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\s233\ri720\tldot\tx8280\tqr\tx8640 \f20 \sbasedon0\snext0 toc 1;}{\s243\tqc\tx4320\tqr\tx8640 \f20 \sbasedon0\snext243 footer;}{\f20 \sbasedon222\snext0 Normal,font: times ;}{\s2\fi-720\li720 \f20 \sbasedon0\snext2 ref;}}{\info{\title Sundar's Thesis}
{\author sundar}}\margl1440\margr1440\widowctrl\ftnbj \sectd \pgnrestart\linemod0\linex0\cols1\endnhere\titlepg {\footer \pard\plain \s243\tqc\tx4320\tqr\tx8640 \f20 \par 
}\pard\plain \qc \f20 \line \line \line \line \line \line \line \line \par 
\pard \qc\li540\ri740 {\b\fs36 Vibration Analysis of Heme Porphyrin}{\b \line \line }Vikram C. Sundar\line May 16, 1997\par 
\pard \qc \line \line \line \line \line \line \line \line Dr. Stephen F. Sontum\line Thesis Advisor\line \line Submitted in partial fulfillment of the requirements for\line {\b Honors}\line in\line Chemistry and Biochemistry\line Middlebury College\line 
\line \line \line \line \line \line Approved:\line \line \line {\ul \~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\line \line \line \~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\line \line \line \~
\~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\~\line \line }Committee in Charge\par 
\pard \sect \sectd \pgnrestart\pgnlcrm\linemod0\linex0\cols1\endnhere {\footer \pard\plain \s243\tqc\tx4320\tqr\tx8640 \f20 \tab \chpgn \par 
}\pard\plain \qc \f20 {\b\fs28 Table of Contents}\par 
\pard\plain \s233\ri720\tldot\tx8280\tqr\tx8640 \f20 {Abstract}\tab 1\par 
Chapter 1-Introduction\tab 2\par 
\pard\plain \s232\li720\ri720\tldot\tx8280\tqr\tx8640 \f20 Myoglobin\tab 2\par 
Spiro Group's Arguments\tab 6\par 
Kitagawa Group's Argument\tab 7\par 
Molecular Dynamics\tab 8\par 
Molecular Models\tab 9\par 
Molecular Dynamics\tab 9\par 
Other Heme Force Fields\tab 10\par 
Goals\tab 12\par 
\pard\plain \s233\ri720\tldot\tx8280\tqr\tx8640 \f20 Chapter 2-Methods and Materials\tab 14\par 
\pard\plain \s232\li720\ri720\tldot\tx8280\tqr\tx8640 \f20 General\tab 14\par 
AMBER 4.1\tab 14\par 
Molecular Mechanics Force Fields\tab 18\par 
\pard\plain \s231\li1440\ri720\tldot\tx8280\tqr\tx8640 \f20 Bond and Angle Parameters\tab 18\par 
\pard\plain \s230\li2160\ri720\tldot\tx8280\tqr\tx8640 \f20 Sundar/Sontum_old Modeling Method\tab 19\par 
Sundar/Sontum_new Modeling Approach\tab 20\par 
\pard\plain \s231\li1440\ri720\tldot\tx8280\tqr\tx8640 \f20 Dihedral Parameters (Bond torsion)\tab 20\par 
Non-bonded Parameters\tab 22\par 
\pard\plain \s232\li720\ri720\tldot\tx8280\tqr\tx8640 \f20 Normal Mode Analysis\tab 22\par 
\pard\plain \s231\li1440\ri720\tldot\tx8280\tqr\tx8640 \f20 NMODE\tab 22\par 
NMANAL\tab 22\par 
\pard\plain \s232\li720\ri720\tldot\tx8280\tqr\tx8640 \f20 Consistent Force Fields\tab 23\par 
\pard\plain \s231\li1440\ri720\tldot\tx8280\tqr\tx8640 \f20 Optimization Procedures\tab 23\par 
Symmetry\tab 24\par 
Potential Energy Distribution  (nfit algorithm)\tab 25\par 
Calc. File\tab 26\par 
Observed File\tab 26\par 
Matching Algorithm (NFIT_12)\tab 27\par 
Orbital Visualization\tab 28\par 
\pard\plain \s230\li2160\ri720\tldot\tx8280\tqr\tx8640 \f20 NMODE_P and RUN.VIS\tab 28\par 
\pard\plain \s232\li720\ri720\tldot\tx8280\tqr\tx8640 \f20 Force Constant Optimization\tab 31\par 
\pard\plain \s231\li1440\ri720\tldot\tx8280\tqr\tx8640 \f20 Ravine Algorithm\tab 32\par 
SIMPLEX Algorithm\tab 32\par 
\pard\plain \s232\li720\ri720\tldot\tx8280\tqr\tx8640 \f20 Force Field Selection\tab 33\par 
IBELLY OPTION\tab 33\par 
\pard\plain \s233\ri720\tldot\tx8280\tqr\tx8640 \f20 Chapter 3- Results Small Molecules\tab 35\par 
\pard\plain \s232\li720\ri720\tldot\tx8280\tqr\tx8640 \f20 Results and Discussion\tab 35\par 
Relaxation of United Ethyl Approximation\tab 36\par 
Non-United Nickel Octaethyl Porphyrin\tab 37\par 
Force Field Development for Benzene, Toluene and Ethylbenzene.\tab 38\par 
\pard\plain \s231\li1440\ri720\tldot\tx8280\tqr\tx8640 \f20 Deuterated Benzene\tab 41\par 
Toluene\tab 42\par 
Ethylbenzene\tab 44\par 
\pard\plain \s232\li720\ri720\tldot\tx8280\tqr\tx8640 \f20 Improper Torsion Terms.\tab 47\par 
Conclusion Transferred over to NiOEP.\tab 49\par 
\pard\plain \s233\ri720\tldot\tx8280\tqr\tx8640 \f20 {Chapter 4- Results Old Force Field}\tab 50\par 
\pard\plain \s232\li720\ri720\tldot\tx8280\tqr\tx8640 \f20 Nickel Octaethyl Porphyrin\tab 50\par 
Vibration Features\tab 50\par 
\pard\plain \s231\li1440\ri720\tldot\tx8280\tqr\tx8640 \f20 Nickel Nitrogen Constant\tab 53\par 
Angle Bending Constants\tab 54\par 
\pard\plain \s232\li720\ri720\tldot\tx8280\tqr\tx8640 \f20 Structural Fits\tab 55\par 
Dihedral (Proper and Improper) Parameters\tab 58\par 
\pard\plain \s231\li1440\ri720\tldot\tx8280\tqr\tx8640 \f20 Proper Torsion Parameters\tab 58\par 
IMPROPER Torsion\tab 60\par 
\pard\plain \s232\li720\ri720\tldot\tx8280\tqr\tx8640 \f20 Force Constants vs. Bond Lengths\tab 61\par 
Transferability\tab 63\par 
Conclusion\tab 64\par 
\pard\plain \s233\ri720\tldot\tx8280\tqr\tx8640 \f20 Chapter 5   New Approach to Modeling\tab 66\par 
\pard\plain \s232\li720\ri720\tldot\tx8280\tqr\tx8640 \f20 Vibrational Fit.\tab 66\par 
\pard\plain \s231\li1440\ri720\tldot\tx8280\tqr\tx8640 \f20 Sundar/Sontum_old vs. Sundar/Sontum_new Angle Force Constants\tab 68\par 
Nickel-Nitrogen Force Constant\tab 69\par 
\pard\plain \s232\li720\ri720\tldot\tx8280\tqr\tx8640 \f20 Bond length vs. Force Constants\tab 70\par 
Geometric Fit\tab 71\par 
Transferability\par 
\pard\plain \s233\ri720\tldot\tx8280\tqr\tx8640 \f20 Chapter 6 Heme Porphyrin Analysis\tab 76\par 
\pard\plain \s232\li720\ri720\tldot\tx8280\tqr\tx8640 \f20 Introduction\tab 76\par 
\pard\plain \s231\li1440\ri720\tldot\tx8280\tqr\tx8640 \f20 Fe-N Force Constant\tab 76\par 
Peripheral Heme groups\tab 78\par 
\pard\plain \s232\li720\ri720\tldot\tx8280\tqr\tx8640 \f20 Spiro/Kitagawa Controversy\tab 79\par 
\pard\plain \s231\li1440\ri720\tldot\tx8280\tqr\tx8640 \f20 Isolated Heme Calculations\par 
Myoglobin Protein Effects\tab 82\par 
\pard\plain \s233\ri720\tldot\tx8280\tqr\tx8640 \f20 {Chapter 7- Conclusions and Future Work}\tab 85\par 
\pard\plain \s232\li720\ri720\tldot\tx8280\tqr\tx8640 \f20 Conclusions\tab 85\par 
Future Work\tab 86\par 
\pard\plain \s233\ri720\tldot\tx8280\tqr\tx8640 \f20 {References}\tab 87\par 
{Appendix A}\par 
\pard\plain \s232\li720\ri720\tldot\tx8280\tqr\tx8640 \f20 {Prep Files}\tab 1\par 
Benzene Prep File\tab 1\par 
Ethyl Benzene Prep File\tab 1\par 
Heme-Histidine Prep File\tab 2\par 
Nickel octaethyl porphine Prep File\tab 4\par 
Nickel  porphine Prep File\tab 6\par 
\pard\plain \s233\ri720\tldot\tx8280\tqr\tx8640 \f20 {Appendix B}\par 
\pard\plain \s232\li720\ri720\tldot\tx8280\tqr\tx8640 \f20 {PDB Files}\tab 9\par 
Benzene PDB File\tab 9\par 
Ethyl Benzene PDB File\tab 9\par 
Ethyl Benzene PDB File\tab 9\par 
Nickel octa ethyl porphine PDB File\tab 11\par 
Nickel porphine PDB File\tab 12\par 
\pard\plain \s233\ri720\tldot\tx8280\tqr\tx8640 \f20 {Appendix C}\par 
\pard\plain \s232\li720\ri720\tldot\tx8280\tqr\tx8640 \f20 {Scale}\tab 14\par 
\pard\plain \s233\ri720\tldot\tx8280\tqr\tx8640 \f20 {Appendix D}\par 
\pard\plain \s232\li720\ri720\tldot\tx8280\tqr\tx8640 \f20 {Obs Files}\tab 19\par 
Benzene Obs File\tab 19\par 
Ethyl Benzene Obs File\tab 19\par 
Nickel Octa Ethyl Porphine Obs File\tab 20\par 
Nickel Octa Ethyl Porphine D4h Obs File\tab 23\par 
Toluene Obs File\tab 24\par 
Sample Run Nmode Script\tab 25\par 
\pard\plain \s233\ri720\tldot\tx8280\tqr\tx8640 \f20 {Appendix E}\par 
\pard\plain \s232\li720\ri720\tldot\tx8280\tqr\tx8640 \f20 {Symmetry Files}\tab 27\par 
Benzene Symmetry File\tab 27\par 
Ethyl Benzene Symmetry File\tab 27\par 
Nickel Octa Ethyl Porphine Symmetry File\tab 28\par 
Nickel Octa Ethyl Porphine D4h Symmetry File\tab 29\par 
Toluene Symmetry File\tab 30\par 
\pard\plain \s233\ri720\tldot\tx8280\tqr\tx8640 \f20 {Appendix F}\par 
\pard\plain \s232\li720\ri720\tldot\tx8280\tqr\tx8640 \f20 {Potential Files}\tab 32\par 
Benzene Potential File\tab 32\par 
Ethyl Benzene Potential File\tab 32\par 
Heme Potential File\tab 33\par 
Heme Sundar New Potential File\tab 36\par 
\pard \s232\li720\ri720\tldot\tx8280\tqr\tx8640 Heme Sundar Old Potential File\tab 38\par 
Toluene Potential File\tab 40\par 
\pard\plain \f20 \sect \sectd \pgnrestart\linemod0\linex0\cols1\endnhere \pard\plain \qc\sl480 \f20 {\v\fs28 {\tc\tcl1\pard\plain \qc\sl480 \f20 {\b\fs28 Abstract}}}{\b\fs28 \par 
}\pard {\fs28 \par 
}\pard {\fs28 \tab 
The Spiro and Kitagawa groups have made two different sets of frequency assignments for the bending frequency of carbon monoxide in carboxymyoglobin. A computational resolution to this controversy has been attempted in this thesis by developing a force fi
eld for the heme porphyrin (protoporphyrin IX). Our analyses support the Spiro group's assignment of 574 cm}{\up6 -1}{\fs28  to this bending frequency. Th
e successful development of the heme force field was done by transferring over force fields developed for smaller molecules like nickel octaethyl porphyrin (NiOEP), ethylbenzene and benzene.Trends observed in such analysis recommend the use of specific dih
edral terms for modeling out of plane motions, and expansion of the dihedral set to model ethyl groups attached to aromatic systems  Furthermore, exclusion of  improper torsion terms in the potential equation is suggested unless hyperconjugation effects ne
ed to be simulated. Finally, an alternative approach to modeling strained systems is developed, in which unstrained values for structural parameters are used.\par 
}\pard \page \par 
\pard \qc\sl360 {\v\fs28 {\tc\tcl1\pard\plain \qc\sl360 \f20 {\b\v\fs28 Chapter 1-}{\b\fs28 Introduction}}}{\b\fs28 \par 
}\pard \qc\sl360 \par 
\pard \fi1440\sl360 Nur die F\'9flle f\'9fhrt die Klarheit,\par 
\pard \fi1440\sl360\tx360 Denn im Abgrund wohnt die Wahrheit!\par 
\pard \fi1440\sl360 \tab \tab \tab   (Frederich Schiller)\par 
\pard \sl480 \tab Literally translated, this famous saying of Schiller's would mean,  "only completeness leads to clarity because the truth lies in an abyss".  According to Schiller in order to determine the truth the entire picture is needed. 
Only with such a 'completed' picture is it possible to discard plausible explanations in favor of the correct explanation, and be certain that the truth, wherever it may be, has been discovered. \par 
\tab 
This saying is particularly appropriate in molecular spectroscopy, where spectra provide insights into real molecules, and one needs to see the 'entire' picture to be confident of one's interpretations of a spectrum.  There are often a variety of possible
 explanations, and hence disputes persist regarding the interpretation of such spectral data. This thesis is an attempt towards resolving one such dispute.\par 
\pard \sl480 \tab 
The focus of this thesis is to computationally probe the vibrations of carboxyheme in the hope of identifying the bending frequency of the carboxyheme linkage. A computational approach will be taken, so that an alternate method is available to reproduce e
xperimental results. Successful assignment of this bending band, in turn, will allow an estimation of the energy required to bend the iron-carbon linkage, and resolve  a controversy surrounding the interpretations of carboxymyoglobin spectra. \par 
\pard \sl480 \par 
\pard \sl480 {\v {\tc\tcl2\pard\plain \sl480 \f20 {\b Myoglobin}}}\par 
\pard \sl480 \tab 
Myglobin is a relatively small sized protein, which has a single polypeptide chain containing 153 amino-acid residues.Myoglobin's primary function is oxygen storage, and it is particularly abundant in diving mammals such as whales and seals. X-ray crystal
 structures reveal that the backbone of the myoglobin molecule consists of eight relatively straight structure segments set off by bends (Figure 1.1).{\up9 {\object\objicemb{\*\objname ICEmbdObject2}{\*\objdata 
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s structure is similar to subunits of another protein, hemoglobin. The same heme group (Protoporphyrin IX), from which both proteins derive their oxygen transporting and storing properties, is noncovalently bound to the interior of  myoglobin and hemoglobi
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\pard \sl480\keepn {\b Figure 1.1 Spermwhale Myoglobin and Protoporphyrin IX Core}\par 
\pard \sl480 \tab  The heme group belongs to the most abundant class of porphyrin derivatives known as protoporphyrins.  Protoporphyrins consist of four pyrrole rings bound to a central metal atom, four 
methyl groups, two vinyl groups and two propionic acid groups. In protoporphyrin IX,  the four pyrrole groups bind to iron metal center to form a square planar complex. Two more ligands can attach at the axial positions, one of which, in myoglobin, is nitr
ogen from a proximal-side histadine (His 64)  residue (Figure 1.2){\b .}{\up9 {\object\objicemb{\*\objname ICEmbdObject6}{\*\objdata 
0000006300000ca3685610000832cf454e524600000000004a00af9f15160038e630010100000000000131000100000000000c000a000120010009000000000000000000010000000300000000000000124c65686e696e6765722c2031393735202333}{\result {\pict\macpict\picw0\pich0 000a0000000000000000
}}}}{\fs18\up9 1}{{\object\objicemb{\*\objname ICEmbdObject7}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900af9f15160038e630}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}
 The final, axial ligand varies, and determines the function of heme. In myoglobin, this sixth ligand is dioxygen allowing this protein to store oxygen. \par 
\pard \sl480 \par 
\pard \sl480\keepn {{\pict\macpict\picw440\pich268 
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000003000bfe002a0a00000406000300000c020010000102000e0100000900040007030400040100fffff8ff0007000202000681008100e100040e00000304fe0000ff}}{\b \par 
}\pard \sl480\keepn {\b Figure 1.2 Protoporphyrin IX along with Histidine 64 Residue}\par 
\pard \sl480  \tab 
Apart from the dioxygen ligand, the iron metal center of the heme porphyrin can bind to other gaseous ligands, of which carbon monoxide is a particularly important example. Carbon monoxide is often used as a substitute for the dioxygen ligand in spectros
copic studies of heme, since both these gases bind to heme forming low-spin complexes, which induce similar changes in the protein structure.{\up9 {\object\objicemb{\*\objname ICEmbdObject8}{\*\objdata 
0000006000000ca3685610000832cf454e524600000000004700af9f1bc4003a780a010100000000000132000100000000000c000a0001200200090000000000000000000100000010000000000000000f537069726f2c203139393420233136}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}{
\fs18\up9 2}{{\object\objicemb{\*\objname ICEmbdObject9}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900af9f1bc4003a780a}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}
 However, carbon monoxide has the advantage of possessing a permanent dipole, wh
ich allows the ligand to be followed through resonance Raman and infrared spectroscopy. Therefore, the carbon monoxide ligand is used to probe "structure-function" relationships between oxygen and heme.{\up9 {\object\objicemb{\*\objname ICEmbdObject10}
{\*\objdata 0000006100000ca3685610000832cf454e524600000000004800af9f1bdc003a7da9010100000000000133000100000000000c000a00012003000900000000000000000001000000060000000000000010416c62657274792c2031393932202336}{\result {\pict\macpict\picw0\pich0 
000a0000000000000000}}}}{\fs18\up9 3}{{\object\objicemb{\*\objname ICEmbdObject11}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900af9f1bdc003a7da9}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}\par 
\pard \sl480 \tab 
Despite these aforementioned similarities, it is also known that these two ligands differ  in their electronic structure and modes of binding. The binding affinity of  carbon monoxide to heme is extremely environment sensitive, as the residues surrounding
 heme control the porphyrin's binding affinity to carbon monoxide. While CO binds 10{\up6 3} ~ 10{\up6 4} times more strongly than oxygen to free heme porphyrins,{\up9 {\object\objicemb{\*\objname ICEmbdObject12}{\*\objdata 
0000006100000ca3685610000832cf454e524600000000004800af9f1c81003aa478010100000000000134000100000000000c000a00012004000900000000000000000001000000070000000000000010436f6c6c6d616e2c2031393736202337}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}
{\fs18\up9 4}{{\object\objicemb{\*\objname ICEmbdObject13}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900af9f1c81003aa478}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}
 within the myoglobin protein environment carbon monoxide binds only 30 times stronger that the dioxygen ligand. \par 
\pard \sl480 \tab The cause of this environment controlled difference in binding affinities of CO has been the object of much debate.{\up9 {\object\objicemb{\*\objname ICEmbdObject14}{\*\objdata 
0000006000000ca3685610000832cf454e524600000000004700af9f1caf003aaf1a010100000000000135000100000000000c000a0001200500090000000000000000000100000017000000000000000f537069726f2c203139393420233233}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}{
\fs18\up9 5}{{\object\objicemb{\*\objname ICEmbdObject15}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900af9f1caf003aaf1a}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}
 The original  X-ray structures of a sperm-whale myoglobin bound to CO ligand was interpreted to indicate that the Fe-C-O angle of binding was not linear, as in the free heme porphyrin,{\up9 {\object\objicemb{\*\objname ICEmbdObject16}{\*\objdata 
0000005f00000ca3685610000832cf454e524600000000004600af9f1cee003abe13010100000000000136000100000000000c000a000120060009000000000000000000010000000a000000000000000e50656e672c203139373620233130}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}{
\fs18\up9 6}{{\object\objicemb{\*\objname ICEmbdObject17}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900af9f1cee003abe13}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}} but rather bent{\b .}{\up9 {\object\objicemb{\*\objname 
ICEmbdObject18}{\*\objdata 0000006100000ca3685610000832cf454e524600000000004800af9f1d3b003ad012010100000000000137000100000000000c000a000120070009000000000000000000010000000900000000000000104b75726979616e2c2031393932202339}{\result 
{\pict\macpict\picw0\pich0 000a0000000000000000}}}}{\fs18\up9 7}{{\object\objicemb{\*\objname ICEmbdObject19}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900af9f1d3b003ad012}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}
 The argument, therefore, was that the protein imposed steric hindrances on the binding of CO ligand, forcing it to bind in a bent fashion. As a bent binding structure is not favorable for backbonding between the Fe d{\fs20\dn4 xy} and CO {\dn4 \'b9}{
\up6 *} orbitals (Figure 1.3), the binding affinity is reduced. In the case of the oxygen binding, the angle of binding of the ligand to the heme porphyrin is bent, irrespective of whether the porphyrin was within the protein environment or not.{\up9 
{\object\objicemb{\*\objname ICEmbdObject20}{\*\objdata 0000006000000ca3685610000832cf454e524600000000004700af9f1d6e003adc2d010100000000000135000100000000000c000a0001200500090000000000000000000100000017000000000000000f537069726f2c203139393420233233
}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}{\fs18\up9 5}{{\object\objicemb{\*\objname ICEmbdObject21}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900af9f1d6e003adc2d}{\result {\pict\macpict\picw0\pich0 
000a0000000000000000}}}}  Therefore, its binding affinity is not affected by the protein environment.    \par 
\pard \sl480 \par 
\pard \sl480\keepn \tab {{\pict\macpict\picw250\pich122 
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\pard \sl480\keepn {\b Figure 1.3   Backbonding possible between  d}{\b\fs20\dn4 xy}{\b  and \'b9* orbitals. \par 
}\pard \sl480 \par 
\pard \sl480 \tab 
While this explanation seems plausible at first glance, some deficiencies of this model have been pointed out. Anfinrud and coworkers concluded, using the technique of photo-selection spectroscopy, that the Fe-C-O geometry is nearly linear under physiolog
ically relevant conditions.{\up9 {\object\objicemb{\*\objname ICEmbdObject22}{\*\objdata 
0000005900000ca3685610000832cf454e524600000000004000af9f1d99003ae616010100000000000138000100000000000c000a000120080009000000000000000000010000000800000000000000084c696d2c20202338}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}{\fs18\up9 8}{
{\object\objicemb{\*\objname ICEmbdObject23}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900af9f1d99003ae616}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}
 Spiro and coworkers point to the prohibitive cost of distorting the Fe-C-O angle away
 from linear. Reduction of binding overlap resulting from bending the Fe-C-O linkage would increase the energy of the Fe-C-O linkage. This energy could not possibly be supplied by the protein matrix, which would more likely adopt a different conformer.{
\up9 {\object\objicemb{\*\objname ICEmbdObject24}{\*\objdata 0000006000000ca3685610000832cf454e524600000000004700af9f1db9003aedb3010100000000000135000100000000000c000a0001200500090000000000000000000100000017000000000000000f537069726f2c203139393420233233
}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}{\fs18\up9 5}{{\object\objicemb{\*\objname ICEmbdObject25}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900af9f1db9003aedb3}{\result {\pict\macpict\picw0\pich0 
000a0000000000000000}}}} Finally, recent X-ray structure determinations of other forms of myoglobin indicate that the angle of CO ligand binding to the Fe (II) center is around 169\'fb,{\up9 {\object\objicemb{\*\objname ICEmbdObject26}{\*\objdata 
0000006200000ca3685610000832cf454e524600000000004900af9f1de2003af76a010100000000000139000100000000000c000a000120090009000000000000000000010000000b00000000000000115175696c6c696e2c203139393320233131}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}
}}}{\fs18\up9 9}{{\object\objicemb{\*\objname ICEmbdObject27}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900af9f1de2003af76a}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}} and not between 120-140\'fb
 as in the sperm whale myoglobin.{\up9 {\object\objicemb{\*\objname ICEmbdObject28}{\*\objdata 
0000006100000ca3685610000832cf454e524600000000004800af9f1e02003afedd010100000000000137000100000000000c000a000120070009000000000000000000010000000900000000000000104b75726979616e2c2031393932202339}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}
{\fs18\up9 7}{{\object\objicemb{\*\objname ICEmbdObject29}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900af9f1e02003afedd}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}} As yet the actual cause of this di
fferential binding is not fully known. Other  factors proposed include the displacement of the iron atom from the heme plane, electrostatic interactions between the ligand and its surroundings in the heme pocket, the solvent content, and the polarity of th
e distal pocket.{\up9 {\object\objicemb{\*\objname ICEmbdObject30}{\*\objdata 
0000006200000ca3685610000832cf454e524600000000004900af9f1e16003b037e010100000000000139000100000000000c000a000120090009000000000000000000010000000b00000000000000115175696c6c696e2c203139393320233131}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}
}}}{\fs18\up9 9}{{\object\objicemb{\*\objname ICEmbdObject31}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900af9f1e16003b037e}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}} \par 
\pard \sl480 \tab An important argument against the bent FeCO model involves the energy required to bend the FeCO linkage. Spiro and coworkers indicate that this energy is too large to allow the sterically hindered model. A rough measure of this energy
 could be obtained from the FeCO bending frequency. This mode of vibration corresponds to the energy required to bend the FeCO linkage and reflects the amount of destabilization caused by moving away from the linear FeCO model (Figure 1.4a). However, there
 exists a disagreement over the assignment of the vibrational frequency caused by this bending motion. The Spiro and Kitagawa groups make particularly compelling cases for different assignments of this frequency. Since resolution of this controversy will b
e the focus of this study, it is necessary to explain the rationale behind their different assignments.\par 
\pard \sl480 {\v {\tc\tcl2\pard\plain \sl480 \f20 {\b Spiro Group's Arguments}}}\par 
\pard \sl480 \tab Spiro's group{\up9 {\object\objicemb{\*\objname ICEmbdObject32_1}{\*\objdata 
0000006000000ca3685610000832cf454e524600000000004700afa22ec30045e26f010100000000000132000100000000000c000a0001200200090000000000000000000100000010000000000000000f537069726f2c203139393420233136}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}{
\fs18\up9 2}{{\object\objicemb{\*\objname ICEmbdObject33_2}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900afa22ec30045e26f}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}
 analyzed resonance infrared spectral data obtained from model   metalloporphyrin-carbon monoxide systems. They assigned a band at 574 cm{\fs20\up6 -1 }to the bending motion of the Fe-C-O, and another band at 494 cm{\up6 -}{\fs20\up6 1}
 to the stretching motion of Fe-C. Their reasoning is that the band at 574 cm{\fs20\up6 -1} displays a "zig-zag" decrease in  frequency when different, isotopically substituted carbon monoxide ligands are used.{\up9 {\object\objicemb{\*\objname 
ICEmbdObject0}{\*\objdata 0000006100000ca3685610000832cf454e524600000000004800afa208520000d9fa01010000000000023130000100000000000c000a0001200a00090000000000000000000100000028000000000000000f537069726f2c203139383820233430}{\result 
{\pict\macpict\picw0\pich0 000a0000000000000000}}}}{\fs18\up9 10}{{\object\objicemb{\*\objname ICEmbdObject1}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900afa208520000d9fa}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}
 Specifically, while this band is very sensitive to changes in the weight of the carbon atom in the carbon monoxide ligand, it is less sensitive to changes in the mass of the oxygen atom.  As Figure 1.4 shows, in the bending mode of the FeCO linkage, the c
arbon atom experiences the maximum displacement, while the oxygen atom remains relatively stationary. Therefore, the 574 cm{\fs20\up6 -1} band was assigned to the bending of the carbon monoxide ligand. The band at 494 cm{\fs20\up6 -1} d
isplays a monotonous decrease in frequency; decreasing as the weight of the carbon monoxide increases. Furthermore, the shift in this bands frequency is not as sensitive as the 574 cm{\fs20\up6 -1}
 band to changes in the mass of the carbon atom. This frequency shifting pattern is expected for the stretching motion of Fe-CO bond,  in which the entire CO unit undergoes displacement.  The 494 cm{\fs20\up6 -1}
 band was assigned  to the stretching motion of the Fe-CO linkage.\par 
\pard \sl480 \par 
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\pard \keepn {\b Figure 1.4 Motion of CO in Bending and Stretching Modes\par 
}\pard \keepn {\b \tab \tab a. Only Carbon atom moves in }{\b\f23 d(}{\b FeCO) bending motion.\par 
\tab \tab b. The entire CO unit moves in }{\b\f23 u}{\b (FeCO) stretching motion.}\par 
\pard \par 
\pard \sl480 \tab The reasoning behind this unusually high assignment (574 cm{\fs20\up6 -1}) for a bending frequency (even higher than the corresponding stretching frequency mode at 494 cm{\fs20\up6 -1}
) involves a strong back-bonding argument. Spiro used this argument to disprove the idea of having a sterically bent Fe-C-O set up within the myoglobin protein environment (Figure 1.3).{\up9 {\object\objicemb{\*\objname ICEmbdObject34}{\*\objdata 
0000006000000ca3685610000832cf454e524600000000004700af9f26cb003d0f4c010100000000000135000100000000000c000a0001200500090000000000000000000100000017000000000000000f537069726f2c203139393420233233}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}{
\fs18\up9 5}{{\object\objicemb{\*\objname ICEmbdObject35}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900af9f26cb003d0f4c}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}} This resistance is reflected in the high bendin
g constants, which would follow from a high 574 cm{\fs20\up6 -1}
 frequency assignment to the bending frequency. On the other hand, the stretching of the Fe-C linkage does not destroy the backbonding overlap. As it is energetically less demanding than the bending motion of the ligand bound to the porphyrin, the stretchi
ng frequency itself is below that of the bending motion. \par 
\pard \sl480 \par 
\pard \sl480 {\v {\tc\tcl2\pard\plain \sl480 \f20 {\b Kitagawa Group's Argument}}}\par 
\pard \sl480 \tab The primary focus of the Kitagawa group{\up9 {\object\objicemb{\*\objname ICEmbdObject36_3}{\*\objdata 
0000007f00000ca3685610000832cf454e524600000000006600afa22ee80045eb32010100000000000531312c3132000100000000000c000a0001200b000900000000000000000002000000110000002700000000000000264b697461676177612c2031393935202331373b204b697461676177612c203139393420233339
}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}{\fs18\up9 11,12}{{\object\objicemb{\*\objname ICEmbdObject37_4}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900afa22ee80045eb32}{\result {\pict\macpict\picw0\pich0 
000a0000000000000000}}}} is the analysis of the heme porphyrin in its bound state to the CO ligand within its protein environment. They contend that the assignment of the 574 cm{\up6 -1}
 band is better explained as a combination band of the Fe-C-O bending mode (360 cm{\up6 -1)},  and an internal porphyrin skeletal mode  (200 cm{\fs20\up6 -1}).{\up9 {\object\objicemb{\*\objname ICEmbdObject38}{\*\objdata 
0000006300000ca3685610000832cf454e524600000000004a00af9f2f60003cb25501010000000000023133000100000000000c000a0001200d0009000000000000000000010000001d000000000000001154737562616b692c203139383220233239}{\result {\pict\macpict\picw0\pich0 000a0000000000000000
}}}}{\fs18\up9 13}{{\object\objicemb{\*\objname ICEmbdObject39}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900af9f2f60003cb255}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}
  The fundamental band at 360 cm-1 is very weak in intensity and is submerged within other, much stronger bands seen in that region. This group also uses isotopic shift data to identify this bending motion. The characteristic "zig-zag" pattern that Spiro's
 group used to justify their assignment of the band at 574 cm-1 as a bending mode, is also observed for this 360 cm{\fs20\up6 -1} band. However, the shift in frequency seen is much smaller for the 360 cm{\fs20\up6 -1} band than that seen for the 574 cm{
\fs20\up6 -1} band. Selection rule arguments, which forbid the FeCO fundamental bending mode from being resonance Raman active, are used to rule out the Spiro group assignment of the 574 cm{\fs20\up6 -1}
 band as being a fundamental bending mode. Any combination band or overtone of a fundamental, however, can be RR active. As the Kitagawa group observed the 574 cm{\fs20\up6 -1}
 band using resonance Raman spectroscopy, this frequency was assigned as a combination mode.  Having assigned the 574 cm{\fs20\up6 -1}
 band as an overtone, the Kitagawa group then assigns a band at 360 cm-1 to be the fundamental bending motion of the Fe-C-O linkage. This assignment allows the bending frequency to be lower than the corresponding stretching frequency.  \par 
\pard \sl480 \tab {\b  }Ab initio calculations done by Kitagawa's group on a simplified 2 amidinato ligand system,{\up9 {\object\objicemb{\*\objname ICEmbdObject54}{\*\objdata 
0000006400000ca3685610000832cf454e524600000000004b00afa20b7e000198a201010000000000023134000100000000000c000a0001200e0009000000000000000000010000001200000000000000124b697461676177612c203139393420233138}{\result {\pict\macpict\picw0\pich0 
000a0000000000000000}}}}{\fs18\up9 14}{{\object\objicemb{\*\objname ICEmbdObject55}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900afa20b7e000198a2}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}} indicate that the ene
rgy required to bend the Fe-C-O bond is not so large that it could not be bent by steric interactions. Consequently, it was possible to assign a lower frequency (360 cm{\up6 -}{\fs20\up6 1}) frequency to this bending interaction.\par 
\pard \sl480 \tab As a another twist to this controversy, the 360 cm{\fs20\up6 -1}
 band identified as the bending fundamental by Kitagawa finds a different assignment in Spiro's work. This band is assigned by Spiro et al. to an internal porphyrin motion coupled to the the CO ligand's motions.  {\b  \par 
}\pard \sl480 {\b \par 
}\pard \sl480 {\v {\tc\tcl2\pard\plain \sl480 \f20 {\b Molecular Dynamics}}}{\b \par 
}\pard \sl480 \tab One of the key differences between the arguments provided by Kitagawa's and Spiro's groups is that Spiro's observations were drawn from model compounds {\ul outside}
 the myoglobin environment, while Kitagawa's conclusions were drawn from spectroscopic data obtained of heme complexes {\ul within}
 the protein environment. As such it is impossible to determine the validity of either one of their assignments on the merits of their arguments alone. Each of their respective conclusions are consistent with the spectroscopic evidence 
they provide. In addition, as the actual spectroscopic conditions themselves are different, it is not possible to reconcile their difference in the conclusions from experimental data alone. \par 
\pard \sl480 \tab 
In such cases a molecular model, which accurately simulated the vibrational and structural characteristics of the carboxyheme porphyrin would clearly be useful. The Spiro/ Kitagawa controversy regarding FeCO bending frequency, could be resolved by computa
tionally recreating the isotopic-shift experiments done by both t
he Spiro and Kitagawa groups.  Not only could the carbon-isotope sensitive bands be determined, but also the types of motions causing these bands be identified. Thus the correct FeCO bending frequency could be identified, and the effects of the protein env
ironment on this band can be evaluated. \par 
\pard \sl480 \tab  \par 
\pard \sl480 {\v {\tc\tcl2\pard\plain \sl480 \f20 {\b Molecular Models}}}{\b \par 
}\pard \sl480 {\b \tab } For spectroscopic purposes two particular types of modeling systems, vibrational  and molecular mechanic force fields,  have become predominant among biochemical and organic chemists.{\up9 {\object\objicemb{\*\objname 
ICEmbdObject40}{\*\objdata 0000006400000ca3685610000832cf454e524600000000004b00af9f2ffc003cd6d601010000000000023135000100000000000c000a0001200f000900000000000000000001000000130000000000000012416c6c696e6765722c203139383220233139}{\result 
{\pict\macpict\picw0\pich0 000a0000000000000000}}}}{\fs18\up9 15}{{\object\objicemb{\*\objname ICEmbdObject41}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900af9f2ffc003cd6d6}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}{\b 
 } 
These modeling systems are referred to as force fields because they use analytical potential energy functions, within the framework of classical mechanics, to predict restoring forces and the vibrational frequencies of the modeled molecules. Of these two m
ethods the method of molecular dynamics has been adopted in this thesis, as it allows easier transfer of force fields between similar molecules. Therefore,  a description of the molecular dynamics force-field is done with the understanding that there exist
s another modeling philosophy.\par 
\pard \sl480 \tab \par 
\pard \sl480 {\v {\tc\tcl2\pard\plain \sl480 \f20 {\b Molecular Dynamics}}}\par 
\pard \sl480 \tab Most force fields{\up9 {\object\objicemb{\*\objname ICEmbdObject42_5}{\*\objdata 
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}}}}{\fs18\up9 16}{{\object\objicemb{\*\objname ICEmbdObject43_6}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900afa22f310045fc48}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}
 build of off the assumption that the molecule is at its minimum energy, and that it is only slightly perturbed from this minimum energy configuration. The resulting potential function can be described by a harmonic function (linear dependence on a square 
term) between the perturbation and the corresponding restoring force. Use of Newton's equation of motion establishes  secular equations between  observed frequencies and these re
storing force constants. Given a set of force constants, the vibrational frequencies can be calculated by solving for the eigenvalues corresponding to the matrix of these secular equations.{\up9 {\object\objicemb{\*\objname ICEmbdObject44}{\*\objdata 
0000006200000ca3685610000832cf454e524600000000004900af9f31d9003d471301010000000000023137000100000000000c000a000120110009000000000000000000010000001f00000000000000104465636975732c203139353520233331}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}
}}}{\fs18\up9 17}{{\object\objicemb{\*\objname ICEmbdObject45}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900af9f31d9003d4713}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}
 The force constants are then varied until the calculated frequencies correspond to the experimentally observed ones. At the end of such force-constant optimization, a consistent force field is said to have been obtained, as this force field is consistent 
with experimentally observed data. {\fs20\up6 \par 
}\pard \sl480 \tab The actual molecular mecha
nics program used in this thesis is called AMBER (Assisted Molecular Building with Energy Refinement).  Peter Kollman, in creating the AMBER model for generating molecular mechanics force fields, placed an emphasis on more "explicitly stated algorithms". 
{\up9 {\object\objicemb{\*\objname ICEmbdObject46}{\*\objdata 
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}}}}{\fs18\up9 18}{{\object\objicemb{\*\objname ICEmbdObject47}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900af9f31e9003d4adb}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}
 Parameters developed using this program, therefore, are done so with explicit information regarding their transferability. As this thesis aims to develop a force field for protoporphyrin IX using data obtained from other, simpler molecules,  the AMBER 
molecular mechanics package was chosen.  Futhermore, this package allows analysis of the internal coordinates or parameters responsible for each of the frequency.  This added information will help in identifying the frequency of the FeCO bending motion.
\par 
\pard \sl480 \par 
\pard \sl480 {\v {\tc\tcl2\pard\plain \sl480 \f20 {\b Other Heme Force Fields}}}\par 
\pard \sl480  \tab Li and Marques{\up9 {\object\objicemb{\*\objname ICEmbdObject48_7}{\*\objdata 
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2c2031393931202332323b204d6172717565732c203139393520233235}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}{\fs18\up9 19-22}{{\object\objicemb{\*\objname ICEmbdObject49_8}{\*\objdata 
0000002200000ca3685610000832cf454e522d00000000000900afa22f5c0046064c}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}} used different  force fields to model the heme porphyrin.{\fs20\up6  }
Marques parametrized iron porphyrins using molecular dynamic force fields, but concentrated on representing the actual shapes of various heme porph
yrin as given by their crystal structures. Thus Marques' emphasis allowed him to calculate and accurately predict the geometry of various heme complexes depending on the stress placed on them. \par 
\pard \sl480 \tab 
 Li on the other hand, chose to concentrate on modeling vibrational features of nickel octaethyl porphyrin (NiOEP) (Figure 1.6 ). He used a vibrational force to classify the vibrations according to their normal modes.  He modeled the NiOEP molecule becaus
e it is structurally similar to the heme porphyrin. Although N
iOEP has a different metal center, it has the same porphyrin core as protoporphyrin IX. The advantage of using NiOEP, however, is that it is easier to obtain pure and isolated from the myoglobin protein. Li succeeded in breaking the various motions into in
-plane and out-of-plane motions. He concluded that such a model could then be used to model the interactions of the heme itself. At 360 cm{\up6 -1}
 he observed an out-of-plane (OOP) frequency which he assigned to the a doming motion of the porphyrin (Figure 1.7).
 He suggested that this frequency could be important in the dynamics of the protein-ligand interactions, as this OOP mode could couple with motions of the ligands.\par 
\pard \sl480 \par 
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1eec0000fff50000fffd0000ffeb0000ffbe00fa66a000fa6681008100f400001bee0001fffff300fdffeb00feffbc0000669a00006681008100f1000000ff}}{\b Figure 1.6  Nickel Octaethyl Porphyrin\par 
}\pard \sl480 \par 
\pard \sl480\keepn {{\pict\macpict\picw339\pich223 
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a20000668d0000ff}}\par 
\pard \sl480\keepn {\b Figure 1.7  Out of Plane Motion of NiOEP at 360 cm}{\b\fs20\up6 -1}{\b .\par 
}\pard \sl480 \par 
\pard \sl480 {\v {\tc\tcl2\pard\plain \sl480 \f20 {\b Goals}}}\par 
\pard \sl480 \tab 
The general goal of this thesis project, that  of developing of a model to describe the interactions of CO with the heme porphyrin, builds of off the studies done by Li and Marquis. The force field aimed for in this thesis should accurate
ly represent both the actual geometry and the vibrational features of heme porphyrin. \par 
\pard \sl480 \tab Specifically, the force field developed by Maggie Zraly and Jason Dimmig will be optimized.{\up9 {\object\objicemb{\*\objname ICEmbdObject50}{\*\objdata 
0000007a00000ca3685610000832cf454e524600000000006100af9f32e3003d859f010100000000000532332c3234000100000000000c000a000120170009000000000000000000020000001a0000001b00000000000000215a72616c792c2031393935202332363b2044696d6d69672c203139393520233237}{\result 
{\pict\macpict\picw0\pich0 000a0000000000000000}}}}{\fs18\up9 23,24}{{\object\objicemb{\*\objname ICEmbdObject51}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900af9f32e3003d859f}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}
 Jason Dimmig succeeded in  optimizating of the in plane vibrations of the NiOEP against the vibrational data obtained by Li. The out-of-plane (OOP) modes however, are still left to be optimized. Optimization of parameters describing these modes of vibrati
ons will be the immediate focus of this thesis. As a molecular dynamic
 force field is being used, the fully-optimized parameters for NiOEP should transfer over to Protoporphyrin IX.  The transferability of these parameters will tested against the structural data of various other porphyrins. If these parameters are truly tran
sferable, then they should reproduce the structural characteristics of these other porphyrin, in different environments.  Thereafter these parameters will be transferred over to the heme porphyrin itself, and due allowances will be made for the structural 
differences between the protoporphyrin and NiOEP.  Parametrizing the heme porphyrin with parameters from NiOEP should be relatively easy. Only the additional groups would have to parametrized; and even these parameters could be transferred from other small
er and simpler molecules. \par 
\pard \sl480 \tab  From the force field thus obtained, the various frequencies of the  porphyrin bound to the CO will be calculated. The Spiro/Kitagawa controversy will be addressed by computationally recreating the isotopic-shift experiments tha
t both these groups have performed. The FeCO bend band will be identified within and outside of the myoglobin protein, and the effects of the protein environment will be examined.  Such analysis will help complete the "picture" of the vibration spectrum of
 the heme porphyrin, and allow clearer understanding of the real molecule, whose vibrations are represented in the carboxyheme vibration spectrum.  \par 
\pard \par 
\pard \qc\sl480 \page {\v {\tc\tcl1\pard\plain \qc\sl480 \f20 {\b\v Chapter 2-}{\b Methods and Materials}}}\par 
\pard \sl480 {\v {\tc\tcl2\pard\plain \sl480 \f20 {\b General}}}\par 
\pard \sl480 \tab The primary goal of this project, that of analyzing the 
normal modes of vibration of carboxymyoglobin, required the development of a force field, which accurately reproduced the vibrational and structural features of this porphyrin.  The general philosophy of this project has been to develop consistent force fi
elds for smaller molecules and transfer these force fields to larger molecules until it was possible to model protoporphyrin IX itself.  It was hoped that this approach would allow testing of new modeling methods  on smaller molecules, in which the smaller
 numbers of variables and vibrational frequencies make such testing tractable. \par 
\pard \sl480 \tab 
As transferability of parameters  was critical to this project, a molecular mechanics package was chosen. Inherently, molecular mechanics packages allow easier transfer of force fields between molecules. Furthermore, a well-tested, modeling package was so
ught that used explicitly stated algorithms. Limitations of such a model would be known and unrealistic levels of accuracy would not be aspired for.  Lastly, the mechanics pack
age needed to be flexible enough, to allow transfer of molecules into a protein environment. \par 
\pard \sl480 \par 
\pard \sl480\keepn {\v {\tc\tcl2\pard\plain \sl480\keepn \f20 {\b AMBER 4.1}}}{\b \par 
}\pard \sl480\keepn \tab The AMBER 4.1 software,{\up9 {\object\objicemb{\*\objname ICEmbdObject22_9}{\*\objdata 
0000006400000ca3685610000832cf454e524600000000004b00afa35fb80040a7d901010000000000023235000100000000000c000a00012019000900000000000000000001000000200000000000000012506561726c6d616e2c203139393420233332}{\result {\pict\macpict\picw0\pich0 
000a0000000000000000}}}}{\fs18\up9 25}{{\object\objicemb{\*\objname ICEmbdObject23_10}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900afa35fb80040a7d9}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}
 developed by the research groups of Peter Kollman and David Case, satisfied the aforementioned requirements and was used to create the porphyrin force field. This software program was designed to perform molecular dynamics calculations on protein, and has
 programmed into it general force fields for proteins. Therefore, upon development of a consistent force-field for the 
carboxyheme porphyrin, it would be possible to transfer the porphyrin force field into the protein environment. Analysis of the Fe-CO bending motions ({\f23 d(}FeCO)) could then be performed outside and inside the myoglobin protein.\par 
\pard \sl480 \tab The version of AMBER, AMBER 4.1, used in this thesis is an updated version of the software used by Jason Dimmig to model nickel porphine (NiP). It retains all the features described by Jason Dimmig in his thesis{\b .}
 A short summary of these features will given here, as the details may be obtained elsewhere.{\up9 {\object\objicemb{\*\objname ICEmbdObject0_11}{\*\objdata 
0000006400000ca3685610000832cf454e524600000000004b00af9f3f270040674d01010000000000023235000100000000000c000a00012019000900000000000000000001000000200000000000000012506561726c6d616e2c203139393420233332}{\result {\pict\macpict\picw0\pich0 
000a0000000000000000}}}}{\fs18\up9 25}{{\object\objicemb{\*\objname ICEmbdObject1_12}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900af9f3f270040674d}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}\par 
\pard \sl480 \tab 
The AMBER 4.1 package consists of different modules,  which allow users to input a molecule's structure and internal parameters, move the molecule to its lowest energy structure, and then calculate the normal modes associated with this equilibrated struct
ure. The PREP, LINK, EDIT and PARM modules allow the user to build the molecule. The SANDER module minimizes the molecule to its equilibrium structure, and the NMODE and NMANAL modules compute and classify the normal mode frequenci
es (orbitals) associated with this structure. \par 
\pard \sl480 \tab 
In the PREP module the internal topology of a molecule is defined. Parameters used to describe this topology include bond distances, bond angles and proper torsion (dihedral) angles between adjacent atoms. Figure 2.1 show a part of the internal topology, 
which would be generated by the PREP module to describe the connectivity between six atoms.  Improper torsion terms, which help maintain the planarity in a molecule, are usually defined between four non-consec
utive atoms. As ambiguity exists regarding improper torsion parameters, these parameters need to be explicitly stated.  Therefore, the desired improper terms are explicitly listed at the end of the PREP file. A separate PREP file is needed for each differe
nt residue in a molecule. As AMBER 4.1 has PREP files for standard amino-acid residues, new PREP files were only created for non-standard residues (like NiOEP and heme porphyrin). All the non-standard prep files used are listed in Appendix A.\par 
\pard \sl480 \par 
\pard \sl480\keepn \tab \tab \tab \tab {{\pict\macpict\picw189\pich284 
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0554696d6573000000ff}}\par 
\pard \sl480\keepn \par 
\pard \keepn {\b Figure 2.1 Internal Topology defined by the PREP module.\par 
\tab        Bond Stretch between atoms 1 & 2.\par 
\tab        Angle Bending between atoms 1, 2, & 3. \par 
                Proper Dihedral torsion between atoms 6, 1, 2, & 4.\par 
                Improper Torsion (Explicitly defined) between atoms 5, 1, 6, & 2.\par 
}\pard \sl480 {\b \tab \par 
}\pard \sl480 \tab After the various PREP files were created, the LINK module was used to connect the individual residue PREP files. In the LINK input file, the residues are listed in the order that they need to be connected. A protein 
chain results from connecting standard residues. Non-standard residues like the heme porphyrin are also connected to proteins using the LINK module. \par 
\pard \sl480 \tab 
As the LINK module writes out the molecular topology only in terms of the molecules internal parameters, the EDIT module is required to fix the location of the atoms in Cartesian coordinate space. The EDIT module takes the output from the LINK module, and
 transforms the molecule's coordinates from internal to cartesian (x, y, and z) ones. Protein Database (PD
B) files are usually used by the EDIT module as a reference, with which to place the atoms in Cartesian coordinate space. The PDB files for the heme porphyrin were extracted from PDB files of myoglobin. The porphyrin coordinates were rotated and translated
 so that the metal center was located at the origin. The porphyrin plane was oriented parallel to the xy plane, such that the z direction was perpendicular to the porphyrin plane. All PDB files used in this thesis have been listed in Appendix B. \par 
\pard \sl480 \tab Atoms in
 the EDIT input file are with those in the PDB file using unique atom labels specified in the PDB and PREP files, and then missing atoms are filled in. In defining the porphyrins, opposite pyrrole ring nitrogens were defined the same, while adjacent ones h
ad different labels. Thus, two sets of atom labels were used for the pyrrole nitrogen atoms. Once the matching of atoms labels has been completed, a new PDB file is written out by the EDIT module. Finally, a topology file describing the connectivity of the
 residues is also created by the EDIT module.\par 
\pard \sl480 \tab 
The topology output from the EDIT module serves as an input to the PARM module. The PARM module assigns parameters to the various internal coordinates of the molecules determined by the previous modules. Values for these internal parameters are taken eith
er from standard AMBER files or user-defined "frcmod" files. The output file (prmtop file) generated by the PARM module contains information on both the connectivity as well as the parameters describing the mol
ecule's topology. This output is used by other AMBER modules. The sets of values for the internal parameters which is are used by the PARM module is the force field that one seeks to optimize for molecules. Values for parameters that were not optimized wer
e taken from the standard AMBER force field.{\up9 {\object\objicemb{\*\objname ICEmbdObject2_13}{\*\objdata 
0000006300000ca3685610000832cf454e524600000000004a00af9f66c90049b70a01010000000000023138000100000000000c000a000120120009000000000000000000010000001800000000000000114b6f6c6c6d616e2c203139393520233234}{\result {\pict\macpict\picw0\pich0 000a0000000000000000
}}}}{\fs18\up9 18}{{\object\objicemb{\*\objname ICEmbdObject3_14}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900af9f66c90049b70a}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}} \par 
\pard \sl480 \tab Vibration frequency calculations require that a molecule be at its energetic minimum (equilibrium structure), in order for harmonic approximations to be valid. Therefore, before any vibration analysis coul
d be done, the SANDER module was used to minimize the energy of the molecule. This module uses a first-derivative, conjugate-gradient algorithm to arrive at a minimum energy structure. The atoms defined by the PARM and EDIT modules are relaxed along a pote
ntial gradient, until an energetically minimized structure is reached. Minimization was stopped when the this gradient fell below 10{\fs20\up6 -4} kcal \'81{\fs20\up6 -1}
. While this minimization technique is effective for proteins, it is not sensitive enough to reach a minimum stru
cture for porphyrins and other smaller molecules modeled in this thesis. After minimizing with the SANDER module, a second-derivative, Newton-Raphson minimization technique was utilized to lock in onto the local minimum structures for these smaller molecul
es. The stopping criteria with this method could be more stringent than, and therefore, minimization was stopped when the potential gradient fell below 10{\fs20\up6 -5} kcal \'81{\fs20\up6 -1}
. This combination of first and second derivative techniques was chosen, as a second-derivative technique is likely to diverge if the molecule is not near equilibrium {\up9 {\object\objicemb{\*\objname ICEmbdObject4_15}{\*\objdata 
0000006400000ca3685610000832cf454e524600000000004b00af9f67d00049f4b701010000000000023135000100000000000c000a0001200f000900000000000000000001000000130000000000000012416c6c696e6765722c203139383220233139}{\result {\pict\macpict\picw0\pich0 
000a0000000000000000}}}}{\fs18\up9 15}{{\object\objicemb{\*\objname ICEmbdObject5_16}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900af9f67d00049f4b7}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}.\par 
\pard \sl480 \tab After minimization, the NMODE was used to calculate the various normal modes of the molecule, and the NMANAL module was used to analyze these normal modes. \par 
\pard \sl480 \par 
\pard \sl480\keepn {\v {\tc\tcl2\pard\plain \sl480\keepn \f20 {\b Molecular Mechanics Force Fields}}}{\b \par 
}\pard \sl480\keepn \tab The AMBER force field evolves out of the following potential energy function.\par 
\tab \par 
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7402816902816f02816e0281730000004a00a0008dff}}}}\pard \sl480\keepn \par 
\pard \sl480\keepn {\b Equation 2.1 AMBER Potential Equation. }\par 
\pard \sl480 \par 
\pard \sl480\keepn {\v {\tc\tcl3\pard\plain \sl480\keepn \f20 {\b Bond and Angle Parameters}}}{\b \par 
}\pard \sl480\keepn \tab The first two terms represent the classical physics, harmonic approximation tha
t is made in a molecular mechanics models. Perturbations away from equilibrium are resisted by a restoring force, which raises the potential energy of the molecule. This rise in potential energy depends both on the restoring force constant (K{\dn4 r} or K
{\f23\dn4 f}) as well as the square of the perturbation away from equilibrium.  Therefore, the values of K{\dn4 r} and K{\f23\dn4 f} are dependent on the choice of r{\dn4 eq} and {\f23 f}{\dn4 eq}
 values. In this thesis, two modeling approaches were employed, each of which exploited the interdependance of force constants and equilibrium values in different ways.\par 
\pard \sl480\keepn \par 
\pard \sl480 {\v {\tc\tcl4\pard\plain \sl480 \f20 {\b Sundar/Sontum_old Modeling Method}}}{\b \par 
}\pard \sl480 {\b \tab }In the first method, r{\dn4 eq} and {\f23 f}{\dn4 eq}
 values were taken from X-ray crystal structures of the molecules. Therefore for NiOEP, crystal structure values used by Li et. al. were used. The force constants were then varied to obtain a good vibrational fit. Finally, the structural parameters were ag
ain varied till a good structural fit was also obtained. The emphasis of this method was to obtain vibrational fits by varying the force constants, while a geometric fit was obtained by mostly varying the equilibrium structural (r{\dn4 eq} and {\f23 f}{
\dn4 eq}) constants.\par 
\pard \sl480 \par 
\pard \sl480\keepn {\v {\tc\tcl4\pard\plain \sl480\keepn \f20 {\b Sundar/Sontum_new Modeling Approach}}}\par 
\pard \sl480\keepn \tab The second approach was fundamentally different from the previous one, as force constants were also varied to get a good geometric fit. Instead of crystal structure values,.equilibrium bond distances (r{\dn4 eq} and {\f23 f}{\dn4 
eq}) were set to unstrained bond lengths, while equilibrium angles were set using hybridization arguments. Therefore, the Ni-N and Fe-N bond lengths were set to 1.86 \'81 and 1.93 \'81 respectively.{\up9 {\object\objicemb{\*\objname ICEmbdObject24_17}
{\*\objdata 
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}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}{\fs18\up9 26,27}{{\object\objicemb{\*\objname ICEmbdObject25_18}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900afa367de004291f6}{\result {\pict\macpict\picw0\pich0 
000a0000000000000000}}}}  Other bond lengths within the porphyrin were set using bond order arguments and a linear scaling formula developed by Kollman et. al.{\up9 {\object\objicemb{\*\objname ICEmbdObject26_19}{\*\objdata 
0000006300000ca3685610000832cf454e524600000000004a00afa3690e0042d96b01010000000000023138000100000000000c000a000120120009000000000000000000010000001800000000000000114b6f6c6c6d616e2c203139393520233234}{\result {\pict\macpict\picw0\pich0 000a0000000000000000
}}}}{\fs18\up9 18}{{\object\objicemb{\*\objname ICEmbdObject27_20}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900afa3690e0042d96b}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}
 Using this formula the CC-CB, CC-N, CB-CB, CC-CD distances were set to 1.38, 1.38, 1.35, 1.44 \'81 respectively. All sp{\fs20\up6 2} and sp{\fs20\up6 3} hyridized-atom equilibrium angles were set to 120\'a1 and 109.5\'a1
 respectively. As the equilibrium angles were not set crystal structure values, the minimized structure's parameters was more s
ensitive to force constant values than before. Therefore, the choice of force constants in the Sundar/Sontum_new modeling approach depended on both structural and vibrational fits. The units for the stretching and bending constants are kcal mol {
\fs20\up6 -1} A{\fs20\up6 -2} and kcal mol{\fs20\up6 -1} respectively.\par 
\pard \sl480 \par 
\pard \sl480 {\v {\tc\tcl3\pard\plain \sl480 \f20 {\b Dihedral Parameters (Bond torsion)}}}{\b \par 
}\pard \sl480 \tab These bond rotation terms restrict rotation around bonds. The potential energy of rotation around a bond is given by this Fourier series expansion around the equilibrium dihedral angle. In equation 2.1, V{\dn4 n}
 is the potential barrier to rotation in kcal Mol{\fs20\up6 -1}, n is the periodicity, {\f23 f} the rotation away from the equilibrium angle, and  {\f23 g }
the equilibrium dihedral angle. An additional redundancy factor, m, was also included in the PARM input file, although this term is not explicitly seen in the above force-field equation. This additional term is included to allow direct comparison of the to
tal barrier to rotation around a bond with values listed in the literature.  The dihedral Fourier series expans
ion reduces to a single term around each dihedral for relatively simple rotational potentials; for a double bond this dihedral Fourier expansion reduces to a single 2 fold (n=2) term. For more complicated types of rotational potentials,  like in ethylbenze
ne, a combination of these terms was required. Other molecular modeling packages, like Spartan, were used to determine the exact shape of the rotational potential. Fourier analysis was done to decompose this potential into its key components, and the impor
tant terms were input into the PARM input file. \tab \par 
\pard \sl480 \tab 
To help maintain planarity in molecules another, "improper" torsion term was also defined. These terms raise the potential energy of the molecule, if the angle between two planes defined by four non-consecutive atoms is distorted away from its predefined,
 equilibrium value.  As there exist a variety of plane definitions, which are possible between four non-consecutive atoms (Figure 2.2), these improper torsion terms need to be explicitly defined in the PREP
 module. Furthermore, as there is no consistent functional dependence between the distortion and the resultant rise in potential energy caused by these improper torsion terms, care was taken while different improper terms were compared. Usually scaling fac
tors were used while converting between various impropers defined on the same four atoms. Maggie Zraly had calculated the relevant scaling factors for improper torsion parameters listed in the literature.{\up9 {\object\objicemb{\*\objname 
ICEmbdObject12_21}{\*\objdata 0000006100000ca3685610000832cf454e524600000000004800afa225430007a6a901010000000000023233000100000000000c000a000120170009000000000000000000010000001a000000000000000f5a72616c792c203139393520233236}{\result 
{\pict\macpict\picw0\pich0 000a0000000000000000}}}}{\fs18\up9 23}{{\object\objicemb{\*\objname ICEmbdObject13_22}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900afa225430007a6a9}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}
 These scaling factors were used when improper torsion parameters listed in the literature needed to be used within the framework of the AMBER  force field.\par 
\pard \sl480 \par 
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\par 
\pard \keepn \tab {\b Figure 2.2 Different Improper Torsion Terms Possible on same Four Atoms\par 
\tab \tab i.  Angle defined by planes containing atoms 2, 1, &4 and 3, 1, & 4.\par 
\tab \tab ii. Angle defined by planes containing atoms 2, 1, &3 and 4, 2, & 3. }\par 
\pard \sl480 \par 
\pard \sl480\keepn {\v {\tc\tcl3\pard\plain \sl480\keepn \f20 {\b Non-bonded Parameters}}}{\b \par 
}\pard \sl480\keepn \tab These non-bonded parameters help to bring a molecule into its best spatial orientation. The physical effects represented by these parameters are Van der
 Waals and electrostatic forces. In AMBER 4.1, these parameters are defined between sets of atoms that are separated by at least 4 bonds. Steric interactions between atoms that 4 bond distances away are accounted for with this term.. As these parameters ar
e sensitive to the net atomic charges,  these charges needed to be carefully set. Usually, these charges were set to values obtained from semi-empirical calculations done in Spartan  or values present in the standard AMBER 4.1 force field (parm94.dat).{
\up9 {\object\objicemb{\*\objname ICEmbdObject14_23}{\*\objdata 
0000006400000ca3685610000832cf454e524600000000004b00afa2257d0007b46701010000000000023235000100000000000c000a00012019000900000000000000000001000000200000000000000012506561726c6d616e2c203139393420233332}{\result {\pict\macpict\picw0\pich0 
000a0000000000000000}}}}{\fs18\up9 25}{{\object\objicemb{\*\objname ICEmbdObject15_24}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900afa2257d0007b467}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}. \tab \par 
\pard \sl480 \par 
\pard \sl480 {\v {\tc\tcl2\pard\plain \sl480 \f20 {\b Normal Mode Analysis}}}{\b \par 
}{\v {\tc\tcl3\pard\plain \sl480 \f20 {\b NMODE}}}\par 
\pard \sl480 \tab This module was designed to perform "molecular mechanics calculations on proteins and nucleic acids".{\fs20\up6 25}
 In this thesis, this functionality has been extended to include other, much smaller molecules like benzene, ethylbenzene and the heme porphyrin. The NMODE module uses first and second derivative information to perform vibrational analyses of molecules aro
und their equilibrium structure.{\up9 {\object\objicemb{\*\objname ICEmbdObject16_25}{\*\objdata 
0000006400000ca3685610000832cf454e524600000000004b00afa2259b0007bb6b01010000000000023235000100000000000c000a00012019000900000000000000000001000000200000000000000012506561726c6d616e2c203139393420233332}{\result {\pict\macpict\picw0\pich0 
000a0000000000000000}}}}{\fs18\up9 25}{{\object\objicemb{\*\objname ICEmbdObject17_26}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900afa2259b0007bb6b}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}
 The vibrational frequencies are obtained by solving the Wilson-GF matrix composed of the various input force field constants.{\up9 {\object\objicemb{\*\objname ICEmbdObject18_27}{\*\objdata 
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}}}{\fs18\up9 17}{{\object\objicemb{\*\objname ICEmbdObject19_28}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900afa225a90007bea5}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}{\b  }
The NMODE module writes out the x, y and z displacement vectors of  the eigenvector solutions to the Wilson-GF matrix, along with the  vibrational frequencies associated with these normal modes. \par 
\pard \sl480 \tab \par 
\pard \sl480 {\v {\tc\tcl3\pard\plain \sl480 \f20 {\b NMANAL}}}\par 
\pard \sl480 \tab 
The NMANAL module was used to analyze the eigenvector data output from the NMODE module. These vectors were projected onto the various internal coordinates of the molecule, and the dependence of a particular eigenvector on these internal coordinat
es was determined. This dependence is known as the potential energy distribution (PED) of a particular mode or orbital, and provides an estimation of the "character" of a particular normal mode. If a mode of motion were comprised entirely of C-H stretches,
 then a large fraction of this mode's PED would contain contributions from C-H bond coordinates. Such a mode's character would then be classified as "primarily stretching" or "having significant stretching character".  A sample script controlling both the 
NMODE as well as the NMANAL programs is listed in Appendix D. \par 
\pard \sl480 \par 
\par 
\pard \sl480 {\v {\tc\tcl2\pard\plain \sl480 \f20 {\b Consistent Force Fields}}}\par 
\pard \sl480 \tab 
The force field defined in the PARM module was optimized by comparing the normal mode frequencies generated by the NMODE module with experimentally observed frequencies. The various constants contained in the force field were changed, either by hand or us
ing an algorithm, until the difference between the theoretically calculated and experimentally observed frequencies was minimized. Upon minimization of this differ
ence, a consistent force field was said to have been obtained, as such a force field was consistent with experimentally observed data. The focus of this thesis was to generate a consistent force field for the NiOEP molecule. Transferability of this optimiz
ed force field was emphasized for two reasons: the NiOEP force field had to be transferred to the heme porphyrin; new approaches towards developing force fields needed to be tested on smaller molecules like benzene, toluene and ethylbenzene, and the result
s of such testing needed to be transferred over to  the nickel porphyrin. \par 
\pard \sl480 \par 
\pard \sl480 {\v {\tc\tcl3\pard\plain \sl480 \f20 {\b Optimization Procedures}}}{\b \par 
}\pard \sl480 \tab Fundamentally the Wilson-GF matrix in molecular mechanics is under-determined, as the total number of normal modes is smaller than the number of force constants present in the GF matrix{\b .}{\up9 {\object\objicemb{\*\objname 
ICEmbdObject20_29}{\*\objdata 0000006400000ca3685610000832cf454e524600000000004b00afa226190007d90401010000000000023135000100000000000c000a0001200f000900000000000000000001000000130000000000000012416c6c696e6765722c203139383220233139}{\result 
{\pict\macpict\picw0\pich0 000a0000000000000000}}}}{\fs18\up9 15}{{\object\objicemb{\*\objname ICEmbdObject21_30}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900afa226190007d904}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}
  It is possible to arrive at similar, optimized frequency matches with different force fields (i.e. different sets of force constants yield the same set of frequencies). There exists another problem which  becomes ac
ute as the size of the modeled molecule increases. For an N-atom molecule, the total number of normal modes is 3N-6. As these various modes span the same frequency range (approximately 3000 cm{\up6 -1}
 in porphyrin systems), in bigger molecules it is difficult to assign and match correct normal modes to observed frequencies. This misalignment problem is particularly acute in the 400 cm{\up6 -1} to 1100 cm{\up6 -1}
 range, where dihedral, bending and stretching frequencies are found. While isotopic shift data and structural featu
res of the modeled molecule helped to increase the criteria with which to select a particular force field, additional considerations were needed to help make  correct matches between calculated and observed frequencies. \par 
\pard \sl480 \par 
\pard \sl480\keepn {\v {\tc\tcl3\pard\plain \sl480\keepn \f20 {\b Symmetry}}}{\b \par 
}\pard \sl480\keepn \tab 
All the molecules, whose force fields were optimized, possessed inherent symmetry and belonged to a symmetry point group. Group theoretical considerations classify a molecule's normal modes into irreducible representations (symmetry types).  Symmetry cons
iderations preclude n
ormal modes belonging to different irreducible representations from mixing . Therefore, optimization of the force field was done within each irreducible representation, where assignments of frequencies became easier. Additional algorithms were developed to
 combine the output from the NMANAL and NMODE modules with these symmetry considerations.  A description of these algorithms follows. \par 
\pard \sl480  \par 
\pard \sl480\keepn {\b Symmetry Program (nsym)\par 
}\pard \sl480\keepn \tab Normal modes belonging to the same symmetry type transform in the same fashion under individua
l, symmetry operations. Within an irreducible representation, the dot product of eigenvectors transformed by a symmetry operation with untransformed eigenvectors are the same.  Normal modes that were symmetric and anti-symmetric with respect to the symmetr
y operation have dot product values of 1 and -1 respectively. Degenerate normal modes, on the other hand, have dot products that were 0, 1 nor -1. The dot products of four operations was exploited by the nsym algorithm,  which classified various normal mod
es into their symmetry types.  A 'syminfo' input file was created, in which matrices corresponding to four symmetry operations in the molecules point group were defined. The dot products of eigenvector transformation were then computed by the nsym algorith
m. As the syminfo file also contained the expected dot products for each of the irreducible representations, the eigenvectors generated by the NMODE module could be classified by the nsym algorithm. The expected number of normal modes within each irreducib
le representation was also present in the input file. This input was used by the nsym module as a check. If there were problems in assigning the symmetry type, the nsym module calculated a flake index which quantified the difference between the actual and 
calculated dot products. The symmetry types of molecular vibrations which had high flake indices were reassigned in a random fashion until the number normal modes assigned to each symmetry type matched the input in the syminfo file. Serious problems in sym
metry matches indicate imbalances in the force field itself, hence the symmetry criterion helped develop well-balanced force fields.  The syminfo files used for the different molecules are listed in Appendix E.\par 
\pard \sl480 \par 
\pard \sl480\keepn {\v {\tc\tcl3\pard\plain \sl480\keepn \f20 {\b Potential Energy Distribution  (nfit algorithm)}}}{\b \par 
}\pard \sl480\keepn \tab 
Another criterion considered while making normal mode assignments was the "character" of the various vibrations.  As mentioned before, the NMANAL module computes the sensitivity of the various normal modes to the internal coordinates (bonds etc.).
  This sensitivity is quantified by the NMANAL module as a percentage of the total potential energy of the normal mode. An algorithm was developed which used the PED data computed by the NMANAL module to determine the character of all the normal modes. If 
a normal mode were only dependent upon torsion coordinates, then it was given a character of 40. Similarly, pure bending and stretching normal modes were assigned characters of 30 and 20 respectively.  Normal modes, in which different internal coordinates 
mixed, did not have pure 20, 30, or 40 character values, instead their characters were determined by the nfit algorithm as a weighted average of their PED values.  Such classification of orbitals was done because literature data was often classified using 
PED distribution values. Therefore, in our observed files, experimentally observed data was also classified according to their characters. Normal modes which were pure dihedral, bend or stretch in character were assigned values of 40, 30 and 20 respectivel
y. For orbitals that were mixed in their character, Table 2.1 list the classification that was used to separate out mixed character, observed frequencies. \par 
\pard \sl480\keepn {\b Table 2.1 Character Classification Used}{\b\fs20 .\par 
}\trowd \trgaph80\trleft-80 \clbrdrt\brdrth \clbrdrl\brdrth \clshdng0\cellx4384\clbrdrt\brdrth \clbrdrr\brdrth \clshdng0\cellx8848\pard \sl480\keepn\intbl Bond Character (=X)\cell Associated Value\cell \pard \intbl {\ul \row }\trowd \trgaph80\trleft-80 
\clbrdrt\brdrs \clbrdrl\brdrs \clshdng0\cellx4384\clbrdrt\brdrs \clbrdrr\brdrs \clshdng0\cellx8848\pard \sl480\keepn\intbl Bond and Dihedral mix\cell 15{\fs20  < X < }20{\fs20 .}\cell \pard \intbl {\ul \row }\trowd \trgaph80\trleft-80 \clbrdrl\brdrs 
\clshdng0\cellx4384\clbrdrr\brdrs \clshdng0\cellx8848\pard \sl480\keepn\intbl Bond and Bend mix\cell 20 < X < 30.\cell \pard \intbl {\ul \row }\pard \sl480\keepn\intbl Dihedral and Angle mix\cell 30 < X < 40.\cell \pard \intbl {\ul \row }\trowd 
\trgaph80\trleft-80 \clbrdrl\brdrs \clbrdrb\brdrs \clshdng0\cellx4384\clbrdrb\brdrs \clbrdrr\brdrs \clshdng0\cellx8848\pard \sl480\keepn\intbl Dihedral and Angle mix\cell 40 < X < 45 .\cell \pard \intbl {\ul \row }\pard \sl480 \par 
\pard \sl480 {\v {\tc\tcl3\pard\plain \sl480 \f20 {\b Calc. File}}}\par 
\pard \sl480 \tab Once the calculated normal modes had been classified according to their symmetry types and character, they were compi
led into a file called the calc.file. In this file, the calculated frequencies were listed in increasing order of their frequencies, along with their irreducible representation (symmetry) and bond character (character). Finally, frequencies belonging to th
e same symmetry type were ranked in increasing order of their frequency (position). This ranking constituted the "position" of the normal modes.   Classification and ordering of the frequencies within the calc.file became necessary to have a systematic met
hod of comparing calculated and experimental frequencies. \par 
\pard \sl480 \par 
\pard \sl480 {\v {\tc\tcl3\pard\plain \sl480 \f20 {\b Observed File}}}{\b \par 
}\pard \sl480 {\b \tab }
Experimentally observed frequencies were listed in an observed file, in which the character, position and frequency of these observed frequencies were listed.  As the format of the observed frequencies was similar to that of the calculated frequencies  lis
ted in the calc.file, it was possible to develop algorithms which matched calculated and observed normal modes. \par 
\pard \sl480 \par 
\pard \sl480\keepn {\v {\tc\tcl3\pard\plain \sl480\keepn \f20 {\b Matching Algorithm (NFIT_12)}}}\par 
\pard \sl480\keepn \tab The nfit_12 algorithm matched
 the various orbitals generated by the NMODE and classified by other modules and algorithms in the calc.file to those listed in an observed file. It made these assignments by comparing the symmetry, character, position and frequency of the calculated orbit
als within the calc.file with those values specified in the observed file. This algorithm was set up such that it was possible to weight the relative importance of each of these factors (symmetry, character, position and frequency) while making the assignm
ents.  The formula used by this algorithm to determine the best possible assignment is given by Equation 2.2:\par 
\pard \sl480\keepn   {\b MATCH=  \{W}{\b\fs20\dn4 1}{\b (}{\b\f23 s}{\b\fs20\dn4 obs}{\b\f23 -s}{\b\fs20\dn4 calc}{\b\f23 ) \}}{\b\f23\fs20\up6 2}{\b\f23  + \{}{\b W}{\b\fs20\dn4 2}{\b\f23 (t}{\b\fs20\dn4 obs}{\b\f23 -t}{\b\fs20\dn4 calc}{\b\f23 )\}}{
\b\f23\fs20\up6 2}{\b + \{W}{\b\fs20\dn4 3}{\b (P}{\b\fs20\dn4 calc}{\b -P}{\b\fs20\dn4 obs}{\b )\}}{\b\fs20\up6 2}{\b  + \tab \tab \tab \tab \{W}{\b\fs20\dn4 4}{\b (}{\b\f23 u}{\b\fs20\dn4 calc}{\b\f23 -u}{\b\fs20\dn4 obs}{\b\f23 )\} }{\b\f23\fs20\up6 2}
{\b\f23 \par 
}\pard \sl480\keepn {\b Equation 2.2  Equation Used to Determine the Best Possible Orbital Match up.}{\b\f23  \par 
}\pard \sl480 \tab In equation 2.2, w refers to weights for each of the individual match criteria. {\f23 s} represents the symmetry types of the observed and calculated frequencies being matched together. Similarly, {\f23 t, }P and {\f23 u}
 refer to the character, posit
ion and frequency classifications of the observed and calculated frequencies. The nfit_12 algorithm used the MATCH equation to compare calculated and observed frequencies. All the frequencies were assigned so that the value of the MATCH equation was minimi
zed. It was possible to control the types of matches being made by altering the weights associated with each individual match criteria. As group theoretical considerations do not allow mixing of normal modes between different symmetries, it became necessar
y to prevent the matching of observed and calculated frequencies belonging to different symmetries. Setting weights associated with the symmetry matches to values much larger than those associated with the character, position and frequency matches ensured 
that matching of orbitals between symmetries did not occur. Typically the following sets of weights were used: w{\fs20\dn4 1}=300,  w{\fs20\dn4 2}=5.0,  w{\fs20\dn4 3}=1.0, w{\fs20\dn4 4}=0. The weight associated with the frequencies of the orbitals (w{
\fs20\dn4 4}) was kept at zero, so that mixing of orbitals between symmetries was avoided when the force fields was not optimized.\par 
\pard \sl480 \tab 
The nfit_12 matching algorithm had several filters that could be applied to further control the type of assignments that occurred. One option was to allow "redundancy" matches between observed and calculated frequencies (ioption=0). Several calculated fre
quencies could be matched to a single observed frequency. Therefore, each calculated frequency was compared to all the observed frequencies to find the minimum value for the MATCH equation
.  Thus, matches could be completed even when the number of calculated orbitals with a particular character did not match the number of normal modes listed in the observed file. It was hoped that once the parameters were sufficiently optimized, the charact
ers of the calculated orbitals would automatically correspond to those listed in the observed file. Another consistently used, matching option was the "lockout" match (ioption=1), which removed redundancies by locking out the calculated frequencies. Theref
ore, the observed set continually got smaller as the matches progressed. The problem with this option, however, was that if a misasignment occurred in the low lying frequencies, the error was carried forward to all subsequent matches also. To correct for t
his deficiency, another option was developed (ioption=2). This option contained an additional refinement. Once a frequency had been assigned with the lockout match (ioption=1), the remaining frequencies were reordered, from to low to high, before any furth
er assignments were done. The nsymm algorithm with ioption=2 was mostly used, as this option consistently gave the best match. \par 
\pard \sl480 \par 
\pard \sl480\keepn {\v {\tc\tcl3\pard\plain \sl480\keepn \f20 {\b Orbital Visualization}}}{\b \par 
}\pard \sl480\keepn \tab 
While the nfit algorithm helped to classify the various vibration into bond, bend or dihedral characters, it did not provide any information regarding the actual dihedral, bend or stretch parameters that were involved with these orbitals.  Two additional 
methods were developed to help visualize, or determine the "shape" of, the calculated orbitals. \par 
\pard \sl480\keepn {\v {\tc\tcl4\pard\plain \sl480\keepn \f20 {\b NMODE_P and RUN.VIS}}}{\b \par 
}\pard \sl480\keepn \tab 
The nmode_p module projected each of the atom eigenvectors for a particular normal mode on to the x-y plane. The value of this projection was then written out, and could be compared to eigenvector diagrams determined by Spiro's group for the nickel porphy
rins. This module proved to be adequate in visualizing pure "out of plane" (OOP) motions of normal modes, but inplane motions could not be tracked by this module. Another program was developed to look at the 3 dimensional shapes of the 
various normal modes.\par 
\pard \sl480 \tab 
The Run.vis script subtracted a certain proportion of an normal mode eigenvector, produced by the NMODE module, from the equilibrium position of the atoms.  The resultant difference was then written out in a PDB format along with the equilibrium positions
 of the atoms. A superimposed figure was then obtained by visualizing the output PDB file using RASMOL. Thus, the 3-dimensional displacement occurring in a particular normal mode was visualized.  Figures 2.3 and 2.4 show the sample vi
sualization of normal modes, as seen using the run_p and Run.vis scripts.  \par 
\pard \keepn \par 
\pard \keepn {\f22\fs20     ............................................................    \par 
     .                 -3                     2                 .    \par 
     .                       -1        42                       .    \par 
     .                    -1               1                    .    \par 
     .                  -1  -1           1   0                  .    \par 
     .                  -1                   0                  .    \par 
     .                          0    0                          .    \par 
     .                                                          .    \par 
     .               2                          -3              .    \par 
     .  1                     0        -1                    -1 .    \par 
     .       7 6         1                  -2        -5-7      .    \par 
     .     1                       0                      -1    .    \par 
     .    -2                                             0 3    .    \par 
     .   -9            2                      -2            10  .    \par 
     .           2                                  -2          .    \par 
     .                    2        0       -2                   .    \par 
     .           2                                  -2          .    \par 
     .   -10           2                      -2            9   .    \par 
     .    -30                                            0 2    .    \par 
     .     1                       0                      -1    .    \par 
     .       7 5         2                  -1        -6 7      .    \par 
     .  1                     1        0                     -1 .    \par 
     .               3                          -2              .    \par 
     .                                                          .    \par 
     .                          0    0                          .    \par 
     .                  0                    1                  .    \par 
     .                  0   -1           1   1                  .    \par 
     .                    -1               1                    .    \par 
     .                       --4       1                        .    \par 
     .                 -2                     3                 .    \par 
     ............................................................    \par 
}\pard \keepn {\b \par 
Figure 2.3 Run_p output for OOP mode Vibration\par 
\tab \tab \tab Numbers refer to Eigenvector Projections on the xy plane.}\par 
\pard \keepn {{\pict\macpict\picw640\pich480 
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ec00fed008cec9c7c5c3c3bfc1bffebc03bfc1c1c9fdd018cbcecbc96660524b3e30292922151c15150e15151c1c446066ef001fd0cec9c5c1bcbcbab8b66666604444371c3e3730221c1c0e150e070e070e1c308100b00000ba8e0004ffff00fffffd00fcff010000feff0000feff030000fffffe0001fffffe0001fffffe
00fcff010000fbff050000ffff0000feff0000feff0000fbff0000feffee0000ffba0004d0c7c7d0d0fe66186052443e3e3729302929222929303752523e37302229222937ef00fed004cecec9c7c7fec306c1c3c1c3c7ce00f9d0086666594b3e37302929fe1cfe15031c1c223eed0016d0cec9c7c3bfbcbcbab6b8666660
60443744373729221cfe15050e150e151c378100b00000c58e00fcfffe0005ffff0000fffffe0006ffff0000ffff00fefffe0003ffff0000fefffe0007ffff0000ffff0000fcff0000fefffe0007ffff0000ffff0000feff0000feff0200ffffef0000ffba0004c7bfc70000fe660860524b443e3e303730fe290930373752
37292922151cfe15011c30f100fdd005cec9c9c7c3c5fcc301c7cefc0017d000006666594b3e3e30292922151c15150e150e1515223eee0008d0d0cbc7c3c1bfbcbcfeb80db66666594b3e3729221c1c0e150efe07030e1515378100b10000c88e0004ffff00fffffe0005ffff0000fffffe0009ffff0000ffff0000fffffe
0001fffffe0001fffffe0009ffff0000ffff0000fffffc0001fffffe0011ffff0000ffff0000ffff0000ffff0000fffff00000ffba0002d0c7c7fd00fe66046044221c4bfe3e0a373e373e4b60224437221cfe15040e15151c30f100fdd004cececbc7c9fec702c9c9d0f7000b666660524b3e373730222922fe1c03222929
4bee0017d0d0cbc7c3c3bfbcbcbab6b8b6b6b466605244372929221cfe15060e070e15151c378100b10000be8e0001fffffb0005ffff0000fffffe0009ffff0000ffff0000fffffe0001fffffe0001fffffe0009ffff0000ffff0000fffffc0001fffffe0011ffff0000ffff0000ffff0000ffff0000fffff10000ffb90002
c7bfc7fd00fe66064444221c1c3e44fc3e0f4b601c2244371c0e150e070e070e1c30f100fbd006cbcecbc9cbced0f600fe6605594b3e3e3737fe2906221c222929304bed0020d0d0cec9c7c3c1c1bfbabcbab8b86660524b3e30292922151c15150e15151c1c3e8100b10000b68e0001fffffb0005ffff0000fffffe0009ff
ff0000ffff0000fffffe0001fffffe0001fffffe0009ffff0000ffff0000fffffc0001fffffe0011ffff0000ffff0000ffff0000ffff0000fffff10000ffba0002d0c7c7fb00086666444422301c1c22fe4b0852526644371c224437fe15050e150e151c37ef00f8d0f400fe660f6052443e3e3729302929222929303752ed
00fed005cbc7c3c3c1c1febc0abab86666594b3e37302929fe1cfe15031c1c223e8100b10000b88e0001fffffe0008ffff00ffff0000fffffe0002ffff00feff030000fffffe0001fffffe0001fffffe0009ffff0000ffff0000fffffc0001fffffe0002ffff00feff0b0000ffff0000ffff0000ffffa90002d0bfc7fb0017
666044221c221c37445952596066444b44601c22440e150efe07030e151537ec0000d0f000fe660860524b443e3e303730fe290330373752ed00fed01ecec9c5c3c3c1bcbfbcbc6666594b3e3e30292922151c15150e150e1515223e8100b20000868f00f9ff010000fcfffd00f7ff0000fdff0000fdfffe00fdff010000fd
fffe00fdfffe00efffaa0002c7bfc7fb000866444422221c222244fc660660666644601c22fe15060e070e15151c37d900fe66046060524b4bfe3e05373e373e4b60ec00fed016cec9c7c5c3c3bfc1bfbcbc666660524b3e373730222922fe1c032229294b8100b1000065820001ffff8100ea0002d0c7c7fa000366444422
fe1c042244d0cbcefe660f606666446022151c15150e15151c1c3ed900fd66056052524b3e44fc3e014b60eb00fed004cecec9c7c7fec301c1c3fe6605594b3e3e3737fe2906221c222929304b8100b1000060820001ffff8100ea0002c7bfc7fb00086666444422301c3744fdd0fd66046066664429fe1cfe15031c1c223e
d800fd66046060594b52fe4b02525266ea00fdd005cec9c9c7c3c5fec3fe660f6052443e3e37293029292229293037528100b10000628300fdff8100ef0005c30000d0c7c7fa0020666044221c221c37440000d06666594b3e6660292922151c15150e150e1515223ed800fb660659605952596066e800fdd004cececbc7c9
fec7fe660860524b443e3e303730fe2903303737528100b100005781008100f10009c9c3c1bfbabcbabcc1c7fa000866444422221c222244fd000b666660524b3e373730222922fe1c032229294bd500f866e500fbd005cbcecbc9cbcefe66046060524b4bfe3e05373e373e4b608100b000005181008100f30007cec5c1bc
bcbab6b8feb601b8bffb000366444422fe1c012244fd00fe6605594b3e3e3737fe2906221c222929304bd1000066df00f8d00000fd66056052524b3e44fc3e014b608100b000004f81008100f40006d0c7c3c1bcbab8feb604b4b6b6b8bffd0008663e44221c221c3744fc00fe660f6052443e3e3729302929222929303752
aa0000d0fb00fd66046060594b52fe4b025252668100af0000558100dc00fbffef0001fffff90001ffffbe001cd0c9c3c1bfbab8b8b4b6b4b2b4b2b4b8bf523e37302229222937222244fc00fe660860524b443e3e303730fe290330373752a200fb6606596059525960668100ae00004b8100db0005ffff0000ffffeb0001
ffffb90007d0cbc5c1c1bcbab8feb60bb4b6b4b6604437292922151cfe15021c3044fb00fe66046060524b4bfe3e05373e373e4b609f00f8668100ac00004a8100db0001fffffe0001ffffec0001ffffba000bd0cbc7c3c1bcbab8b8b4b6b4feb206664b3e3729221cfe15040e15151c30fb00fd66056052524b3e44fc3e01
4b609b0000668100a80000628100db0001fffffe0001fffffe00fefffd00fdff050000ffff0000fdff030000fffffd00fefffe00fbffcf0008d0cec9c5c1bcbcbab8feb612b4b266523e3730221c1c0e150e070e070e1c30fb00fd66046060594b52fe4b0252526681008100c000006a8100db0005ffff0000fffffe000cff
ff00ffff0000ffff00ffff00fefffe0003ffff0000fefffe0004ffff00fffffe00feff0200ffffd00015d0cec9c7c3bfbcbcbab6b8b6b6b4665944373729221cfe15050e150e151c37fa00fb66065960595259606681008100bf0000608100db00fcfffe0001fffffe0004ffff00fffffc0001fffffe0001fffffe0005ffff
0000fffffe0009ffff0000ffff0000ffffd00008d0d0cbc7c3c1bfbcbcfeb80cb666594b3e3729221c1c0e150efe07030e151537f900f86681008100bd0000638100db0001fffffb0001fffffe0003ffff0000fefffe0001fffffe0001fffffe0005ffff0000fffffe0009ffff0000ffff0000ffffd10016d0d0cbc7c3c3bf
bcbcbab6b8b6b666605244372929221cfe15060e070e15151c37f500006681008100b900005e8100db0001fffffb0001fffffe0001fffffd0005ffff0000fffffe0001fffffe0005ffff0000fffffe0009ffff0000ffff0000ffffd0001fd0d0cec9c7c3c1c1bfbabcbab86660524b3e30292922151c15150e15151c1c3e81
008100ac00005a8100db0001fffffa000fffff00ffff0000ffff00ffff0000fffffe00fdff0200fffffe0004ffff00fffffe0005ffff0000ffffd000fed005cbc7c3c3c1c1febc09ba6666594b3e37302929fe1cfe15031c1c223e81008100ac00004c8100dc00fcfffb00fefffe00fdff010000fdfffe0002ffff00fdfffe
00fefffe00f9ffd100fed01dcec9c5c3c3c1bcbfbc6666594b3e3e30292922151c15150e150e1515223e81008100ad00002c81008100f600fed015cec9c7c5c3c3bfc1bfbc666660524b3e373730222922fe1c032229294b81008100ac00002b81008100f500fed004cecec9c7c7fec300c1fe6605594b3e3e3737fe290622
1c222929304b81008100ac00002a81008100f500fdd007cec9c9c7c3c5c3c3fe660f6052443e3e372930292922292930375281008100ac00002981008100f400fdd006cececbc7c9c7c7fe660860524b443e3e303730fe29033037375281008100ac00002581008100f300fbd004cbcecbc9cbfe66046060524b4bfe3e0537
3e373e4b6081008100ab00001c81008100f100f8d0fd66056052524b3e44fc3e014b6081008100ab00001e81008100ed0000d0fc00fd66046060594b52fe4b0252526681008100aa00001681008100e600fb66065960595259606681008100a900000e81008100e400f86681008100a700000e81008100e000006681008100
a300000a81008100810081008100000a81008100810081008100000a81008100810081008100000a81008100810081008100000a81008100810081008100000a81008100810081008100000a81008100810081008100000a81008100810081008100000a81008100810081008100000a81008100810081008100000a810081
00810081008100000a81008100810081008100000a81008100810081008100000a81008100810081008100000a81008100810081008100000a81008100810081008100000a81008100810081008100000a81008100810081008100000a81008100810081008100000a81008100810081008100000a81008100810081008100
000a81008100810081008100000a81008100810081008100000a81008100810081008100000a81008100810081008100000a810081008100810081000000ff}}{\b Figure 2.4  Run.vis Output for an O.O.P. Normal Mode. \par 
}\pard \keepn Light trace represents the NiOEP Molecule at its Equilibrium Position.\par 
Dark Trace shows the NiOEP molecule at Maximum Displacement in this particular Normal Mode{\b .}\par 
\pard \sl480\keepn {\v {\tc\tcl2\pard\plain \sl480\keepn \f20 {\b Force Constant Optimization}}}{\b \par 
}\pard \sl480\keepn \tab 
A non-linear, weighted optimization procedure was used to improve the correlation between calculated and observed frequencies, once these two sets of frequencies were matched correctly using the MATCH equation.  The following formula was used to determine
 correlation between  correctly assigned frequencies. \par 
\pard \sl480\keepn {\dn54 {\object\objemb{\*\objname Embedded_Object_2}{\*\objclass Equation}{\*\objdata 0102000002000000090000004571756174696f6e0000000000000000008b010000
02000101000a04010101028120028120028120028120028120028120028120028120028120028463030f00000b110102813200000a02863d031d000001128377030f01000b011283690011000a02822802846e030f01000b011282651282781282700011000a02862d02846e030f01000b0112836312836112836c12836300
11000a028229030f00000b11010288320000000112836612837212836512837100110d0286e500000a010965c001028720028720028720028720028720028720028720028720028720028720028720028720028720028720028720028720028720028720028720028720028720028177028168028165028172028165028720
028177030f01000b010965c001028169000b11000965c00102863d02872002817702816502816902816702816802817402872002816102817302817302816902816702816e02816502816402872002817402816f02872002816102872002816602817202816502817102817502816502816e02816302817902872002816d02
8161028174028163028168000000
01020000050000000d0000004d45544146494c455049435400ec09000014f6ffffa80100000800ec09ec095621010009000003bf00000000005a00000000001500000026060f001f00ffffffff0400150000004d7245640f004d6963726f736f6674204472617700005a00000026060f00a9004d72456402009f0000009d00
0100840084008002a5010000000000000100030000000000ffffff0000000000ffffff000100000100000001000000000001000000000000010c0048656c7600a20203008a00ff00290003015f0b020011000301af0d0200120003100000000000ffffff00c0c0c00080808000ff00000080000000ffff00008080000000ff
00000080000000ffff00008080000000ff0000008000ff00ff0080008000000e00000026060f0012004d7245640300080000000000000040024002050000000b0200000000050000000c0240024002030000001e000400000003010800050000000102ffffff00050000000902000000000400000007010300040000000401
0d0004000000060101000400000002010200030000001e00040000002701ffff040000002701ffff0300000000008b46048b56068946f88956fa8b46088b560a8946fc8956fe837efa007507817ef800}{\result {\pict\macpict\picw361\pich62 
0ae800000000003e01691101a10064000eb77870720000001b0000000c0000a0008c01000a00000000003e0169070000000022003e01690000a000bea100c0000d63757272656e74706f696e740da000bf22000000000000a000be2c000800140554696d65730300140d00102e0004ff0000002b0210092020202020202020
202c000900170653796d626f6c03001704022924016303001404000d000c280009003001320300170d00102b0c07013d0300140402292001770d000c2b0a04016904000d0010280010006c012803001704022906016e03001404000d000c2b0904036578700300170d00102800100091012d0402290c016e0300140d000c2b
09040463616c6304000d001028001000bc01290d000c28000900c201320402280020004a046672657103001704000d0012280012004d01e503001404010d000e280037000215202020202020202020202020202020202020202020040029490577686572650401292201200400290401772b0b050169030017280037008501
3d0300140401290c01200400290406776569676874040129260120040029030861737369676e65640401293001200400290402746f0401290b012004002903016104012906012004002904096672657175656e637904012938012004002903056d61746368a100c0075e3330206469637420626567696e0a63757272656e74
706f696e742033202d3120726f6c6c20737562206e65672033203120726f6c6c207375622031313535322064697620313938342033202d3120726f6c6c206578636820646976207363616c652063757272656e74706f696e74207472616e736c617465203634203431207472616e736c6174650a3020343835206d6f766574
6f0a2f66732030206465660a2f7366207b6578636820647570202f667320657863682064656620647570206e6567206d6174726978207363616c65206d616b65666f6e7420736574666f6e747d206465660a2f6631207b66696e64666f6e7420647570202f63662065786368206465662073667d206465660a2f6e73207b63
662073667d206465660a353132202f54696d65732d526f6d616e2066310a28202020202020202020292073686f770a3131353220343835206d6f7665746f0a2f6632207b66696e64666f6e74206d6174726978206475702032202e323220707574206d616b65666f6e7420647570202f63662065786368206465662073667d
206465660a353132202f53796d626f6c2066320a2863292073686f770a3134383920323631206d6f7665746f0a333834202f54696d65732d526f6d616e2066310a2832292073686f770a3138353820343835206d6f7665746f0a353132202f53796d626f6c2066310a283d292073686f770a3238393420343835206d6f7665
746f0a353132202f54696d65732d4974616c69632066310a2877292073686f770a3332323820363133206d6f7665746f0a333834206e730a2869292073686f770a3333393920343835206d6f7665746f0a353132202f54696d65732d526f6d616e2066310a285c28292073686f770a3336303620343835206d6f7665746f0a
353132202f53796d626f6c2066320a286e292073686f770a3338393420363133206d6f7665746f0a333834202f54696d65732d526f6d616e2066310a28657870292073686f770a3435393120343835206d6f7665746f0a353132202f53796d626f6c2066310a282d292073686f770a3439383020343835206d6f7665746f0a
353132202f53796d626f6c2066320a286e292073686f770a3532363420363135206d6f7665746f0a333834202f54696d65732d4974616c69632066310a2863616c63292073686f770a3539373520343835206d6f7665746f0a353132202f54696d65732d526f6d616e2066310a285c29292073686f770a3631353720323631
206d6f7665746f0a333834202f54696d65732d526f6d616e2066310a2832292073686f770a3233333220393834206d6f7665746f0a333834202f54696d65732d4974616c69632066310a2866726571292073686f770a3234303520353338206d6f7665746f0a353736202f53796d626f6c2066310a285c333435292073686f
770a302031373230206d6f7665746f0a343438202f54696d65732d426f6c642066310a28202020202020202020202020202020202020202020292073686f770a323335322031373230206d6f7665746f0a343438202f54696d65732d526f6d616e2066310a287768657265292073686f770a333434342031373230206d6f76
65746f0a343438202f54696d65732d426f6c642066310a2820292073686f770a333535362031373230206d6f7665746f0a343438202f54696d65732d526f6d616e2066310a2877292073686f770a333930352031383932206d6f7665746f0a2869292073686f770a343230392031373230206d6f7665746f0a343438202f53
796d626f6c2066310a283d292073686f770a343539332031373230206d6f7665746f0a343438202f54696d65732d426f6c642066310a2820292073686f770a343730352031373230206d6f7665746f0a343438202f54696d65732d526f6d616e2066310a28776569676874292073686f770a353932322031373230206d6f76
65746f0a343438202f54696d65732d426f6c642066310a2820292073686f770a363033342031373230206d6f7665746f0a343438202f54696d65732d526f6d616e2066310a2861737369676e6564292073686f770a373537342031373230206d6f7665746f0a343438202f54696d65732d426f6c642066310a282029207368
6f770a373638362031373230206d6f7665746f0a343438202f54696d65732d526f6d616e2066310a28746f292073686f770a383033342031373230206d6f7665746f0a343438202f54696d65732d426f6c642066310a2820292073686f770a383134362031373230206d6f7665746f0a343438202f54696d65732d526f6d61
6e2066310a2861292073686f770a383334342031373230206d6f7665746f0a343438202f54696d65732d426f6c642066310a2820292073686f770a383435362031373230206d6f7665746f0a343438202f54696d65732d526f6d616e2066310a286672657175656e6379292073686f770a31303234342031373230206d6f76
65746f0a343438202f54696d65732d426f6c642066310a2820292073686f770a31303335362031373230206d6f7665746f0a343438202f54696d65732d526f6d616e2066310a286d61746368292073686f770a656e640aa000bfa1006401974d4154480001018b571e02000101000a04010101028120028120028120028120
028120028120028120028120028120028463030f00000b110102813200000a02863d031d000001128377030f01000b011283690011000a02822802846e030f01000b011282651282781282700011000a02862d02846e030f01000b0112836312836112836c1283630011000a028229030f00000b1101028832000000011283
6612837212836512837100110d0286e500000a010965c001028720028720028720028720028720028720028720028720028720028720028720028720028720028720028720028720028720028720028720028720028720028177028168028165028172028165028720028177030f01000b010965c001028169000b11000965
c00102863d02872002817702816502816902816702816802817402872002816102817302817302816902816702816e02816502816402872002817402816f02872002816102872002816602817202816502817102817502816502816e02816302817902872002816d0281610281740281630281680000004f67a0008dff}}}
}\pard \sl480\keepn \par 
\pard \sl480\keepn {\b Equation 2.3  Average Weighted Standard Deviation Equation.}\par 
\pard \sl480 \par 
\pard \sl480 \tab The weights were usually assigned depending on the accuracy of the observed frequency.  The weights were calculated using the formula {\dn26 {\object\objemb{\*\objname Embedded_Object_10}{\*\objclass Equation}{\*\objdata 0102000002000000
090000004571756174696f6e0000000000000000003700000002000101000a01028177030f01000b010281690011000a02863d03290000010288310001028473030f00000b1101028832000000000000
01020000050000000d0000004d45544146494c455049435400ec09000014f6ffffa80100000800ec09ec095621010009000003bf00000000005a00000000001500000026060f001f00ffffffff0400150000004d7245640f004d6963726f736f6674204472617700005a00000026060f00a9004d72456402009f0000009d00
0100840084008002a5010000000000000100030000000000ffffff0000000000ffffff000100000100000001000000000001000000000000010c0048656c7600a20203008a00ff00290003015f0b020011000301af0d0200120003100000000000ffffff00c0c0c00080808000ff00000080000000ffff00008080000000ff
00000080000000ffff00008080000000ff0000008000ff00ff0080008000000e00000026060f0012004d7245640300080000000000000040024002050000000b0200000000050000000c0240024002030000001e000400000003010800050000000102ffffff00050000000902000000000400000007010300040000000401
0d0004000000060101000400000002010200030000001e00040000002701ffff040000002701ffff0300000000008b46048b56068946f88956fa8b46088b560a8946fc8956fe837efa007507817ef800}{\result {\pict\macpict\picw69\pich30 
047600000000001e00451101a10064000eb77870720000000d0000000c0000a0008c01000a00000000001e0045070000000022001e00450000a000bea100c0000d63757272656e74706f696e740da000bf22000000000000a000be2c000800140554696d65730300140d00102e0004ff0000002b011101770d000c2b0d0401
692c000900170653796d626f6c0300170d00102800110016013d03001428000c0027013103001704022b0910017303001404000d000c280015003b013207000100012200010036ee1aa100c0035a3330206469637420626567696e0a63757272656e74706f696e742033202d3120726f6c6c20737562206e65672033203120
726f6c6c20737562203232303820646976203936302033202d3120726f6c6c206578636820646976207363616c652063757272656e74706f696e74207472616e736c617465203634202d32383632207472616e736c6174650a2d31302033343036206d6f7665746f0a2f66732030206465660a2f7366207b65786368206475
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}, where {\dn4 {\object\objemb{\*\objname Embedded_Object_11}{\*\objclass Equation}{\*\objdata 0102000002000000090000004571756174696f6e0000000000000000000c00000002000101000a010284730000
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0d0004000000060101000400000002010200030000001e00040000002701ffff040000002701ffff0300000000008b46048b56068946f88956fa8b46088b560a8946fc8956fe837efa007507817ef800}{\result {\pict\macpict\picw13\pich11 
022900000000000b000d1101a10064000eb7787072000000020000000c0000a0008c01000a00000000000b000d070000000022000b000d0000a000bea100c0000d63757272656e74706f696e740da000bf22000000000000a000be2c000900170653796d626f6c03001704020d00102e0004ff0000002b01090173a100c001
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 was the uncertainty in the observed frequency. Some of the frequencies listed by Li et. al, were not observed by them, but rather predicted by their own vibrational force field. Therefore, while these frequencies were listed in the observed file, the weig
hts associated with these frequencies was set to zero. While some degree of "hand-tweaking" of the various force constants was done, to get the order of these frequencies to approximately match the obser
ved frequencies, coupling between parameters prevented extensive use of this method. Therefore, two algorithms were developed, which did such "hand-tweaking" in a controlled, iterative fashion.\par 
\pard \sl480   \par 
\pard \sl480\keepn {\v {\tc\tcl3\pard\plain \sl480\keepn \f20 {\b Ravine Algorithm}}}{\dn4 \par 
}\pard \sl480\keepn \tab This algorithm{\up9 {\object\objicemb{\*\objname ICEmbdObject22_13}{\*\objdata 
0000006500000ca3685610000832cf454e524600000000004c00afa236700047b02b01010000000000023238000100000000000c000a0001201c0009000000000000000000010000002a0000000000000013426576696e67746f6e2c203139363920233432}{\result {\pict\macpict\picw0\pich0 
000a0000000000000000}}}}{\fs18\up9 28}{{\object\objicemb{\*\objname ICEmbdObject23_14}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900afa236700047b02b}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}
 allowed systematic variation of sets of parameters, in a manner that reduces the {\f23 c}{\f23\fs20\up6 2}.  As the name suggest this algorithm runs on a {\f23 c}{\f23\fs20\up6 2}
contour map and connects the "ravines" which exist in this map.  It steps along the largest gradient on the contour map to reduce the {\f23 c}{\f23\fs20\up6 2}. A central assumption made when using this technique is that the various valleys in the {\f23 c
}{\f23\fs20\up6 2}
 contour map are interconnected. In the event that these ravines were not interconnected, the algorithm was started from different positions on the contour map (different values for the parm sets) in the hope that all minimum value contours would be locate
d.\par 
\pard \sl480 \par 
\pard \sl480\keepn {\v {\tc\tcl3\pard\plain \sl480\keepn \f20 {\b SIMPLEX Algorithm}}}{\b \par 
}\pard \sl480\keepn \tab While the ravine algorithm located the different local minima present in the {\f23 c}{\f23\fs20\up6 2} contour, a more sophisticated algorithm{\up9 {\object\objicemb{\*\objname ICEmbdObject24_15}{\*\objdata 
0000006000000ca3685610000832cf454e524600000000004700afa236910047b7db01010000000000023239000100000000000c000a0001201d0009000000000000000000010000002b000000000000000e4d6561642c203139363520233433}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}{
\fs18\up9 29}{{\object\objicemb{\*\objname ICEmbdObject25_16}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900afa236910047b7db}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}} was required to loc
ate the absolute minima within each of these valleys. This requirement was satisfied with the simplex algorithm. The disadvantage of this method, however, was that it was capable of locating the absolute minima only within a single valley. Therefore, a com
bination of the ravine and simplex algorithms were used to search for global {\f23 c}{\f23\fs20\up6 2} minima.\par 
\pard \sl480 \par 
\pard \sl480\keepn {\v {\tc\tcl2\pard\plain \sl480\keepn \f20 {\b Force Field Selection}}}{\b \par 
}\pard \sl480\keepn \tab Once many such minima had been located from different starting points in the {\f23 c}{\f23\fs20\up6 2} space, the physical viability of the force fields responsible for each of the {\f23 c}{\f23\fs20\up6 2}
 minima was considered.  The shapes of the calculated orbitals were visualized using either the run_p or run.vis programs. Consistency in the shapes between the calculated and observed frequencies was sought, and hence some optimized force fields were excl
uded. Structural features of the molecule, upon application of the optimized force-field were analyzed. If an optimized and consistent force field were the truly the best one possible, it should reproduce experimentally observed vibrational modes {\ul and
}
 structural features of that molecule. This stringent, evaluation criteria allowed us to discard various optimized parameter sets in favor of one,  more general parameter set for the NiOEP molecule. Lastly, force fields which displayed intuitive consistenc
y and trends between the values of the various parameters were favored. The final force field selected for the NiOEP molecule satisfies all these requirements and proved to be transferable over to the heme porphyrin. The optimized heme porphy
rin force field was placed in different environments to see if this force field could reproduce the structural features of the heme residue in different environments. The final optimized force fields are listed in Appendix F.{\b \par 
}\pard \sl480 \par 
\pard \sl480\keepn {\v {\tc\tcl2\pard\plain \sl480\keepn \f20 {\b IBELLY OPTION}}}{\b \par 
}\pard \sl480\keepn \tab 
In order to analyze the effects of the protein environment on the normal modes of the carboxyheme, it was necessary to freeze out the movements of the rest of the protein. By freezing out the movements of the protein, it should be possible to concentrate 
our frequen
cy analysis on the carboxyheme segment, while at the same time taking into account the steric and electronic effects of the rest of the protein on the porphyrin normal modes. Freezing out of the rest of the protein would have been done by using the "belly"
 option provided in the AMBER package. However, glitches in the operation of this option, particularly in the nmode module,  prevented the use of this function.  Therefore, no analysis was possible inside the protein. \par 
\pard \par 
\pard \qc\sl480 \page {\v {\tc\tcl1\pard\plain \qc\sl480 \f20 {\b Chapter 3- Results Small Molecules}}}{\b \par 
}\pard \sl480 {\v {\tc\tcl2\pard\plain \sl480 \f20 {\b Results and Discussion}}}{\b \par 
}\pard \sl480 {\b \tab }
The primary goal of this project was to develop and utilize a consistent force field for heme porphyrins. As we started this development with nickel porphyrins, a requirement of transferability was imposed on all optimized force fields, so that the eventua
l transfer of nickel porphyrin force fields to heme would be simple. \par 
\pard \sl480 \tab Jason Dimmig had completed the optimization of a transferable force field which accurately simulated the inplane motions of nickel porphyrin (NiP) using a united ethyl approximation of nickel octaethyl porphyrin (NiOEPz).{\up9 
{\object\objicemb{\*\objname ICEmbdObject16_31}{\*\objdata 0000006200000ca3685610000832cf454e524600000000004900afa373e40045654c01010000000000023234000100000000000c000a000120180009000000000000000000010000001b000000000000001044696d6d69672c203139393520233237
}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}{\fs18\up9 24}{{\object\objicemb{\*\objname ICEmbdObject17_32}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900afa373e40045654c}{\result {\pict\macpict\picw0\pich0 
000a0000000000000000}}}} Figure 3.1 shows the simplification  made by Dimmig.   \par 
\pard \qc\keepn {{\pict\macpict\picw487\pich316 
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000008810081008100990000ff}}{\b Figure 3.1  Comparison of Structural Features Between NiOEPz and NiOEP.\par 
}\pard \sl480 \tab 
As figure 3.1 shows, the ethyl groups at the periphery of the NiOEP were assumed to be single point masses in the NiEOPz model, with a combined mass of 29 amu. This approximation allowed two simplifications: the NiOEPz molecule was planar and hence the ou
t-of-plane (OOP) and inplane (IP) modes were decoupled
; and, the number vibrational frequencies being modeled was reduced from 255 to 111.  Dimmig succeeded in optimizing IP parameters (bond stretch and angle bend) of the porphyrin core  and attempted to complete such optimization for the out-of-plane paramet
ers. Complete optimization, however, was not possible because of the united ethyl approximation made in the NiOEPz model. Jason Dimmig states in his thesis, " our  biggest problem with the CZ atom seems to be that we are optimizing on full ethyl observed d
ata with a united ethyl atom."{\up9 {\object\objicemb{\*\objname ICEmbdObject0_33}{\*\objdata 
0000006200000ca3685610000832cf454e524600000000004900afa2350b000b5bd601010000000000023234000100000000000c000a000120180009000000000000000000010000001b000000000000001044696d6d69672c203139393520233237}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}
}}}{\fs18\up9 24}{{\object\objicemb{\*\objname ICEmbdObject1_34}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900afa2350b000b5bd6}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}
 All modes associated with the internal motions of the ethyl group, could not be simulated by united ethyl atoms. The immediate focus in this thesis was to complete development of the  NiOEP force field, after having relaxed the united atom approximation m
ade in Jason Dimmig's thesis. The transferable force field developed by Jason Dimmig{\up9 {\object\objicemb{\*\objname ICEmbdObject18_35}{\*\objdata 
0000006200000ca3685610000832cf454e524600000000004900afa3740000456bee01010000000000023234000100000000000c000a000120180009000000000000000000010000001b000000000000001044696d6d69672c203139393520233237}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}
}}}{\fs18\up9 24}{{\object\objicemb{\*\objname ICEmbdObject19_36}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900afa3740000456bee}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}
 was used as a starting point for the optimization procedure.\par 
\pard \sl480 \par 
\pard \sl480 {\v {\tc\tcl2\pard\plain \sl480 \f20 {\b Relaxation of United Ethyl Approximation}}}{\b \par 
}\pard \sl480 {\b \tab }Our strategy was to relax
 the united ethyl approximation in a step-wise fashion i.e. first move to a united methyl-methylene (NiOEPx), then to a united methyl-non-united methylene (NiOEPy) used in Li's force field development, and finally to a fully non-united ethyl atom (NiOEP) (
Figure 3.2). \par 
\pard \sl480\keepn \tab {{\pict\macpict\picw352\pich141 
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\pard \qc\sl480\keepn {\b Figure 3.2 Step-wise Relaxation of United Ethyl Approximation\par 
}\pard \qc\sl480 \par 
\pard \sl480 \tab While each of the models shown in Figure 3.2 (NiOEPz, NiOEPx and NiOEPy) were useful as approximations, the problems arising from the oversimplification of the ethyl groups pe
rsisted. Specifically, internal ethyl group vibrations were not calculated in the correct frequency range. Reasons for such poor correlation became apparent when simulations were performed on  other computation packages. One set of simulations done  on eth
ylbenzene using Spartan suggested strong coupling between the vibrations of methyl and methylene hydrogens. Additionally, Kincaid et. al. point out the coupling between the vibrations of ethyl group hydrogen atoms in porphyrin systems.{\up9 
{\object\objicemb{\*\objname ICEmbdObject2_37}{\*\objdata 
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}}}}{\fs18\up9 30}{{\object\objicemb{\*\objname ICEmbdObject3_38}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900afa2368a000bb5fb}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}  None of the app
roximate models (NiOEPz, NiOEPx and NiOEPy) include the methyl hydrogens, which can couple in the required fashion. Existence of such coupling prompted complete relaxation of the united ethyl approximation, and optimizations on NiOEP were attempted. 
\par 
\pard \sl480 \par 
\pard \sl480 {\v {\tc\tcl2\pard\plain \sl480 \f20 {\b Non-United Nickel Octaethyl Porphyrin}}}\par 
\pard \sl480 \tab Optimization of the full NiOEP force field proved difficult, because of the increased numbers of normal modes (255). These difficulties were circumvented by analyzing a smaller molecule, ethylbenzene, which contained 
an ethyl group at the periphery of an aromatic ring.  Figure 3.3 displays the similarities between ethylbenzene and NiOEP.\par 
\pard \sl480 \par 
\pard \sl480\keepn {\b Figure 3.3\par 
}\pard \qc\sl480\keepn {{\pict\macpict\picw466\pich296 
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fe000012f80001ffffbf0001ffff810081008100fe000012f70001ffffc10001ffff810081008100fd000008810081008100af000008810081008100af000008810081008100af000008810081008100af000008810081008100af000008810081008100af000008810081008100af000008810081008100af000008810081
008100af000008810081008100af000008810081008100af000008810081008100af000008810081008100af000008810081008100af000008810081008100af0000ff}}{\b Figure 3.3  Structural Similarities between NiOEP and Ethylbenzene\par 
}\pard \sl480  \tab 
As our main interest in smaller molecules was to develop a force-field which reproduced the vibration frequencies of an ethyl group connected to an aromatic ring. Figure 3.3 demonstrates the suitability of ethylbenzene. This molecule also has an ethyl gr
oup attached to an aromatic ring, much like NiOEP its
elf, and allows easier understanding of force field requirements for modeling the ethyl group. Additionally, the smaller number of vibration frequencies in ethylbenzene allowed us to test out different modeling approaches, before selecting a method to use 
in NiOEP. The results of such analysis will be described in the following sections. \par 
\pard \sl480  {\b \par 
}\pard \sl480 {\v {\tc\tcl2\pard\plain \sl480 \f20 {\b Force Field Development for Benzene, Toluene and Ethylbenzene.}}}{\b \par 
}\pard \sl480 {\b \tab }Before ethylbenzene could be modeled, existing force fields for benzene and toluene needed to be revi
sed. The standard AMBER force fields for both these molecules produced poor vibrational fits,  which in turn, caused poor vibrational fits for ethylbenzene. The existing force fields for benzene and toluene were corrected, and information extracted from su
ch corrections gave us a clearer insight into the nature of the OOP parameters used in the AMBER force field. These conclusions are discussed in the next few sections.\par 
\pard \sl480 \par 
\pard \sl480 {\v .c3 }{\b Benzene}\par 
\pard \sl480 \tab As mentioned before, the standard AMBER force field produced a poor vibrat
ional fit. When the calculated frequencies were analyzed using the NMANAL, run_p and run.vis programs, it became apparent that the primary problems were in the OOP modes of vibrations. The philosophy of Kollman et al. in modeling the OOP modes of benzene w
as to simplify the parameters required as much as possible.{\up9 {\object\objicemb{\*\objname ICEmbdObject4_39}{\*\objdata 
0000006300000ca3685610000832cf454e524600000000004a00afa23939000c572d01010000000000023138000100000000000c000a000120120009000000000000000000010000001800000000000000114b6f6c6c6d616e2c203139393520233234}{\result {\pict\macpict\picw0\pich0 000a0000000000000000
}}}}{\fs18\up9 18}{{\object\objicemb{\*\objname ICEmbdObject5_40}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900afa23939000c572d}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}
 Dihedral terms were defined with wild cards, so that a single dihedral term would suffice for all the dihedral definitions around a bond. Such emphasis on simplicity affected the accuracy of t
he benzene force field. As a correction we developed a  new force field for benzene in which dihedrals were specifically defined.  Figure 3.4 illustrates the nature of the change effected in the standard AMBER dihedral parameters. \par 
\pard \sl480\keepn {\b \par 
}\pard \qc\keepn {{\pict\macpict\picw472\pich177 
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2032353934206c0d63700d660d6e700d313233322033383230204d0d313231322033383230206c0d313231322033303230206c0d313233322033303230206c0d63700d660d6e700d313936322034333639204d0d313935322034333837206c0d313336312034303436206c0d313337312034303238206c0d63700d660d6e70
0d323032352034323630204d0d323031352034323738206c0d313432342033393337206c0d313433342033393139206c0d63700d660d6e700d323836372034303431204d0d323837372034303539206c0d323237382034343035206c0d323236382034333837206c0d63700d660d6e700d333032392033303230204d0d3330
34392033303230206c0d333034392033383230206c0d333032392033383230206c0d63700d660d6e700d323930332033303230204d0d323932332033303230206c0d323932332033383230206c0d323930332033383230206c0d63700d660d6e700d323836392032373935204d0d323835392032383133206c0d3232383520
32343831206c0d323239352032343633206c0d63700d660d6e700d323132302031393030204d0d323134302031393030206c0d323134302032323630206c0d323132302032323630206c0d63700d660d6e700d3737312034323236204d0d3736312034323038206c0d313034392034303432206c0d31303539203430363020
6c0d63700d660d6e700d323134302034393630204d0d323132302034393630206c0d323132302034353830206c0d323134302034353830206c0d63700d660d6e700d333434352034313737204d0d333433352034313935206c0d333138312034303437206c0d333139312034303239206c0d63700d660d6e700d3334333520
32363634204d0d333434352032363832206c0d333137352032383339206c0d333136352032383231206c0d63700d660d6e700d3738362032363635204d0d3739362032363437206c0d313035302032373934206c0d313034302032383132206c0d63700d660d67720d636f756e74206f72696773746b207375627b507d7270
20656e640d6368656d7361766520726573746f72650da000bfa0008c2c000c00150948656c76657469636103001504010d000a2e0004ffff010010533063a5533063a52b4c27024341a0008da0008c280041001e024341a0008da0008c2a34024341a0008da0008c2b2e1a024341a0008da0008c2800750079024341a0008d
a0008c2800410079024341a0008da0008c0400280009004f024841a0008da0008c2800850000024841a0008da0008c2b4f29024841a0008da0008c2800850096024841a0008da0008c2800320096024841a0008da0008c2800320000024841a0008da0008c2c000800140554696d65730300140d000c28001d00c410414d42
455220444948454452414c200d2a0d0b582d2043412d43412d5820a0008da0008c28004000c3194e657720466f726365204669656c6420444948454452414c0d2a0d0c48412d43412d43412d48410d2a0d0c43412d43412d43412d48410d2a0d0b48412d43412d43412d4841a0008da0008c28001b017b0f414d4245522069
6d70726f7065720d2a0d0b582d20582d2043412d4841a0008da0008c28003f017a10204e657720466f7263652066696c650d2a0d0a496d70726f706572200d2a0d044e4f4e45a0008da10064051c43484d4400005354524700540018010401ef0015000a0014000c0078000c00280258005000140005000100000036ffffff
ffffff094c085c000000000b5904d0000000010f7204d000000002117e085c000000030f720be9000000040b590be90000000506f4085c0000000c0a2d02c800000016109e02c80000000e13d6085c00000010109e0df1000000120a2d0df100000014ffff0003000100030002000300030003000400030005000300060003
000700030008000300090003000a0003000b0003ffff0000000102080006000100020101000700020003020800080003000401010009000400050208000a000000050101000b000000060101000d0001000701010017000200080101000f00030009010100110004000a010100130005000b01010015ffff00030001000300
02000300030003000400030005000300060003000700030008000300090003000a0003000b0003ffffffff00000f02434100010f02434100020f02434100030f02434100040f02434100050f02434100060f02484100070f02414800080f02414800090f024841000a0f024841000b0f024841ffffffff000c000100000015
610c000a00030992085c000100000018000000000000091007d0099c08d400010002fffa000c000100000015610c000a00030b9f0be90001000000190000000000000b180b540ba40c5800010002fffb000c000100000015610c000a00030fb80be900010000001a0000000000000f280b540fb40c5800010002fffc000c00
0100000015610c000a000311c4085c00010000001b000000000000113007d011bc08d400010002fffd000c000100000015610c000a00030fb804d000010000001c0000000000000f28044c0fb4055000010002fffe000c000100000015610c000a00030b9f04d000010000001d0000000000000b18044c0ba4055000010002
fff9000c0001000000156000000a00030744080c00000000001e00000000000006b808200744091000010002fff4000c0001000000156000000a00030a7d0da100000000001f00000000000009ec0dac0a780e9c00010002fff5000c0001000000156000000a000310ee0da100000000002000000000000010680dac10f40e
9c00010002fff6000c0001000000156000000a00031426080c000000000021000000000000139c08201428091000010002fff7000c0001000000156044000a000310ee0307ffff000000220000000000001068020810f402f800010002fff8000c00010000001560c0000a00030a7d0307ffff0000002300000000000009ec
02080a7802f800010002001b000c0001000000140000000c000308d411300000000000240000011b00010834113009d8198c00020010001b414d42455220444948454452414c200d582d2043412d43412d582001003c000c000100000014000c000c00030b90111c0000000000250000000000010af0111c0e9c1c70000400
1900250031003c4e657720466f726365204669656c6420444948454452414c0d48412d43412d43412d48410d43412d43412d43412d48410d48412d43412d43412d4841001a000c00010000001400ad000c000308ac1f7c000000000027000000000001080c1f7c09b026840002000f001a414d42455220696d70726f706572
0d582d20582d2043412d4841001e000c0001000000140000000c00030b7c1f680000000000280000000000010adc1f680d84253000030010001a001e204e657720466f7263652066696c650d496d70726f706572200d4e4f4e450000000200150948656c76657469636100140554696d65730000a100640004574f5244a000
8dff}}{\b Figure 3.4  OOP Force Field Parameters in the Standard AMBER and New Parameter Sets}\par 
\pard \sl480 \tab Our force field for benzene contained specific definitions for proper dihedrals in that we broke the standard X-CA-CA-X dihedral  of AMBER into CA-CA-CA-CA, HA-CA-CA-CA and HA-CA-CA-HA. When th
e dihedral terms were not grouped, we noticed that good vibrational fit were possible without improper terms. This trend will be discussed separately in a future section of this chapter. The improved frequency correlation arising from this change is listed
 in Table 3.1, in which fits obtained with the new force field are contrasted with ones obtained with the standard AMBER force field.  \par 
\pard \sl480 \par 
\pard \keepn {\b Table 3.1 Frequencies Calculated from New and Standard AMBER Force Fields.}\par 
\pard \sl480\keepn \par 
\trowd \trqc\trgaph80\trleft-80 \clbrdrt\brdrs \clbrdrl\brdrs \clshdng0\cellx1216\clbrdrt\brdrs \clshdng0\cellx2512\clbrdrt\brdrs \clshdng0\cellx3808\clbrdrt\brdrs \clshdng0\cellx5104\clbrdrt\brdrs \clshdng0\cellx6400\clbrdrt\brdrs \clbrdrr\brdrs 
\clshdng0\cellx7696\pard \sl480\keepn\intbl {\b\fs20 Symmetry\par 
type}{\b \cell }\pard \sl480\keepn\intbl {\b\fs20 Observed Frequency (cm}{\b\fs18\up6 -1}{\b\fs20 )}{\b \cell }\pard \sl480\keepn\intbl {\b\fs20 New Force Field Frequency (cm}{\b\fs18\up6 -1}{\b\fs20 )}{\b \cell }\pard \sl480\keepn\intbl {\b\fs20 
Difference (%)}{\b \cell }\pard \sl480\keepn\intbl {\b\fs20 AMBER Force Field  (cm}{\b\fs18\up6 -1}{\b\fs20 )}{\b \cell }\pard \sl480\keepn\intbl {\b\fs20 Difference (%)\cell }\pard \intbl \row \trowd \trqc\trgaph80\trleft-80 \clbrdrl\brdrs \clshdng0
\cellx1216\clshdng0\cellx2512\clshdng0\cellx3808\clshdng0\cellx5104\clshdng0\cellx6400\clbrdrr\brdrs \clshdng0\cellx7696\pard \sl480\keepn\intbl {\f23 c}{\f23\fs20\up6 2}\cell \cell 1384.3\cell \pard \sl480\keepn\intbl \cell \pard \sl480\keepn\intbl 
4879.8\cell \cell \pard \intbl \row \pard \sl480\keepn\intbl a2u\cell 673.0\cell 688.7\cell \pard \sl480\keepn\intbl 2.3 %\cell \pard \sl480\keepn\intbl 700.7\cell 4.1%\cell \pard \intbl \row \pard \sl480\keepn\intbl b2g\cell 703.0\cell 686.3\cell \pard 
\sl480\keepn\intbl 2.3%\cell \pard \sl480\keepn\intbl 663.3\cell 5.6\cell \pard \intbl \row \pard \sl480\keepn\intbl eu\cell 995.0\cell 996.2\cell \pard \sl480\keepn\intbl 0.1%\cell \pard \sl480\keepn\intbl 1195.6\cell 20.1\cell \pard \intbl \row \trowd 
\trqc\trgaph80\trleft-80 \clbrdrl\brdrs \clbrdrb\brdrs \clshdng0\cellx1216\clbrdrb\brdrs \clshdng0\cellx2512\clbrdrb\brdrs \clshdng0\cellx3808\clbrdrb\brdrs \clshdng0\cellx5104\clbrdrb\brdrs \clshdng0\cellx6400\clbrdrb\brdrs \clbrdrr\brdrs \clshdng0
\cellx7696\pard \sl480\keepn\intbl b2u\cell 1329.0\cell 1666.6\cell \pard \sl480\keepn\intbl 25.4%\cell \pard \sl480\keepn\intbl 1729.0\cell 30.1%\cell \pard \intbl \row \pard \sl480 \tab Improvements to the standard force field are evident from the {
\f23 c}{\f23\fs20\up6 2 }values listed in Table 3.1, which have fallen from 4879.8 to 1384.3.  Focusing on the calculated differences, it is apparent that the correlation has improved across the symmetries. The a2u, b2g and e2
u symmetry frequencies are all OOP modes of vibration, so improvements in these frequencies supports the use of the more detailed OOP parameter set.  The b2u symmetry observed frequency at 1329 cm{\fs20\up6 -1}
 is an IP frequency (Kekule Mode), which could not be modeled by either of parameter sets. The poor correlation in this frequency reflects an inherent deficiency in the AMBER potential equation (Eq. 2.1), in which off diagonal terms from the force matrix a
re incompletely represented. This frequency was therefore excluded from all {\f23 c}{\f23\fs20\up6 2} calculations.  {\b \par 
}\pard \sl480 \tab 
Further analysis of the specific dihedral terms  offers a reason for the improved correlation in OOP mode frequencies. Table 3.2 tabulates the dihedral parameters defined in the new benzene force field and compares them to values listed in the standard be
nzene force field.\par 
\pard \sl480 \par 
\pard \qc\sl480\keepn {\b Table 3.2 Torsion Parameters Comparison.\par 
}\trowd \trqc\trgaph80\trleft-80 \clbrdrt\brdrs \clbrdrl\brdrs \clshdng0\cellx2800\clbrdrt\brdrs \clshdng0\cellx4960\clbrdrt\brdrs \clbrdrr\brdrs \clshdng0\cellx7120\pard \sl480\keepn\intbl {\b Proper Dihedral Used}\cell \pard \sl480\keepn\intbl {\b 
New Force Field (kcal/ mol)}\cell {\b Standard Force Field (Kcal/ mol)}\cell \pard \intbl \row \trowd \trqc\trgaph80\trleft-80 \clbrdrl\brdrs \clshdng0\cellx2800\clshdng0\cellx4960\clbrdrr\brdrs \clshdng0\cellx7120\pard \sl480\keepn\intbl {\b\fs20 
CA-CA-CA-CA (1)}{\fs20 \cell }\pard \qc\sl480\keepn\intbl 4.178\cell N.A.\cell \pard \intbl \row \pard \sl480\keepn\intbl {\b\fs20 CA-CA-CA-HA (2)}{\fs20 \cell }\pard \qc\sl480\keepn\intbl 8.063\cell N.A\cell \pard \intbl \row \pard \sl480\keepn\intbl {
\b\fs20 HA-CA-CA-HA (1)}{\fs20 \cell }\pard \qc\sl480\keepn\intbl 2.292\cell N.A\cell \pard \intbl \row \pard \sl480\keepn\intbl {\b\fs20 X -CA-CA-X     (4)}{\fs20 \cell }\pard \qc\sl480\keepn\intbl N.A\cell 14.50\cell \pard \intbl \row \pard 
\sl480\keepn\intbl {\b Improper Dihedrals \par 
Used\cell }\pard \qc\sl480\keepn\intbl \cell \cell \pard \intbl \row \trowd \trqc\trgaph80\trleft-80 \clbrdrl\brdrs \clbrdrb\brdrs \clshdng0\cellx2800\clbrdrb\brdrs \clshdng0\cellx4960\clbrdrb\brdrs \clbrdrr\brdrs \clshdng0\cellx7120\pard 
\sl480\keepn\intbl {\b\fs20 X- X- CA- HA}\cell \pard \qc\sl480\keepn\intbl 0.000\cell 1.100\cell \pard \intbl \row \trowd \trqc\trgaph80\trleft-80 \clbrdrl\brdrs \clbrdrb\brdrs \clshdng0\cellx2800\clbrdrb\brdrs \clshdng0\cellx4960\clbrdrb\brdrs \clbrdrr
\brdrs \clshdng0\cellx7120\pard \sl480\keepn\intbl {\b Total}\cell \pard \qc\sl480\keepn\intbl 14.542\cell 15.474*\cell \pard \intbl \row \pard \qc\keepn {\b \par 
}\pard \keepn Values in ( ) refer to the redundancy factor (m) around the central bond\par 
* Total contains scaled contribution from IMPROPER terms \par 
\pard \par 
\pard \sl480 \tab 
As Table 3.2 shows, the sum of the specific dihedrals (14.542 kcal/ mol) defined in our new force field is similar to that in the standard force field (15.474 kcal/ mol). Such consistency is reassuring, because the total potential barrier around a bond sh
ould be in
dependent of the internal distribution of such a barrier. Therefore, by breaking away from the general dihedral restriction employed in the standard AMBER force field, we have introduced more flexibility into our force field. This flexibility, in turn, is 
reflected in better vibrational fits for the OOP modes.  \par 
\pard \sl480 \par 
\pard \sl480\keepn {\v {\tc\tcl3\pard\plain \sl480\keepn \f20 {\b Deuterated Benzene}}}{\b \par 
}\pard \sl480\tx0 {\b \tab }Before the benzene force field was transferred over to toluene, it transferability was tested on deuterated benzene. The physical effects of deuteration were simulated by ch
anging the mass of the hydrogen atom within the force field from one to two amu, and by optimizing on the parameters that controlled the vibrations of the deuterium atom. Table 3.3 shows the vibrational fit for some samples normal modes using the AMBER and
 new force fields. \par 
\pard \sl480\tx0 \par 
\pard \keepn\tx0 {\b Table 3.3 Sample Frequencies Calculated Using the New and Standard AMBER Force Fields}\par 
\trowd \trgaph80\trleft-80 \clbrdrt\brdrs \clbrdrl\brdrs \clshdng0\cellx2080\clbrdrt\brdrs \clshdng0\cellx4240\clbrdrt\brdrs \clshdng0\cellx6400\clbrdrt\brdrs \clbrdrr\brdrs \clshdng0\cellx8560\pard \sl480\keepn\tx0\intbl {\b Symmetry}\cell {\b 
New Force Field\par 
(cm}{\b\fs20\up6 -1}{\b )}\cell \pard \sl480\keepn\tx0\intbl {\b AMBER Force Field (cm}{\b\fs20\up6 -1}{\b )}\cell \pard \sl480\keepn\tx0\intbl {\b Observed Frequency (cm}{\b\fs20\up6 -1}{\b )}{\up9 {\object\objicemb{\*\objname ICEmbdObject6_41}
{\*\objdata 0000005f00000ca3685610000832cf454e524600000000004600afa23a6d000c9f9501010000000000023331000100000000000c000a0001201f00090000000000000000000100000021000000000000000d4c61752c203139373020233333}{\result {\pict\macpict\picw0\pich0 
000a0000000000000000}}}}{\fs18\up9 31}{{\object\objicemb{\*\objname ICEmbdObject7_42}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900afa23a6d000c9f95}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}\cell \pard \intbl \row 
\trowd \trgaph80\trleft-80 \clbrdrl\brdrs \clshdng0\cellx2080\clshdng0\cellx4240\clshdng0\cellx6400\clbrdrr\brdrs \clshdng0\cellx8560\pard \sl480\keepn\tx0\intbl {\f23 c}{\f23\fs20\up6 2}\cell 807.9\cell 2716.7\cell \cell \pard \intbl \row \pard 
\sl480\keepn\tx0\intbl a2u\cell 499.8\cell 514.5\cell 497.0\cell \pard \intbl \row \pard \sl480\keepn\tx0\intbl b2g\cell 582.4\cell 584.8\cell 599.0\cell \pard \intbl \row \pard \sl480\keepn\tx0\intbl eu\cell 820.8\cell 959.3\cell 830.0\cell \pard \intbl 
\row \trowd \trgaph80\trleft-80 \clbrdrl\brdrs \clbrdrb\brdrs \clshdng0\cellx2080\clbrdrb\brdrs \clshdng0\cellx4240\clbrdrb\brdrs \clshdng0\cellx6400\clbrdrb\brdrs \clbrdrr\brdrs \clshdng0\cellx8560\pard \sl480\keepn\tx0\intbl b2u\cell 1647.7\cell 1705.4
\cell 1282.0\cell \pard \intbl \row \pard \qc\tx0 \par 
\pard \sl480\tx0 \tab  The improvements made to the standard AMBER benzene parameter set are evident in this table, as the {\f23 c}{\f23\fs20\up6 2}{\f23  }
 value for the fit has decreased from 2716.7 to 807.9. Furthermore, the improvements in correlation have happened in the same symmetry as in benzene, supporting our break from general dihedral definitions. Examining Table 3.3 reveals that the b2u frequency
  is modeled incorrectly, again highlighting the inherent deficiency in the AMBER force field equation mentioned in the previous section.  Maintaining consistency with the approach used in the previous section, this b2u frequency was not included in any {
\f23 c}{\f23\fs20\up6 2} calculations.  \par 
\pard \sl480 {\b \par 
}\pard \sl480\keepn {\v {\tc\tcl3\pard\plain \sl480\keepn \f20 {\b Toluene}}}\par 
\pard \sl480 \tab 
Attempts  to transfer the entire, newly-optimized benzene force field to toluene met with repeated failure. Further investigation revealed that this  lack of transferability between the sets was concentrated around the apex carbon atom.  While the entire 
toluene PREP file is listed in Appendix A, changes made to atom labels are summarized in figure 3.5. \par 
\pard \sl480\keepn \par 
\pard \sl480\keepn \tab {{\pict\macpict\picw371\pich159 
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667d622f527b6e756c6c206465667d622f642f646566204c2f612f616464204c2f616c2f616c6f6164204c2f61732f6173746f7265204c2f61742f6174616e204c2f63702f636c6f736570617468204c2f63762f6375727665746f204c2f63772f63757272656e746c696e657769647468204c2f6370742f63757272656e74
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33323535206c0d323336302033313238206c0d323337302033313130206c0d63700d660d6e700d333130372033313030204d0d333131372033313138206c0d323837352033323539206c0d323836352033323431206c0d63700d660d6e700d333037312033303338204d0d333038312033303536206c0d3238333920333139
37206c0d323832392033313739206c0d63700d660d6e700d333234302032353430204d0d333236302032353430206c0d333236302032393030206c0d333234302032393030206c0d63700d660d6e700d323837382032323237204d0d323838382032323039206c0d333130382032333337206c0d333039382032333535206c
0d63700d660d6e700d323834322032323839204d0d323835322032323731206c0d333037322032333939206c0d333036322032343137206c0d63700d660d6e700d323538372032323030204d0d323539372032323138206c0d323335352032333539206c0d323334352032333431206c0d63700d660d6e700d323732302031
353337204d0d323733302031353330206c0d323734302031353335206c0d323734302032303030206c0d323732302032303030206c0d63700d665b3120342032373330203134373620323733302031303430205d42640d0d6e700d323237332031333335204d0d323333332031323331206c0d323732382031353136206c0d
323733302031353330206c0d323732302031353337206c0d63700d660d6e700d333031362031313630204d0d333130302031323434206c0d323734302031353335206c0d323733302031353330206c0d323732382031353136206c0d63700d660d6e700d333736352032313231204d0d333737352032313339206c0d333339
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343430206c0d63700d660d6e700d313639352033333339204d0d313638352033333231206c0d323036372033313030206c0d323037372033313138206c0d63700d660d6e700d313638352032313339204d0d313639352032313231206c0d323036382032333337206c0d323035382032333535206c0d63700d660d67720d63
6f756e74206f72696773746b207375627b507d727020656e640d6368656d7361766520726573746f72650d0000a000bf00a0008c002c000c00150948656c76657469636100030015000d000a002e0004ffff0100002b687d0243410000a0008d00a0008c002a1e02434100a0008d00a0008c002b1a0f0243410000a0008d00
a0008c0028009b009c0243410000a0008d00a0008c0028007d009c0243410000a0008d00a0008c0028006e00820243430000a0008d00a0008c0028003200850248430000a0008d00a0008c0028004100640248430000a0008d00a0008c0028003b009a0248430000a0008d00a0008c002c000800140554696d657300030014
000d000c002b663e24434320646566696e6974696f6e206368616e6765642066726f6d20434120746f2043430d00002a0d2a746f2061696420696e207472616e736665726162696c697479206265747765656e2062656e7a656e650d002a0d0b616e6420746f6c75656e650000a0008d00a10064040a43484d440000535452
47002a005100c901c40015000a0014000c0078000c00280258005000140005000100000036ffffffffffff098808ac000000000be008ac000000010d0c0ab4000000020be00cbc0000000309880cbc00000004085c0ab40000000506040ab40000000c03ac0ab40000000e04d808ac00000010045c0c5c00000012085c0ec4
0000001d0d0c0ec40000001f0f640ab4000000210d0c06a400000023085c06a400000025ffff0003000100030002000300030003000400030005000300060003000700030008000300090003000a0003000b0003000c0003000d0003000e0003ffff0000000102080006000100020101000700020003020800080003000401
010009000400050208000a000000050101000b000500060101000d000600070104000f000600080107001100060009010700130004000a0101001e0003000b010100200002000c010100220001000d010100240000000e01010026ffff00030001000300020003000300030004000300050003000600030007000300080003
00090003000a0003000b0003000c0003000d0003000e0003ffffffff00000f02434100010f02434100020f02434100030f02434100040f02434100050f02434300070f02484300080f02434800090f024843ffffffff000c0001000000156086000a000309ce08ac000100000014000000000000094c083409d80924000100
02fffe000c000100000015605f000a00030c2608ac0001000000150000000000000ba408340c30092400010002fffd000c000100000015602e000a00030d520ab40001000000160000000000000cd00a3c0d5c0b2c00010002fffc000c000100000015602e000a00030c260cbc0001000000170000000000000ba40c440c30
0d3400010002fffb000c000100000015602e000a000309ce0cbc000100000018000000000000094c0c4409d80d3400010002fffa000c0001000000156086000a000308a20ab400010000001900000000000008200a3c08ac0b4000010002fff8000c000100000015600c000a000303f20a6400000000001a00000000000003
700a7803fc0b7c00010002fff7000c0001000000156000000a0003051e08ecffff0000001b000000000000049c07e4052808e800010002fff6000c000100000015600c000a000304a20c0c00000000001c00000000000004100c1c049c0d20000100020059000c0001000000140000000c0003097414000000000000270000
0000000108d414000b7c232800030024004e0059434320646566696e6974696f6e206368616e6765642066726f6d20434120746f2043430d746f2061696420696e207472616e736665726162696c697479206265747765656e2062656e7a656e650d616e6420746f6c75656e65ce0000000200150948656c76657469636100
140554696d6573000000ff}}\par 
\pard \qc\keepn \tab {\b Figure 3.5 Atom Definitions Used in Toluene.}\par 
\pard \sl480 \tab 
Once the apex carbon atom of the phenyl  ring shown in figure 3.5 was redefined as CC, we were able to transfer parameters developed for the benzene CA atoms over to the remaining CA atoms in the phenyl ring of toluene. Additionally, we continued with the
 use of specific dihedral definitions to describe parameters containing the CC atom. Good vibrational fits could then be obtained by optimizing only the CC and methyl parameters.  Table 3.4{\b  }
compares the vibration fits obtained using our optimized and the standard AMBER force fields. \par 
\pard \sl480 \par 
\pard \keepn {\b Table 3.4  Frequencies Calculated for Toluene using New and Standard AMBER Force Fields.}\par 
\pard \keepn \par 
\trowd \trqc\trgaph80\trleft-80 \clbrdrt\brdrs \clbrdrl\brdrs \clshdng0\cellx1216\clbrdrt\brdrs \clshdng0\cellx2656\clbrdrt\brdrs \clshdng0\cellx3952\clbrdrt\brdrs \clshdng0\cellx5248\clbrdrt\brdrs \clshdng0\cellx6544\clbrdrt\brdrs \clbrdrr\brdrs 
\clshdng0\cellx7840\pard \sl480\keepn\intbl {\b\fs20 Symmetry}\cell \pard \sl480\keepn\intbl {\b\fs20 Observed Frequencies}{\fs20\up9 {\object\objicemb{\*\objname ICEmbdObject8_43}{\*\objdata 
0000005f00000ca3685610000832cf454e524600000000004600afa23ac6000cb49101010000000000023332000100000000000c000a0001202000090000000000000000000100000023000000000000000d4c61752c203139373320233335}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}{
\fs18\up9 32}{\fs20 {\object\objicemb{\*\objname ICEmbdObject9_44}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900afa23ac6000cb491}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}{\b\fs20 \par 
}\pard \sl480\keepn\intbl {\b\fs20 (cm}{\b\fs18\up6 -1}{\b\fs20 )}{\b\fs18 \cell }\pard \sl480\keepn\intbl {\b\fs20 New Force Field Frequencies\par 
}\pard \sl480\keepn\intbl {\b\fs20 (cm}{\b\fs18\up6 -1}{\b\fs20 )}{\b\fs18 \cell }{\b\fs20 Difference\par 
(%)\cell }\pard \sl480\keepn\intbl {\b\fs20 AMBER Force Field (cm}{\b\fs18\up6 -1}{\b\fs20 ) \cell }\pard \sl480\keepn\intbl {\b\fs20 Difference (%) \cell }\pard \intbl \row \trowd \trqc\trgaph80\trleft-80 \clbrdrl\brdrs \clshdng0\cellx1216\clshdng0
\cellx2656\clshdng0\cellx3952\clshdng0\cellx5248\clshdng0\cellx6544\clbrdrr\brdrs \clshdng0\cellx7840\pard \sl480\keepn\intbl {\f23 c}{\f23\fs20\up6 2} \cell \pard \sl480\keepn\intbl \cell \pard \sl480\keepn\intbl 1214\cell \cell 7418\cell \cell \pard 
\intbl \row \pard \sl480\keepn\intbl a1\cell \pard \sl480\keepn\intbl 220.0\cell \pard \sl480\keepn\intbl 214.5\cell \pard \qc\sl480\keepn\intbl 2.5%\cell \pard \sl480\keepn\intbl 222.3\cell \pard \qc\sl480\keepn\intbl 1.0%\cell \pard \intbl \row \pard 
\sl480\keepn\intbl \cell \pard \sl480\keepn\intbl 467.0\cell \pard \sl480\keepn\intbl 474.8\cell \pard \qc\sl480\keepn\intbl 1.5%\cell \pard \sl480\keepn\intbl 455.6\cell \pard \qc\sl480\keepn\intbl 2.4%\cell \pard \intbl \row \pard \sl480\keepn\intbl a2
\cell \pard \sl480\keepn\intbl 44.0\cell \pard \sl480\keepn\intbl 43.5\cell \pard \qc\sl480\keepn\intbl 1.1%\cell \pard \sl480\keepn\intbl 34.9\cell \pard \qc\sl480\keepn\intbl 20.6%\cell \pard \intbl \row \trowd \trqc\trgaph80\trleft-80 \clbrdrl\brdrs 
\clbrdrb\brdrs \clshdng0\cellx1216\clbrdrb\brdrs \clshdng0\cellx2656\clbrdrb\brdrs \clshdng0\cellx3952\clbrdrb\brdrs \clshdng0\cellx5248\clbrdrb\brdrs \clshdng0\cellx6544\clbrdrb\brdrs \clbrdrr\brdrs \clshdng0\cellx7840\pard \sl480\keepn\intbl \cell 
\pard \sl480\keepn\intbl 348.0\cell \pard \sl480\keepn\intbl 365.7\cell \pard \qc\sl480\keepn\intbl 4.8%\cell \pard \sl480\keepn\intbl 405.5\cell \pard \qc\sl480\keepn\intbl 16.5%\cell \pard \intbl \row \pard \sl480 \tab \par 
\pard \sl480 \tab Table 3.4 summarizes the improvements made with the new force field ({\f23 c}{\f23\fs20\up6 2} value has fallen from 7418 to 1214). The high {\f23 c}{\f23\fs20\up6 2}
 value with the standard AMBER force field reflects the inherent non-transferability of benzene parameters over to the apex carbon atom, and the poor vibration fits for the lower lying frequencies in the a2 symmetry. The improvement matches in the low lyin
g frequencies again supports the break in dihedral parameters employed in our new force field. Once again, while no improper terms were required for the CA atoms,  one
 was needed around the CC atom. This interesting exception will be revisited later in this chapter. \par 
\pard \sl480 \par 
\pard \sl480\keepn {\v {\tc\tcl3\pard\plain \sl480\keepn \f20 {\b Ethylbenzene}}}\par 
\pard \sl480 \tab 
Our success in transferring most of the benzene force field over to toluene, encouraged us to transfer the toluene force field over to ethylbenzene.  Although optimizing the ethylbenzene force field with an additional atom should have been easy, especiall
y with the new CC atom definition employed in toluene's force field, considerable difficulties were encountered in trying to optimize the
 low lying frequencies. Table 3.5 lists two low lying frequencies, both of which could not be optimized simultaneously.  \par 
\pard \sl480 \par 
\pard \keepn {\b Table 3.5 Calculated and Observed Low Lying Frequencies in Ethylbenzene.}\par 
\trowd \trgaph80\trleft-80 \clbrdrt\brdrs \clbrdrl\brdrs \clshdng0\cellx2800\clbrdrt\brdrs \clshdng0\cellx5680\clbrdrt\brdrs \clbrdrr\brdrs \clshdng0\cellx8560\pard \sl480\keepn\intbl {\b Symmetry}\cell {\b Observed}\cell {\b Calculated}\cell \pard 
\intbl \row \trowd \trgaph80\trleft-80 \clbrdrl\brdrs \clshdng0\cellx2800\clshdng0\cellx5680\clbrdrr\brdrs \clshdng0\cellx8560\pard \sl480\keepn\intbl a1\cell 150.7\cell 152.0\cell \pard \intbl \row \trowd \trgaph80\trleft-80 \clbrdrl\brdrs \clbrdrb
\brdrs \clshdng0\cellx2800\clbrdrb\brdrs \clshdng0\cellx5680\clbrdrb\brdrs \clbrdrr\brdrs \clshdng0\cellx8560\pard \sl480\keepn\intbl a2\cell 45.0\cell 115.9\cell \pard \intbl \row \pard \sl480 \tab \par 
\pard \sl480 \tab 
Analysis of the two frequencies listed in Table 3.5 revealed that they depended on the same parameter (CA-CC-CT-CT). It was not possible to reduce the CA-CC-CT-CT dihedral and improve the a2 frequency match, without worsening the a1 match. Visualizatio
n of  both these orbitals revealed that they were dependent on the rotation of the ethyl group attached to the phenyl ring.{\b  }
We found that improvements to this fit were possible if an additional term was included in  the proper torsion Fourier expansion  of  the AMBER force field equation (equation 2.1). Specifically, an additional, fourth order term (n=4) term had to be employe
d around the CA-CC-CT-CT dihedral. Table 3.6 lists the fit of these low lying frequencies once the fourth order term had been includ
ed. This vibrational fit has been compared to the fit obtained without the inclusion of the fourth order dihedral potential term. \par 
\pard \sl480\keepn \par 
\pard \qc\keepn {\b Table 3.6  Ethyl Group Frequencies With and Without the Inclusion of the fourth Order Fourier Expansion.}\par 
\trowd \trqc\trgaph80\trleft-80 \clbrdrt\brdrs \clbrdrl\brdrs \clshdng0\cellx2080\clbrdrt\brdrs \clshdng0\cellx4240\clbrdrt\brdrs \clshdng0\cellx6400\clbrdrt\brdrs \clbrdrr\brdrs \clshdng0\cellx8560\pard \sl480\keepn\intbl {\b Symmetry}\cell \pard 
\sl480\keepn\intbl {\b fourth Order Term Included (cm}{\b\fs20\up6 -1}{\b )}\cell {\b fourth Order Term Excluded (cm}{\b\fs20\up6 -1}{\b )}\cell {\b Observed Frequency (cm}{\b\fs20\up6 -1}{\b )}{\up9 {\object\objicemb{\*\objname ICEmbdObject10_45}
{\*\objdata 0000005f00000ca3685610000832cf454e524600000000004600afa23c55000d124501010000000000023332000100000000000c000a0001202000090000000000000000000100000023000000000000000d4c61752c203139373320233335}{\result {\pict\macpict\picw0\pich0 
000a0000000000000000}}}}{\fs18\up9 32}{{\object\objicemb{\*\objname ICEmbdObject11_46}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900afa23c55000d1245}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}\cell \pard \intbl \row 
\trowd \trqc\trgaph80\trleft-80 \clbrdrl\brdrs \clshdng0\cellx2080\clshdng0\cellx4240\clshdng0\cellx6400\clbrdrr\brdrs \clshdng0\cellx8560\pard \sl480\keepn\intbl a1\cell 148.2\cell 152.0\cell 150.7\cell \pard \intbl \row \trowd \trqc\trgaph80\trleft-80 
\clbrdrl\brdrs \clbrdrb\brdrs \clshdng0\cellx2080\clbrdrb\brdrs \clshdng0\cellx4240\clbrdrb\brdrs \clshdng0\cellx6400\clbrdrb\brdrs \clbrdrr\brdrs \clshdng0\cellx8560\pard \sl480\keepn\intbl a2\cell 48.7\cell 115.8\cell 45.0\cell \pard \intbl \row \pard 
\sl480 \tab Table 3.6 displays the importance of including the fourth order potential term to model the rotation barrier of the ethyl gr
oup, when this group is attached to benzene (an aromatic molecule). The fourth order  affects the a2 term more significantly than the a1 term, and, counter intuitively,  causes the a2 frequency to {\i decrease}
. Both these changes, however, improve the correlation between calculated and observed frequencies. It is important  to understand the underlying reasons for such an improvement, especially because NiOEP also has ethyl groups attached to an aromatic ring. 
Conclusions regarding the rotation of the ethyl group in ethylbenzene should be applicable in the case of NiOEP as well. \par 
\pard \sl480 \tab Investigation of literature{\up9 {\object\objicemb{\*\objname ICEmbdObject12_47}{\*\objdata 
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000a0000000000000000}}}}{\fs18\up9 33}{{\object\objicemb{\*\objname ICEmbdObject13_48}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900afa23c5f000d14b1}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}
 and abinitio calculations done using Spartan yielded an explanation for the additional dihedral term that is required. Figure 3.6 shows the rotational potential seen for ethylbenzene around the CC-CT bond, as calculated by Spartan. \par 
\pard \sl480 \par 
\pard \keepn {{\pict\macpict\picw452\pich496 
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7279290002000c00010000001400040008000324510caa00000000002200000000000123dc0ca824540d5c0001000243430000000100140554696d6573000000ff}}\tab \par 
\pard \qc\keepn {\b Figure 3.6 Rotational Potential in Ethylbenzene.}\par 
\pard \sl480 \tab While at first glance the rotational potential around the CC-CT bond in figure 3.6 may look like a simple two fold potent
ial (n=2 in dihedral expansion), closer inspection reveals that the maxima of this curve does not resemble the corresponding minima. Additional Fourier analysis of this potential barrier (also shown in figure 3.6) reveals that this term was composed of two
 distinct rotational potentials- a dominant two fold and a minor four fold term. In the standard AMBER force field,{\up9 {\object\objicemb{\*\objname ICEmbdObject14_49}{\*\objdata 
0000006300000ca3685610000832cf454e524600000000004a00afa23ccc000d2e4801010000000000023138000100000000000c000a000120120009000000000000000000010000001800000000000000114b6f6c6c6d616e2c203139393520233234}{\result {\pict\macpict\picw0\pich0 000a0000000000000000
}}}}{\fs18\up9 18}{{\object\objicemb{\*\objname ICEmbdObject15_50}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900afa23ccc000d2e48}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}
 only a two fold term is used to model the ethylbenzene rotation barrier, explaining the inability of this force field to reproduce the low-lying orbitals correctly.\par 
\pard \sl480 \tab The coefficients obtained from this analysis were used as starting V{\fs20\dn4 n}
 values. Optimization of the expanded set of dihedral terms was then done using ravine and simplex algorithms, until the frequency matches were improved.  Table 3.7 compares the theoretically calculated and final torsion potential values that were used.
\par 
\pard \sl480 \par 
\pard \keepn {\b Table 3.7 Comparison of Spartan Calculated and Optimized Torsion Parameter Values}\par 
\trowd \trqc\trgaph80\trleft-80 \clbrdrt\brdrs \clbrdrl\brdrs \clshdng0\cellx2080\clbrdrt\brdrs \clshdng0\cellx4240\clbrdrt\brdrs \clbrdrr\brdrs \clshdng0\cellx6400\pard \sl360\keepn\intbl {\b Parameter Type}\cell \pard \sl360\keepn\intbl {\b 
Calculated Barrier (kcal/Mol)}\cell {\b Final Potential (V}{\b\fs20\dn4 n}{\b ) Values used. (Kcal/mol)}\cell \pard \intbl \row \trowd \trqc\trgaph80\trleft-80 \clbrdrl\brdrs \clshdng0\cellx2080\clshdng0\cellx4240\clbrdrr\brdrs \clshdng0\cellx6400\pard 
\sl480\keepn\intbl n=4\cell 0.284\cell 0.560\cell \pard \intbl \row \trowd \trqc\trgaph80\trleft-80 \clbrdrl\brdrs \clbrdrb\brdrs \clshdng0\cellx2080\clbrdrb\brdrs \clshdng0\cellx4240\clbrdrb\brdrs \clbrdrr\brdrs \clshdng0\cellx6400\pard 
\sl480\keepn\intbl n=2\cell 2.258\cell 2.308\cell \pard \intbl \row \pard \sl480 \tab 
Table 3.7 indicates that while the  final second order dihedral term used corresponds to those calculated by Spartan, the optimized fourth order term is almost double the Spartan calculated value. One possible reason, for such a trend is the existence of 
other, higher order dihedral terms which describe this rotational parameter. The magnitudes of these terms are small, but maybe the fourth order term is compensating for these absent higher order terms. Ther
efore, as long as higher order Fourier expansion terms are present, barriers calculated by Spartan seem to be transferable to the AMBER potential set. \par 
\pard \sl480 \tab  \par 
\pard \sl480 {\v {\tc\tcl2\pard\plain \sl480 \f20 {\b Improper Torsion Terms.}}}\par 
\pard \sl480 \tab 
As indicated consistently during the discussions of proper dihedral parameters earlier in this chapter, an interesting observation concerning the use of improper terms was made. These observations are now summarized and trends extracted from such a summar
y.\par 
\pard \sl480 \tab As mentioned in chapter two, improper terms help maintain the planari
ty of molecules. However, there is no consistent functional dependence between perturbations and the rise in potential energy caused by improper torsion terms. As a result, when literature values of improper terms are compared, their values have to be scal
ed by different scaling factors before they can be used within the AMBER framework.  \par 
\pard \sl480 \tab Our observation concerns the need to use these improper terms. In our analysis of benzene and its deuterated analog, toluene and ethylbenzene, we found that an improper 
term was needed only in toluene and ethylbenzene, and furthermore, this improper was required only around the CC atom. In the case of benzene such impropers were not required. It seems like the excluded improper terms around CA atoms are compensated for by
 the extended proper dihedral set. Table 3.8  lists the optimized frequency fits possible in ethylbenzene and toluene with and without the use of the CC improper term.\par 
\pard \sl480 \par 
\pard \qc\keepn  {\b Table 3.8 Effects of Using Improper Term Defined Around CC Atom in Toluene and Ethylbenzene}\par 
\trowd \trgaph80\trleft-80 \clbrdrt\brdrs \clbrdrl\brdrs \clshdng0\cellx2800\clbrdrt\brdrs \clshdng0\cellx5680\clbrdrt\brdrs \clbrdrr\brdrs \clshdng0\cellx8560\pard \sl480\keepn\intbl \cell \pard \sl480\keepn\intbl {\b 
Optimized Force Field with CC Improper}\cell {\b Optimized Force Field without CC Improper}\cell \pard \intbl \row \trowd \trgaph80\trleft-80 \clbrdrl\brdrs \clshdng0\cellx2800\clshdng0\cellx5680\clbrdrr\brdrs \clshdng0\cellx8560\pard \sl480\keepn\intbl {
\f23 c}{\f23\fs20\up6 2}{\f23  }(Toluene){\f23 \cell }1214.0\cell 1485.3\cell \pard \intbl \row \trowd \trgaph80\trleft-80 \clbrdrl\brdrs \clbrdrb\brdrs \clshdng0\cellx2800\clbrdrb\brdrs \clshdng0\cellx5680\clbrdrb\brdrs \clbrdrr\brdrs \clshdng0\cellx8560
\pard \sl480\keepn\intbl {\f23 c}{\f23\fs20\up6 2}{\f23  (}Ethyl benzene)\cell 851.3\cell 929.8\cell \pard \intbl \row \pard \qc \tab {\b \par 
}\par 
\pard \sl480 \tab  The higher  {\f23 c}{\f23\fs20\up6 2}{\f23  } values in table 3.8 shows the need for  improper terms around the CC atom. An additional F-series test  confirmed that the fall in {\f23 c}{\f23\fs20\up6 2}{\f23  }
 value was statistically significant at the 90% level. One possible reason for this could be understood by considering the CC atom and the CC-CT bond in toluene and ethylbenzene.\par 
\pard \sl480 \tab  Clearly, the CC atom is not
 like the rest of the CA atoms in the phenyl ring. This is evidenced by the fact that CA parameters (from benzene) do not yield good vibrational fits when transferred over to this CC atom. Additionally, the CC-CT bond in both ethylbenzene and toluene is a 
single bond, which could hyperconjugate with the CT-HC bond  (Figure 3.7).  The resulting partial double bond character of this bond is not modeled by any of the other terms present in the AMBER force field equation. Therefore, it is possible that improper
 terms are required to represent hyperconjugation effects within the AMBER force field. \par 
\pard \sl480\keepn \par 
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0a00030f281a680000000000160000000000000e9c1a7c0f281b8000010002fff6000c0001000000156092000a00030d201b440000000000170000000000000c941b580d201c5c00010002fff8000c0001000000156092000a000307bc1bbc00000000001800000000000007301bd007bc1f68000100080000000200140554
696d657300150948656c766574696361000000ff}}\par 
\pard \sl480\keepn \par 
\pard \qc\keepn {\b Figure 3.7 Possible Hyper conjugation Between CC-CM Bond and CM-HC bonds}\par 
\pard \sl480 \tab \par 
\pard \sl480 {\v {\tc\tcl2\pard\plain \sl480 \f20 {\b Conclusion Transferred over to NiOEP.}}}\par 
\pard \sl480 \tab 
Our modeling of ethylbenzene in its entirety has enabled us to probe and better  understand the nature of OOP parameters. Conclusions derived from such analysis were used while modeling NiOEP's OOP parameters.  Important conclusions that were transferred 
include the following. Just as in benzene, di
hedral definitions were made more specific and improper terms were excluded unless hyperconjugation were possible. A fourth order dihedral term was included to describe the rotation of the ethyl group. Finally, the parameters developed for the ethyl group 
were used as a starting point for optimizing ethyl group parameters in NiOEP. \par 
\pard \par 
\pard \qc\sl480 \page {\v\fs28 {\tc\tcl1\pard\plain \qc\sl480 \f20 {\b\fs28 Chapter 4- Results Old Force Field}}}{\b \par 
}\pard \sl480\keepn {\v {\tc\tcl2\pard\plain \sl480\keepn \f20 {\b Nickel Octaethyl Porphyrin}}}\par 
\pard \sl480 \tab After obtaining a good potential set for the ethyl group, a consistent force field for NiOEP (Sundar/Sont
um_old) was developed by transferring these ethyl group parameters over to the averaged, transferable porphyrin force field developed by Jason Dimmig. Thereafter, another consistent force field (Sundar/Sontum_new) was also sucessfully developed. Each of th
ese force fields result from the fundamentally different modeling approaches described in the methods section. The feasibility of each of the force fields was then evaluated against the criteria mentioned at the end of the methods section. While both of th
ese force fields satisfy these requirements, the  Sundar/Sontum_new force field is intuitively more appealing and hence favored. The force field developed first (Sundar/Sontum_old) is evaluated in this chapter. Examination of the Sundar/Sontum_new force fi
eld is left for the nextchapter. \par 
\pard \sl480 \par 
\pard \sl480\keepn {\v {\tc\tcl2\pard\plain \sl480\keepn \f20 {\b Vibration Features}}}\par 
\pard \sl480 {\b \tab }The most important requirement  of the Sundar/Sontum_old force field was that it reproduce the vibrational features of NiOEP. As the Sundar/Sontum_old force field is vibrationally consistent, its o
ptimized parameters were compared to other porphyrin force fields, in order to evaluate the feasibility of these optimized parameters. Such a comparison is done in Table 4.1, where bond force constants in the Sundar/Sontum_old, united ethyl Dimmig/ Sontum 
and three other force fields are compared.\par 
\pard \sl480 \par 
\pard \qc\sl480\keepn {\b Table 4.1 Bond Force Constants for NiOEP \par 
}\pard \keepn \par 
\trowd \trgaph80\trleft-80 \clbrdrt\brdrs \clbrdrl\brdrs \clbrdrb\brdrs \clshdng0\cellx1360\clbrdrt\brdrs \clbrdrb\brdrs \clshdng0\cellx2800\clbrdrt\brdrs \clbrdrb\brdrs \clshdng0\cellx4240\clbrdrt\brdrs \clbrdrb\brdrs \clshdng0\cellx5680\clbrdrt\brdrs 
\clbrdrb\brdrs \clshdng0\cellx7120\clbrdrt\brdrs \clbrdrb\brdrs \clbrdrr\brdrs \clshdng0\cellx8560\pard \sl360\keepn\intbl {\b \cell }\pard \sl360\keepn\intbl {\b\ul Sundar/ Sontum\par 
}\pard \sl360\keepn\intbl {\b\ul Old\cell }\pard \sl360\keepn\intbl {\b\ul Dimmig/ Sontum (Averaged)  \cell }\pard \sl360\keepn\intbl {\b\ul Spiro}{\up9 {\object\objicemb{\*\objname ICEmbdObject18_51}{\*\objdata 
000000a100000ca3685610000832cf454e524600000000008800afa23b8d0048e3db010100000000000831392d32312c3333000100000000000c000a0001201300090000000000000000000400000024000000140000001500000016000000000000003d4a6f7267656e73656e2c2031393935202333363b204c692c203139
3930202332303b204c692c2031393930202332313b204c692c203139393120233232}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}{\fs18\up9 19-21,33}{{\object\objicemb{\*\objname ICEmbdObject19_52}{\*\objdata 
0000002200000ca3685610000832cf454e522d00000000000900afa23b8d0048e3db}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}{\b\ul \cell }\pard \sl360\keepn\intbl {\b\ul Karplus}{\up9 {\object\objicemb{\*\objname ICEmbdObject20_53}{\*\objdata 
0000006300000ca3685610000832cf454e524600000000004a00afa23b8d0048e3dd01010000000000023334000100000000000c000a000120220009000000000000000000010000002500000000000000114b6172706c75732c203139393020233337}{\result {\pict\macpict\picw0\pich0 000a0000000000000000
}}}}{\fs18\up9 34}{{\object\objicemb{\*\objname ICEmbdObject21_54}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900afa23b8d0048e3dd}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}{\b\ul \cell AMBER}{\up9 {\object\objicemb
{\*\objname ICEmbdObject22_55}{\*\objdata 0000006300000ca3685610000832cf454e524600000000004a00afa23b8d0048e3de01010000000000023138000100000000000c000a000120120009000000000000000000010000001800000000000000114b6f6c6c6d616e2c203139393520233234}{\result 
{\pict\macpict\picw0\pich0 000a0000000000000000}}}}{\fs18\up9 18}{{\object\objicemb{\*\objname ICEmbdObject23_56}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900afa23b8d0048e3de}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}{
\b\ul \cell }\pard \intbl {\b \row }\trowd \trgaph80\trleft-80 \clbrdrt\brdrs \clbrdrl\brdrs \clshdng0\cellx1360\clbrdrt\brdrs \clshdng0\cellx2800\clbrdrt\brdrs \clshdng0\cellx4240\clbrdrt\brdrs \clshdng0\cellx5680\clbrdrt\brdrs \clshdng0\cellx7120
\clbrdrt\brdrs \clbrdrr\brdrs \clshdng0\cellx8560\pard \sl480\keepn\intbl {\b\f23 c}{\b\f23\fs20\up6 2}{\b  }\cell 1656.\cell 1537.\cell 5840.\cell 2684.\cell 7288.\cell \pard \intbl {\b \row }\trowd \trgaph80\trleft-80 \clbrdrl\brdrs \clshdng0\cellx1360
\clshdng0\cellx2800\clshdng0\cellx4240\clshdng0\cellx5680\clshdng0\cellx7120\clbrdrr\brdrs \clshdng0\cellx8560\pard \sl480\keepn\intbl {\b\fs20 BONDS}{\fs20 \cell \cell \cell \cell \cell \cell }\pard \intbl {\b \row }\pard \sl480\keepn\intbl {\b\fs20 
NI-NP\cell }{\fs20 157.246\cell 145.000\cell 121.000\cell 270.200\cell 50.000\cell }\pard \intbl {\b \row }\pard \sl480\keepn\intbl {\b\fs20 NP-CC\cell }{\fs20 297.322\cell 313.538\cell 427.500\cell 377.200\cell 428.00\cell }\pard \intbl {\b \row }\pard 
\sl480\keepn\intbl {\b\fs20 CC-CB\cell }{\fs20 260.679\cell 287.400\cell 391.000\cell 299.800\cell 416.000\cell }\pard \intbl {\b \row }\pard \sl480\keepn\intbl {\b\fs20 CC-CD\cell }{\fs20 327.507\cell 361.863\cell 502.000\cell 360.000\cell 500.000\cell 
}\pard \intbl {\b \row }\pard \sl480\keepn\intbl {\b\fs20 CB-CB\cell }{\fs20 413.607\cell 426.790\cell 512.000\cell 340.700\cell 546.000\cell }\pard \intbl {\b \row }\pard \sl480\keepn\intbl {\b\fs20 CD-HM\cell }{\fs20 356.507\cell 361.107\cell 361.000
\cell 367.600\cell 367.000\cell }\pard \intbl {\b \row }\pard \sl480\keepn\intbl {\b\fs20 CB-CX\cell }{\fs20 282.851\cell 410.766*\cell 302.300\cell 441.300\cell 317.000\cell }\pard \intbl {\b \row }\pard \sl480\keepn\intbl {\b\fs20 CX-CY\cell }{\fs20 
329.418\cell N.A.\cell 331.000\cell 441.300\cell 310.000\cell }\pard \intbl {\b \row }\pard \sl480\keepn\intbl {\b\fs20 CX-HE\cell }{\fs20 337.442\cell N.A.\cell 328.000\cell 367.000\cell 340.000\cell }\pard \intbl {\b \row }\trowd \trgaph80\trleft-80 
\clbrdrl\brdrs \clbrdrb\brdrs \clshdng0\cellx1360\clbrdrb\brdrs \clshdng0\cellx2800\clbrdrb\brdrs \clshdng0\cellx4240\clbrdrb\brdrs \clshdng0\cellx5680\clbrdrb\brdrs \clshdng0\cellx7120\clbrdrb\brdrs \clbrdrr\brdrs \clshdng0\cellx8560\pard 
\sl480\keepn\intbl {\b\fs20 CY-HN\cell }{\fs20 337.442\cell N.A.\cell N.A.\cell 367.000\cell 340.000\cell }\pard \intbl {\b \row }\pard \sl480 \tab The {\f23 c}{\f23\fs20\up6 2}{\f23  }
values listed in Table 4.1 represent the fit each of individual force field when u
sed in the AMBER force field package. Several approximations were made while evaluating the Spiro, Karplus and AMBER force fields. Firstly, the Spiro force field listed here does not include the non-transferable, off-diagonal terms used by the actual Spiro
 vibrational force field. Additionally, as the Spiro  force field was developed for a united methyl model (NiOEPy in our naming scheme), internal methyl group parameters (CY-HN) were approximated from the standard AMBER force field.  The Karplus and AMBER 
force fields were developed for the heme porphryin, so the Ni-N constant listed under each of these force fields is the Fe-N constant transferred from protoporphyrin IX, and ethyl group parameters are approximated with standard AMBER values.\par 
\pard \sl480 \tab  Our goal was to improve the force constants listed in the standard AMBER force field, so that vibrations of porphyrin systems are better simulated. As Table 4.1 shows this goal has been achieved. The {\f23 c}{\f23\fs20\up6 2}
 for the Sundar/Sontum_old is only higher than that of the Dimmig/Sontum force field. Even in this case, however, the frequency and character fits of the low lying frequencies is better. Therefore, even with a higher {\f23 c}{\f23\fs20\up6 2}
 value, the Sundar/Sontum_old force field gives better vibrational fits. Furthermore, the average root mean square (rms) error of our force field,  40.69 cm{\fs20\up6 -1}
, is, we believe, the lowest error limit possible using the AMBER force field equation. Actually, any rms values around 40  cm{\fs20\up6 -1} is believed to be at the lower limits of the AMBER force field for the f
ollowing reasons. Kollman et al. in their papers are content with AMBER force fields which have root mean square errors of 40.{\up9 {\object\objicemb{\*\objname ICEmbdObject24_57}{\*\objdata 
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Even in our own investigations of smaller molecules like toluene and ethylbenzene, our best optimized force fields had rms errors in the 40 cm{\fs20\up6 -1} range.\par 
\pard \sl480 \tab Not surprisingly, the correlation between parameters and {\f23 c}{\f23\fs20\up6 2}
 values in the Sundar/ Sontum and Dimmig/Sontum force fields is the best. The similarity of these values reflects the inherent transferability of both the force fields.
 No ethyl group parameters had been developed by Dimmig, therefore, standard AMBER values were used instead.\par 
\pard \sl480  \tab 
If the Dimmig/Sontum force field is excluded, then the Sundar/ Sontum_old force field matches up best with the Karplus force field. Our Ni-N constant is 42% smaller, while our CB-CB force constant is 18% larger. These trends are similar to those observed
 by Dimmig in his thesis, reinforcing the transferability of that united atom force field to the Sundar/Sontum_old force field. The ethyl group par
ameters do not match up between the Sundar/Sontum_old and Karplus force fields. Karplus' force field has both the CX-CY and CB-CX constants set to 441 kcal/mol, which although higher than values used in the Spiro and AMBER force fields, match the optimized
 constants in the Dimmig/Sontum united ethyl model. We believe that  Karplus did not develop parameters for the ethyl group, but chose instead to transfer united ethyl parameters{\b . \par 
}\pard \sl480 {\b \tab }Various attributes of each of the listed force field become apparent, when
 Table 4.1 is examined closer. For example, the simplicity of the standard, AMBER force field is appealing. Fundamentally, the development of AMBER bond force constants was done by "linear interpolation between pure single and double bond values using the 
observed bond distances."{\up9 {\object\objicemb{\*\objname ICEmbdObject28_59}{\*\objdata 
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 The result of such a modeling philosophy is the correspondence seen between bond orders and force constants. As a result, the CB-CB bond  (bond order= 1.75) has the largest constant (546.0 kcal/ Mol{\fs20\up6 -1}), while the CX-CY bond (b
ond order=1.0) has the lowest force constant (310.0 kcal/ Mol{\fs20\up6 -1}). The problem with the standard force field, however, is the poor vibrational fit it gives when used to describe the vibrational frequencies of the NiOEP. The high {\f23 c}{
\f23\fs20\up6 2} value obtained with the standard force field indicates the "poorness" of the vibrational fit.\par 
\pard \sl480 \tab Lastly, as mentioned before, comparison of the Spiro force field within the AMBER framework cannot be done effectively . Spiro's vibrational force field had interaction constants, which 
do not have an analog within the AMBER force field philosophy. While non-bonded terms attempt to simulate off-diagonals terms, there is no simple, direct relationship between non-bonded and off-diagonal terms. Not surprisingly, high {\f23 c}{
\f23\fs20\up6 2} values result when the Spiro force field is placed within our AMBER force field framework, reflecting the inherrent non-transferability of this force field.\par 
\pard \sl480 \par 
\pard \sl480\keepn {\v {\tc\tcl3\pard\plain \sl480\keepn \f20 {\b Nickel Nitrogen Constant}}}\par 
\pard \sl480 \tab The range  seen in literature for the nickel-nitrogen constant (Ni-N) is from 50 to 270 kcal/ mol. Dimmig determined that the range of force constants for this parameter in his model  was between 120 and 280 kcal/mol. {\up9 
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000a0000000000000000}}}}
 However, no convincing reason could be developed for setting the value of this constant at 145 kcal/ Mol. We experienced a similar problem with our force field. The range of values that the Sundar/Sontum_force field allows for the Ni-N force contast in be
tween 120 and 280 kcal/ Mol. A choice of 157 kcal/ Mol was made by final optimization  of the force field, once the values
 for all the other parameters had been chosen. Resolution of the nickel-nitrogen force constant  ambiguity led to the development of Sundar/Sontum_new force field, and so this ambiguity is reconsidered in the next chapter.\par 
\pard \sl480 \par 
\pard \sl480\keepn {\v {\tc\tcl3\pard\plain \sl480\keepn \f20 {\b Angle Bending Constants}}}\par 
\pard \sl480 \tab 
The other set of inplane parameters directly transferred from Dimmig's optimized united atom model were the angle bending constants.   Table 4.2 lists the angle constants from the four force fields listed in Table 4.1. Again, the transferable Dimmig/ Sont
um force field was the starting point in the development of the Sundar/Sontum_old force field. \par 
\pard \qc\sl480\keepn {\b Table 4.2  Angle Force Constants\par 
}\pard \keepn \par 
\trowd \trgaph80\trrh320\trleft-80 \clbrdrt\brdrs \clbrdrl\brdrs \clshdng0\cellx1480\clbrdrt\brdrs \clshdng0\cellx3040\clbrdrt\brdrs \clshdng0\cellx4600\clbrdrt\brdrs \clshdng0\cellx6160\clbrdrt\brdrs \clshdng0\cellx7720\clbrdrt\brdrs \clbrdrr\brdrs 
\clshdng0\cellx9280\pard \qc\keepn\intbl {\b \cell }\pard \qc\keepn\intbl {\b Sundar/ Sontum_old\cell }\pard \qc\keepn\intbl {\b Dimmig/ Sontum (Averaged)\cell }\pard \qc\keepn\intbl {\b Spiro\cell Karplus\cell AMBER\cell }\pard \intbl \row \trowd 
\trgaph80\trrh320\trleft-80 \clbrdrl\brdrs \clshdng0\cellx1480\clshdng0\cellx3040\clshdng0\cellx4600\clshdng0\cellx6160\clshdng0\cellx7720\clbrdrr\brdrs \clshdng0\cellx9280\pard \keepn\intbl {\b ANGLES}\cell \cell \cell \cell \cell \cell \pard \intbl 
\row \pard \keepn\intbl NP-NI-NP\cell \pard \qr\keepn\intbl 0.000\cell 0.000\cell 0.000\cell 0.000\cell 0.000\cell \pard \intbl \row \pard \keepn\intbl NO-NI-NP\cell \pard \qr\keepn\intbl 8.780\cell 29.454\cell 18.000\cell 50.000\cell 0.000\cell \pard 
\intbl \row \pard \keepn\intbl NI-NP-CC\cell \pard \qr\keepn\intbl 87.705\cell 64.740\cell 22.000\cell 96.150\cell 0.000\cell \pard \intbl \row \pard \keepn\intbl NP-CC-CB\cell \pard \qr\keepn\intbl 117.615\cell 121.926\cell 99.000\cell 122.00\cell 70.000
\cell \pard \intbl \row \pard \keepn\intbl NP-CC-CD\cell \pard \qr\keepn\intbl 36.191\cell 27.753\cell 60.000\cell 88.000\cell 70.000\cell \pard \intbl \row \pard \keepn\intbl CB-CC-CD\cell \pard \qr\keepn\intbl 36.191\cell 27.753\cell 60.000\cell 61.600
\cell 70.000\cell \pard \intbl \row \pard \keepn\intbl CC-NP-CC\cell \pard \qr\keepn\intbl 130.413\cell 127.505\cell 117.00\cell 139.300\cell 70.000\cell \pard \intbl \row \pard \keepn\intbl CC-CB-CB\cell \pard \qr\keepn\intbl 90.796\cell 60.050\cell 
99.000\cell 30.080\cell 70.000\cell \pard \intbl \row \pard \keepn\intbl CC-CD-CC\cell \pard \qr\keepn\intbl 166.070\cell 157.490\cell 79.000\cell 94.200\cell 70.000\cell \pard \intbl \row \pard \keepn\intbl CC-CD-HM\cell \pard \qr\keepn\intbl 32.014
\cell 29.167\cell 36.000\cell 12.700\cell 35.000\cell \pard \intbl \row \pard \keepn\intbl CC-CB-CX\cell \pard \qr\keepn\intbl 29.230\cell 76.366\cell 86.000\cell 65.000\cell 70.000\cell \pard \intbl \row \pard \keepn\intbl CB-CB-CX\cell \pard 
\qr\keepn\intbl 29.230\cell 76.366\cell 56.000\cell 65.000\cell 70.000\cell \pard \intbl \row \pard \keepn\intbl CB-CX-CY\cell \pard \qr\keepn\intbl 93.004\cell N.A.\cell 54.000\cell 70.000\cell 70.000\cell \pard \intbl \row \pard \keepn\intbl CB-CX-HE
\cell \pard \qr\keepn\intbl 55.062\cell N.A.\cell 45.000\cell \cell 50.000\cell \pard \intbl \row \pard \keepn\intbl CX-CY-HE\cell \pard \qr\keepn\intbl 35.847\cell N.A.\cell N.A.\cell N.A.\cell 50.000\cell \pard \intbl \row \pard \keepn\intbl CY-CX-HE
\cell \pard \qr\keepn\intbl 35.847\cell N.A.\cell 45.000\cell N.A.\cell 50.000\cell \pard \intbl \row \pard \keepn\intbl HE-CX-HE\cell \pard \qr\keepn\intbl 31.560\cell N.A.\cell 39.000\cell N.A.\cell 35.000\cell \pard \intbl \row \trowd 
\trgaph80\trrh320\trleft-80 \clbrdrl\brdrs \clbrdrb\brdrs \clshdng0\cellx1480\clbrdrb\brdrs \clshdng0\cellx3040\clbrdrb\brdrs \clshdng0\cellx4600\clbrdrb\brdrs \clshdng0\cellx6160\clbrdrb\brdrs \clshdng0\cellx7720\clbrdrb\brdrs \clbrdrr\brdrs \clshdng0
\cellx9280\pard \keepn\intbl HN-CY-HN\cell \pard \qr\keepn\intbl 31.560\cell N.A.\cell N.A.\cell N.A.\cell 35.000\cell \pard \intbl \row \pard \keepn {\fs20 *Listed force constants have units of Kcal / mol. \par 
}\pard \sl480 \tab 
The same approximations mentioned in the discussion of the bond parameters were made with these force field parameters also. As table 4.2 shows, the Sundar/ Sontum angle bending constants closely correspond to the Dimmig/ Sontum force field, supporting th
e inherent transferability of these two force fields. As expected, force constants concerning the ethyl groups do not correspond between these two force fields as they represent different groups(united atom vs. non-united ethyl group). In the S
undar/Sontum_old force field, values for these ethyl parameters were transferred over from ethylbenzene and the optimized. Such additional optimization did not change the values of these ethyl group parameters by much, reinforcing the transferability of th
e ethylbenzene force field.\par 
\tab As seen in Dimmig's thesis, the CC-CD-CC constants value is much higher than corresponding values in other force fields. Also N-CC-CD and CB-CC-CD angle constants are much smaller than those listed in the Spiro, Karplus and AMB
ER force fields. Dimmig suggested that such a trend was indicative a trade-off between the CC-CD-CC parameter and the N-CC-CD/ CB-CC-CD set of parameters.  These arguments seem to be valid in the Sundar/Sontum_old force field as well. While such an explana
tion seems reasonable, wide fluctuations in angle constants are avoided with the Sundar/Sontum_new force field. Another possible explanation for the observed fluctuations in the angle force constant will be offered in the next chapter, when the Sundar/Sont
um_new force field is compared to the Sundar/Sontum_old force field. \par 
\pard \sl480 \tab 
Again, the simplicity of the AMBER force field is appealing. Unlike the other four force fields, bending constants within the standard AMBER force field do not vary by much. AMBER philosophy emphasises simplicity in force field development, Hence force co
nstants in the standard, AMBER force field are 70, 50 or 30 kcal/ mol.  The chief deficiency of the standard force field, however, is the poor vibrational fit to NiOEP  is poor as indicated by the high {\f23 c}{\f23\fs20\up6 2}
 value. The Sundar/Sontum_new force field will be shown to represent a compromise between the Dimmig/Sontum and AMBER force fields; retaining some of the AMBER simplicity, while still producing good vibrational fits. {\b \par 
}\pard \sl480 \par 
\pard \sl480\keepn {\v {\tc\tcl2\pard\plain \sl480\keepn \f20 {\b Structural Fits}}}\par 
\pard \sl480 \tab 
Apart from a good vibrational fit, it was necessary that force field parameters (bond and angle constants) also gave a good structural fit for the porphyrin molecule. Dimmig et. al. determined that such a fit was best possible if the porphyrin had some s
train built into it. Accordingly, the equilibrium bond (r{\fs20\dn4 eq} in equation 2.1) and angle ({\f23 q}{\fs20\dn4 eq}
 in equation 2.1) were not taken from the crystal structure of NiOEP. The final equilibrium angles used by Dimmig for the CC-CD-CC and CC-N-CC values were set so that  the minimized structure of NiOEP reproduced the same bond distances and angles like the 
crystal structure. According to Dimmig, "the strained set was found to be easily transferable".{\up9 {\object\objicemb{\*\objname ICEmbdObject0_63}{\*\objdata 
0000006200000ca3685610000832cf454e524600000000004900afa28653000d918201010000000000023234000100000000000c000a000120180009000000000000000000010000001b000000000000001044696d6d69672c203139393520233237}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}
}}}{\fs18\up9 24}{{\object\objicemb{\*\objname ICEmbdObject1_64}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900afa28653000d9182}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}
 Our optimized force field (Sundar/Sontum_old) reflects this philo
sophy. The final bond and angle parameters used are not taken from the NiOEP crystal structure. Instead these were assigned until the right geometric and vibrational fits was obtained.  Table 4.3 lists the equilibrium values (r{\fs20\dn4 eq} and {\f23 q}{
\fs20\dn4 eq} in equation 2.1) used, the results of energy minimization using these parameters, and the corresponding results obtained from the crystal structure of NiOEP. \par 
\pard \qc\sl480\keepn {\b Table 4.3\tab Structural and Angle Parameters}\par 
\pard \keepn \par 
\trowd \trqc\trgaph80\trleft-80 \clbrdrt\brdrth \clbrdrl\brdrth \clshdng0\cellx2080\clbrdrt\brdrth \clshdng0\cellx4240\clbrdrt\brdrth \clshdng0\cellx6400\clbrdrt\brdrth \clbrdrr\brdrth \clshdng0\cellx8560\pard \keepn\intbl \cell \pard \qc\keepn\intbl {\b 
Equilibrium Values\par 
}\pard \qc\keepn\intbl {\b  (\'81 or \'a1)}\cell \pard \qc\keepn\intbl {\b Minimized NiOEP\par 
}\pard \qc\keepn\intbl {\b  (\'81 or \'a1)}\cell \pard \qc\keepn\intbl {\b Crystal Structure NiOEP\par 
}\pard \qc\keepn\intbl {\b  (\'81 or \'a1)}{\up9 {\object\objicemb{\*\objname ICEmbdObject30_65}{\*\objdata 
0000005e00000ca3685610000832cf454e524600000000004500afa23b8e0048e3e101010000000000023139000100000000000c000a0001201300090000000000000000000100000014000000000000000c4c692c203139393020233230}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}{
\fs18\up9 19}{{\object\objicemb{\*\objname ICEmbdObject31_66}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900afa23b8e0048e3e1}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}\cell \pard \intbl \row \trowd 
\trqc\trgaph80\trrh-430\trleft-80 \clbrdrt\brdrs \clbrdrl\brdrs \clshdng0\cellx2080\clbrdrt\brdrs \clshdng0\cellx4240\clbrdrt\brdrs \clshdng0\cellx6400\clbrdrt\brdrs \clbrdrr\brdrs \clshdng0\cellx8560\pard \keepn\intbl BONDS\cell \cell \cell \cell \pard 
\intbl \row \trowd \trqc\trgaph80\trrh-430\trleft-80 \clbrdrl\brdrs \clshdng0\cellx2080\clshdng0\cellx4240\clshdng0\cellx6400\clbrdrr\brdrs \clshdng0\cellx8560\pard \keepn\intbl Ni-N\cell 1.958\cell 1.968\cell 1.958\cell \pard \intbl \row \pard 
\keepn\intbl N-CC\cell 1.376\cell 1.381\cell 1.376\cell \pard \intbl \row \pard \keepn\intbl CC-CB\cell 1.443\cell 1.453\cell 1.443\cell \pard \intbl \row \pard \keepn\intbl CC-CD\cell 1.371\cell 1.377\cell 1.371\cell \pard \intbl \row \pard \keepn\intbl 
CB-CB\cell 1.346\cell 1.350\cell 1.346\cell \pard \intbl \row \pard \keepn\intbl CB-CX\cell 1.495\cell 1.516\cell 1.510\cell \pard \intbl \row \pard \keepn\intbl CX-CY\cell 1.501\cell 1.512\cell 1.506\cell \pard \intbl \row \pard \keepn\intbl CD-HM\cell 
1.090\cell 1.086\cell 1.090\cell \pard \intbl \row \pard \keepn\intbl CX(Y)-HE(N)\cell 1.100\cell 1.100\cell 1.100\cell \pard \intbl \row \pard \keepn\intbl ANGLES\cell \cell \cell \cell \pard \intbl \row \pard \keepn\intbl NP-NI-NP\cell 180.000\cell 
179.822\cell 180.000\cell \pard \intbl \row \pard \keepn\intbl NO-NI-NP\cell   90.000\cell 90.000\cell   90.000\cell \pard \intbl \row \pard \keepn\intbl NI-N-CC\cell 120.000\cell 127.795\cell 128.000\cell \pard \intbl \row \pard \keepn\intbl N-CC-CB
\cell 120.000\cell 111.122\cell 111.500\cell \pard \intbl \row \pard \keepn\intbl NO-CC-CD\cell 121.800\cell 125.018\cell 124.000\cell \pard \intbl \row \pard \keepn\intbl CB-CC-CD\cell 118.200\cell 123.860\cell 124.100\cell \pard \intbl \row \pard 
\keepn\intbl CC-N-CC\cell 108.000\cell 104.411\cell 104.000\cell \pard \intbl \row \pard \keepn\intbl CC-CB-CB\cell 120.000\cell 106.673\cell 106.500\cell \pard \intbl \row \pard \keepn\intbl CC-CD-CC\cell 124.000\cell 124.375\cell 125.000\cell \pard 
\intbl \row \pard \keepn\intbl CC-CB-CX\cell 120.000\cell 127.537\cell 125.500\cell \pard \intbl \row \pard \keepn\intbl CB-CB-CX\cell 120.000\cell 125.787\cell 128.000\cell \pard \intbl \row \trowd \trqc\trgaph80\trrh-430\trleft-80 \clbrdrl\brdrs 
\clbrdrb\brdrs \clshdng0\cellx2080\clbrdrb\brdrs \clshdng0\cellx4240\clbrdrb\brdrs \clshdng0\cellx6400\clbrdrb\brdrs \clbrdrr\brdrs \clshdng0\cellx8560\pard \keepn\intbl CB-CX-CY\cell 109.500\cell 110.103\cell 109.500\cell \pard \intbl \row \pard \sl480 
\tab 
A good force field upon minimization should reproduce the crystal structure values for the various bond and angle, since a good geometry implies a good energy fit for the molecule as well. As Table 4.3 shows, the Sundar/Sontum_old force field reproduces b
oth the bond lengths and bond angles seen in the X-ray crystal structure of the NiOEP molecule.  The average errors in the bond lengths and angles listed in table 4.3 are 0.006 \'81 and 0.461\'a1
 respectively. Such accuracy is better than currently available in literature. Other force fields, like Marques' MM2 force field reproduced porphyrin bond and angle parameters with errors of 0.015 \'81 and 1.5\'a1 respectively.{\up9 {\object\objicemb
{\*\objname ICEmbdObject32}{\*\objdata 0000006300000ca3685610000832cf454e524600000000004a00afa23b8e0048e3e201010000000000023232000100000000000c000a000120160009000000000000000000010000001900000000000000114d6172717565732c203139393520233235}{\result 
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\par 
\pard \sl480 \par 
\pard \sl480 {\v {\tc\tcl2\pard\plain \sl480 \f20 {\b Dihedral (Proper and Improper) Parameters}}}{\b \par 
}{\v {\tc\tcl3\pard\plain \sl480 \f20 {\b Proper Torsion Parameters}}}\par 
\pard \sl480 \tab Unlike the IP parameters already described in this chapter, the OOP parameters developed in this thesis do n
ot correspond to those developed by Dimmig. We broke away from using a single dihedral to describe all the proper dihedrals around a bond. Dimmig had also grouped his dihedrals into either cis or trans sets. We chose to define specific dihedrals for all th
e possible dihedrals. Table 4.4 shows the effects of this additional relaxation on the dihedral parameters used in the Sundar/Sontum_old force field. The proper dihedrals terms possible around the CB-CB bond are listed, and the values for these term in the
 Sundar/Sontum_old, Dimmig/Sontum and AMBER force fields are compared. \par 
\pard \sl480 \par 
\pard \qc\sl480\keepn {\b Table 4.4 Different Dihedral Parameters Definition Used. \par 
}\pard \keepn \par 
\trowd \trqc\trgaph80\trleft-80 \clbrdrt\brdrth \clbrdrl\brdrth \clshdng0\cellx2800\clbrdrt\brdrth \clshdng0\cellx4600\clbrdrt\brdrth \clshdng0\cellx6400\clbrdrt\brdrth \clbrdrr\brdrth \clshdng0\cellx8200\pard \sl360\keepn\intbl {\b Parameter}\cell \pard 
\sl360\keepn\intbl {\b\fs20 AMBER (kcal/mol)}{\fs20\up9 {\object\objicemb{\*\objname ICEmbdObject34_67}{\*\objdata 
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}}}}{\fs18\up9 18}{\fs20 {\object\objicemb{\*\objname ICEmbdObject35_68}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900afa23b8e0048e3e3}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}{\fs20 \cell }\pard \sl360\keepn\intbl {
\b\fs20 Dimmig/ Sontum (kcal/mol)}{\fs20\up9 {\object\objicemb{\*\objname ICEmbdObject36}{\*\objdata 
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}}}{\fs18\up9 24}{\fs20 {\object\objicemb{\*\objname ICEmbdObject37}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900afa23b8e0048e3e4}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}{\fs20 \cell }{\b\fs20 
Sundar/ Sontum_old (kcal/ mol)}{\fs20 \cell }\pard \intbl \row \trowd \trqc\trgaph80\trleft-80 \clbrdrt\brdrs \clbrdrl\brdrs \clshdng0\cellx2800\clbrdrt\brdrs \clshdng0\cellx4600\clbrdrt\brdrs \clshdng0\cellx6400\clbrdrt\brdrs \clbrdrr\brdrs \clshdng0
\cellx8200\pard \sl480\keepn\intbl {\b CC-CB-CB-CC\cell }\pard \qc\sl480\keepn\intbl   5.70\cell 9.127\cell    7.759\cell \pard \intbl \row \trowd \trqc\trgaph80\trleft-80 \clbrdrl\brdrs \clshdng0\cellx2800\clshdng0\cellx4600\clshdng0\cellx6400\clbrdrr
\brdrs \clshdng0\cellx8200\pard \sl480\keepn\intbl {\b CX(Z)-CB-CB-CX(Z)\cell }\pard \qc\sl480\keepn\intbl   5.70\cell 9.127\cell    5.579\cell \pard \intbl \row \pard \sl480\keepn\intbl {\b CC-CB-CB-CX(Z)\cell }\pard \qc\sl480\keepn\intbl   5.70\cell 
0.02\cell    3.475\cell \pard \intbl \row \pard \sl480\keepn\intbl {\b IMPROPER TERM\cell }\pard \qc\sl480\keepn\intbl 1.00\cell 0.961\cell 4.314\cell \pard \intbl \row \trowd \trqc\trgaph80\trleft-80 \clbrdrl\brdrs \clbrdrb\brdrs \clshdng0\cellx2800
\clbrdrb\brdrs \clshdng0\cellx4600\clbrdrb\brdrs \clshdng0\cellx6400\clbrdrb\brdrs \clbrdrr\brdrs \clshdng0\cellx8200\pard \sl480\keepn\intbl {\b Total\cell }\pard \qc\sl480\keepn\intbl 21.80*\cell 19.106*\cell  20.645* \cell \pard \intbl \row \pard 
\keepn \tab {\fs20 * scaling formula used to account for improper term.}\par 
\pard \sl480 \tab As  the last row of table 4.4 shows, consistency in the
 total rotation potential  is maintained. The scaling procedure used to account for the improper terms is explained in Appendix C. Thus in the Sundar/Sontum_old force field, just as with smaller molecule force fields, the barrier to rotation has been distr
ibuted non-uniformly between such specific dihedrals term, and the additional flexibility has lead to better vibrational fits of the OOP modes. As a final check on the developed OOP force field, the intuitive consistency of the various parameters was evalu
ated. Just as bond force constants depend on the internuclear separation of atoms, i.e on the bond order, similarly we would also expect the total rotation potential around each bond to reflect the associated bond order.  We summed up all the specific dihe
drals around each bond and compared them to values listed in the AMBER force field. Table 4.5 lists the total potentials around each of the bonds and optimized values listed in the AMBER force field. The last column contains expected values based on bond o
rders. These values were used as a starting point for final values listed in the AMBER potential.\par 
\pard \qc\sl480\keepn {\b Table 4.5 Total Rotation Potentials.\par 
}\trowd \trgaph80\trleft-80 \clbrdrt\brdrth \clbrdrl\brdrth \clshdng0\cellx2800\clbrdrt\brdrth \clshdng0\cellx4672\clbrdrt\brdrth \clshdng0\cellx6544\clbrdrt\brdrth \clbrdrr\brdrth \clshdng0\cellx8416\pard \sl480\keepn\intbl {\b Parameter }\cell \pard 
\sl480\keepn\intbl {\b Total Potential }\cell \pard \sl480\keepn\intbl {\b AMBER potential}{\up9 {\object\objicemb{\*\objname ICEmbdObject2_69}{\*\objdata 
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000a0000000000000000}}}}{\b\fs18\up9 25}{{\object\objicemb{\*\objname ICEmbdObject3_70}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900afa28d5f000f3962}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}\cell \pard 
\qc\sl480\keepn\intbl {\b Expected Values}{\up9 {\object\objicemb{\*\objname ICEmbdObject4_71}{\*\objdata 
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}}}}{\b\fs18\up9 18}{{\object\objicemb{\*\objname ICEmbdObject5_72}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900afa28d6f000f3d22}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}{\b \cell }\pard \intbl {\b \row }\trowd 
\trgaph80\trleft-80 \clbrdrt\brdrs \clbrdrl\brdrs \clshdng0\cellx2800\clbrdrt\brdrs \clshdng0\cellx4672\clbrdrt\brdrs \clshdng0\cellx6544\clbrdrt\brdrs \clbrdrr\brdrs \clshdng0\cellx8416\pard \sl480\keepn\intbl {\b X-NO-Ni-X   (1.00)}\cell \pard 
\qc\sl480\keepn\intbl    7.122*\cell \pard \qc\sl480\keepn\intbl     0.00\cell \pard \qc\sl480\keepn\intbl N.A.\cell \pard \intbl {\b \row }\trowd \trgaph80\trleft-80 \clbrdrl\brdrs \clshdng0\cellx2800\clshdng0\cellx4672\clshdng0\cellx6544\clbrdrr\brdrs 
\clshdng0\cellx8416\pard \sl480\keepn\intbl {\b X-CB-CX-X  (1.00)\cell }\pard \qc\sl480\keepn\intbl    3.468*\cell \pard \qc\sl480\keepn\intbl     1.10\cell \pard \qc\sl480\keepn\intbl 0.00\cell \pard \intbl {\b \row }\pard \sl480\keepn\intbl {\b 
X-CX-CY-X  (1.00)\cell }\pard \qc\sl480\keepn\intbl   1.254\cell \pard \qc\sl480\keepn\intbl    1.10* \cell \pard \qc\sl480\keepn\intbl 0.00\cell \pard \intbl {\b \row }\pard \sl480\keepn\intbl {\b X-CB-CB-X  (1.75)\cell }\pard \qc\sl480\keepn\intbl 
20.645*\cell \pard \qc\sl480\keepn\intbl   21.80*\cell \pard \qc\sl480\keepn\intbl 22.50\cell \pard \intbl {\b \row }\pard \sl480\keepn\intbl {\b X-CB-CC-X  (1.25)\cell }\pard \qc\sl480\keepn\intbl 11.101*\cell \pard \qc\sl480\keepn\intbl   16.95*\cell 
\pard \qc\sl480\keepn\intbl 7.50\cell \pard \intbl {\b \row }\pard \sl480\keepn\intbl {\b X-CC-NO-X  (1.50)\cell }\pard \qc\sl480\keepn\intbl 16.663*\cell \pard \qc\sl480\keepn\intbl   15.95*\cell \pard \qc\sl480\keepn\intbl 10.00\cell \pard \intbl {\b 
\row }\trowd \trgaph80\trleft-80 \clbrdrl\brdrs \clbrdrb\brdrs \clshdng0\cellx2800\clbrdrb\brdrs \clshdng0\cellx4672\clbrdrb\brdrs \clshdng0\cellx6544\clbrdrb\brdrs \clbrdrr\brdrs \clshdng0\cellx8416\pard \sl480\keepn\intbl {\b X-CC-CD-X   (1.50)\cell 
}\pard \qc\sl480\keepn\intbl  10.259*\cell \pard \qc\sl480\keepn\intbl   11.95*\cell \pard \qc\sl480\keepn\intbl 14.50\cell \pard \intbl {\b \row }\pard \keepn {\fs20 * improper terms accounted for using a scaling formula.\par 
units are kcal/mol\par 
( ) refer to approximate bond orders\par 
}\pard \sl480 \tab 
The total rotation potentials in almost all the cases agree with the values listed within the AMBER potential.Such consistency is reassuring as the total barrier to rotation around a bond should not depend on the distribution of the barrier. Most of the t
erms listed in the AMBER potential had improper terms, and the effects of these improper terms were accounted for by using a scaling formula (Appendix C).
 Thus, just as in the case of the benzene derivative (chapter III), the OOP parameters in Sundar/Sontum_old reflects a more dynamic and flexible force field.  \par 
\pard \sl480 \tab 
Closer examination of Table 4.5, however, reveals 2 disagreement between dihedral parameters in the AMBER and Sundar/Sontum_old force fields. The AMBER force field has the proper dihedrals around both NO-Ni and CB-CX bonds set to zero. In our potential se
t, these parameters need definite values. These divergences are genuine, in that they reflect possible deficiencies in standard AMBER OOP parameter set itself, and need to be examined individually. \par 
\pard \sl480 \tab 
In the case of the dihedral defined around the Ni-N bond, the Sundar/Sontum_old force field diverges from the trend seen in the Karplus, Spiro and AMBER force fields. In all of these force fields, this dihedral has been set to zero. Vibrationally, the X-N
-NI-X dihedrals control the frequency of the a low energy ruffling mode of the porphyrin.  In our investigations of this mode, we found that a definite v
alue for this Ni-N dihedral was required, to make this ruffling mode energetically demanding (i.e. have a non-zero vibrational frequency). The problem of zero frequency ruffling motion is particulary evident in the Karplus force field, which doesn't seem t
o have any other terms, which could restrict the ruffling motion. Our final X-N-Ni-X dihedral parameter was determined by matching the calculated ruffling mode frequency to the corresponding  experimentally observed frequency.\par 
\pard \sl480 \tab The other parameter that doe
s not correspond between the AMBER and Sundar/Sontum force fields is the total X-CB-CX-X torsion potential. AMBER has the proper dihedral around this bond set to zero. The only contribution to this term therefore is from an improper torsion term defined ar
ound the CB atom. Our analyses of ethylbenzene (Chapter 3) indicate, however, that there is non-zero proper dihedral rotation barrier around the CB-CX bond.  We believe, therefore, that this term has been  incorrectly set in the standard AMBER force field.
 \par 
\pard \sl480 \par 
\pard \sl480 {\v {\tc\tcl3\pard\plain \sl480 \f20 {\b IMPROPER Torsion}}}\par 
\pard \sl480 \tab 
The last conclusion derived from our modeling of ethylbenzene was also transferred over to the porphyrin. With the additional flexibility in the proper dihedral set, we were able to eliminate the use of improper terms around most of the atom centers. Agai
n, as we had observed in our analysis of ethylbenzene, we needed these improper terms only when hyperconjugation was possible. Therefore, use of improper terms was eliminated from the CD position of the porphyrin core. All other OOP
 modes could be satisfactorily reproduced using our specific, unrestricted proper dihedral parameter set. \par 
\pard \sl480  \par 
\pard \sl480 {\v {\tc\tcl2\pard\plain \sl480 \f20 {\b Force Constants vs. Bond Lengths}}}\par 
\pard \sl480 \tab 
After vibrational and structural consistency, another requirement of the final force field was that it display some intuitive consistency in the final parameters developed. Intuitively, one expects an inverse correlation to exist between bond lengths and 
associated force constants. Increasing the distance between atoms reduces their interaction with each other (r
educes the bond order), hence one would expect the force constant to go down. While no linear relationship is expected, as the mass of the atoms at either ends of bond also needs to considered, a rough trend is expected. Relationships between the bond dist
ances separating pairs of atoms and the force constant associated with these bond lengths were probed for the final force field. Figure 4.1 displays the trend seen in minimized structure, equilibrium bond lengths and force constants for the Sundar/ Sontum,
 Dimmig/ Sontum and Spiro force fields. \par 
\pard \sl480 \par 
\pard \sl480\keepn {{\pict\macpict\picw482\pich332 
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0200ff00b7ff0000fbff0000feff0000d3ff010000f9ff0000feff0000bdff0000faff0000fdff0000bbff0000f9ff0300ffff00b8ff0000faff0300ff0000b9ff0000f8ff0200ff00b7ff0000fbff0000feff0000d3ff010000f9ff0000feff0000bdff0000faff0000fdff0000bbff0000f9ff0300ffff00b8ff0000faff
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ff0000fdff0000bbff0000f9ff0000feff0000bbff0000f8ff0000feff0000d2ff0000f9ff0000feff0000bdff0000f7ff0000b9ff0000f6ff0000b8ff0000faff0000fdff0000bbff0000f9ff0000feff0000bbff0000f8ff0000feff000000c0d2ff0000f9ff0000feff0000bdff0000f8ff0000b8ff0000f6ff0000b8ff
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ff0000faff0000fdff0000bbff0000f9ff0000feff0000bcff0000f7ff0000feff000000c9d2ff0000f9ff0000feff0000bdff0000f9ff0000b7ff0000f6ff0000b8ff0000f9ff0300ffff00baff0000f9ff0000feff0000bdff0000fdff0000fbff0000feff0000d2ff0000f9ff0000feff0000bdff0000f9ff0000b7ff00
00f6ff0000b8ff0000f9ff0300ffff00baff0000f9ff0000feff0000bdff0000fdff0000fbff0000feff0000d2ff0000f9ff0000feff0000bdff0000f9ff0000b7ff0000f6ff0000b8ff0000f9ff0300ffff00baff0000f9ff0000feff0000bdff0000fdff0000fbff0000feff000000ddd2ff0000f9ff0000feff0000bdff
0000faff0000fdff0000bcfffe00feff0000fbff0000b9fffe00feff0000fdff010000bafffe00feff0000fdfffe00bcfffc00feff0000fdfffe00d1ff0000f9ff0000feff0000bdff0000faff0000fdff0000bcfffe00feff0000fbff0000b9fffe00feff0000fdff010000bafffe00feff0000fdfffe00bcfffc00feff00
00fdfffe00d1ff0000f9ff0000feff0000bdff0000faff0000fdff0000bcfffe00feff0000fbff0000b9fffe00feff0000fdff010000bafffe00feff0000fdfffe00bcfffc00feff0000fdfffe0000ff005ad2ff0000f9ff0000feff0000befffe00feff0200fffffc0081ff81ff81fffeff0000f9ff0000feff0000befffe
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00fbff0000eaff0300ffff00f9ff0000fcff0000fcff000081ff81ff81ffedff0000feff0000f0ff0000fbff0000eaff0300ffff00f9ff0000fcff0000fcff000081ff81ff81ffedff0000feff0000f0ff0000fbff0000eaff0300ffff00f9ff0000fcff0000fcff000081ffb0ff00d881ffbeff0000feff0000fefffe0005
ffff00ff0000fefffe00fbff0000fbff070000ffff00ff0000feff040000ff00fffe0000fffe00fbff0000fdff0200ff00fdff000081ff81ff81ffedff0000feff0000fefffe0005ffff00ff0000fefffe00fbff0000fbff070000ffff00ff0000feff040000ff00fffe0000fffe00fbff0000fdff0200ff00fdff000081ff
81ff81ffedff0000feff0000fefffe0005ffff00ff0000fefffe00fbff0000fbff070000ffff00ff0000feff040000ff00fffe0000fffe00fbff0000fdff0200ff00fdff000081ffb0ff00e181ffbefffd00feff0000feff0b00ffff00ffff00ff00ffff00fbff0000fcff0e00ffff00ffff00ffff00ff00ffff00feff0600
ffff00ffff00fdff0000fcff0200ff00fcff000081ff81ff81ffeefffd00feff0000feff0b00ffff00ffff00ff00ffff00fbff0000fcff0e00ffff00ffff00ffff00ff00ffff00feff0600ffff00ffff00fdff0000fcff0200ff00fcff000081ff81ff81ffeefffd00feff0000feff0b00ffff00ffff00ff00ffff00fbff00
00fcff0e00ffff00ffff00ffff00ff00ffff00feff0600ffff00ffff00fdff0000fcff0200ff00fcff000081ffb1ff00ea81ffbeff0000feff0300ffff00feff0b00ffff00ffff00ff00ffff00fbff0000fcfffd000affff00ffff00ff00ffff00feff0600ffff00ffff00fdff0000fdff0000feff0000fdff000081ff81ff
81ffeeff0000feff0300ffff00feff0b00ffff00ffff00ff00ffff00fbff0000fcfffd000affff00ffff00ff00ffff00feff0600ffff00ffff00fdff0000fdff0000feff0000fdff000081ff81ff81ffeeff0000feff0300ffff00feff0b00ffff00ffff00ff00ffff00fbff0000fcfffd000affff00ffff00ff00ffff00fe
ff0600ffff00ffff00fdff0000fdff0000feff0000fdff000081ffb1ff00db81ffbeff0000feff0300ffff00feff0b00ffff00ffff00ff00ffff00fbff0000fcff0000fcff0700ffff00ffff0000fdff0600ffff00ffff00fdff0000fdfffc00fdff000081ff81ff81ffeeff0000feff0300ffff00feff0b00ffff00ffff00
ff00ffff00fbff0000fcff0000fcff0700ffff00ffff0000fdff0600ffff00ffff00fdff0000fdfffc00fdff000081ff81ff81ffeeff0000feff0300ffff00feff0b00ffff00ffff00ff00ffff00fbff0000fcff0000fcff0700ffff00ffff0000fdff0600ffff00ffff00fdff0000fdfffc00fdff000081ffb1ff00ed81ff
beff0000feff0300ffff00feff0b00ffff00ffff00ff00ffff00fbff0000feff0d00ff00ffff00ffff00ffff00ff00fbff0600ffff00ffff00fdff0000feff0000fcff0000feff000081ff81ff81ffeeff0000feff0300ffff00feff0b00ffff00ffff00ff00ffff00fbff0000feff0d00ff00ffff00ffff00ffff00ff00fb
ff0600ffff00ffff00fdff0000feff0000fcff0000feff000081ff81ff81ffeeff0000feff0300ffff00feff0b00ffff00ffff00ff00ffff00fbff0000feff0d00ff00ffff00ffff00ffff00ff00fbff0600ffff00ffff00fdff0000feff0000fcff0000feff000081ffb1ff00cf81ffbffffc00fdfffe0001fffffe0003ff
0000fffd00fdfffb0005ffff0000fffffe0003ff0000fffe00fdfffe0000fffe00fdff0400ffff0000fefffe0001ff0081ff81ff81ffeefffc00fdfffe0001fffffe0003ff0000fffd00fdfffb0005ffff0000fffffe0003ff0000fffe00fdfffe0000fffe00fdff0400ffff0000fefffe0001ff0081ff81ff81ffeefffc00
fdfffe0001fffffe0003ff0000fffd00fdfffb0005ffff0000fffffe0003ff0000fffe00fdfffe0000fffe00fdff0400ffff0000fefffe0001ff0081ffb0ff004281ff90ff0000feff0000f3ff0000f6ff000081ff81ff81ffbfff0000feff0000f3ff0000f6ff000081ff81ff81ffbfff0000feff0000f3ff0000f6ff0000
81ffb0ff003681ff8ffffe00f1ff0000f8ff000081ff81ff81ffbdfffe00f1ff0000f8ff000081ff81ff81ffbdfffe00f1ff0000f8ff000081ffafff0000ff}}\tab {\b Figure 4.1 Force Constant vs. Bond Length Trends}\par 
\pard \sl480 \tab 
The Spiro force field displays the expected intuitive trend between bond lengths and force constants. The Dimmig/ Sontum force field resembles the Spiro force field, even though force constants are consistently lower. Dimmig explained this in terms of the
 inverse relationship he had observed between averaged stretching and bending constants. As the Dimmig/ Sontum force field consistently has higher angle bending co
nstants than the Spiro force field, lower bond force constants in the Dimmig/ Sontum force field were explained as another manifestation of this inverse trend. The only point which remained to be explained in the Dimmig/ Sontum force field was the CB-CZ bo
nd length/ force constant relationship.  The force constant was {\i higher}
  for this bond in the Dimmig/ Sontum force field than in the Spiro force field. The greater  mass of the united ethyl atom (29 amu) as compared to the methyl atom used by Spiro was used
 to explain this discrepancy. It was hoped that when the united ethyl approximation was relaxed this inconsistent point would be corrected.{\up9 {\object\objicemb{\*\objname ICEmbdObject6_73}{\*\objdata 
0000006200000ca3685610000832cf454e524600000000004900afa292c900107f2501010000000000023234000100000000000c000a000120180009000000000000000000010000001b000000000000001044696d6d69672c203139393520233237}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}
}}}{\fs18\up9 24}{{\object\objicemb{\*\objname ICEmbdObject7_74}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900afa292c900107f25}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}} \par 
\pard \sl480 \tab 
The inherent transferability of the Sundar/ Sontum and Dimmig/ Sontum force field is also evident from Figure 4.1. Almost all points in both these force fields coincide. As expected, lack of correspondence such correspondence is observed in parameters ass
ociated with the united ethyl approximation ( at bond length ~1.5 \'81).  The Sundar/Sontum_old force constant around ~1.5 \'81
 are no longer greater than those listed in Spiro's force field. Such reordering supports Dimmig's hypothesis that the high united ethyl force constant (CB-CZ) was the result of the increased united ethyl mass.  \par 
\tab Changing from a united ethyl model to our full NiOEP model, however, has not regained the relationship between force constants and bond lengths. Figure 4.1 shows a rise in the force constant around 1.5 \'81
 for the Sundar/Sontum force field, even though bond lengths increase. All the bonds around ~1.5 \'81
 are carbon-carbon bonds. The masses at either ends of the bonds are the same, and hence our intuitive feel for the force constant/ bond length relation should be satisfied. The resolution of this problem forms a basis for favoring the Sundar/
Sontum_new force field (Chapter 5). \par 
\pard \sl480 \par 
\pard \sl480 {\v {\tc\tcl2\pard\plain \sl480 \f20 {\b Transferability}}}\par 
\pard \sl480 \tab Our final force field  reproduces the vibrational and structural features of NiP.  Core porphyrin values from Sundar/ Sontum_old were transferred to NiP and parameters for the hydrogen atom were ta
ken from the Dimmig optimized porphyrin force field.  Table 4.3 lists {\f23 c}{\fs20\up6 2}
 values obtained when the Sundar/Sontum force field was applied to NiP. Minimized structural parameter values are also listed and compared to crystal structure values for this porphyrin. \par 
\pard \qc\sl480\keepn {\b Table 4.1  NiOEP force fields when applied to NiP\par 
}\pard \keepn \par 
\trowd \trqc\trgaph80\trleft-80 \clbrdrt\brdrth \clbrdrl\brdrth \clshdng0\cellx1936\clbrdrt\brdrth \clshdng0\cellx3952\clbrdrt\brdrth \clbrdrr\brdrth \clshdng0\cellx5968\pard \sl480\keepn\intbl {\b \cell }\pard \sl480\keepn\intbl {\b Minimized Values
\cell Crystal Structure}{\up9 {\object\objicemb{\*\objname ICEmbdObject40_75}{\*\objdata 
0000005e00000ca3685610000832cf454e524600000000004500afa23b8e0048e3e501010000000000023231000100000000000c000a0001201500090000000000000000000100000016000000000000000c4c692c203139393120233232}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}{
\fs18\up9 21}{{\object\objicemb{\*\objname ICEmbdObject41_76}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900afa23b8e0048e3e5}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}{\b \cell }\pard \intbl {\b \row }\trowd 
\trqc\trgaph80\trleft-80 \clbrdrt\brdrs \clbrdrl\brdrs \clshdng0\cellx1936\clbrdrt\brdrs \clshdng0\cellx3952\clbrdrt\brdrs \clbrdrr\brdrs \clshdng0\cellx5968\pard \sl480\keepn\intbl {\b\f23 c}{\b\fs20\up6 2}{\b =2421.37\cell }\cell \cell \pard \intbl {\b 
\row }\trowd \trqc\trgaph80\trleft-80 \clbrdrl\brdrs \clshdng0\cellx1936\clshdng0\cellx3952\clbrdrr\brdrs \clshdng0\cellx5968\pard \sl480\keepn\intbl {\b Bond\cell }\cell \cell \pard \intbl {\b \row }\pard \sl480\keepn\intbl {\b Ni-N\cell }1.960\cell 
1.955\cell \pard \intbl {\b \row }\pard \sl480\keepn\intbl {\b N-CC\cell }1.381\cell 1.380\cell \pard \intbl {\b \row }\pard \sl480\keepn\intbl {\b CC-CB\cell }1.443\cell 1.440\cell \pard \intbl {\b \row }\pard \sl480\keepn\intbl {\b CB-CB\cell }1.343
\cell 1.352\cell \pard \intbl {\b \row }\pard \sl480\keepn\intbl {\b CC-CD\cell }1.379\cell 1.383\cell \pard \intbl {\b \row }\pard \sl480\keepn\intbl {\b ANGLES\cell }\cell \cell \pard \intbl {\b \row }\pard \sl480\keepn\intbl {\b CC-N-CC\cell }104.063
\cell 104.8\cell \pard \intbl {\b \row }\pard \sl480\keepn\intbl {\b N-CC-CB\cell }111.176\cell 110.7\cell \pard \intbl {\b \row }\pard \sl480\keepn\intbl {\b CC-CB-CB\cell }106.792\cell 106.8\cell \pard \intbl {\b \row }\pard \sl480\keepn\intbl {\b 
N-CC-CD\cell }125.036\cell 126.5\cell \pard \intbl {\b \row }\trowd \trqc\trgaph80\trleft-80 \clbrdrl\brdrs \clbrdrb\brdrs \clshdng0\cellx1936\clbrdrb\brdrs \clshdng0\cellx3952\clbrdrb\brdrs \clbrdrr\brdrs \clshdng0\cellx5968\pard \sl480\keepn\intbl {\b 
CC-CD-CC\cell }123.992\cell 121.4\cell \pard \intbl {\b \row }\pard \sl480 \tab The {\f23 c}{\fs20\up6 2} values of 2421 is comparable to the best fit obtained by Jason Dimmig with his transferable force field ({\f23 c}{\fs20\up6 2}
 =2207.8). The average errors in bond lengths (0.005 \'81) and angles (1.45\'a1) are again comparable with values obtained by others.{\up9 {\object\objicemb{\*\objname ICEmbdObject42}{\*\objdata 
0000006300000ca3685610000832cf454e524600000000004a00afa23b8e0048e3e601010000000000023232000100000000000c000a000120160009000000000000000000010000001900000000000000114d6172717565732c203139393520233235}{\result {\pict\macpict\picw0\pich0 000a0000000000000000
}}}}{\fs18\up9 22}{{\object\objicemb{\*\objname ICEmbdObject43}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900afa23b8e0048e3e6}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}\par 
\pard \sl480 \tab \par 
\pard \sl480\keepn {\v {\tc\tcl2\pard\plain \sl480\keepn \f20 {\b Conclusion}}}{\b \par 
}\pard \sl480\keepn {\b \tab }In conclusion, the Sundar/Sontum_old force field represents a transferable force field for the NiOEP porphyrin, developed by transferring parameters from ethylbenzen
e and the Dimmig/Sontum averaged force fields. Dihedral terms were reoptimized keeping in mind the conclusions arrived at in the previous chapter.  The combined force field that resulted (Sundar/Sontum_old) produces better vibrational fits that other force
 fields present in the literature. Additionally, this force field is dynamic enough to reproduce the structural parameters of NiP as well. However, problems that still persist in this force field, have led to the development another force field (Sundar/Son
tum_new). These problems will be reexamined in the following chapter (Chapter 5), where features of the new force field will be elaborated. \par 
\pard \par 
\par 
\pard \qc\sl480 \page {\v {\tc\tcl1\pard\plain \qc\sl480 \f20 {\b Chapter 5   New Approach to Modeling}}}\par 
\pard \sl480 \tab 
The problems in our optimized force field (Sundar/ Sontum_old) mentioned in the previous chapter need to be summarized. A great range in force constants is evident in the angle bending constants (Table 4.2). This trend is evident in both the Sundar/ Sontu
m force field as well the Dimmig/ Sontum force field. While such a rang
e did yield a better vibrational fit than the Spiro, Karplus or standard AMBER force fields, the simplicity characteristic of the AMBER force field is missing. Trends between bond lengths and force constants, which one would expect intuitively, also are no
t maintained across the range of bond lengths (Figure 4.1). While in the Dimmig/ Sontum force field such discrepancies were explained as the result of the increased CZ mass (Figure 4.1), such inconsistencies still persist in the Sundar/Sontum_old force fie
ld, where such mass arguments are no longer valid. As the Sundar/ Sontum force field is derived from the Dimmig/ Sontum force field, it is probable that there is a deficiency in that model as well. Finally, the Ni-N bond constant could not be selected with
out ambiguity. A range of values for this force constant is admissible within the Sundar/Sontum_old force field. To overcome the above mentioned problems another modeling philosophy was employed.  The specifics of the modeling approach have been described 
in the methods section (Chapter 2). The results of using this modeling philosophy are evaluated in the following sections. \par 
\pard \sl480 \par 
\pard \sl480 {\v {\tc\tcl2\pard\plain \sl480 \f20 {\b Vibrational Fit}.}}\par 
\pard \sl480 \tab 
Any new force field has to reproduce the vibrations of NiOEP if it is to be useful for the primary goal of this project. Table 5.1 compares the bond stretch parameters in the Sundar/ Sontum (new) force field with values in the present standard AMBER, Sund
ar/ Sontum (old), Spiro and Karplus force fields. \par 
\pard \sl480\keepn \page {\b Table 5.1 Inplane Force Constant Comparison.}\par 
\trowd \trqc\trgaph80\trleft-80 \clbrdrt\brdrs \clbrdrl\brdrs \clshdng0\cellx1288\clbrdrt\brdrs \clshdng0\cellx2656\clbrdrt\brdrs \clshdng0\cellx4024\clbrdrt\brdrs \clshdng0\cellx5392\clbrdrt\brdrs \clshdng0\cellx6760\clbrdrt\brdrs \clbrdrr\brdrs 
\clshdng0\cellx8128\pard \sl360\keepn\intbl \cell \pard \sl360\keepn\intbl {\ul Sundar/ Sontum (new)}\cell \pard \sl360\keepn\intbl {\ul Sundar/ Sontum (old)\cell }\pard \sl360\keepn\intbl {\ul Spiro} {\up9 {\object\objicemb{\*\objname ICEmbdObject0_77}
{\*\objdata 
0000008500000ca3685610000832cf454e524600000000006c00afa294ed0010ffe5010100000000000531392d3231000100000000000c000a0001201300090000000000000000000300000014000000150000001600000000000000284c692c2031393930202332303b204c692c2031393930202332313b204c692c203139
393120233232}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}{\fs18\up9 19-21}{{\object\objicemb{\*\objname ICEmbdObject1_78}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900afa294ed0010ffe5}{\result {\pict\macpict\picw0\pich0 
000a0000000000000000}}}}\cell {\ul Karplus}{\up9 {\object\objicemb{\*\objname ICEmbdObject2_79}{\*\objdata 
0000006300000ca3685610000832cf454e524600000000004a00afa294f9001102a901010000000000023334000100000000000c000a000120220009000000000000000000010000002500000000000000114b6172706c75732c203139393020233337}{\result {\pict\macpict\picw0\pich0 000a0000000000000000
}}}}{\fs18\up9 34}{{\object\objicemb{\*\objname ICEmbdObject3_80}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900afa294f9001102a9}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}\cell \pard \sl360\keepn\intbl {\ul AMBER}{\up9 
{\object\objicemb{\*\objname ICEmbdObject4_81}{\*\objdata 
0000006300000ca3685610000832cf454e524600000000004a00afa295040011054d01010000000000023138000100000000000c000a000120120009000000000000000000010000001800000000000000114b6f6c6c6d616e2c203139393520233234}{\result {\pict\macpict\picw0\pich0 000a0000000000000000
}}}}{\fs18\up9 18}{{\object\objicemb{\*\objname ICEmbdObject5_82}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900afa295040011054d}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}{\ul \cell }\pard \intbl \row \trowd 
\trqc\trgaph80\trrh-430\trleft-80 \clbrdrl\brdrs \clshdng0\cellx1288\clshdng0\cellx2656\clshdng0\cellx4024\clshdng0\cellx5392\clshdng0\cellx6760\clbrdrr\brdrs \clshdng0\cellx8128\pard \sl480\keepn\intbl {\b\f23 c}{\b\f23\fs20\up6 2}{\b  }\cell 1352\cell 
1656\cell 5840.171\cell 2684.301\cell \cell \pard \intbl \row \pard \sl480\keepn\intbl {\b BONDS}\cell \cell \cell \cell \cell \cell \pard \intbl \row \pard \sl480\keepn\intbl NI-NP\cell 80.308\cell 157.246\cell 121.000\cell 270.200\cell 50.000\cell 
\pard \intbl \row \pard \sl480\keepn\intbl NP-CC\cell 335.9\cell 297.322\cell 427.500\cell 377.200\cell 428.00\cell \pard \intbl \row \pard \sl480\keepn\intbl CC-CB\cell 330.6\cell 260.679\cell 391.000\cell 299.800\cell 416.000\cell \pard \intbl \row 
\pard \sl480\keepn\intbl CC-CD\cell 365.3\cell 327.507\cell 502.000\cell 360.000\cell 500.000\cell \pard \intbl \row \pard \sl480\keepn\intbl CB-CB\cell 460.6\cell 413.607\cell 512.000\cell 340.700\cell 546.000\cell \pard \intbl \row \pard 
\sl480\keepn\intbl CD-HM\cell 363.59\cell 356.507\cell 361.000\cell 367.600\cell 367.000\cell \pard \intbl \row \pard \sl480\keepn\intbl {\b ANGLES}\cell \cell \cell \cell \cell \cell \pard \intbl \row \pard \sl480\keepn\intbl NP-NI-NP\cell 0.000\cell 
0.000\cell 0.000\cell 0.000\cell 0.000\cell \pard \intbl \row \pard \sl480\keepn\intbl NO-NI-NP\cell 9.981\cell 8.780\cell 18.000\cell 50.000\cell 0.000\cell \pard \intbl \row \pard \sl480\keepn\intbl NI-NP-CC\cell 80.289\cell 87.705\cell 22.000\cell 96.1
50\cell 0.000\cell \pard \intbl \row \pard \sl480\keepn\intbl NP-CC-CB\cell 101.511\cell 117.615\cell 99.000\cell 122.00\cell 70.000\cell \pard \intbl \row \pard \sl480\keepn\intbl NP-CC-CD\cell 43.77\cell 36.191\cell 60.000\cell 88.000\cell 70.000\cell 
\pard \intbl \row \pard \sl480\keepn\intbl CB-CC-CD\cell 49.662\cell 36.191\cell 60.000\cell 61.600\cell 70.000\cell \pard \intbl \row \pard \sl480\keepn\intbl CC-NP-CC\cell 62.010\cell 130.413\cell 117.00\cell 139.300\cell 70.000\cell \pard \intbl \row 
\pard \sl480\keepn\intbl CC-CB-CB\cell 72.582\cell 90.796\cell 99.000\cell 30.080\cell 70.000\cell \pard \intbl \row \pard \sl480\keepn\intbl CC-CD-CC\cell 92.601\cell 166.070\cell 79.000\cell 94.200\cell 70.000\cell \pard \intbl \row \pard 
\sl480\keepn\intbl CC-CD-HM\cell 31.413\cell 32.014\cell 36.000\cell 12.700\cell 35.000\cell \pard \intbl \row \pard \sl480\keepn\intbl CC-CB-CX\cell 26.414\cell 29.230\cell 86.000\cell 65.000\cell 70.000\cell \pard \intbl \row \trowd 
\trqc\trgaph80\trrh-430\trleft-80 \clbrdrl\brdrs \clbrdrb\brdrs \clshdng0\cellx1288\clbrdrb\brdrs \clshdng0\cellx2656\clbrdrb\brdrs \clshdng0\cellx4024\clbrdrb\brdrs \clshdng0\cellx5392\clbrdrb\brdrs \clshdng0\cellx6760\clbrdrb\brdrs \clbrdrr\brdrs 
\clshdng0\cellx8128\pard \sl480\keepn\intbl CB-CB-CX\cell 26.414\cell 29.230\cell 56.000\cell 65.000\cell 70.000\cell \pard \intbl \row \pard {\fs20 * Bond Force Constant units Kcal mol}{\fs18\up6 -1}{\fs20  \'81}{\fs18\up6 -2}{\fs20 \par 
* Angle Force Constant units kcal mol}{\fs18\up6 -1}{\fs20  }\par 
\pard \sl480 \tab Only the
 core porphyrin parameters have been listed in Table 5.1. The remaining ethyl group (bond and angle parameters) did not change much between the old and new force fields. No significant changes were required in the OOP parameters, hence these parameters hav
e not been listed. The same restrictions and approximations described in the previous chapter were employed while listing the Karplus, AMBER and Spiro force fields. The {\f23 c}{\f23\fs20\up6 2}
 values reflect the success of each of the force fields in reproducing the experimentally observed frequencies when used in the AMBER software package.  The low {\f23 c}{\fs20\up6 2}
 value obtained with the Sundar/ Sontum_new force field is indicative of the better vibrational fit obtained with this force field.  \par 
\tab 
Unlike the Sundar/ Sontum_old force field, some parameters of the Sundar/ Sontum_new force field find good matches in the Karplus force field, while the AMBER  provides better matches for the Ni-N force constant and the angle force constants. The NiN forc
e constant itself is more like force constants set in the AMBER force field for heme porphyrins,{\up9 {\object\objicemb{\*\objname ICEmbdObject6_83}{\*\objdata 
0000006300000ca3685610000832cf454e524600000000004a00afa2956c00111d9f01010000000000023138000100000000000c000a000120120009000000000000000000010000001800000000000000114b6f6c6c6d616e2c203139393520233234}{\result {\pict\macpict\picw0\pich0 000a0000000000000000
}}}}{\fs18\up9 18}{{\object\objicemb{\*\objname ICEmbdObject7_84}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900afa2956c00111d9f}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}
 and should allow easier transfer of the NiOEP force field into the heme porphyrin. The rough trend seen in the bond constants, seems to indicate that these constants are indicative of the bond orders.  Therefore, while the  CB-CB bond (bond order =1.75) h
as the highest force constant, the CC-CB bond (bond order=1.25) has the lowest force constant.  \par 
\pard \sl480 \tab Closer examination of the angle force constants and the Ni-N bond force constants reveal the chief dif
ferences between the Sundar/ Sontum_new and Sundar/ Sontum_old force fields. Each of these differences need to be examined separately, in order to highlight the different modeling philosophies reflected by the Sundar/Sontum_old and Sundar/Sontum_new force 
fields. \par 
\pard \sl480 \par 
\pard \sl480\keepn {\v {\tc\tcl3\pard\plain \sl480\keepn \f20 {\b Sundar/Sontum_old vs. Sundar/Sontum_new Angle Force Constants}}}\par 
\pard \sl480\keepn \tab The angle force constants in the new force field do not display the same the fluctuation across the force field, as they did in the old force field. The fundamental effects of the
 changes made between the old and new force fields need to be examined to understand the reason for these for constants decreasing in the new force field.\par 
\pard \sl480 \tab The AMBER force field equation controlling the minimized bond lengths and angles contains the following two terms.\par 
\pard \sl480\keepn {\dn38 {\object\objemb{\*\objname Embedded_Object_85}{\*\objclass Equation}{\*\objdata 0102000002000000090000004571756174696f6e00000000000000000020010000
02000101000a01128345030f01000b0112837412836f12837412836112836c0011000a02863d031d00000112834b030f01000b011283720011000a02822812837202862d128372030f01000b011283651283710011000a028229030f00000b110102883200000a02862b031d00000112834b030f01000b010284710011000a
02822802847102862d028471030f01000b011283651283710011000a028229030f00000b11010288320000000112836112836e12836712836c12836512837300110d0286e500000b0112836212836f12836e12836412837300110d0286e5000a02862b12836412836912836812836512836412837212836112836c12837302
862b12836e12836f12836e02825f12836212836f12836e1283641283651283640000
01020000050000000d0000004d45544146494c455049435400ec09000014f6ffffa80100000800ec09ec095621010009000003bf00000000005a00000000001500000026060f001f00ffffffff0400150000004d7245640f004d6963726f736f6674204472617700005a00000026060f00a9004d72456402009f0000009d00
0100840084008002a5010000000000000100030000000000ffffff0000000000ffffff000100000100000001000000000001000000000000010c0048656c7600a20203008a00ff00290003015f0b020011000301af0d0200120003100000000000ffffff00c0c0c00080808000ff00000080000000ffff00008080000000ff
00000080000000ffff00008080000000ff0000008000ff00ff0080008000000e00000026060f0012004d7245640300080000000000000040024002050000000b0200000000050000000c0240024002030000001e000400000003010800050000000102ffffff00050000000902000000000400000007010300040000000401
0d0004000000060101000400000002010200030000001e00040000002701ffff040000002701ffff0300000000008b46048b56068946f88956fa8b46088b560a8946fc8956fe837efa007507817ef800}{\result {\pict\macpict\picw427\pich35 
09dc00000000002301ab1101a10064000eb7787072000000130000000c0000a0008c01000a00000000002301ab070000000022002301ab0000a000bea100c0000d63757272656e74706f696e740da000bf22000000000000a000be2c000800140554696d657303001404020d000e2e0004ff0000002b021001450d000c2b08
0305746f74616c2c000900170653796d626f6c03001704000d000e2800100025013d0300140402292b014b0d000c2b0903017204000d000e2800100060012804022906017203001704002909012d0300140402290a01720d000c2b060302657104000d000e280010008d01290d000c280009009201320300170d000e2b0b07
012b03001404022922014b0300170d000c2b0a03017103001404000d000e28001000d201280300170402290501710400290c012d0402290a01710300140d000c2b080302657104000d000e280010010301290d000c28000901080132040228001f00a706616e676c657303001704000d001028001100b101e503001404020d
000c28001f003105626f6e647303001704000d0010280011003901e50d000e2800100112012b0300140402290b09646968656472616c7303001704002938012b0300140402290b036e6f6e04002916015f0402290906626f6e646564a100c006c63330206469637420626567696e0a63757272656e74706f696e742033202d
3120726f6c6c20737562206e65672033203120726f6c6c207375622031333636342064697620313132302033202d3120726f6c6c206578636820646976207363616c652063757272656e74706f696e74207472616e736c617465203634203535207472616e736c6174650a3720343537206d6f7665746f0a2f667320302064
65660a2f7366207b6578636820647570202f667320657863682064656620647570206e6567206d6174726978207363616c65206d616b65666f6e7420736574666f6e747d206465660a2f6631207b66696e64666f6e7420647570202f63662065786368206465662073667d206465660a2f6e73207b63662073667d20646566
0a343438202f54696d65732d4974616c69632066310a2845292073686f770a32373420353731206d6f7665746f0a333834206e730a28746f74616c292073686f770a3131343720343537206d6f7665746f0a343438202f53796d626f6c2066310a283d292073686f770a3235303020343537206d6f7665746f0a343438202f
54696d65732d4974616c69632066310a284b292073686f770a3238313420353639206d6f7665746f0a333834206e730a2872292073686f770a3330333920343537206d6f7665746f0a343438202f54696d65732d526f6d616e2066310a285c28292073686f770a3332313320343537206d6f7665746f0a343438202f54696d
65732d4974616c69632066310a2872292073686f770a3334393620343537206d6f7665746f0a343438202f53796d626f6c2066310a282d292073686f770a3338333720343537206d6f7665746f0a343438202f54696d65732d4974616c69632066310a2872292073686f770a3430323120353639206d6f7665746f0a333834
206e730a286571292073686f770a3434363020343537206d6f7665746f0a343438202f54696d65732d526f6d616e2066310a285c29292073686f770a3436323420323631206d6f7665746f0a333834202f54696d65732d526f6d616e2066310a2832292073686f770a3439363220343537206d6f7665746f0a343438202f53
796d626f6c2066310a282b292073686f770a3630363820343537206d6f7665746f0a343438202f54696d65732d4974616c69632066310a284b292073686f770a3633373520353732206d6f7665746f0a2f6632207b66696e64666f6e74206d6174726978206475702032202e323220707574206d616b65666f6e7420647570
202f63662065786368206465662073667d206465660a333834202f53796d626f6c2066320a2871292073686f770a3636373020343537206d6f7665746f0a343438202f54696d65732d526f6d616e2066310a285c28292073686f770a3638333520343537206d6f7665746f0a343438202f53796d626f6c2066320a28712920
73686f770a3732303020343537206d6f7665746f0a343438202f53796d626f6c2066310a282d292073686f770a3735333220343537206d6f7665746f0a343438202f53796d626f6c2066320a2871292073686f770a3737393120353639206d6f7665746f0a333834202f54696d65732d4974616c69632066310a2865712920
73686f770a3832333020343537206d6f7665746f0a343438202f54696d65732d526f6d616e2066310a285c29292073686f770a3833393420323631206d6f7665746f0a333834202f54696d65732d526f6d616e2066310a2832292073686f770a3533313020393435206d6f7665746f0a333834202f54696d65732d4974616c
69632066310a28616e676c6573292073686f770a3536323720353036206d6f7665746f0a353132202f53796d626f6c2066310a285c333435292073686f770a3135303620393435206d6f7665746f0a333834202f54696d65732d4974616c69632066310a28626f6e6473292073686f770a3137383320353036206d6f766574
6f0a353132202f53796d626f6c2066310a285c333435292073686f770a3837333220343537206d6f7665746f0a343438206e730a282b292073686f770a3930373920343537206d6f7665746f0a343438202f54696d65732d4974616c69632066310a28646968656472616c73292073686f770a313038363720343537206d6f
7665746f0a343438202f53796d626f6c2066310a282b292073686f770a313132313020343537206d6f7665746f0a343438202f54696d65732d4974616c69632066310a286e6f6e292073686f770a313139313720343537206d6f7665746f0a343438202f54696d65732d526f6d616e2066310a285f292073686f770a313232
313120343537206d6f7665746f0a343438202f54696d65732d4974616c69632066310a28626f6e646564292073686f770a656e640aa000bfa10064012c4d415448000101203cd602000101000a01128345030f01000b0112837412836f12837412836112836c0011000a02863d031d00000112834b030f01000b0112837200
11000a02822812837202862d128372030f01000b011283651283710011000a028229030f00000b110102883200000a02862b031d00000112834b030f01000b010284710011000a02822802847102862d028471030f01000b011283651283710011000a028229030f00000b11010288320000000112836112836e1283671283
6c12836512837300110d0286e500000b0112836212836f12836e12836412837300110d0286e5000a02862b12836412836912836812836512836412837212836112836c12837302862b12836e12836f12836e02825f12836212836f12836e1283641283651283640000ffffa0008dff}}}}\pard \sl480\keepn   {\b  
\tab \tab \tab \tab \tab \tab \tab \tab \tab \tab \tab Eq. 5.1}\par 
\pard \sl480 \tab Given a set of K{\fs20\dn4 r}, K{\f23\fs20\dn4 q}, r{\fs20\dn4 eq} and {\f23 q}{\fs20\dn4 eq} values, the molecule is brought to its minimum energy structure by varying r and {\f23 q}
 values before any vibrational analysis is done. Restoring forces, upon which the calculated frequencies depend, therefore depend on force constants (K{\fs20\dn4 r} or {\f23 q}{\fs20\dn4 eq}) and perturbation \{ (r-r{\fs20\dn4 eq}){\fs20\up6 2}  or ({
\f23 q}- {\f23 q}{\fs20\dn4 eq}{\f23 )}{\f23\fs20\up6 2}\} away from equilibrium. Previously, in the old force field approach, as indeed in Spiro's and Karplus' force fields, r{\fs20\dn4 eq} and {\f23 q}{\fs20\dn4 eq}
 values were set to crystal structure values. A large force constant is required to produce the required restoring force. In the new force field, a different approach was taken. Unstrained r{\fs20\dn4 eq} and {\f23 q}{\fs20\dn4 eq}
 values, determined by procedures described in the methods section, were used. This approach leads to fewer fluctuations in the angle force constants. \par 
\pard \sl480 \par 
\pard \sl480 {\v {\tc\tcl3\pard\plain \sl480 \f20 {\b Nickel-Nitrogen Force Constant}}}\par 
\pard \sl480 \tab 
 The carboxyheme group we would like to examine has carbon monoxide bound to the metal center of the heme porphyrin. As a result any coupling of the porphyrin normal modes to the ligand vibrations will be transmitted through this metal center. Good assign
ment of this Ni-N force constant becomes critical, as the flexibility of the heme porphyrin core, and its effectiveness in transmitting potential cou
pling motions depend intimately on this choice. In the Sundar/Sontum_old force field this force constant could take on a range of values and still yield good vibrational and structural fits. The new modelling approach adopted in the Sundar/Sontum_new force
 field eliminates such ambiguity. We adjusted the value of the Ni-N force constant until a good structural fit for the Ni-N, minimized bond distance is obtained. Thereafter, other force constants were optimized to get good structural and vibrational fits. 
 The additional, structural-fit criterion imposes restrictions on the choice of the Ni-N force constant, thereby eliminating the ambiguity that existed in the Sundar/Sontum_old force field.  Lastly, the Ni-N force constant is closer to the Fe-N force const
ant used in the AMBER force field. \par 
\pard \sl480 \par 
\pard \sl480 {\v {\tc\tcl2\pard\plain \sl480 \f20 {\b Bond length vs. Force Constants}}}\par 
\pard \sl480 \tab A good vibrational fit was the first requirement of the optimized force field, and since the Sundar/ Sontum (new) force field satisfies this requirement,  other stipulations, those o
f intuitive consistency and transferability, were applied to this force field.\par 
\pard \sl480 \tab 
The intuitive trend that one would expect between force constants and bond lengths was described in the previous chapter. The existence of such a trend in the new optimized force field would support adopting the Sundar/Sontum (new) force field over the Su
ndar/ Sontum (old) force field. Figure 5.1 is a graph, in which force constants have been plotted against minimized bond\par 
\pard \sl480 lengths for the Sundar/ Sontum (new), Sundar/ Sontum (old) and Spiro force fields. \par 
\pard \qc\sl480\keepn {{\pict\macpict\picw502\pich361 
982000000000016901f6001102ff0c00fffe55b4004800000048000000000000016901f6019206f00001000a00000000016901f6009b000000ff87d800000000016901f6000000040000000000480000004800000010002000030008000000000192ddc40000000000000000016901f600000000016901f60040000a000000
00016901f6002ae1fff90081ff81ff81ffbdfff700e1fff90081ff81ff81ffbdfff700e1fff90081ff81ff81ffbdfff700002ae1fff90081ff81ff81ffbdfff700e1fff90081ff81ff81ffbdfff700e1fff90081ff81ff81ffbdfff7000054f1ff010000fefffe00fefffe0001fffff90081ff81ff81ffbdfff700f1ff0100
00fefffe00fefffe0001fffff90081ff81ff81ffbdfff700f1ff010000fefffe00fefffe0001fffff90081ff81ff81ffbdfff700005df2ff0000fdff0000feff0200ff00feff0100fff90081ff81ff81ffbdfff700f2ff0000fdff0000feff0200ff00feff0100fff90081ff81ff81ffbdfff700f2ff0000fdff0000feff02
00ff00feff0100fff90081ff81ff81ffbdfff700005df3ff0000fcff0000feff0200ff00feff0100fff90081ff81ff81ffbdfff700f3ff0000fcff0000feff0200ff00feff0100fff90081ff81ff81ffbdfff700f3ff0000fcff0000feff0200ff00feff0100fff90081ff81ff81ffbdfff700005df3fffd0002ffff00feff
0200ff00feff0100fff90081ff81ff81ffbdfff700f3fffd0002ffff00feff0200ff00feff0100fff90081ff81ff81ffbdfff700f3fffd0002ffff00feff0200ff00feff0100fff90081ff81ff81ffbdfff700006ff3ff0000feff0200ff00feff0200ff00feff0100fffe00fcff810081008100bd00fbfffd00f3ff0000fe
ff0200ff00feff0200ff00feff0100fffe00fcff810081008100bd00fbfffd00f3ff0000feff0200ff00feff0200ff00feff0100fffe00fcff810081008100bd00fbfffd0000d5f3ff0000feff0200ff00feff0200ff00feff0100fffe0000fffd00d8ff0000d3ff0000d4ff0000d4ff0000d4ff0000d4ff0000d4ff0000d4
ff0000d3ff0000d9fffc0000fffd00f3ff0000feff0200ff00feff0200ff00feff0100fffe0000fffd00d8ff0000d3ff0000d4ff0000d4ff0000d4ff0000d4ff0000d4ff0000d4ff0000d3ff0000d9fffc0000fffd00f3ff0000feff0200ff00feff0200ff00feff0100fffe0000fffd00d8ff0000d3ff0000d4ff0000d4ff
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feff0000afff0000faff0000feff0000b5ff0000f9ff0000feff0100ff00d9e2ff0000faff0000feff0000b6ff0000f7ff0000afff0000faff0000feff0000b4ff0000faff0000feff0000afff0000faff0000feff0000b6ff0000feff0000fcff0000feff0000e1ff0000faff0000feff0000b6ff0000f7ff0000afff0000
faff0000feff0000b4ff0000faff0000feff0000afff0000faff0000feff0000b6ff0000feff0000fcff0000feff0000e1ff0000faff0000feff0000b6ff0000f7ff0000afff0000faff0000feff0000b4ff0000faff0000feff0000afff0000faff0000feff0000b6ff0000feff0000fcff0000feff0100ff00c3e2ff0000
faff0000feff0000b6ff0000f8ff0000aeff0000fafffc00b4ff0000faff0000feff0000afff0000faff0000feff0000b6fffd00feff0000fefffe00e0ff0000faff0000feff0000b6ff0000f8ff0000aeff0000fafffc00b4ff0000faff0000feff0000afff0000faff0000feff0000b6fffd00feff0000fefffe00e0ff00
00faff0000feff0000b6ff0000f8ff0000aeff0000fafffc00b4ff0000faff0000feff0000afff0000faff0000feff0000b6fffd00feff0000fefffe0001ffff009ee2ff0000faff0000feff0000b6ff0000f9ff0000adff0000f6ff0000b5fffe00feff0000fefffe00affffe00feff0000fefffe0086ff0000faff0000fe
ff0000b6ff0000f9ff0000adff0000f6ff0000b5fffe00feff0000fefffe00affffe00feff0000fefffe0086ff0000faff0000feff0000b6ff0000f9ff0000adff0000f6ff0000b5fffe00feff0000fefffe00affffe00feff0000fefffe00a5ff007ae2ff0000faff0000feff0000b6ff0000faff0000feff0000b1fffe00
feff0000fbff000081ff81ffceff0000faff0000feff0000b6ff0000faff0000feff0000b1fffe00feff0000fbff000081ff81ffceff0000faff0000feff0000b6ff0000faff0000feff0000b1fffe00feff0000fbff000081ff81ffedff005ae2ff0000faff0000feff0000b7fffe00feff0200fffffd0081ff81ff81ffef
ff0000faff0000feff0000b7fffe00feff0200fffffd0081ff81ff81ffefff0000faff0000feff0000b7fffe00feff0200fffffd0081ff81ff8eff0038e3fffe00feff0000fefffe0081ff81ff81ff98fffe00feff0000fefffe0081ff81ff81ff98fffe00feff0000fefffe0081ff81ff81ffb6ff001881ff81ff81ff81ff
81ff81ff81ff81ff81ff81ff81ff9fff002081ff81ffd5fffd0081ff81ff81ff8ffffd0081ff81ff81ff8ffffd0081ffbbff002081ff81ffd5fffd0081ff81ff81ff8ffffd0081ff81ff81ff8ffffd0081ffbbff002081ff81ffd5fffd0081ff81ff81ff8ffffd0081ff81ff81ff8ffffd0081ffbbff001881ff81ff81ff81
ff81ff81ff81ff81ff81ff81ff81ff9fff006c81ff9cfffc00f0ff010000fcfffe00e9ff010000f8ff0000fdff0000fdff000081ff81ff81ffd9fffc00f0ff010000fcfffe00e9ff010000f8ff0000fdff0000fdff000081ff81ff81ffd9fffc00f0ff010000fcfffe00e9ff010000f8ff0000fdff0000fdff000081ffbeff
007b81ff9bff0000feff0000f0ff0000fbff0000eaff0300ffff00f9ff0000fcff0000fcff000081ff81ff81ffd9ff0000feff0000f0ff0000fbff0000eaff0300ffff00f9ff0000fcff0000fcff000081ff81ff81ffd9ff0000feff0000f0ff0000fbff0000eaff0300ffff00f9ff0000fcff0000fcff000081ffbfff00d8
81ff9bff0000feff0000fefffe0005ffff00ff0000fefffe00fbff0000fbff070000ffff00ff0000feff040000ff00fffe0000fffe00fbff0000fdff0200ff00fdff000081ff81ff81ffd9ff0000feff0000fefffe0005ffff00ff0000fefffe00fbff0000fbff070000ffff00ff0000feff040000ff00fffe0000fffe00fb
ff0000fdff0200ff00fdff000081ff81ff81ffd9ff0000feff0000fefffe0005ffff00ff0000fefffe00fbff0000fbff070000ffff00ff0000feff040000ff00fffe0000fffe00fbff0000fdff0200ff00fdff000081ffbfff00e181ff9bfffd00feff0000feff0b00ffff00ffff00ff00ffff00fbff0000fcff0e00ffff00
ffff00ffff00ff00ffff00feff0600ffff00ffff00fdff0000fcff0200ff00fcff000081ff81ff81ffdafffd00feff0000feff0b00ffff00ffff00ff00ffff00fbff0000fcff0e00ffff00ffff00ffff00ff00ffff00feff0600ffff00ffff00fdff0000fcff0200ff00fcff000081ff81ff81ffdafffd00feff0000feff0b
00ffff00ffff00ff00ffff00fbff0000fcff0e00ffff00ffff00ffff00ff00ffff00feff0600ffff00ffff00fdff0000fcff0200ff00fcff000081ffc0ff00ea81ff9bff0000feff0300ffff00feff0b00ffff00ffff00ff00ffff00fbff0000fcfffd000affff00ffff00ff00ffff00feff0600ffff00ffff00fdff0000fd
ff0000feff0000fdff000081ff81ff81ffdaff0000feff0300ffff00feff0b00ffff00ffff00ff00ffff00fbff0000fcfffd000affff00ffff00ff00ffff00feff0600ffff00ffff00fdff0000fdff0000feff0000fdff000081ff81ff81ffdaff0000feff0300ffff00feff0b00ffff00ffff00ff00ffff00fbff0000fcff
fd000affff00ffff00ff00ffff00feff0600ffff00ffff00fdff0000fdff0000feff0000fdff000081ffc0ff00db81ff9bff0000feff0300ffff00feff0b00ffff00ffff00ff00ffff00fbff0000fcff0000fcff0700ffff00ffff0000fdff0600ffff00ffff00fdff0000fdfffc00fdff000081ff81ff81ffdaff0000feff
0300ffff00feff0b00ffff00ffff00ff00ffff00fbff0000fcff0000fcff0700ffff00ffff0000fdff0600ffff00ffff00fdff0000fdfffc00fdff000081ff81ff81ffdaff0000feff0300ffff00feff0b00ffff00ffff00ff00ffff00fbff0000fcff0000fcff0700ffff00ffff0000fdff0600ffff00ffff00fdff0000fd
fffc00fdff000081ffc0ff00ed81ff9bff0000feff0300ffff00feff0b00ffff00ffff00ff00ffff00fbff0000feff0d00ff00ffff00ffff00ffff00ff00fbff0600ffff00ffff00fdff0000feff0000fcff0000feff000081ff81ff81ffdaff0000feff0300ffff00feff0b00ffff00ffff00ff00ffff00fbff0000feff0d
00ff00ffff00ffff00ffff00ff00fbff0600ffff00ffff00fdff0000feff0000fcff0000feff000081ff81ff81ffdaff0000feff0300ffff00feff0b00ffff00ffff00ff00ffff00fbff0000feff0d00ff00ffff00ffff00ffff00ff00fbff0600ffff00ffff00fdff0000feff0000fcff0000feff000081ffc0ff00cf81ff
9cfffc00fdfffe0001fffffe0003ff0000fffd00fdfffb0005ffff0000fffffe0003ff0000fffe00fdfffe0000fffe00fdff0400ffff0000fefffe0001ff0081ff81ff81ffdafffc00fdfffe0001fffffe0003ff0000fffd00fdfffb0005ffff0000fffffe0003ff0000fffe00fdfffe0000fffe00fdff0400ffff0000feff
fe0001ff0081ff81ff81ffdafffc00fdfffe0001fffffe0003ff0000fffd00fdfffb0005ffff0000fffffe0003ff0000fffe00fdfffe0000fffe00fdff0400ffff0000fefffe0001ff0081ffbfff004481ff81ffedff0000feff0000f3ff0000f6ff000081ff81ff81ffabff0000feff0000f3ff0000f6ff000081ff81ff81
ffabff0000feff0000f3ff0000f6ff000081ffbfff003881ff81ffecfffe00f1ff0000f8ff000081ff81ff81ffa9fffe00f1ff0000f8ff000081ff81ff81ffa9fffe00f1ff0000f8ff000081ffbeff0000ff}}\tab {\b Figure 5.1 Bond Length vs. Force Constants}\par 
\pard \sl480 \tab As figure 5.1 shows, the intuitive trend that is expected between force constants and bond lengths is present in the new force field. Particularly around ~1.5 \'81
 bond lengths,  where such a trend was not maintained by the Sundar/ Sontum_old force field, th
is trend has been regained. The intuitive relationship between bond parameters and associated force constants is another reason for favoring the Sundar/ Sontum _new force field over the Sundar/Sontum_old force field.\par 
\pard \sl480 \par 
\pard \sl480\keepn {\v {\tc\tcl2\pard\plain \sl480\keepn \f20 {\b Geometric Fit}}}\par 
\pard \sl480\keepn \tab 
A good geometric fit for NiOEP is also necessary, as inaccurate geometric fits are indicative of a poor energy fit for the molecule itself. Therefore, the ability of the Sundar/ Sontum (new) force field to reproduce crystal structure values of the porphyr
in was examined. Table 5.2 lists the structural parameters input, the minimized molecules parameter values and the actual crystal structure values.\par 
\pard \sl480\keepn {\b Table 5.2 Geometrical Fit.}\par 
\trowd \trqc\trgaph80\trleft-80 \clbrdrt\brdrth \clbrdrl\brdrth \clshdng0\cellx1936\clbrdrt\brdrth \clshdng0\cellx3952\clbrdrt\brdrth \clshdng0\cellx5968\clbrdrt\brdrth \clbrdrr\brdrth \clshdng0\cellx7984\pard \keepn\intbl {\b\fs20 \cell }\pard 
\keepn\intbl {\b\fs20 Equilibrium Values (\'81)\cell }\pard \qc\keepn\intbl {\b\fs20 Minimized NiOEP (\'81)\cell }\pard \keepn\intbl {\b\fs20 Crystal Structure NiOEP (\'81)\cell }\pard \intbl \row \trowd \trqc\trgaph80\trrh-430\trleft-80 \clbrdrt\brdrs 
\clbrdrl\brdrs \clshdng0\cellx1936\clbrdrt\brdrs \clshdng0\cellx3952\clbrdrt\brdrs \clshdng0\cellx5968\clbrdrt\brdrs \clbrdrr\brdrs \clshdng0\cellx7984\pard \keepn\intbl {\b\fs20 BONDS\cell }{\fs20 \cell \cell \cell }\pard \intbl \row \trowd 
\trqc\trgaph80\trrh-430\trleft-80 \clbrdrl\brdrs \clshdng0\cellx1936\clshdng0\cellx3952\clshdng0\cellx5968\clbrdrr\brdrs \clshdng0\cellx7984\pard \keepn\intbl {\b\fs20 Ni-N\cell }{\fs20 1.860\cell 1.961\cell 1.958\cell }\pard \intbl \row \pard 
\keepn\intbl {\b\fs20 N-CC\cell }{\fs20 1.380\cell 1.381\cell 1.376\cell }\pard \intbl \row \pard \keepn\intbl {\b\fs20 CC-CB\cell }{\fs20 1.440\cell 1.450\cell 1.443\cell }\pard \intbl \row \pard \keepn\intbl {\b\fs20 CC-CD\cell }{\fs20 1.380\cell 1.378
\cell 1.371\cell }\pard \intbl \row \pard \keepn\intbl {\b\fs20 CB-CB\cell }{\fs20 1.350\cell 1.356\cell 1.346\cell }\pard \intbl \row \pard \keepn\intbl {\b\fs20 CB-CX\cell }{\fs20 1.501\cell 1.515\cell 1.510\cell }\pard \intbl \row \pard \keepn\intbl {
\b\fs20 CX-CY\cell }{\fs20 1.506\cell 1.512\cell 1.506\cell }\pard \intbl \row \pard \keepn\intbl {\b\fs20 CD-HM\cell }{\fs20 1.090\cell 1.086\cell 1.090\cell }\pard \intbl \row \pard \keepn\intbl {\b\fs20 CX(Y)-HE(N)\cell }{\fs20 1.100\cell 1.100\cell 
1.100\cell }\pard \intbl \row \pard \keepn\intbl {\b\fs20 ANGLES\cell }{\fs20 \cell \cell \cell }\pard \intbl \row \pard \keepn\intbl {\b\fs20 NP-NI-NP\cell }{\fs20 180.00\cell 179.818\cell 180.000\cell }\pard \intbl \row \pard \keepn\intbl {\b\fs20 
NO-NI-NP\cell }{\fs20  90.00\cell     90.00\cell   90.000\cell }\pard \intbl \row \pard \keepn\intbl {\b\fs20 NI-N-CC\cell }{\fs20 120.00\cell 127.502\cell 128.000\cell }\pard \intbl \row \pard \keepn\intbl {\b\fs20 N-CC-CB\cell }{\fs20 120.00\cell 
110.752\cell 111.500\cell }\pard \intbl \row \pard \keepn\intbl {\b\fs20 NO-CC-CD\cell }{\fs20 120.00\cell 126.421\cell 124.000\cell }\pard \intbl \row \pard \keepn\intbl {\b\fs20 CB-CC-CD\cell }{\fs20 120.00\cell 122.826\cell 124.100\cell }\pard \intbl 
\row \pard \keepn\intbl {\b\fs20 CC-N-CC\cell }{\fs20 120.00\cell 104.995\cell 104.000\cell }\pard \intbl \row \pard \keepn\intbl {\b\fs20 CC-CB-CB\cell }{\fs20 120.00\cell 106.750\cell 106.500\cell }\pard \intbl \row \pard \keepn\intbl {\b\fs20 CC-CD-CC
\cell }{\fs20 120.00\cell 122.153\cell 125.000\cell }\pard \intbl \row \pard \keepn\intbl {\b\fs20 CC-CB-CX\cell }{\fs20 120.00\cell 125.982\cell 125.500\cell }\pard \intbl \row \pard \keepn\intbl {\b\fs20 CB-CB-CX\cell }{\fs20 120.00\cell 127.266\cell 
128.000\cell }\pard \intbl \row \trowd \trqc\trgaph80\trrh-430\trleft-80 \clbrdrl\brdrs \clbrdrb\brdrs \clshdng0\cellx1936\clbrdrb\brdrs \clshdng0\cellx3952\clbrdrb\brdrs \clshdng0\cellx5968\clbrdrb\brdrs \clbrdrr\brdrs \clshdng0\cellx7984\pard 
\keepn\intbl {\b\fs20 CB-CX-CY\cell }{\fs20 109.5\cell 110.240\cell 109.500\cell }\pard \intbl \row \pard \sl480 \tab 
It is evident from table 5.2 that the Sundar/ Sontum_new force field is capable of reproducing the structural characteristics of the NiOEP molecule as well. The minimized Ni-N bond length is only 0.003 \'81
 larger than the crystal structure values, again reinforcing our choice of 80.308 kcal/ Mol for this force constant.  The averaged error between the observed and calculated structural parameters are small (0.006 \'81 for bond lengths and 1.201\'a1
 for angles).  The relatively large error in the minimized angles seems to result from the angles associated with the CD atom, particularly the C
C-CD-CC angle. However, the structural fit around this angle for the NiP (next section) is good, indicating a possible deficiency in the our model itself. On average, however, these errors are lower than those obtained in previous studies.{\up9 
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}}}}{\fs18\up9 22}{{\object\objicemb{\*\objname ICEmbdObject9_87}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900afa29e6900133a4c}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}} \par 
\pard \sl480 \par 
\pard \sl480\keepn {\v {\tc\tcl2\pard\plain \sl480\keepn \f20 {\b Transferability\:}}}\par 
\pard \sl480\keepn \tab 
The last criterion applied on the Sundar/ Sontum (new) force field was one of transferability. As described in the previous chapter, the core porphyrin parameters were transferred to NiP. The vibrational and structural fits obtained upon transfer of this 
force field was examined. Table 5.3 lists the {\f23 c}{\f23\fs20\up6 2} value,  structural parameters obtained upon minimization, and crystal structure values for NiP.\par 
\pard \sl480 \par 
\pard \sl480\keepn {\b Table 5.3 Structural and Vibrational Fits for NiP}\par 
\trowd \trqc\trgaph80\trleft-80 \clbrdrt\brdrth \clbrdrl\brdrth \clshdng0\cellx1936\clbrdrt\brdrth \clshdng0\cellx3952\clbrdrt\brdrth \clbrdrr\brdrth \clshdng0\cellx5968\pard \sl360\keepn\intbl {\b \cell }\pard \sl360\keepn\intbl {\b Minimized Values
\cell Crystal Structure\cell }\pard \intbl {\b \row }\trowd \trqc\trgaph80\trleft-80 \clbrdrt\brdrs \clbrdrl\brdrs \clshdng0\cellx1936\clbrdrt\brdrs \clshdng0\cellx3952\clbrdrt\brdrs \clbrdrr\brdrs \clshdng0\cellx5968\pard \sl360\keepn\intbl {\b\f23 c}{
\b\fs20\up6 2}{\b =2733\cell }\cell \cell \pard \intbl \row \trowd \trqc\trgaph80\trleft-80 \clbrdrl\brdrs \clshdng0\cellx1936\clshdng0\cellx3952\clbrdrr\brdrs \clshdng0\cellx5968\pard \sl360\keepn\intbl {\b Bond\cell }\cell \cell \pard \intbl \row \pard 
\sl360\keepn\intbl {\b Ni-N\cell }1.959\cell 1.955\cell \pard \intbl \row \pard \sl360\keepn\intbl {\b N-CC\cell }1.377\cell 1.380\cell \pard \intbl \row \pard \sl360\keepn\intbl {\b CC-CB\cell }1.443\cell 1.440\cell \pard \intbl \row \pard 
\sl360\keepn\intbl {\b CB-CB\cell }1.353\cell 1.352\cell \pard \intbl \row \pard \sl360\keepn\intbl {\b CC-CD\cell }1.375\cell 1.383\cell \pard \intbl \row \pard \sl360\keepn\intbl {\b ANGLES\cell }\cell \cell \pard \intbl \row \pard \sl360\keepn\intbl {
\b CC-N-CC\cell }105.571\cell 104.8\cell \pard \intbl \row \pard \sl360\keepn\intbl {\b N-CC-CB\cell }110.279\cell 110.7\cell \pard \intbl \row \pard \sl360\keepn\intbl {\b CC-CB-CB\cell }106.936\cell 106.8\cell \pard \intbl \row \pard \sl360\keepn\intbl 
{\b N-CC-CD\cell }127.0\cell 126.5\cell \pard \intbl \row \trowd \trqc\trgaph80\trleft-80 \clbrdrl\brdrs \clbrdrb\brdrs \clshdng0\cellx1936\clbrdrb\brdrs \clshdng0\cellx3952\clbrdrb\brdrs \clbrdrr\brdrs \clshdng0\cellx5968\pard \sl360\keepn\intbl {\b 
CC-CD-CC\cell }121.408\cell 121.4\cell \pard \intbl \row \pard \sl480  \tab The transferability of the Sundar/Sontum_new force field is evident in table 5.3. Average errors in the listed bond lengths and angles are 0.005 \'81 and 0.455\'a1
 respectively. Again, such errors are below those obtained by others in the literature.{\up9 {\object\objicemb{\*\objname ICEmbdObject10_88}{\*\objdata 
0000006300000ca3685610000832cf454e524600000000004a00afa29f290013677701010000000000023232000100000000000c000a000120160009000000000000000000010000001900000000000000114d6172717565732c203139393520233235}{\result {\pict\macpict\picw0\pich0 000a0000000000000000
}}}}{\fs18\up9 22}{{\object\objicemb{\*\objname ICEmbdObject11_89}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900afa29f2900136777}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}} Additionally, these errors are compa
rable with those obtained with the Sundar/ Sontum_old force field (0.005 \'81 and 1.45\'a1).  Lastly, the {\f23 c}{\fs20\up6 2} value with this force field is higher than that calculated with the Dimmig/Sontum force field. This higher {\f23 c}{\fs20\up6 2
} value reflects the emphasis of this thesis- a good vibrational fit for NiOEP, and the linear weighting scheme (all weights set to 1) used while calculating the {\f23 c}{\fs20\up6 2}
 values for NiP. Therefore, even though key frequencies find better matches with the Sundar/Sontum_new force field, such better correspondence is not reflected in the {\f23 c}{\fs20\up6 2}{\b\fs20\up6  }value.\par 
\pard \sl480 \tab 
The Sundar/Sontum_new force field satisfies all the requirements of the new force field. It is transferable between NiOEP and NiP, accurately reproducing structural and vibrational features for both of these molecules. Large fluctuations in angle force co
nstants are avoided, and intuitive trends are observed in the bond constants. All of these factors strongly recommend usage of the new modeling approach described in the methods section. This transferable Sundar/Sont
um_new force field was transferred over to the heme porphyrin, once appropriate force constants for the Fe-N bond had been determined. \par 
\pard \par 
\pard \qc\sl480 \page {\v {\tc\tcl1\pard\plain \qc\sl480 \f20 {\b Chapter 6 Heme Porphyrin Analysis}}}{\b \par 
}\pard \sl480 {\v {\tc\tcl2\pard\plain \sl480 \f20 {\b Introduction}}}\par 
\pard \sl480 \tab 
As the Sundar/Sontum_new force field for NiOEP proved to be a consistent, transferable force field, a heme force field could be developed from it. Obviously, force field parameters had to be determined for parameters associated with the iron-metal center 
and additional functional groups at the periphery of protoporph
yrin IX. Fortunately, the inherent modeling philosophy of the Sundar/Sontum_new force field made the choice of the Fe-N force constants relatively straightforward, and standard force field parameters could be used for the additional peripheral groups. As i
ndicated previously, the choice of the metal-nitrogen force constant is critical, as the flexibility of the porphyrin core and its ability to couple vibrationally with attached ligands depend intimately on an appropriate choice of this constant.  We set th
e value of the Fe-N force constant to 71.0 kcal/ Mol in the heme porphyrin, quite similar to the Ni-N force constant selected in the Sundar/Sontum_new force field. Our justifications for this force constant choice will be elaborated in the next section.
\par 
\pard \sl480 \par 
\pard \sl480 {\v {\tc\tcl3\pard\plain \sl480 \f20 {\b Fe-N Force Constant}}}\par 
\pard \sl480 \tab The ambiguity in nickel-nitrogen force constant, present with the Sundar/Sontum_old force field, was satisfactorily resolved with the Sundar/Sontum_new force field, especially as our choice of this constant was controlled by both st
ructural and vibrational requirements imposed on the force field. The inherent transferability of our new force field and available structural data on iron porphyrin system were exploited to yield experimentally consistent values for iron related parameter
s. The Fe-N force constant was varied until the iron-nitrogen distance in iron octaethyl porphyrin (FeOEP) agreed with average structural values calculated for iron porphyrin systems.  The final values chosen for the Fe-N constant was 71.0 Kcal/mol, while 
the unstrained equilibrium distance was set to 1.93 \'81.  The reason for the choosing an equilibrium distance of 1.93 \'81
 was described in the methods section.  Table 6.1 lists the structural parameters calculated for iron octaethyl porphyrin, when the above m
entioned parameter values were chosen, and average observed values for intermediate spin, four coordinate iron (II) complexes.{\up9 {\object\objicemb{\*\objname ICEmbdObject0_90}{\*\objdata 
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\pard \sl480\keepn {\b Table 6.1 Structural Parameters for Iron Octaethyl Porphyrin (FeOEP)\par 
}\trowd \trgaph80\trleft-80 \clbrdrt\brdrth \clbrdrl\brdrth \clshdng0\cellx2440\clbrdrt\brdrth \clshdng0\cellx4960\clbrdrt\brdrth \clbrdrr\brdrth \clshdng0\cellx7480\pard \sl480\keepn\intbl {\b\fs20 Parameter}\cell {\b\fs20 Calculated (\'81)}\cell {
\b\fs20 Observed (\'81)}{\fs20\up9 {\object\objicemb{\*\objname ICEmbdObject2_92}{\*\objdata 
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}}}}{\fs18\up9 22}{{\object\objicemb{\*\objname ICEmbdObject48}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900afa1e3c40004405d}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}\cell \pard \intbl \row \trowd \trgaph80\trleft-80 
\clbrdrt\brdrs \clbrdrl\brdrs \clshdng0\cellx2440\clbrdrt\brdrs \clshdng0\cellx4960\clbrdrt\brdrs \clbrdrr\brdrs \clshdng0\cellx7480\pard \sl480\keepn\intbl Fe-N{\fs20\dn4 p}\cell 1.979 \'81\cell 1.979 (0.015)\cell \pard \intbl \row \trowd 
\trgaph80\trleft-80 \clbrdrl\brdrs \clshdng0\cellx2440\clshdng0\cellx4960\clbrdrr\brdrs \clshdng0\cellx7480\pard \sl480\keepn\intbl N{\fs20\dn4 p}-Fe-N{\fs20\dn4 p} (trans)\cell 180.00 \'a1\cell 179.1\'a1 (0.9)\cell \pard \intbl \row \trowd 
\trgaph80\trleft-80 \clbrdrl\brdrs \clbrdrb\brdrs \clshdng0\cellx2440\clbrdrb\brdrs \clshdng0\cellx4960\clbrdrb\brdrs \clbrdrr\brdrs \clshdng0\cellx7480\pard \sl480\keepn\intbl N{\fs20\dn4 p}-Fe-N{\fs20\dn4 p} (cis)\cell 90.0\'a1\cell 90.0\'a1 (0.3)\cell 
\pard \intbl \row \pard \sl480 \tab 
 As table 6.1 demonstrates, our FeOEP structural parameters match average observed values, thus our choice of Fe-N force constant value of 110.308 kcal/ mol is experimentally consistent. We chose to fit our FeOEP values to averaged, four coordinate iron p
orphyrin values, so that the Fe-N parameter would be more easily transferred to the heme porphyrin. \par 
\tab Once the consistency of the iron related parameters was ensured
, as a further check we compared the remaining porphyrin parameters with their mean values  in Fe(II)and Fe(III) porphyrins. The results of such comparison are shown in Table 6.2, in which non-iron related structural parameters are compared with their aver
aged values. \par 
\pard \sl480 \par 
\pard \sl480\keepn {\b Table 6.2 Non-Iron Structural Parameters in FeOEP}\par 
\trowd \trgaph80\trleft-80 \clbrdrt\brdrth \clbrdrl\brdrth \clshdng0\cellx2656\clbrdrt\brdrth \clshdng0\cellx5392\clbrdrt\brdrth \clbrdrr\brdrth \clshdng0\cellx8128\pard \sl480\keepn\intbl {\b\fs20 Parameter}{\fs20 \cell }\pard \sl480\keepn\intbl {
\b\fs20 Calculated}{\fs20 \cell }{\b\fs20 Average Observed}{\fs20\up9 {\object\objicemb{\*\objname ICEmbdObject4_95}{\*\objdata 
0000006300000ca3685610000832cf454e524600000000004a00afa1e3d50004443a01010000000000023232000100000000000c000a000120160009000000000000000000010000001900000000000000114d6172717565732c203139393520233235}{\result {\pict\macpict\picw0\pich0 000a0000000000000000
}}}}{\fs18\up9 22}{\fs20 {\object\objicemb{\*\objname ICEmbdObject5_96}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900afa1e3d50004443a}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}{\fs20 \cell }\pard \intbl \row \trowd 
\trgaph80\trleft-80 \clbrdrt\brdrth \clbrdrl\brdrs \clshdng0\cellx2656\clbrdrt\brdrth \clshdng0\cellx5392\clbrdrt\brdrth \clbrdrr\brdrs \clshdng0\cellx8128\pard \sl480\keepn\intbl {\b\fs20 BOND \cell }\pard \sl480\keepn\intbl {\fs20 \cell \cell }\pard 
\intbl \row \trowd \trgaph80\trleft-80 \clbrdrl\brdrs \clshdng0\cellx2656\clshdng0\cellx5392\clbrdrr\brdrs \clshdng0\cellx8128\pard \sl480\keepn\intbl {\b\fs20 N-CC}{\fs20 \cell }\pard \sl480\keepn\intbl {\fs20 1.379\cell 1.380 (0.013)\cell }\pard \intbl 
\row \pard \sl480\keepn\intbl {\b\fs20 CC-CD}{\fs20 \cell }\pard \sl480\keepn\intbl {\fs20 1.382\cell 1.389 (0.016)\cell }\pard \intbl \row \pard \sl480\keepn\intbl {\b\fs20 CC-CB}{\fs20 \cell }\pard \sl480\keepn\intbl {\fs20 1.450\cell 1.439 (0.018)
\cell }\pard \intbl \row \trowd \trgaph80\trleft-80 \clbrdrl\brdrs \clbrdrb\brdrs \clshdng0\cellx2656\clbrdrb\brdrs \clshdng0\cellx5392\clbrdrb\brdrs \clbrdrr\brdrs \clshdng0\cellx8128\pard \sl480\keepn\intbl {\b\fs20 CB-CB}{\fs20 \cell }\pard 
\sl480\keepn\intbl {\fs20 1.358\cell 1.350 (0.022)\cell }\pard \intbl \row \trowd \trgaph80\trleft-80 \clbrdrt\brdrs \clbrdrl\brdrs \clshdng0\cellx2656\clbrdrt\brdrs \clshdng0\cellx5392\clbrdrt\brdrs \clbrdrr\brdrs \clshdng0\cellx8128\pard 
\sl480\keepn\intbl {\b\fs20 ANGLE}{\fs20 \cell }\pard \sl480\keepn\intbl {\fs20 \cell \cell }\pard \intbl \row \trowd \trgaph80\trleft-80 \clbrdrl\brdrs \clshdng0\cellx2656\clshdng0\cellx5392\clbrdrr\brdrs \clshdng0\cellx8128\pard \sl480\keepn\intbl {
\b\fs20 CC-N-CC}{\fs20 \cell }\pard \sl480\keepn\intbl {\fs20 105.584\cell 105.8 (1.1)\cell }\pard \intbl \row \pard \sl480\keepn\intbl {\b\fs20 N-CC-CB}{\fs20 \cell }\pard \sl480\keepn\intbl {\fs20 110.375\cell 109.9 (1.1)\cell }\pard \intbl \row \pard 
\sl480\keepn\intbl {\b\fs20 CC-CB-CB\cell }\pard \sl480\keepn\intbl {\fs20 106.833\cell 107.2 (1.0)\cell }\pard \intbl \row \pard \sl480\keepn\intbl {\b\fs20 CC-CD-CC\cell }\pard \sl480\keepn\intbl {\fs20 122.606\cell 124.6 (1.8)\cell }\pard \intbl \row 
\pard \sl480\keepn\intbl {\b\fs20 N-CC-CD\cell }\pard \sl480\keepn\intbl {\fs20 126.489\cell 125.4 (1.3)\cell }\pard \intbl \row \trowd \trgaph80\trleft-80 \clbrdrl\brdrs \clbrdrb\brdrs \clshdng0\cellx2656\clbrdrb\brdrs \clshdng0\cellx5392\clbrdrb\brdrs 
\clbrdrr\brdrs \clshdng0\cellx8128\pard \sl480\keepn\intbl {\b\fs20 CB-CC-CD\cell }\pard \sl480\keepn\intbl {\fs20 123.135\cell 124.6 (1.8)\cell }\pard \intbl \row \pard \sl480  \par 
\pard \sl480 \tab As Table 6.2 shows, structurally the FeOEP parameters agree with averaged experimental values for iron porphyrins. Standard errors between the calculated and averaged values are 0.008 \'81 and 1.33 \'a1
 respectively for bonds and angles. Such agreement reinforces the structural consistency of the Sundar/Sontum_new force field and the Fe-N constants, that were chosen. \par 
\pard \sl480 \par 
\pard \sl480 {\v {\tc\tcl3\pard\plain \sl480 \f20 {\b Peripheral Heme groups}}}\par 
\pard \sl480 \tab 
The other major group that still remained to be modeled was the vinyl group at the periphery of the porphyrin molecule. Specifically, the rotational potential of the vinyl group was modeled by examining styrene. Our interest in the rotational potential of
 the vinyl group was raised, primarily because of the trend observed in our examinations of ethylbenzene. To summarize, the standard AMBER force field has the rotational potentials around a CC-CX bond set to zero. As d
iscussed in chapter 3, this value is unrealistically low, because semi-empirical calculations done with Spartan indicate otherwise. Therefore, the default rotational potential around the vinyl-porphyrin bond, which is set to zero in AMBER, was recalculated
. In a manner similar to the method used in ethylbenzene (chapter 3), we calculated the torsional barrier around the vinyl-benzene bond in styrene using Spartan. Fourier analysis of this potential revealed the existence of predominant two-fold term, which 
was then transferred over to styrene's force field and optimized. The total torsion barrier (V{\fs20\dn4 n}
 in equation 2.1) optimized on styrene was 1.624 kcal/mol. Lack of vibrational data on for  heme porphyrins precluded further optimization on the porphyrin. But, as the two-fold rotational potential from ethylbenzene had proved itself to be transferable to
 NiOEP (chapter 3), we felt confident transferring the two fold rotational potential parameters over from styrene to heme. A more complete analysis of styrene, however remains to be done. \par 
\pard \sl480 \par 
\pard \sl480\keepn {\v {\tc\tcl2\pard\plain \sl480\keepn \f20 {\b Spiro/Kitagawa Controversy}}}{\b \par 
}\pard \sl480\keepn {\v {\tc\tcl3\pard\plain \sl480\keepn \f20 {\b Isolated Heme Calculations\:}}}\par 
\pard \sl480\keepn \tab 
Our final heme force field was used to address the original questions posed by the different frequency assignments made by the Spiro and Kitagawa groups.  With a consistent force field, we computationally recreated the isotopic shift experiments performed
 by the Spiro and Kitagawa groups, and addressed the Spiro/Kitagawa  controversy from another perspective. First, we varied Fe-C and C-O force constants, until our calculated {\f23 u}(Fe-CO) and {\f23 u}
(C-O) frequencies matched experimentally observed ones. Then we set the Fe-C-O bending force constant, until either the Spiro or Kitagawa assigned bending frequency was matched. Thereafter, we varied the mass of both the carbon and oxygen atoms in the carb
on monoxide ligand, and analyzed, using the NMANAL module, the effects of such mass changes on the vibrational frequencies. Our hope was to simulate the isotopic shift patterns seen by either one of the groups for the {\f23 d}(FeCO) freq
uency. Table 6.2 summarizes the results of such isotopic shift simulations, after either Spiro or Kitagawa assignment of {\f23 d}(FeCO) frequency had been matched.  \par 
\pard \sl480 \page {\b \par 
}\page \tab  Along with the Spiro and Kitagawa assignments and isotopic shift data,{\up9 {\object\objicemb{\*\objname ICEmbdObject6_97}{\*\objdata 
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 calculated values for these frequencies have also been listed in Table 6.4. The absolute shift in frequency upon isotopic substitution is listed for individual group experiments and our simulations. Unlike the observed frequencies, we noticed multiple ban
ds in the same 
frequency, which were sensitive to changes into the CO ligand mass.  To make our comparison and analysis of subsequent data easier, only bands which had at least a 10% PED on one of the FeCO parameters, are listed in table 6.4. The PED values for the vario
us bands were obtained from the NMANAL module's output . The {\f23 u}(CO) and {\f23 u}
(FeC) frequencies assignments are not disputed in the literature, as both groups have assigned comparable values to these bands. These bands, however, are included in table 6.4 to gauge the accuracy the heme force field. \par 
\pard \sl480 \tab It is immediately evident, that the force field accurately reproduces the observed {\f23 u}(CO) frequencies and shift patterns. Such accuracy, however, eludes force field calculations when the {\f23 u}
(FeC) frequencies are examined. While the absolute frequency is reproduced accurately, when either the Spiro or Kitagawa frequencies assignment is simulated, the isotopic shift pattern is not reproduced in either cases. The magnitude of isotopic shifts is 
calculated to be much smaller in our force field than is actually observed. Further analysis of the bands around 500 cm{\fs20\up6 -1} revealed one possible explanation for this discrepancy. The PED of the {\f23 u}
(FeC) frequency in both sets of simulations is not 100% FeC stretch, i.e. the character is not entirely a FeC bond stretch.  Though too small, the monotonically decreasing pattern observed by the Kitagawa and Spiro groups for  this frequency is simulated- 
{\f23 u}(FeC) decreases as the mass of the CO unit is raised. \par 
\pard \sl480 \tab The results of our {\f23 d}(FeCO) simulati
ons are more clear cut. By varying the Fe-C-O angle force constant, we reproduce the characteristic "zig-zag" pattern of frequency shifting for either the Spiro or Kitagawa group.  Our Kitagawa group assignment simulations are deficient, however, in that w
e are not able to simulate the right magnitude of isotopic shift patterns for the {\f23 d}(FeCO) frequency. Furthermore, multiple bands are calculated to be sensitive to such isotopic substitution. By reducing the {\f23 d}
(FeCO) force constant to reproduce the approxima
te magnitude for the Kitagawa group assignments, more mixing of the bending mode is observed. Physically, such increased mixing is evident from the multiple, isotopic-substitution sensitive bands. Additionally, the magnitude of the {\f23 d}
(FeCO) shift upon increasing the mass of the carbon atom in CO is much smaller in our simulations than observed by the Kitagawa group. Analyzing the PED of this vibrational mode provides an explanation. The PED of this bending frequency is not 100% {\f23 
d}(FeCO), instead the {\f23 d}(FeCO) bending character is dispersed over multiple frequencies.  In the case of the Spiro simulations, only three {\f23 d}
(FeCO) frequencies are seen. Not much coupling of the bending mode takes place; the character of the FeCO bending mode is close to 60% for one of the bands. As a result this bending frequency bands displays the same magnitude in its shift pattern. Therefor
e, the Spiro group's assignments seem to be favored by our model. \par 
\pard \sl480 \par 
\pard \sl480\keepn {\v {\tc\tcl3\pard\plain \sl480\keepn \f20 {\b Myoglobin Protein Effects}}}\line {\v ;}\tab As indicated in the methods section, analysis of
 carboxyheme vibrations was not done within the protein itself. A glitch in the AMBER NMODE module prevented such simulations. Instead, we used results calculated by Maggie Zraly to predict possible geometrical repercussions of modeling the Kitagawa and Sp
iro group assignments. \par 
\pard \sl480 \tab In order to reproduce either the Kitagawa or Spiro group assignments for the {\f23 d}
(FeCO) motion, we varied the Fe-C-O bend constant. Table 6.5 lists the final sets of parameter values required to simulate the Kitagawa and Spiro group assignments.\par 
\pard \sl480 \par 
\pard \sl480\keepn {\b Table 6.5  Final Force Constants}\par 
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\cellx8776\pard \sl480\keepn\intbl {\b \cell }\pard \sl480\keepn\intbl {\b K(Fe-C)\cell K(C-O)\cell K(Fe-C-O)\cell }\pard \intbl \row \trowd \trgaph80\trleft-80 \clbrdrt\brdrs \clbrdrl\brdrs \clshdng0\cellx1864\clbrdrt\brdrs \clshdng0\cellx4168\clbrdrt
\brdrs \clshdng0\cellx6472\clbrdrt\brdrs \clbrdrr\brdrs \clshdng0\cellx8776\pard \sl480\keepn\intbl {\b Spiro\cell }\pard \sl480\keepn\intbl 160\cell 1044\cell 68.00\cell \pard \intbl \row \trowd \trgaph80\trleft-80 \clbrdrl\brdrs \clbrdrb\brdrs \clshdng0
\cellx1864\clbrdrb\brdrs \clshdng0\cellx4168\clbrdrb\brdrs \clshdng0\cellx6472\clbrdrb\brdrs \clbrdrr\brdrs \clshdng0\cellx8776\pard \sl480\keepn\intbl {\b Kitagawa\cell }\pard \sl480\keepn\intbl 160\cell 1044\cell 22.00\cell \pard \intbl \row \pard 
\keepn {\fs20 * Bond Force constant units Kcal mol}{\fs20\up6 -1}{\fs20  \'81}{\fs20\up6 -2}{\fs20  \par 
* Angle Force constant units Kcal mol}{\fs20\up6 -1}{\fs20 \par 
}\pard \sl480 \tab As Table 6.5 indicates, the only force constant that was changed between our simulations of the Kitagawa and Spiro group results was the Fe-C-O angle force constants. The value of this force constant is 68. kcal mol{\fs20\up6 -1}
 in the case of the Spiro simulations, while a force constant of 22 kcal mol{\fs20\up6 -1} was required to reproduce the Kitagawa group assignments. \par 
\pard \sl480 \tab Different researchers have considered with the effect of the protein on the CO ligand's orientation within the protein. Recent crystal structures indicate that this linkage is linear.{\up9 {\object\objicemb{\*\objname ICEmbdObject10_99}
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 Maggie Zraly determined a relationship between the Fe-C-O force constant and the angle of the FeCO linkage would adopt within the myoglobin protein. She computed the effects of the protein framework upon minimization on the FeCO linkage for a given set of
 force constants. Figure 6.1 shows the results that she had derived. \par 
\pard \sl480\keepn \par 
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\pard \sl480\keepn {\b Figure 6.1 Fe-C-O Angle vs. Force Constant}{\up9 {\object\objicemb{\*\objname ICEmbdObject8_101}{\*\objdata 
0000006100000ca3685610000832cf454e524600000000004800afa1e54200049a0901010000000000023233000100000000000c000a000120170009000000000000000000010000001a000000000000000f5a72616c792c203139393520233236}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}
{\fs18\up9 23}{{\object\objicemb{\*\objname ICEmbdObject9_102}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900afa1e54200049a09}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}{\b \par 
}\pard \sl480 \tab If figure 6.1 is used to predict the final geometry of the FeCO linkage within the protein environment, then the unreasonableness of the Kitagawa group's assignments is  apparent. The force constant of 28.00 kcal mol{\fs20\up6 -1}
 would cause the FeCO linkage to adopt a bent structure (FeCO angle of 175\'a1).  The Spiro assignment force constant, however, would allow the FeCO linkage to retain a linear geometry within the p
rotein. Thus the Spiro assignment would allow the FeCO geometry predicted by our force field to be consistent with crystal structure.{\up9 {\object\objicemb{\*\objname ICEmbdObject12_103}{\*\objdata 
0000006200000ca3685610000832cf454e524600000000004900afa2ae610016faf9010100000000000139000100000000000c000a000120090009000000000000000000010000000b00000000000000115175696c6c696e2c203139393320233131}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}
}}}{\fs18\up9 9}{{\object\objicemb{\*\objname ICEmbdObject13_104}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900afa2ae610016faf9}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}
 Therefore, even within the protein we would expect our model to geometrically favor the Spiro assignment of the  {\f23 d}(FeCO) frequency. \par 
\pard \par 
\pard \qc \page {\v\fs28 {\tc\tcl1\pard\plain \qc \f20 {\b\fs28 Chapter 7- Conclusions and Future Work}}}{\fs28 \par 
}\pard \sl480 {\fs28 \par 
}\pard \sl480 {\v {\tc\tcl2\pard\plain \sl480 \f20 {\b Conclusions}}}{\b \par 
}\pard \sl480 {\b \tab }The focus of this thesis was to analyze the vibrations of carboxyheme using a consistent, transferable force field. Our interest in this porphyrin system arouse because of the con
troversy surrounding the exact bending frequency for the Fe-CO linkage in the carboxy porphyrin. We have successfully developed a force field for the heme porphyrin, by transferring over a consistent force field from nickel porphyrin system, and analyzed t
he carboxyheme system. Our analysis outside the protein supports the Spiro group's assignments for this frequency. We were unable to perform these calculations within the protein environment, and directly prove the Spiro group assignments.  However, calcul
ations done using results obtained by Zraly reinforce the unreasonableness of the Kitagawa group's assignments. \par 
\pard \sl480 \tab 
In our attempts to develop a consistent force field for nickel octaethyl porphyrin, we examined other smaller molecules. Conclusions from such analyses were then used in our modeling of NiOEP. The main conclusion that were transferred are the following. M
ore specific definitions for dihedral terms help in improving vibrational fits for the OOP modes of vibrations. The overall barrier to rotation
 usually remains constant but the internal distribution of this barrier is non-uniform. The resulting increase in the force field's flexibility helps to improve vibrational fits and exclude improper terms. In fact, improper torsion terms are needed only wh
en hyperconjugation effects need to simulated. \par 
\tab Lastly, we were able to develop two consistent force field for NiOEP. The first force field was developed from the force field developed by Jason Dimmig. The similarity between the two force field (Dimmig/So
ntum and Sundar/Sontum_old) emphasizes the inherent transferability of these force fields. A second force field, reflecting a different modeling philosophy, was also developed. A fundamental change in modeling was effected in the second force field. Equili
brium distances angles were set using unstrained literature values, and force constants were then varied to get good vibrational and structural fits.  Greater uniformity and intuitive consistency is evident in the parameter set, when such a change in model
ing is effected. \par 
\pard \sl480 \par 
\pard \sl480 {\v {\tc\tcl2\pard\plain \sl480 \f20 {\b Future Work}}}\par 
\pard \sl480 \tab 
As indicated in the conclusion, no simulations were possible within the protein environment, and therefore a fundamental goal of this project stills remains to be done. The AMBER force field package has some glitches in it, which do not allow the use of t
he IBELLY option for vibrational analysis. Once these "bugs" have been corrected, analysis within the protein can be concluded. The effects of the protein environment on this linkage can then be fully explored. \par 
\pard \sl480 \tab With the existence of a good parameter set for the heme group, it should be possible to examine other questions concerning the myoglobin and hemoglobin proteins. Specifically, the spectroscopically different vibrational states{\up9 
{\object\objicemb{\*\objname ICEmbdObject0_105}{\*\objdata 0000005d00000ca3685610000832cf454e524600000000004400afa38bf0004b0be4010100000000000138000100000000000c000a0001200800090000000000000000000100000008000000000000000c4c696d2c2031393935202338}{\result 
{\pict\macpict\picw0\pich0 000a0000000000000000}}}}{\fs18\up9 8}{{\object\objicemb{\*\objname ICEmbdObject1_106}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900afa38bf0004b0be4}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}
 of carboxyheme group can be probed computationally. Pathways for ligand escape upon photodissociation may also be examined.{\up9 {\object\objicemb{\*\objname ICEmbdObject2_107}{\*\objdata 
0000006300000ca3685610000832cf454e524600000000004a00afa38c01004b0fc001010000000000023334000100000000000c000a000120220009000000000000000000010000002500000000000000114b6172706c75732c203139393020233337}{\result {\pict\macpict\picw0\pich0 000a0000000000000000
}}}}{\fs18\up9 34}{{\object\objicemb{\*\objname ICEmbdObject3_108}{\*\objdata 0000002200000ca3685610000832cf454e522d00000000000900afa38c01004b0fc0}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}} \par 
\tab Finally, parameter set for other important molecules may be undertaken, using some of the modeling conclusions determined in this project. Thus, modeling of nuc
leic acids can be done and inherent deficiencies in standard parameter describing these molecules may be eliminated, in a manner similar to the corrections done for the heme porphyrin set. \par 
\pard \par 
\sect \sectd \linemod0\linex0\cols1\endnhere \pard\plain \qc \f20 {\v\fs28 {\tc\tcl1\pard\plain \qc \f20 {\b\fs28 References}}}{\b\fs28 \par 
}\pard \qc \par 
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0000000000000000000009650010000c0001005c000000000000000000000a890010000c00010284000000000000000000000a990010000c00010184000000000000000000000a9d0010000c0001005c000000000000000000000a9f0010000c00010284000000000000000000000aa10010000c0001005c00000000000000
0000000adb0010000c00010284000000000000000000000b160010000c0001005c000000000000000000000b5f0010000c00010284000000000000000000000b700010000c00010184000000000000000000000b740010000c0001005c000000000000000000000b760010000c00010284000000000000000000000b770010
000c0001005c000000000000000000000bc00010000c00010284000000000000000000000bde0010000c00010184000000000000000000000be20010000c0001005c000000000000000000000be40010000c00010284000000000000000000000be60010000c0001005c000000000000000000000c120010000c0001028400
0000000000000000000c270010000c00010184000000000000000000000c2b0010000c0001005c000000000000000000000c2d0010000c00010284000000000000000000000c300010000c0001005c000000000000000000000c5c0010000c00010284000000000000000000000c700010000c000101840000000000000000
00000c740010000c0001005c000000000000000000000c760010000c00010284000000000000000000000c790010000c0001005c000000000000000000000cb70010000c00010284000000000000000000000cda0010000c00010184000000000000000000000cde0010000c0001005c000000000000000000000ce0001000
0c00010284000000000000000000000ce20010000c0001005c000000000000000000000d190010000c00010284000000000000000000000d330010000c00010184000000000000000000000d370010000c0001005c000000000000000000000d390010000c00010284000000000000000000000d3c0010000c0001005c0000
00000000000000005d}{\result {\pict\macpict\picw0\pich0 000a0000000000000000}}}}\pard \s2\fi-720\li720 (1)\tab Lehninger, A., L In {\i Biochemistry}; second ed.Worth: New York, 1975; pp 137-138.\par 
(2)\tab Spiro, T. G.; Vogel, K. M.; Hu, S. {\i Journal of the American Chemical Society }{\b 1994}, {\i 116}, 11187-11188.\par 
(3)\tab Alberty, R., A; Silbey, R., J In {\i Physical Chemistry}John Wiley and Sons: New York, 1992; pp 489-491.\par 
(4)\tab Collman, J. P.; Brauman, J. I.; Halbert, T. R.; Suslick, K. S. {\i Proceedings of the National Academy of Science }{\b 1976}, {\i 73}, 3333-3337.\par 
(5)\tab Spiro, T. G.; Li, X. Y.; Ibers, J. A.; Sessler, J. L.; Ray, G. B. {\i Journal of the American Chemical Society }{\b 1994}, {\i 116}, 162-176.\par 
(6)\tab Peng, S., M; Ibers, J., A {\i Journal of the American Chemical Society }{\b 1976}, {\i 98}, 8032.\par 
(7)\tab Kuriyan, J.; Wilz, S.; Karplus, M.; Petsko, G., O {\i Journal of Molecular Biology }{\b 1992}, {\i 196}, 133-154.\par 
(8)\tab Lim, L.; Jackson, T., A {\i Journal of Chemical Physics }{\b 1995}, {\i 102}, 4355\emdash 4366.\par 
(9)\tab Quillin, M., L; Arduini, R., M; Olson, J., S; Phillips {\i Journal of Molecular Biology }{\b 1993}, {\i 234}, 140-155.\par 
(10)\tab Spiro, T. G.; Y, L. X. {\i Journal of the American Chemical Society }{\b 1988}, {\i 111}, 6024\emdash 6033.\par 
(11)\tab Kitagawa, T.; Takashi, O.; Hirota, S. {\i Journal of the American Chemical Society }{\b 1995}, {\i 117}, 821-822.\par 
(12)\tab Kitagawa, T.; Hirota, S.; Ogura, T. {\i Journal of Physical Chemistry }{\b 1994}, {\i 98}, 6652\emdash 6660.\par 
(13)\tab Tsubaki, M.; Srivastava, R. B.; Yu, N. T. {\i Biochemistry }{\b 1982}, {\i 21}, 1132-1140.\par 
(14)\tab Kitagawa, T.; Yamamoto, S.; Minoato, T.; Saito, M.; Jewsbury, P. {\i Journal of the American Chemical Society }{\b 1994}, {\i 116}, 11586-11587.\par 
(15)\tab Allinger, N., L.; Burkert, U. In {\i Molecular Mechanics}American Chemical Society: New York, 1982; Vol. 177; pp 14-56.\par 
(16)\tab Allinger, N., L; Burkert, U. In {\i Molecular Mechanics}; First ed.American Chemical Society: Washington D.C., 1982; Vol. 177; pp ix-xii.\par 
(17)\tab Decius, J.; Cross, P. C.; Wilson, E. B. J. {\i The Theory of Infrared and Raman Vibrational Spectra}; McGraw-Hill Book Company: New York, 1955.\par 
(18)\tab Kollman, P. A.; Cornell, W. D.; Cieplak, P.; Bayly, C. I. {\i Journal of the American Chemical Society }{\b 1995}, {\i 117}, 5179-5197.\par 
(19)\tab Li, X. Y.; Czernuszewicz, R. S.; Kincaid, J. R.; Su, Y. O.; Spiro, T. G. {\i Journal of Physical Chemistry }{\b 1990}, {\i 94}, 31-47.\par 
(20)\tab Li, X. Y.; Czernuszewicz, R. S.; Kincaid, J. R.; Stein, P.; Spiro, T. G. {\i Journal of Physical Chemistry }{\b 1990}, {\i 94}, 47-61.\par 
(21)\tab Li, X. Y.; Zgierski, M. Z. {\i Journal of Physical Chemistry }{\b 1991}, {\i 95}, 4268-4287.\par 
(22)\tab Marques, H. M.; Munro, O. Q.; Markoulides, T. {\i Journal of Chemical Society Faraday Transactions }{\b 1995}, {\i 91}, 1741-1749.\par 
(23)\tab Zraly, M. A. Senior-honors Thesis, Middlebury College, 1995.\par 
(24)\tab Dimmig, J. Senior Thesis, Middlebury College, 1995.\par 
(25)\tab Pearlman, D. A.; Case, D. A.; Caldwell, J. W.; Kollman, P. A. In University of California: San Franscisco, 1994; pp .\par 
(26)\tab Scheidt, W. R.; Reed, C. R. {\i Chemical Review }{\b 1981}, {\i 81}, 543\emdash 555.\par 
(27)\tab Hoard, J. L. ; 199?\par 
(28)\tab Bevington, P. R. {\i Data Reduction and Error Analysis for the Physical Sciences}; McGraw-Hill Book Company: New York, 1969.\par 
(29)\tab Mead, R.; Nelder, J. A. {\i Computer Journal }{\b 1965}, {\i 7}, 308-311.\par 
(30)\tab Kincaid, J. R.; Urban, M. W.; Watanabe, T.; Nakamoto, K. {\i Journal of Physical Chemistry }{\b 1983}, {\i 87}, 3096-3101.\par 
(31)\tab Lau, C. L.; Snyder, R. G. {\i Spectrochimica Acta. }{\b 1970}, {\i 27A}, 2073\emdash 2088.\par 
(32)\tab Lau, C. L.; Snyder, R. G. {\i Spectrochimica Acta }{\b 1973}, {\i ???}, ???\par 
(33)\tab Jorgensen, W. L.; Maxwell, D. S.; Tirado-Rives, J. {\i Journal of Computational Chemistry }{\b 1995}, {\i 16}, 984\emdash 1010.\par 
(34)\tab Karplus, M.; Kuriyan, J.; Kuczera, K. {\i Journal Molecular Biology }{\b 1990}, {\i 213}, 351\emdash 373.{{\object\objicemb{\*\objname ICEmbdObject52}{\*\objdata 0000002200000ca3685610000832cf454e422d00000000000900afa3a8830051c2ae}{\result 
{\pict\macpict\picw0\pich0 000a0000000000000000}}}}\par 
\par 
\pard\plain \f20 \sect \sectd \pgnrestart\linemod0\linex0\cols1\endnhere {\footer \pard\plain \s243\tqc\tx4320\tqr\tx8640 \f20 \tab Appendix - \chpgn \par 
}\pard\plain \qc \f20 {\v\fs28 {\tc\tcl1\pard\plain \qc \f20 {\b\fs28 Appendix A\: Prep Files}}}{\b\fs28 \par 
}\pard \par 
\pard {\v {\tc\tcl2\pard\plain \f20 {\b Benzene Prep File}}}\par 
\pard {\f22\fs18      0    0    2                                                                \par 
                                                                                \par 
    benzene prep file                                                           \par 
benzene.db3                                                                     \par 
BEN  INT     1                                                                  \par 
CORR NOMIT DU   BEG                                                             \par 
   0.00000                                                                      \par 
   1   DUMM  DU    M      0  -1  -2       0.0000      0.0000      0.0000      0.0000\par 
   2   DUMM  DU    M      1   0  -1       1.0000      0.0000      0.0000      0.0000\par 
   3   DUMM  DU    M      2   1   0       1.0000     90.0000      0.0000      0.0000\par 
   4   C1    CA    M      3   2   1       1.4000     90.0000     90.0000     -0.1500\par 
   5   H1    HA    E      4   3   2       1.0900     90.0000      0.0000      0.1500\par 
   6   C2    CA    B      4   3   2       1.4000     90.0000    120.0000     -0.1500\par 
   7   H2    HA    E      6   4   3       1.0900    120.0000    -90.0000      0.1500\par 
   8   C3    CA    B      6   4   3       1.4000    120.0000     90.0000     -0.1500\par 
   9   H3    HA    E      8   6   4       1.0900    120.0000    180.0000      0.1500\par 
  10   C4    CA    B      8   6   4       1.4000    120.0000      0.0000     -0.1500\par 
  11   H4    HA    E     10   8   6       1.0900    120.0000    180.0000      0.1500\par 
  12   C5    CA    B     10   8   6       1.4000    120.0000      0.0000     -0.1500\par 
  13   H5    HA    E     12  10   8       1.0900    120.0000    180.0000      0.1500\par 
  14   C6    CA    S     12  10   8       1.4000    120.0000      0.0000     -0.1500\par 
  15   H6    HA    E     14  12  10       1.0900    120.0000    180.0000      0.1500\par 
\par 
LOOP                                                                            \par 
 C1   C6\par 
\par 
IMPROPER\par 
 C6   C2   C1   H5\par 
 C1   C3   C2   H2\par 
 C4   C2   C3   H3\par 
 C5   C3   C4   H4\par 
 C6   C4   C5   H1\par 
 C5   C1   C6   H6\par 
\par 
DONE                                                                            \par 
STOP                                                                            \par 
}\pard \par 
\pard {\v {\tc\tcl2\pard\plain \f20 {\b Ethyl Benzene Prep File}}}{\b \par 
}\pard {\f22\fs18      0    0    2                                                                \par 
                                                                                \par 
ethybenzene prep file                                                           \par 
toluene.db3                                                                     \par 
TOL  INT     1                                                                  \par 
CORR NOMIT DU   BEG                                                             \par 
   0.00000                                                                      \par 
   1   DUMM  DU    M      0  -1  -2       0.0000      0.0000      0.0000      0.0000\par 
   2   DUMM  DU    M      1   0  -1       1.0000      0.0000      0.0000      0.0000\par 
   3   DUMM  DU    M      2   1   0       1.0000     90.0000      0.0000      0.0000\par 
   4   C1    CA    M      3   2   1       1.5100     90.0000     90.0000     -0.1101\par 
   5   H1    HA    E      4   3   2       1.0900     90.0000      0.0000      0.1399\par 
   6   C2    CA    B      4   3   2       1.4000     90.0000    120.0000     -0.1601\par 
   7   H2    HA    E      6   4   3       1.0900    120.0000    -90.0000      0.1399\par 
   8   C3    CA    B      6   4   3       1.4000    120.0000     90.0000     -0.1601\par 
   9   H3    HA    E      8   6   4       1.0900    120.0000    180.0000      0.1399\par 
  10   C4    CA    B      8   6   4       1.4000    120.0000      0.0000     -0.1601\par 
  11   H4    HA    E     10   8   6       1.0900    120.0000    180.0000      0.1399\par 
  12   C5    CA    B     10   8   6       1.4000    120.0000      0.0000     -0.1601\par 
  13   H5    HA    E     12  10   8       1.0900    120.0000    180.0000      0.1399\par 
  14   C6    CA    S     12  10   8       1.4000    120.0000      0.0000     -0.1601\par 
  15   C7    CT    3     14  12  10       1.5100    120.0000    180.0000     -0.1184\par 
  16   C8    CT    3     14  12  10       1.5260    109.5000     90.0000     -0.1184\par 
  17   H81   HM    E     16  15  14       1.0900    109.5000      0.0000      0.0896\par 
  18   H82   HM    E     16  15  14       1.0900    109.5000    120.0000      0.0896\par 
  19   H83   HM    E     16  15  14       1.0900    109.5000   -120.0000      0.0896\par 
  20   H72   HC    E     15  14  12       1.0900    109.5000    -30.0000      0.0896\par 
  21   H73   HC    E     15  14  12       1.0900    109.5000   -150.0000      0.0896\par 
\par 
                                                                                \par 
                                                                                \par 
LOOP                                                                            \par 
 C1   C6                                                                        \par 
                                                                                \par 
IMPROPER\par 
 C1   C2   H2   C3\par 
 C2   C3   H3   C4\par 
 C3   C4   H4   C5\par 
 C4   C5   H5   C6\par 
 C5   C6   C7   C1\par 
 C6   C1   H1   C2\par 
 H1   C6   C1   C2\par 
 H2   C1   C2   C3\par 
 H3   C2   C3   C4\par 
 H4   C3   C4   C5\par 
 H5   C4   C5   C6\par 
 C7   C5   C6   C1\par 
\par 
\par 
DONE                                                                            \par 
STOP                                                                            \par 
                                                                                \par 
}\pard \par 
\pard {\v {\tc\tcl2\pard\plain \f20 {\b Heme-Histidine Prep File}}}{\b \par 
}\pard \par 
\pard {\f22\fs18     0    0    2                                                                 \par 
                                                                                \par 
    Heme-histidine residue  ALL ATOM, Yves names .1 CO charge nuetron coord\par 
heme_his_co.db3                                                                    \par 
HEM  INT     1                                                                  \par 
CORRECT  NOMIT DU   BEG                                                          \par 
   0.00000                                                                      \par 
   1   DUMM  DU    M      0  -1  -2       0.0000      0.0000      0.0000      0.0000\par 
   2   DUMM  DU    M      1   0  -1       1.4490      0.0000      0.0000      0.0000\par 
   3   DUMM  DU    M      2   1   0       1.5220    111.1000      0.0000      0.0000\par 
   4   N     N     M      3   2   1       1.3350    116.6000    180.0000     -0.4630\par 
   5   HN    H     E      4   3   2       1.0100    119.8000      0.0000      0.2520\par 
   6   CA    CT    M      4   3   2       1.4490    121.9000    180.0000      0.0350\par 
   7   HA    HC    E      6   4   3       1.0900    109.5000    300.0000      0.0480\par 
   8   CB    CT    3      6   4   3       1.5250    111.1000     60.0000     -0.0980\par 
   9   HB2   HC    E      8   6   4       1.0900    109.5000     60.0000      0.0380\par 
  10   HB3   HC    E      8   6   4       1.0900    109.5000    300.0000      0.0380\par 
  11   CG    CC    S      8   6   4       1.5100    115.0000    180.0000     -0.0320\par 
  12   ND1   NA    B     11   8   6       1.3900    122.0000    180.0000     -0.1460\par 
  13   HND   H     E     12  11   8       1.0100    126.0000      0.0000      0.2280\par 
  14   CE1   CR    B     12  11   8       1.3200    108.0000    180.0000      0.2410\par 
  15   HE    HC    E     14  12  11       1.0800    120.0000    180.0000      0.0360\par 
  16   NE2   NB    B     14  12  11       1.1300    109.0000      0.0000     -0.5020\par 
  17   CD2   CV    S     16  14  12       1.3600    110.0000      0.0000      0.1950\par 
  18   HD    HC    E     17  16  14       1.0800    120.0000    180.0000      0.0180\par 
  19   FE    FE    B     16  14  12       2.1000    124.0000    180.0000      0.2500\par 
  20   NA    NP    S     19  16  14       2.0800     98.0000     90.0000     -0.1800\par 
  21   C1A   CC    S     20  19  16       1.3800    125.4000     90.0000      0.0300\par 
  22   C2A   CB    B     21  20  19       1.4100    109.0000    180.0000     -0.0200\par 
  23   CAA   CX    3     22  21  20       1.5100    124.0000    180.0000     -0.1600\par 
  24   HP71  HE    E     23  22  21       1.0900    109.5000     60.0000      0.1000\par 
  25   HP72  HE    E     23  22  21       1.0900    109.5000    300.0000      0.1000\par 
  26   CBA   CY    3     23  22  21       1.5400    111.0000    180.0000     -0.3000\par 
  27   HP73  HN    E     26  23  22       1.0900    109.5000     60.0000      0.1000\par 
  28   HP74  HN    E     26  23  22       1.0900    109.5000    300.0000      0.1000\par 
  29   CGA   C     B     26  23  22       1.5270    109.4000    180.0000      0.3000\par 
  30   O1A   O2    E     29  26  23       1.2600    117.2000     90.0000     -0.5000\par 
  31   O2A   O2    E     29  26  23       1.2600    117.2000    270.0000     -0.5000\par 
  32   C3A   CB    B     22  21  20       1.4100    107.0000      0.0000      0.0200\par 
  33   CMA   CX    3     32  22  21       1.5100    125.0000    180.0000     -0.2650\par 
  34   HM81  HE    E     33  32  22       1.0900    109.5000     60.0000      0.0750\par 
  35   HM82  HE    E     33  32  22       1.0900    109.5000    180.0000      0.0750\par 
  36   HM83  HE    E     33  32  22       1.0900    109.5000    300.0000      0.0750\par 
  37   C4A   CC    S     32  22  21       1.4100    107.0000      0.0000      0.0200\par 
  38   CHB   CD    B     37  32  22       1.3700    127.0000    180.0000     -0.1100\par 
  39   HDM   HM    E     38  37  32       1.0800    120.0000      0.0000      0.1500\par 
  40   C1B   CC    B     38  37  32       1.3700    127.0000    180.0000      0.0300\par 
  41   NB    NO    E     40  38  37       1.3800    124.0000      0.0000     -0.1800\par 
  42   C2B   CB    B     40  38  37       1.4100    127.0000    180.0000      0.0200\par 
  43   CMB   CX    3     42  40  38       1.5100    125.0000      0.0000     -0.2650\par 
  44   HM11  HE    E     43  42  40       1.0900    109.5000     60.0000      0.0750\par 
  45   HM12  HE    E     43  42  40       1.0900    109.5000    180.0000      0.0750\par 
  46   HM13  HE    E     43  42  40       1.0900    109.5000    300.0000      0.0750\par 
  47   C3B   CB    B     42  40  38       1.4100    107.0000    180.0000     -0.0500\par 
  48   CAB   CQ    B     47  42  40       1.5100    126.0000    180.0000     -0.1300\par 
  49   HV2A  HQ    E     48  47  42       1.0800    120.0000      0.0000      0.1500\par 
  50   CBB   CQ    B     48  47  42       1.3300    120.0000    180.0000     -0.3000\par 
  51   HV2C  HQ    E     50  48  47       1.0800    120.0000      0.0000      0.1000\par 
  52   HV2T  HQ    E     50  48  47       1.0800    120.0000    180.0000      0.1000\par 
  53   C4B   CC    S     47  42  40       1.4100    107.0000      0.0000      0.0200\par 
  54   CHC   CD    B     53  47  42       1.3700    127.0000    180.0000     -0.1100\par 
  55   HAM   HM    E     54  53  47       1.0800    120.0000      0.0000      0.1500\par 
  56   C1C   CC    B     54  53  47       1.3700    130.0000    180.0000      0.0300\par 
  57   NC    NP    E     56  54  53       1.3800    124.0000      0.0000     -0.1800\par 
  58   C2C   CB    B     56  54  53       1.4100    127.0000    180.0000      0.0200\par 
  59   CMC   CX    3     58  56  54       1.5100    125.0000      0.0000     -0.2650\par 
  60   HM31  HE    E     59  58  56       1.0900    109.5000     60.0000      0.0750\par 
  61   HM32  HE    E     59  58  56       1.0900    109.5000    180.0000      0.0750\par 
  62   HM33  HE    E     59  58  56       1.0900    109.5000    300.0000      0.0750\par 
  63   C3C   CB    B     58  56  54       1.4100    107.0000    180.0000     -0.0500\par 
  64   CAC   CQ    B     63  58  56       1.5100    126.0000    180.0000     -0.1200\par 
  65   HV4A  HQ    E     64  63  58       1.0800    120.0000      0.0000      0.1500\par 
  66   CBC   CQ    B     64  63  58       1.3300    120.0000    180.0000     -0.3000\par 
  67   HV4C  HQ    E     66  64  63       1.0800    120.0000      0.0000      0.1000\par 
  68   HV4T  HQ    E     66  64  63       1.0800    120.0000    180.0000      0.1000\par 
  69   C4C   CC    S     63  58  56       1.4100    107.0000      0.0000      0.0200\par 
  70   CHD   CD    B     69  63  58       1.3700    127.0000    180.0000     -0.1100\par 
  71   HBM   HM    E     70  69  63       1.0800    120.0000      0.0000      0.1500\par 
  72   C1D   CC    B     70  69  63       1.3700    130.0000    180.0000      0.0300\par 
  73   ND    NO    E     72  70  69       1.3800    124.0000      0.0000     -0.1800\par 
  74   C2D   CB    B     72  70  69       1.4100    127.0000    180.0000      0.0200\par 
  75   CMD   CX    3     74  72  70       1.5100    125.0000      0.0000     -0.2650\par 
  76   HM51  HE    E     75  74  72       1.0900    109.5000     60.0000      0.0750\par 
  77   HM52  HE    E     75  74  72       1.0900    109.5000    180.0000      0.0750\par 
  78   HM53  HE    E     75  74  72       1.0900    109.5000    300.0000      0.0750\par 
  79   C3D   CB    B     74  72  70       1.4100    107.0000    180.0000     -0.0200\par 
  80   C4D   CC    S     79  74  72       1.4100    107.0000      0.0000      0.0200\par 
  81   CHA   CD    S     80  79  74       1.3700    127.0000    180.0000     -0.1100\par 
  82   HGM   HM    E     81  80  79       1.0800    120.0000      0.0000      0.1500\par 
  83   CAD   CX    3     79  74  72       1.5100    124.0000    180.0000     -0.1600\par 
  84   HP61  HE    E     83  79  74       1.0900    109.5000     60.0000      0.1000\par 
  85   HP62  HE    E     83  79  74       1.0900    109.5000    300.0000      0.1000\par 
  86   CBD   CY    3     83  79  74       1.5400    111.0000    180.0000     -0.3000\par 
  87   HP63  HN    E     86  83  79       1.0900    109.5000     60.0000      0.1000\par 
  88   HP64  HN    E     86  83  79       1.0900    109.5000    300.0000      0.1000\par 
  89   CGD   C     B     86  83  79       1.5300    109.4000    180.0000      0.3000\par 
  90   O1D   O2    E     89  86  83       1.2600    117.2000     90.0000     -0.5000\par 
  91   O2D   O2    E     89  86  83       1.2600    117.2000    270.0000     -0.5000\par 
  92   CMX   LC    S     19  16  14       2.1100    180.0000     90.0000      0.1000\par 
  93   OMX   LO    E     92  19  16       1.2000    170.0000      0.0000     -0.1000\par 
  94   C     C     M      6   4   3       1.5220    111.1000    180.0000      0.6160\par 
  95   O     O     E     94   6   4       1.2290    120.5000      0.0000     -0.5040\par 
\par 
                                                                                \par 
LOOP  EXPLICIT                                                                  \par 
 NA   C4A                                                                       \par 
 FE   NB                                                                        \par 
 FE   NC                                                                        \par 
 FE   ND                                                                        \par 
 NB   C4B                                                                       \par 
 NC   C4C                                                                       \par 
 ND   C4D                                                                       \par 
 C1A  CHA                                                                       \par 
 CG   CD2                                                                       \par 
                                                                                \par 
IMPROPER                                                                        \par 
  C1A  CHA  HGM  C4D\par 
  C1D  CHD  HBM  C4C\par 
  C1C  CHC  HAM  C4B\par 
  C1B  CHB  HDM  C4A\par 
  C1A  NA   FE   C4A\par 
  C1B  NB   FE   C4B\par 
  C1C  NC   FE   C4C\par 
  C1D  ND   FE   C4D\par 
  C1A  C2A  CAA  C3A\par 
  C1B  C2B  CMB  C3B\par 
  C1C  C2C  CMC  C3C\par 
  C1D  C2D  CMD  C3D\par 
  C2A  C3A  CMA  C4A\par 
  C2B  C3B  CAB  C4B\par 
  C2C  C3C  CAC  C4C\par 
  C2D  C3D  CAD  C4D\par 
  C1B  NB   CHB  C2B\par 
  C1A  NA   CHA  C2A\par 
  C1D  ND   CHD  C2D\par 
  C1C  NC   CHC  C2C\par 
\par 
DONE                                                                            \par 
STOP                                                                            \par 
}\pard \par 
\pard {\v {\tc\tcl2\pard\plain \f20 {\b Nickel octaethyl porphine Prep File}}}{\b \par 
}\pard {\f22\fs18     0    0    2                                                                                     \par 
                                                                                                    \par 
   Nioep with non-united methyl groups CY 7-14-95 leanear dihedral warning                              \par 
por_beg.db3                                                                                         \par 
POR  INT     1                                                                                      \par 
CORRECT  NOMIT DU   BEG                                                                             \par 
   0.00000                                                                                          \par 
   1   DUMM  DU    M      0  -1  -2       0.0000      0.0000      0.0000      0.0000\par 
   2   DUMM  DU    M      1   0  -1       1.0000      0.0000      0.0000      0.0000\par 
   3   DUMM  DU    M      2   1   0       1.0000     90.0000      0.0000      0.0000\par 
   4   NI    NI    M      3   2   1       2.1100     90.0000     90.0000      0.2219\par 
   5   NA    NP    S      4   3   2       1.9580     90.0000     90.0000     -0.2081\par 
   6   C1A   CC    S      5   4   3       1.3760    128.0000    -90.0000      0.0019\par 
   7   C2A   CB    B      6   5   4       1.4430    111.5000    180.0000     -0.0481\par 
   8   CA1   CX    3      7   6   5       1.4950    128.0000    180.0000     -0.1881\par 
   9   HA1   HE    E      8   7   6       1.1000    109.5000    -30.0000      0.0719\par 
  10   HA2   HE    E      8   7   6       1.1000    109.5000   -150.0000      0.0719\par 
  11   CA2   CY    3      8   7   6       1.5060    109.5000     90.0000     -0.0403\par 
  12   HE1   HN    E     11   8   7       1.1000    109.5000    180.0000      0.0719\par 
  13   HE2   HN    E     11   8   7       1.1000    109.5000    300.0000      0.0719\par 
  14   HE3   HN    E     11   8   7       1.1000    109.5000     60.0000      0.0719\par 
  15   C3A   CB    B      7   6   5       1.3460    106.5000      0.0000     -0.0481\par 
  16   CA3   CX    3     15   7   6       1.4950    125.5000    180.0000     -0.1881\par 
  17   HA3   HE    E     16  15   7       1.1000    109.5000    -30.0000      0.0719\par 
  18   HA4   HE    E     16  15   7       1.1000    109.5000   -150.0000      0.0719\par 
  19   CA4   CY    3     16  15   7       1.5060    109.5000     90.0000     -0.0403\par 
  20   HE4   HN    E     19  16  15       1.1000    109.5000    180.0000      0.0719\par 
  21   HE5   HN    E     19  16  15       1.1000    109.5000    300.0000      0.0719\par 
  22   HE6   HN    E     19  16  15       1.1000    109.5000     60.0000      0.0719\par 
  23   C4A   CC    S     15   7   6       1.4430    106.5000      0.0000      0.0019\par 
  24   CHB   CD    S     23  15   7       1.3710    124.1000    180.0000     -0.1381\par 
  25   HHB   HM    E     24  23  15       1.0900    117.5000      0.0000      0.1219\par 
  26   NB    NO    S      4   3   2       1.9580     90.0000    180.0000     -0.2081\par 
  27   C1B   CC    S     26   4   3       1.3760    128.0000    -90.0000      0.0019\par 
  28   C2B   CB    B     27  26   4       1.4430    111.5000    180.0000     -0.0481\par 
  29   CB1   CX    3     28  27  26       1.4950    128.0000    180.0000     -0.1881\par 
  30   HB1   HE    E     29  28  27       1.1000    109.5000     30.0000      0.0719\par 
  31   HB2   HE    E     29  28  27       1.1000    109.5000    150.0000      0.0719\par 
  32   CB2   CY    3     29  28  27       1.5060    109.5000    -90.0000     -0.0403\par 
  33   HF1   HN    E     32  28  27       1.1000    109.5000    180.0000      0.0719\par 
  34   HF2   HN    E     32  28  27       1.1000    109.5000    300.0000      0.0719\par 
  35   HF3   HN    E     32  28  27       1.1000    109.5000     60.0000      0.0719\par 
  36   C3B   CB    B     28  27  26       1.3460    106.5000      0.0000     -0.0481\par 
  37   CB3   CX    3     36  28  27       1.4950    125.5000    180.0000     -0.1881\par 
  38   HB3   HE    E     37  36  28       1.1000    109.5000     30.0000      0.0719\par 
  39   HB4   HE    E     28  36  28       1.1000    109.5000    150.0000      0.0719\par 
  40   CB4   CY    3     37  36  28       1.5060    109.5000    -90.0000     -0.0403\par 
  41   HF4   HN    E     40  37  36       1.1000    109.5000    180.0000      0.0719\par 
  42   HF5   HN    E     40  37  36       1.1000    109.5000    300.0000      0.0719\par 
  43   HF6   HN    E     40  37  36       1.1000    109.5000     60.0000      0.0719\par 
  44   C4B   CC    S     36  28  27       1.4430    106.5000      0.0000      0.0019\par 
  45   CHC   CD    S     44  36  28       1.3710    124.1000    180.0000     -0.1381\par 
  46   HHC   HM    E     45  44  36       1.0900    117.5000      0.0000      0.1219\par 
  47   NC    NP    S      4   3   2       1.9580     90.0000    270.0000     -0.2081\par 
  48   C1C   CC    S     47   4   3       1.3760    128.0000    -90.0000      0.0019\par 
  49   C2C   CB    B     48  47   4       1.4430    111.5000    180.0000     -0.0481\par 
  50   CC1   CX    3     49  48  47       1.4950    128.0000    180.0000     -0.1881\par 
  51   HC1   HE    E     50  49  48       1.1000    109.5000    -30.0000      0.0719\par 
  52   HC2   HE    E     50  49  48       1.1000    109.5000   -150.0000      0.0719\par 
  53   CC2   CY    3     50  49  48       1.5060    109.5000     90.0000     -0.0403\par 
  54   HG1   HN    E     53  50  49       1.1000    109.5000    180.0000      0.0719\par 
  55   HG2   HN    E     53  50  49       1.1000    109.5000    300.0000      0.0719\par 
  56   HG3   HN    E     53  50  49       1.1000    109.5000     60.0000      0.0719\par 
  57   C3C   CB    B     49  48  47       1.3460    106.5000      0.0000     -0.0481\par 
  58   CC3   CX    3     57  49  48       1.4950    125.5000    180.0000     -0.1881\par 
  59   HC3   HE    E     58  57  49       1.1000    109.5000    -30.0000      0.0719\par 
  60   HC4   HE    E     58  57  49       1.1000    109.5000   -150.0000      0.0719\par 
  61   CC4   CY    3     58  57  49       1.5060    109.5000     90.0000     -0.0403\par 
  62   HG4   HN    E     61  58  57       1.1000    109.5000    180.0000      0.0719\par 
  63   HG5   HN    E     61  58  57       1.1000    109.5000    300.0000      0.0719\par 
  64   HG6   HN    E     61  58  57       1.1000    109.5000     60.0000      0.0719\par 
  65   C4C   CC    S     57  49  48       1.4430    106.5000      0.0000      0.0019\par 
  66   CHD   CD    S     65  57  49       1.3710    124.1000    180.0000     -0.1381\par 
  67   HHD   HM    E     66  65  57       1.0900    117.5000      0.0000      0.1219\par 
  68   ND    NO    S      4   3   2       1.9580     90.0000    360.0000     -0.2081\par 
  69   C1D   CC    S     68   4   3       1.3760    128.0000    -90.0000      0.0019\par 
  70   C2D   CB    B     69  68   4       1.4430    111.5000    180.0000     -0.0481\par 
  71   CD1   CX    3     70  69  68       1.4950    128.0000    180.0000     -0.1881\par 
  72   HD1   HE    E     71  70  69       1.1000    109.5000     30.0000      0.0719\par 
  73   HD2   HE    E     71  70  69       1.1000    109.5000    150.0000      0.0719\par 
  74   CD2   CY    3     71  70  69       1.5060    109.5000    -90.0000     -0.0403\par 
  75   HJ1   HN    E     74  71  70       1.1000    109.5000    180.0000      0.0719\par 
  76   HJ2   HN    E     74  71  70       1.1000    109.5000    300.0000      0.0719\par 
  77   HJ3   HN    E     74  71  70       1.1000    109.5000     60.0000      0.0719\par 
  78   C3D   CB    B     70  69  68       1.3460    106.5000      0.0000     -0.0481\par 
  79   CD3   CX    3     78  70  69       1.4950    125.5000    180.0000     -0.1881\par 
  80   HD3   HE    E     79  78  70       1.1000    109.5000     30.0000      0.0719\par 
  81   HD4   HE    E     79  78  70       1.1000    109.5000    150.0000      0.0719\par 
  82   CD4   CY    3     79  78  70       1.5060    109.5000    -90.0000     -0.0403\par 
  83   HJ4   HN    E     82  79  78       1.1000    109.5000    180.0000      0.0719\par 
  84   HJ5   HN    E     82  79  78       1.1000    109.5000    300.0000      0.0719\par 
  85   HJ6   HN    E     82  79  78       1.1000    109.5000     60.0000      0.0719\par 
  86   C4D   CC    S     78  70  69       1.4430    106.5000      0.0000      0.0019\par 
  87   CHA   CD    S     87  78  70       1.3710    124.1000    180.0000     -0.1381\par 
  88   HHA   HM    E     88  87  78       1.0900    117.5000      0.0000      0.1219\par 
\par 
LOOP  EXPLICIT                                                                                      \par 
 NA   C4A                                                                                           \par 
 NB   C4B                                                                                           \par 
 NC   C4C                                                                                           \par 
 ND   C4D                                                                                           \par 
 CHB  C1B                                                                                           \par 
 CHC  C1C                                                                                           \par 
 CHD  C1D                                                                                           \par 
 CHA  C1A                                                                                           \par 
                                                                                                    \par 
IMPROPER                                                                                            \par 
 C1A  CHA  HHA  C4D                                                                                 \par 
 C1B  CHB  HHB  C4A                                                                                 \par 
 C1C  CHC  HHC  C4B                                                                                 \par 
 C1D  CHD  HHD  C4C                                                                                 \par 
 C1A  NA  NI  C4A                                                                                   \par 
 C1B  NB  NI  C4B                                                                                   \par 
 C1C  NC  NI  C4C                                                                                   \par 
 C1D  ND  NI  C4D                                                                                   \par 
 C2A  C3A  CA3  C4A                                                                                 \par 
 C2B  C3B  CB3  C4B                                                                                 \par 
 C2C  C3C  CC3  C4C                                                                                 \par 
 C2D  C3D  CD3  C4D                                                                                 \par 
 C1A  C2A  CA1  C3A                                                                                 \par 
 C1B  C2B  CB1  C3B                                                                                 \par 
 C1C  C2C  CC1  C3C                                                                                 \par 
 C1D  C2D  CD1  C3D                                                                                 \par 
 C1B  NB  CHB  C2B\par 
 C1C  NC  CHC  C2C\par 
 C1D  ND  CHD  C2D\par 
 C1A  NA  CHA  C2A\par 
\par 
                                                                                                    \par 
DONE                                                                                                \par 
STOP                                                                                                \par 
}\pard \par 
\pard {\v {\tc\tcl2\pard\plain \f20 {\b Nickel  porphine Prep File}}}{\b \par 
}\pard {\f22\fs18     0    0    2                                                                                     \par 
                                                                                                    \par 
    united ethyl (cz) nioep                                                                         \par 
por_beg.db3                                                                                         \par 
POR  INT     1                                                                                      \par 
CORRECT  NOMIT DU   BEG                                                                             \par 
   0.00000                                                                                          \par 
   1   DUMM  DU    M      0  -1  -2       0.0000      0.0000      0.0000      0.0000\par 
   2   DUMM  DU    M      1   0  -1       1.0000      0.0000      0.0000      0.0000\par 
   3   DUMM  DU    M      2   1   0       1.0000     90.0000      0.0000      0.0000\par 
   4   NI    NI    M      3   2   1       2.1100     90.0000     90.0000      0.2500\par 
   5   NA    NP    S      4   3   2       1.9580     90.0000     90.0000     -0.1800\par 
   6   C1A   CC    S      5   4   3       1.3760    128.0000    -90.0000      0.0300\par 
   7   C2A   CB    B      6   5   4       1.4430    111.5000    180.0000     -0.0200\par 
   8   HA2   CZ    E      7   6   5       1.4950    128.0000    180.0000      0.0288\par 
   9   C3A   CB    B      7   6   5       1.3460    106.5000      0.0000     -0.0200\par 
  10   HA3   CZ    E      9   7   6       1.4950    125.5000    180.0000      0.0288\par 
  11   C4A   CC    S      9   7   6       1.4430    106.5000      0.0000      0.0300\par 
  12   CHB   CD    S     11   9   7       1.3710    124.1000    180.0000     -0.1100\par 
  13   HHB   HM    E     12  11   9       1.0900    117.5000      0.0000      0.1500\par 
  14   NB    NO    S      4   3   2       1.9580     90.0000    180.0000     -0.1800\par 
  15   C1B   CC    S     14   4   3       1.3760    128.0000    -90.0000      0.0300\par 
  16   C2B   CB    B     15  14   4       1.4430    111.5000    180.0000     -0.0200\par 
  17   HB2   CZ    E     16  15  14       1.4950    128.0000    180.0000      0.0288\par 
  18   C3B   CB    B     16  15  14       1.3460    106.5000      0.0000     -0.0200\par 
  19   HB3   CZ    E     18  16  15       1.4950    125.5000    180.0000      0.0288\par 
  20   C4B   CC    S     18  16  15       1.4430    106.5000      0.0000      0.0300\par 
  21   CHC   CD    S     20  18  16       1.3710    124.1000    180.0000     -0.1100\par 
  22   HHC   HM    E     21  20  18       1.0900    117.5000      0.0000      0.1500\par 
  23   NC    NP    S      4   3   2       1.9580     90.0000    270.0000     -0.1800\par 
  24   C1C   CC    S     23   4   3       1.3760    128.0000    -90.0000      0.0300\par 
  25   C2C   CB    B     24  23   4       1.4430    111.5000    180.0000     -0.0200\par 
  26   HC2   CZ    E     25  24  23       1.4950    128.0000    180.0000      0.0288\par 
  27   C3C   CB    B     25  24  23       1.3460    106.5000      0.0000     -0.0200\par 
  28   HC3   CZ    E     27  25  24       1.4950    125.5000    180.0000      0.0288\par 
  29   C4C   CC    S     27  25  24       1.4430    106.5000      0.0000      0.0300\par 
  30   CHD   CD    S     29  27  25       1.3710    124.1000    180.0000     -0.1100\par 
  31   HHD   HM    E     30  29  27       1.0900    117.5000      0.0000      0.1500\par 
  32   ND    NO    S      4   3   2       1.9580     90.0000    360.0000     -0.1800\par 
  33   C1D   CC    S     32   4   3       1.3760    128.0000    -90.0000      0.0300\par 
  34   C2D   CB    B     33  32   4       1.4430    111.5000    180.0000     -0.0200\par 
  35   HD2   CZ    E     34  33  32       1.4950    128.0000    180.0000      0.0288\par 
  36   C3D   CB    B     34  33  32       1.3460    106.5000      0.0000     -0.0200\par 
  37   HD3   CZ    E     36  34  33       1.4950    125.5000    180.0000      0.0288\par 
  38   C4D   CC    S     36  34  33       1.4430    106.5000      0.0000      0.0300\par 
  39   CHA   CD    S     38  36  34       1.3710    124.1000    180.0000     -0.1100\par 
  40   HHA   HM    E     39  38  36       1.0900    117.5000      0.0000      0.1500\par 
\par 
LOOP  EXPLICIT                                                                                      \par 
 NA   C4A                                                                                           \par 
 NB   C4B                                                                                           \par 
 NC   C4C                                                                                           \par 
 ND   C4D                                                                                           \par 
CHB   C1B                                                                                           \par 
CHC   C1C                                                                                           \par 
CHD   C1D                                                                                           \par 
CHA   C1A                                                                                           \par 
                                                                                                    \par 
IMPROPER                                                                                            \par 
 C1A  CHA  HHA  C4D                                                                                 \par 
 C1B  CHB  HHB  C4A                                                                                 \par 
 C1C  CHC  HHC  C4B                                                                                 \par 
 C1D  CHD  HHD  C4C                                                                                 \par 
 C1A  NA  NI  C4A                                                                                   \par 
 C1B  NB  NI  C4B                                                                                   \par 
 C1C  NC  NI  C4C                                                                                   \par 
 C1D  ND  NI  C4D                                                                                   \par 
 C2A  C3A  HA3  C4A                                                                                 \par 
 C2B  C3B  HB3  C4B                                                                                 \par 
 C2C  C3C  HC3  C4C                                                                                 \par 
 C2D  C3D  HD3  C4D                                                                                 \par 
 C1A  C2A  HA2  C3A                                                                                 \par 
 C1B  C2B  HB2  C3B                                                                                 \par 
 C1C  C2C  HC2  C3C                                                                                 \par 
 C1D  C2D  HD2  C3D                                                                                 \par 
 C1B  NB  CHB  C2B\par 
 C1C  NC  CHC  C2C\par 
 C1D  ND  CHD  C2D\par 
 C1A  NA  CHA  C2A\par 
\par 
DONE                                                                                                \par 
STOP                                                                                                \par 
}\pard \par 
\pard \qc \page {\v\fs28 {\tc\tcl1\pard\plain \qc \f20 {\b\fs28 Appendix B\: PDB Files}}}{\b\fs28 \par 
}\pard \par 
\pard {\v {\tc\tcl2\pard\plain \f20 {\b Benzene PDB File}}}{\b \par 
}\pard {\b \par 
}\pard {\f22\fs18 HEADER     Benzene pdb file\par 
ATOM      1  C1  TOL     1      -0.704  -1.218   0.000 \par 
ATOM      2  H1  TOL     1      -1.244  -2.154   0.000 \par 
ATOM      3  C2  TOL     1       0.704  -1.218   0.000 \par 
ATOM      4  H2  TOL     1       1.244  -2.154   0.000\par 
ATOM      5  C3  TOL     1       1.406   0.000   0.000\par 
ATOM      6  H3  TOL     1       2.488   0.000   0.000\par 
ATOM      7  C4  TOL     1       0.704   1.218   0.000\par 
ATOM      8  H4  TOL     1       1.244   2.154   0.000\par 
ATOM      9  C5  TOL     1      -0.704   1.218   0.000\par 
ATOM     10  H5  TOL     1      -1.244   2.155   0.000\par 
ATOM     11  C6  TOL     1      -1.406   0.000   0.000\par 
ATOM     12  H6  TOL     1      -2.488   0.000   0.000\par 
}\pard \par 
\pard {\v {\tc\tcl2\pard\plain \f20 {\b Ethyl Benzene PDB File}}}{\b \par 
}\pard \par 
\pard {\f22\fs18 HEADER  Rotated on 27-Jan-97 about    11   12    1\par 
ATOM      1  C1  TOL     1      -0.708   1.218   0.000\par 
ATOM      2  H1  TOL     1      -0.176   2.157   0.017\par 
ATOM      3  C2  TOL     1      -2.114   1.217  -0.038\par 
ATOM      4  H2  TOL     1      -2.654   2.153  -0.042\par 
ATOM      5  C3  TOL     1      -2.817   0.000  -0.071\par 
ATOM      6  H3  TOL     1      -3.898  -0.001  -0.099\par 
ATOM      7  C4  TOL     1      -2.113  -1.217  -0.068\par 
ATOM      8  H4  TOL     1      -2.652  -2.153  -0.095\par 
ATOM      9  C5  TOL     1      -0.707  -1.217  -0.031\par 
ATOM     10  H5  TOL     1      -0.174  -2.158  -0.036\par 
ATOM     11  C6  TOL     1       0.000   0.000   0.000\par 
ATOM     12  C7  TOL     1       1.517   0.000   0.000\par 
ATOM     13  C8  TOL     1       2.121   0.003  -1.406\par 
ATOM     14  H81 TOL     1       1.791  -0.883  -1.949\par 
ATOM     15  H82 TOL     1       1.793   0.893  -1.944\par 
ATOM     16  H83 TOL     1       3.209   0.001  -1.340\par 
ATOM     17  H72 TOL     1       1.871  -0.882   0.536\par 
ATOM     18  H73 TOL     1       1.873   0.877   0.541\par 
}\pard \par 
\pard {\v {\tc\tcl2\pard\plain \f20 {\b Ethyl Benzene PDB File}}}{\b \par 
}\pard {\b \par 
}\pard {\f22\fs18 HEADER    Myoglobin Heme pdb file\par 
ATOM   1491  N   HEM    93      -0.269  -2.440  -6.103                          \par 
ATOM   1492  HN  HEM    93       0.400  -1.686  -6.171                          \par 
ATOM   1493  CA  HEM    93      -1.636  -2.086  -5.787                          \par 
ATOM   1494  HA  HEM    93      -1.971  -2.732  -4.975                          \par 
ATOM   1495  CB  HEM    93      -1.731  -0.554  -5.390                          \par 
ATOM   1496  HB2 HEM    93      -1.354   0.028  -6.232                          \par 
ATOM   1497  HB3 HEM    93      -2.776  -0.268  -5.279                          \par 
ATOM   1498  CG  HEM    93      -1.016  -0.204  -4.092                          \par 
ATOM   1499  ND1 HEM    93       0.241  -0.644  -3.788                          \par 
ATOM   1500  HND HEM    93       0.917  -1.056  -4.416                          \par 
ATOM   1501  CE1 HEM    93       0.560  -0.404  -2.517                          \par 
ATOM   1502  HE  HEM    93       1.571  -0.564  -2.172                          \par 
ATOM   1503  NE2 HEM    93      -0.476   0.000  -1.825                          \par 
ATOM   1504  CD2 HEM    93      -1.443   0.272  -2.878                          \par 
ATOM   1505  HD  HEM    93      -2.466   0.485  -2.605                          \par 
ATOM   1506 FE   HEM    93      -0.502   0.394   0.422                          \par 
ATOM   1507  NA  HEM    93       1.492   0.125   0.462                          \par 
ATOM   1508  C1A HEM    93       2.194  -1.018   0.713                          \par 
ATOM   1509  C2A HEM    93       3.622  -0.722   0.477                          \par 
ATOM   1510  CAA HEM    93       4.750  -1.790   0.532                          \par 
ATOM   1511  HP71HEM    93       5.564  -1.177   0.919                          \par 
ATOM   1512  HP72HEM    93       4.540  -2.626   1.198                          \par 
ATOM   1513  CBA HEM    93       5.219  -2.336  -0.914                          \par 
ATOM   1514  HP73HEM    93       6.205  -2.772  -0.754                          \par 
ATOM   1515  HP74HEM    93       5.174  -1.515  -1.629                          \par 
ATOM   1516  CGA HEM    93       4.196  -3.421  -1.409                          \par 
ATOM   1517  O1A HEM    93       3.275  -2.972  -2.119                          \par 
ATOM   1518  O2A HEM    93       4.072  -4.496  -0.753                          \par 
ATOM   1519  C3A HEM    93       3.833   0.621   0.242                          \par 
ATOM   1520  CMA HEM    93       5.022   1.287  -0.284                          \par 
ATOM   1521  HM81HEM    93       5.289   1.005  -1.302                          \par 
ATOM   1522  HM82HEM    93       4.905   2.370  -0.245                          \par 
ATOM   1523  HM83HEM    93       5.924   1.004   0.259                          \par 
ATOM   1524  C4A HEM    93       2.492   1.120   0.203                          \par 
ATOM   1525  CHB HEM    93       2.140   2.473  -0.090                          \par 
ATOM   1526  HDM HEM    93       2.972   3.145  -0.303                          \par 
ATOM   1527  C1B HEM    93       0.909   3.069  -0.098                          \par 
ATOM   1528  NB  HEM    93      -0.227   2.400   0.178                          \par 
ATOM   1529  C2B HEM    93       0.625   4.446  -0.295                          \par 
ATOM   1530  CMB HEM    93       1.682   5.549  -0.260                          \par 
ATOM   1531  HM11HEM    93       2.340   5.438  -1.122                          \par 
ATOM   1532  HM12HEM    93       1.320   6.517  -0.606                          \par 
ATOM   1533  HM13HEM    93       2.146   5.747   0.706                          \par 
ATOM   1534  C3B HEM    93      -0.760   4.554  -0.275                          \par 
ATOM   1535  CAB HEM    93      -1.487   5.930  -0.240                          \par 
ATOM   1537  CBB HEM    93      -1.115   7.013   0.373                          \par 
ATOM   1538  HV2CHEM    93      -0.292   6.991   1.071                          \par 
ATOM   1539  HV2THEM    93      -1.726   7.872   0.136                          \par 
ATOM   1540  C4B HEM    93      -1.257   3.250  -0.160                          \par 
ATOM   1541  CHC HEM    93      -2.606   2.942  -0.222                          \par 
ATOM   1542  HAM HEM    93      -3.421   3.652  -0.365                          \par 
ATOM   1543  C1C HEM    93      -3.208   1.687   0.041                          \par 
ATOM   1544  NC  HEM    93      -2.460   0.548   0.302                          \par 
ATOM   1545  C2C HEM    93      -4.621   1.487   0.183                          \par 
ATOM   1546  CMC HEM    93      -5.704   2.459   0.255                          \par 
ATOM   1547  HM31HEM    93      -6.688   2.105   0.563                          \par 
ATOM   1548  HM32HEM    93      -5.339   3.197   0.969                          \par 
ATOM   1549  HM33HEM    93      -5.818   2.960  -0.706                          \par 
ATOM   1550  C3C HEM    93      -4.715   0.147   0.398                          \par 
ATOM   1551  CAC HEM    93      -5.949  -0.672   0.686                          \par 
ATOM   1553  CBC HEM    93      -6.961  -0.270   1.527                          \par 
ATOM   1554  HV4CHEM    93      -6.927   0.642   2.105                          \par 
ATOM   1555  HV4THEM    93      -7.796  -0.941   1.668                          \par 
ATOM   1556  C4C HEM    93      -3.425  -0.428   0.350                          \par 
ATOM   1557  CHD HEM    93      -3.160  -1.811   0.542                          \par 
ATOM   1558  HBM HEM    93      -4.032  -2.425   0.766                          \par 
ATOM   1559  C1D HEM    93      -1.921  -2.354   0.535                          \par 
ATOM   1560  ND  HEM    93      -0.741  -1.591   0.704                          \par 
ATOM   1561  C2D HEM    93      -1.745  -3.778   0.850                          \par 
ATOM   1562  CMD HEM    93      -2.900  -4.814   1.017                          \par 
ATOM   1563  HM51HEM    93      -3.333  -4.981   0.030                          \par 
ATOM   1564  HM52HEM    93      -2.618  -5.815   1.344                          \par 
ATOM   1565  HM53HEM    93      -3.696  -4.437   1.660                          \par 
ATOM   1566  C3D HEM    93      -0.419  -3.859   1.220                          \par 
ATOM   1567  C4D HEM    93       0.203  -2.532   1.084                          \par 
ATOM   1568  CHA HEM    93       1.585  -2.245   1.001                          \par 
ATOM   1569  HGM HEM    93       2.245  -3.091   1.192                          \par 
ATOM   1570  CAD HEM    93       0.326  -5.056   1.650                          \par 
ATOM   1571  HP61HEM    93      -0.119  -5.991   1.311                          \par 
ATOM   1572  HP62HEM    93       1.361  -4.981   1.315                          \par 
ATOM   1573  CBD HEM    93       0.313  -5.184   3.204                          \par 
ATOM   1574  HP63HEM    93      -0.679  -5.068   3.640                          \par 
ATOM   1575  HP64HEM    93       0.409  -6.255   3.379                          \par 
ATOM   1576  CGD HEM    93       1.461  -4.568   3.968                          \par 
ATOM   1577  O1D HEM    93       1.356  -4.243   5.168                          \par 
ATOM   1578  O2D HEM    93       2.609  -4.691   3.539                          \par 
ATOM   1579  CMX HEM    93      -0.380   0.955   2.493                          \par 
ATOM   1580  OMX HEM    93      -0.229   1.303   3.552                          \par 
ATOM   1581  C   HEM    93      -2.567  -2.364  -6.942                          \par 
ATOM   1582  O   HEM    93      -3.777  -2.509  -6.766                          \par 
}\pard \par 
\pard {\v {\tc\tcl2\pard\plain \f20 {\b Nickel octa ethyl porphine PDB File}}}{\b \par 
}\pard \par 
\pard {\f22\fs18 HEADER       starting coordinates nioep full\par 
ATOM      1 NI   POR     1       0.000   0.000   0.000                          \par 
ATOM      2  NA  POR     1       1.965   0.000   0.010                          \par 
ATOM      3  C1A POR     1       2.813  -1.083   0.014                          \par 
ATOM      4  C2A POR     1       4.210  -0.678   0.020                          \par 
ATOM      5  CA1 POR     1       5.412  -1.602   0.046                          \par 
ATOM      6  HA1 POR     1       5.191  -2.479   0.671                          \par 
ATOM      7  HA2 POR     1       6.276  -1.093   0.494                          \par 
ATOM      8  CA2 POR     1       5.763  -2.047  -1.355                          \par 
ATOM      9  HE1 POR     1       6.630  -2.724  -1.321                          \par 
ATOM     10  HE2 POR     1       4.911  -2.577  -1.807                          \par 
ATOM     11  HE3 POR     1       6.013  -1.176  -1.978                          \par 
ATOM     12  C3A POR     1       4.210   0.678   0.020                          \par 
ATOM     13  CA3 POR     1       5.412   1.602   0.046                          \par 
ATOM     14  HA3 POR     1       6.276   1.093   0.494                          \par 
ATOM     15  HA4 POR     1       5.191   2.479   0.671                          \par 
ATOM     16  CA4 POR     1       5.763   2.047  -1.355                          \par 
ATOM     17  HE4 POR     1       6.630   2.724  -1.321                          \par 
ATOM     18  HE5 POR     1       6.013   1.176  -1.978                          \par 
ATOM     19  HE6 POR     1       4.911   2.577  -1.807                          \par 
ATOM     20  C4A POR     1       2.813   1.083   0.014                          \par 
ATOM     21  CHB POR     1       2.400   2.400   0.000                          \par 
ATOM     22  HHB POR     1       3.167   3.167   0.000                          \par 
ATOM     23  NB  POR     1       0.000   1.965  -0.010                          \par 
ATOM     24  C1B POR     1       1.083   2.813  -0.014                          \par 
ATOM     25  C2B POR     1       0.678   4.210  -0.020                          \par 
ATOM     26  CB1 POR     1       1.602   5.412  -0.046                          \par 
ATOM     27  HB1 POR     1       2.479   5.191  -0.671                          \par 
ATOM     28  HB2 POR     1       1.093   6.276  -0.494                          \par 
ATOM     29  CB2 POR     1       2.047   5.763   1.355                          \par 
ATOM     30  HF1 POR     1       2.724   6.630   1.321                          \par 
ATOM     31  HF2 POR     1       1.176   6.013   1.978                          \par 
ATOM     32  HF3 POR     1       2.577   4.911   1.807                          \par 
ATOM     33  C3B POR     1      -0.678   4.210  -0.020                          \par 
ATOM     34  CB3 POR     1      -1.602   5.412  -0.046                          \par 
ATOM     35  HB3 POR     1      -1.093   6.276  -0.494                          \par 
ATOM     36  HB4 POR     1      -2.479   5.191  -0.671                          \par 
ATOM     37  CB4 POR     1      -2.047   5.763   1.355                          \par 
ATOM     38  HF4 POR     1      -2.724   6.630   1.321                          \par 
ATOM     39  HF5 POR     1      -2.577   4.911   1.807                          \par 
ATOM     40  HF6 POR     1      -1.176   6.013   1.978                          \par 
ATOM     41  C4B POR     1      -1.083   2.813  -0.014                          \par 
ATOM     42  CHC POR     1      -2.400   2.400   0.000                          \par 
ATOM     43  HHC POR     1      -3.167   3.167   0.000                          \par 
ATOM     44  NC  POR     1      -1.965   0.000   0.010                          \par 
ATOM     45  C1C POR     1      -2.813   1.083   0.014                          \par 
ATOM     46  C2C POR     1      -4.210   0.678   0.020                          \par 
ATOM     47  CC1 POR     1      -5.412   1.602   0.046                          \par 
ATOM     48  HC1 POR     1      -5.191   2.479   0.671                          \par 
ATOM     49  HC2 POR     1      -6.276   1.093   0.494                          \par 
ATOM     50  CC2 POR     1      -5.763   2.047  -1.355                          \par 
ATOM     51  HG1 POR     1      -6.630   2.724  -1.321                          \par 
ATOM     52  HG2 POR     1      -4.911   2.577  -1.807                          \par 
ATOM     53  HG3 POR     1      -6.013   1.176  -1.978                          \par 
ATOM     54  C3C POR     1      -4.210  -0.678   0.020                          \par 
ATOM     55  CC3 POR     1      -5.412  -1.602   0.046                          \par 
ATOM     56  HC3 POR     1      -6.276  -1.093   0.494                          \par 
ATOM     57  HC4 POR     1      -5.191  -2.479   0.671                          \par 
ATOM     58  CC4 POR     1      -5.763  -2.047  -1.355                          \par 
ATOM     59  HG4 POR     1      -6.630  -2.724  -1.321                          \par 
ATOM     60  HG5 POR     1      -6.013  -1.176  -1.978                          \par 
ATOM     61  HG6 POR     1      -4.911  -2.577  -1.807                          \par 
ATOM     62  C4C POR     1      -2.813  -1.083   0.014                          \par 
ATOM     63  CHD POR     1      -2.400  -2.400   0.000                          \par 
ATOM     64  HHD POR     1      -3.167  -3.167   0.000                          \par 
ATOM     65  ND  POR     1       0.000  -1.965  -0.010                          \par 
ATOM     66  C1D POR     1      -1.083  -2.813  -0.014                          \par 
ATOM     67  C2D POR     1      -0.678  -4.210  -0.020                          \par 
ATOM     68  CD1 POR     1      -1.602  -5.412  -0.046                          \par 
ATOM     69  HD1 POR     1      -2.479  -5.191  -0.671                          \par 
ATOM     70  HD2 POR     1      -1.093  -6.276  -0.494                          \par 
ATOM     71  CD2 POR     1      -2.047  -5.763   1.355                          \par 
ATOM     72  HJ1 POR     1      -2.724  -6.630   1.321                          \par 
ATOM     73  HJ2 POR     1      -1.176  -6.013   1.978                          \par 
ATOM     74  HJ3 POR     1      -2.577  -4.911   1.807                          \par 
ATOM     75  C3D POR     1       0.678  -4.210  -0.020                          \par 
ATOM     76  CD3 POR     1       1.602  -5.412  -0.046                          \par 
ATOM     77  HD3 POR     1       1.093  -6.276  -0.494                          \par 
ATOM     78  HD4 POR     1       2.479  -5.191  -0.671                          \par 
ATOM     79  CD4 POR     1       2.047  -5.763   1.355                          \par 
ATOM     80  HJ4 POR     1       2.724  -6.630   1.321                          \par 
ATOM     81  HJ5 POR     1       2.577  -4.911   1.807                          \par 
ATOM     82  HJ6 POR     1       1.176  -6.013   1.978                          \par 
ATOM     83  C4D POR     1       1.083  -2.813  -0.014                          \par 
ATOM     84  CHA POR     1       2.400  -2.400   0.000                          \par 
ATOM     85  HHA POR     1       3.167  -3.167   0.000                          \par 
}\pard \par 
\pard {\v {\tc\tcl2\pard\plain \f20 {\b Nickel porphine PDB File}}}{\b \par 
}\pard \par 
\pard {\f22\fs18 HEADER  Symmetric coordinates Nipor  Jason's\par 
ATOM      1 NI   POR     1       0.000   0.000   0.000                          \par 
ATOM      2  NB  POR     1       0.000   1.974   0.000                          \par 
ATOM      3  C1B POR     1       1.099   2.821   0.000                          \par 
ATOM      4  C2B POR     1       0.675   4.202   0.000                          \par 
ATOM      5  CHB POR     1       2.435   2.435   0.000                          \par 
ATOM      6  HB2 POR     1       1.319   5.070   0.000                          \par 
ATOM      7  HHB POR     1       3.199   3.199   0.000                          \par 
ATOM      8  NA  POR     1       1.974   0.000   0.000                          \par 
ATOM      9  ND  POR     1       0.000  -1.974   0.000                          \par 
ATOM     10  NC  POR     1      -1.974   0.000   0.000                          \par 
ATOM     11  C4A POR     1       2.821   1.099   0.000                          \par 
ATOM     12  C1A POR     1       2.821  -1.099   0.000                          \par 
ATOM     13  C4D POR     1       1.099  -2.821   0.000                          \par 
ATOM     14  C1D POR     1      -1.099  -2.821   0.000                          \par 
ATOM     15  C4C POR     1      -2.821  -1.099   0.000                          \par 
ATOM     16  C1C POR     1      -2.821   1.099   0.000                          \par 
ATOM     17  C4B POR     1      -1.099   2.821   0.000                          \par 
ATOM     18  C3A POR     1       4.202   0.675   0.000                          \par 
ATOM     19  C2A POR     1       4.202  -0.675   0.000                          \par 
ATOM     20  C3D POR     1       0.675  -4.202   0.000                          \par 
ATOM     21  C2D POR     1      -0.675  -4.202   0.000                          \par 
ATOM     22  C3C POR     1      -4.202  -0.675   0.000                          \par 
ATOM     23  C2C POR     1      -4.202   0.675   0.000                          \par 
ATOM     24  C3B POR     1      -0.675   4.202   0.000                          \par 
ATOM     25  CHA POR     1       2.435  -2.435   0.000                          \par 
ATOM     26  CHD POR     1      -2.435  -2.435   0.000                          \par 
ATOM     27  CHC POR     1      -2.435   2.435   0.000                          \par 
ATOM     28  HA3 POR     1       5.070   1.319   0.000                          \par 
ATOM     29  HA2 POR     1       5.070  -1.319   0.000                          \par 
ATOM     30  HD3 POR     1       1.319  -5.070   0.000                          \par 
ATOM     31  HD2 POR     1      -1.319  -5.070   0.000                          \par 
ATOM     32  HC3 POR     1      -5.070  -1.319   0.000                          \par 
ATOM     33  HC2 POR     1      -5.070   1.319   0.000                          \par 
ATOM     34  HB3 POR     1      -1.319   5.070   0.000                          \par 
ATOM     35  HHA POR     1       3.199  -3.199   0.000                          \par 
ATOM     36  HHD POR     1      -3.199  -3.199   0.000                          \par 
ATOM     37  HHC POR     1      -3.199   3.199   0.000                          \par 
}\pard \par 
\pard \qc \page {\v\fs28 {\tc\tcl1\pard\plain \qc \f20 {\b\fs28 Appendix C\: Scale}}}{\b\fs28 \par 
}\pard \par 
\pard {\v c2.}{\b Relative Scale Factors for Improper Torsions\par 
}\pard \par 
\pard \qc {{\pict\macpict\picw311\pich139 
01da00000000008b01371101a10064000c574f524400000000008b013701000a00000000008b013770001e00330011008a013600330048008a0011008a010300330136003300480700030003220081002c69dc220039004e452422005d009445bf070001000120003a004e001d00d907000700070900000000000000002200
3200764000070001000109ffffffffffffffff20001c00da0080002c60001900a1003700b7ffa6ffa6a10096000c0100000001000000000000002c000900170653796d626f6c0300170d000c2e0004000000002b99390166a00097a000aa61001000cd002a00e7009c003022002300da003ba000ada10096000c0100000001
000000000000002c000800140554696d65730300142b4b12017aa00097a100b600040001000422006000954600a100b60004000100010700000000230000070001000160004600a1007a00c30000005aa10096000c01000000010000000000000003001728005400c30171a00097a10096000c010000000100000000000000
03001428008400230141a00097a10096000c01000000010000000000000028004100440142a00097a10096000c0100000001000000000000002b502b0143a00097a10096000c01000000010000000000000028002000df0144a00097ff}}\par 
\pard \par 
\pard \qc V{\fs20\dn4 dih} = \|f(1,2)Vn(1+cos(n{\f23\fs20 f-g}))\par 
\pard The above set  of atoms A-C-D-B is associated with an improper torsion hinged about the bond\line  C-D.  The relative scaling factor between Vn/2 choosen for different  hinge atoms is given by the following ratios:\par 
\pard \qc  V{\fs20\dn4 dih}' = Vn/2'(1+cos(n{\f23\fs20 f}'{\f23\fs20 -g})) = V{\fs20\dn4 dih} =Vn/2(1+cos(n{\f23\fs20 f-g}))\par 
or\par 
\pard \qc Vn/2 = Vn/2' \|f((1+cos(n{\f23\fs20 f}'{\f23\fs20 -g})),(1+cos(n{\f23\fs20 f-g})))\par 
\pard \par 
\pard The relative scaling factor between Spiro's wagging force constants defined in terms of {\f23\fs20 q} and the Amber torsion constants defined in terms of {\f23\fs20 f} are given by the following ratios:\par 
\pard \qc   V{\fs20\dn4 dih} = Vn/2(1+cos(n{\f23\fs20 f-g})) = V{\fs20\dn4 pln} = \|f(1,2) k{\f23\fs18\dn4 q} {\f23\fs20 q}{\f23\fs18\up6 2\par 
}\pard \qc    or \par 
\pard \qc Vn/2 = k{\f23\fs18\dn4 q} \|f({\f23\fs20 q}{\f23\fs18\up6 2},2(1+cos(n{\f23\fs20 f-g})))\par 
\pard The relative scaling factor between Karplus force constants defined in terms of {\f23\fs20 f} and the Amber torsion constants defined in terms of {\f23\fs20 f} are given by the following ratios:\par 
\pard \qc   V{\fs20\dn4 dih} = Vn/2(1+cos(n{\f23\fs20 f-g})) = V{\fs20\dn4 ang} = \|f(1,2) k{\f23\fs18\dn4 f} {\f23\fs20 f}{\f23\fs18\up6 2\par 
}\pard \qc    or \par 
\pard \qc Vn/2 = k{\f23\fs18\dn4 f} \|f({\f23\fs20 f}{\f23\fs18\up6 2},2(1+cos(n{\f23\fs20 f-g})))\par 
\pard Since k{\f23\fs18\dn4 f }={\f23\fs18\dn4  }d{\fs20\up6 2}V{\fs20\dn4 dih}/d{\f23\fs20 f}{\fs20\up6 2} = n{\fs20\up6 2} Vn/2; emplies   Vn/2 = \|f(k{\f23\fs18\dn4 f},n{\fs20\up6 2})  or a factor of .25 for n=2.\par 
\pard \par 
\pard The following program used as input the pdb coordinates of heme, and a set of integers contained in namelist start in file cntrl defining respectively the four atoms of the i
mproper torsion (A,B,C,D), the atom which is wagging (D) and the atom to which the wagging atom is attached(C).\par 
\pard \page \par 
{\v c2.}{\b Resultes from  dihtest2\par 
}\pard \par 
  dihtest2 -c cntrl < pdbout\par 
\pard {\f22\fs18   $start\par 
 nstep\tab =             3\par 
 step\tab =  0.1000000\par 
 norder\tab =             2\par 
 gamma\tab =  180.0000\par 
 rk\tab =  100.0000\par 
 vn2\tab =  25.00000\par 
 $end\par 
    1 Ni pucker          =   11    1    2   29    1    2\par 
    2 Ni wag             =    3    1    2    8    1    2\par 
    3 Ni wag             =    1    3    8    2    1    2\par 
    4 Ni wag             =    8    3    1    2    1    2\par 
    5 Cz wag             =    3    4    5    6    5    4\par 
    6 Cz wag             =    4    3    6    5    5    4\par 
    7 Cz wag             =    4    3    5    6    5    4\par 
    8 Hm wag             =    3   36   37   35   37   36\par 
    9 Hm wag             =   36    3   35   37   37   36\par 
   10 Hm wag             =   36    3   37   35   37   36\par 
   11 Hm wag             =   37    3   36   35   37   36\par 
   12 Cm pucker          =    3   36   37   35   36   37\par 
   13 Cm pucker          =   36    3   35   37   36   37\par 
   14 Cm pucker          =   36    3   37   35   36   37\par 
   15 Ca pucker          =    3    2    4   36    2   36\par 
   16 Ca pucker          =    3   36    4    2    2   36\par 
   17 Ca pucker          =    3   36    2    4    2   36\par 
   18 Ca pucker          =   36    2    3    4    2   36\par 
   19 Ca pucker          =   36    2    4    3    2   36\par 
   20 Ca pucker          =    3    2   36    4    2   36\par 
     ................. CB3 .......... CB2 .............    \par 
     .                                                .    \par 
     .                                                .    \par 
     .                     C3B    C2B                 .    \par 
     .                                                .    \par 
     .          HHC                          HHB      .    \par 
     .                    C4B      C1B                .    \par 
     .              CHC                  CHB          .    \par 
     .                         NB                     .    \par 
      CC2                                              CA3 \par 
     .            C1C                      C4A        .    \par 
     .     C2C                                    C3A .    \par 
     .                                                .    \par 
     .                NC      NI       NA             .    \par 
     .     C3C                                    C2A .    \par 
     .            C4C                      C1A        .    \par 
      CC3                                              CA2 \par 
     .                         ND                     .    \par 
     .              CHD                  CHA          .    \par 
     .                    C1D      C4D                .    \par 
     .          HHD                          HHA      .    \par 
     .                                                .    \par 
     .                     C2D    C3D                 .    \par 
     .                                                .    \par 
     .                                                .    \par 
     ................. CD2 .......... CD3 .............    \par 
   1=NI     2= NA    3= C1A   4= C2A   5= CA2\par 
   6= C3A   7= CA3   8= C4A   9= CHB  10= HHB\par 
  11= NB   12= C1B  13= C2B  14= CB2  15= C3B\par 
  16= CB3  17= C4B  18= CHC  19= HHC  20= NC \par 
  21= C1C  22= C2C  23= CC2  24= C3C  25= CC3\par 
  26= C4C  27= CHD  28= HHD  29= ND   30= C1D\par 
  31= C2D  32= CD2  33= C3D  34= CD3  35= C4D\par 
  36= CHA  37= HHA\par 
\par 
 V dih = 2*(1+cos(n*ang-gamma))\par 
 V pln=  (angle to plane)**2\par 
 V ang=  ang**2\par 
 Use the V dih to tell relative strenghts\par 
 Use the ang/dih to tell strenghts of karplus\par 
 Use the pln/dih to tell strenghts of spiro\par 
\par 
# NB -NI  - NA - ND  with NI  === Ni pucker           ratios\par 
#   z     angle    anglep     V dih     V pln     V ang Vpln/Vdih Vang/Vih\par 
 0.00     0.000     0.000    0.0000    0.0000    0.0000   -1.0000   -1.0000\par 
 0.10     5.828     2.918    0.0412    0.0026    0.0103    0.0629    0.2509\par 
 0.20    11.581     5.820    0.1612    0.0103    0.0409    0.0640    0.2534\par 
\par 
# C1A-NI  - NA - C4A with NI  === Ni wag              ratios\par 
#   z     angle    anglep     V dih     V pln     V ang Vpln/Vdih Vang/Vih\par 
 0.00     0.000     0.000    0.0000    0.0000    0.0000   -1.0000   -1.0000\par 
 0.10     4.556     2.918    0.0252    0.0026    0.0063    0.1028    0.2505\par 
 0.20     9.062     5.820    0.0992    0.0103    0.0250    0.1040    0.2521\par 
\par 
#NI  - C1A- C4A- NA  with NI  === Ni wag              ratios\par 
#   z     angle    anglep     V dih     V pln     V ang Vpln/Vdih Vang/Vih\par 
 0.00     0.000     0.000    0.0000    0.0000    0.0000   -1.0000   -1.0000\par 
 0.10     2.036     2.918    0.0050    0.0026    0.0013    0.5137    0.2501\par 
 0.20     4.067     5.820    0.0201    0.0103    0.0050    0.5130    0.2504\par 
\par 
# C4A- C1A-NI  - NA  with NI  === Ni wag              ratios\par 
#   z     angle    anglep     V dih     V pln     V ang Vpln/Vdih Vang/Vih\par 
 0.00     0.000     0.000    0.0000    0.0000    0.0000   -1.0000   -1.0000\par 
 0.10     2.442     2.918    0.0073    0.0026    0.0018    0.3570    0.2501\par 
 0.20     4.858     5.820    0.0287    0.0103    0.0072    0.3597    0.2506\par 
\par 
# C1A- C2A- CA2- C3A with  CA2=== Cz wag              ratios\par 
#   z     angle    anglep     V dih     V pln     V ang Vpln/Vdih Vang/Vih\par 
 0.00     0.000     0.000    0.0000    0.0000    0.0000   -1.0000   -1.0000\par 
 0.10     5.665     3.811    0.0390    0.0044    0.0098    0.1136    0.2508\par 
 0.20    11.228     7.589    0.1516    0.0175    0.0384    0.1157    0.2532\par 
\par 
# C2A- C1A- C3A- CA2 with  CA2=== Cz wag              ratios\par 
#   z     angle    anglep     V dih     V pln     V ang Vpln/Vdih Vang/Vih\par 
 0.00     0.028     0.000    0.0000    0.0000    0.0000    0.0000    0.2500\par 
 0.10     2.454     3.811    0.0073    0.0044    0.0018    0.6033    0.2502\par 
 0.20     4.899     7.589    0.0292    0.0175    0.0073    0.6013    0.2506\par 
\par 
# C2A- C1A- CA2- C3A with  CA2=== Cz wag              ratios\par 
#   z     angle    anglep     V dih     V pln     V ang Vpln/Vdih Vang/Vih\par 
 0.00     0.000     0.000    0.0000    0.0000    0.0000   -1.0000   -1.0000\par 
 0.10     3.094     3.811    0.0117    0.0044    0.0029    0.3798    0.2502\par 
 0.20     6.130     7.589    0.0456    0.0175    0.0114    0.3847    0.2510\par 
\par 
# C1A- CHA- HHA- C4D with  HHA=== Hm wag              ratios\par 
#   z     angle    anglep     V dih     V pln     V ang Vpln/Vdih Vang/Vih\par 
 0.00     0.000     0.000    0.0000    0.0000    0.0000   -1.0000   -1.0000\par 
 0.10     5.527     5.247    0.0371    0.0084    0.0093    0.2260    0.2508\par 
 0.20    10.893    10.407    0.1429    0.0330    0.0361    0.2309    0.2530\par 
\par 
# CHA- C1A- C4D- HHA with  HHA=== Hm wag              ratios\par 
#   z     angle    anglep     V dih     V pln     V ang Vpln/Vdih Vang/Vih\par 
 0.00     0.000     0.000    0.0000    0.0000    0.0000   -1.0000   -1.0000\par 
 0.10     3.304     5.247    0.0133    0.0084    0.0033    0.6313    0.2503\par 
 0.20     6.585    10.407    0.0526    0.0330    0.0132    0.6271    0.2511\par 
\par 
# CHA- C1A- HHA- C4D with  HHA=== Hm wag              ratios\par 
#   z     angle    anglep     V dih     V pln     V ang Vpln/Vdih Vang/Vih\par 
 0.00     0.000     0.000    0.0000    0.0000    0.0000   -1.0000   -1.0000\par 
 0.10     3.378     5.247    0.0139    0.0084    0.0035    0.6039    0.2503\par 
 0.20     6.650    10.407    0.0536    0.0330    0.0135    0.6150    0.2511\par 
\par 
# HHA- C1A- CHA- C4D with  HHA=== Hm wag              ratios\par 
#   z     angle    anglep     V dih     V pln     V ang Vpln/Vdih Vang/Vih\par 
 0.00     0.000     0.000    0.0000    0.0000    0.0000   -1.0000   -1.0000\par 
 0.10     5.928     5.247    0.0427    0.0084    0.0107    0.1965    0.2509\par 
 0.20    11.732    10.407    0.1654    0.0330    0.0419    0.1995    0.2535\par 
\par 
# C1A- CHA- HHA- C4D with  CHA=== Cm pucker           ratios\par 
#   z     angle    anglep     V dih     V pln     V ang Vpln/Vdih Vang/Vih\par 
 0.00     0.000     0.000    0.0000    0.0000    0.0000   -1.0000   -1.0000\par 
 0.10    14.809     5.247    0.2613    0.0084    0.0668    0.0321    0.2556\par 
 0.20    28.795    10.407    0.9281    0.0330    0.2526    0.0355    0.2722\par 
\par 
# CHA- C1A- C4D- HHA with  CHA=== Cm pucker           ratios\par 
#   z     angle    anglep     V dih     V pln     V ang Vpln/Vdih Vang/Vih\par 
 0.00     0.000     0.000    0.0000    0.0000    0.0000   -1.0000   -1.0000\par 
 0.10     8.834     5.247    0.0943    0.0084    0.0238    0.0889    0.2520\par 
 0.20    17.266    10.407    0.3524    0.0330    0.0908    0.0936    0.2577\par 
\par 
# CHA- C1A- HHA- C4D with  CHA=== Cm pucker           ratios\par 
#   z     angle    anglep     V dih     V pln     V ang Vpln/Vdih Vang/Vih\par 
 0.00     0.000     0.000    0.0000    0.0000    0.0000   -1.0000   -1.0000\par 
 0.10     9.067     5.247    0.0993    0.0084    0.0250    0.0844    0.2521\par 
 0.20    17.701    10.407    0.3698    0.0330    0.0954    0.0892    0.2581\par 
\par 
# C1A- NA - C2A- CHA with  NA === Ca pucker           ratios\par 
#   z     angle    anglep     V dih     V pln     V ang Vpln/Vdih Vang/Vih\par 
 0.00     0.028     0.000    0.0000    0.0000    0.0000    0.0000    0.2500\par 
 0.10     2.334     2.341    0.0066    0.0017    0.0017    0.2516    0.2501\par 
 0.20     4.626     4.673    0.0260    0.0067    0.0065    0.2557    0.2505\par 
\par 
# C1A- CHA- C2A- NA  with  NA === Ca pucker           ratios\par 
#   z     angle    anglep     V dih     V pln     V ang Vpln/Vdih Vang/Vih\par 
 0.00     0.000     0.000    0.0000    0.0000    0.0000   -1.0000   -1.0000\par 
 0.10     2.807     2.341    0.0096    0.0017    0.0024    0.1739    0.2502\par 
 0.20     5.601     4.673    0.0381    0.0067    0.0096    0.1746    0.2508\par 
\par 
# C1A- CHA- NA - C2A with  NA === Ca pucker           ratios\par 
#   z     angle    anglep     V dih     V pln     V ang Vpln/Vdih Vang/Vih\par 
 0.00     0.000     0.000    0.0000    0.0000    0.0000   -1.0000   -1.0000\par 
 0.10     2.911     2.341    0.0103    0.0017    0.0026    0.1618    0.2502\par 
 0.20     5.756     4.673    0.0402    0.0067    0.0101    0.1653    0.2508\par 
\par 
# CHA- NA - C1A- C2A with  NA === Ca pucker           ratios\par 
#   z     angle    anglep     V dih     V pln     V ang Vpln/Vdih Vang/Vih\par 
 0.00     0.000     0.000    0.0000    0.0000    0.0000   -1.0000   -1.0000\par 
 0.10     4.487     2.341    0.0245    0.0017    0.0061    0.0682    0.2505\par 
 0.20     8.888     4.673    0.0955    0.0067    0.0241    0.0697    0.2520\par 
\par 
# CHA- NA - C2A- C1A with  NA === Ca pucker           ratios\par 
#   z     angle    anglep     V dih     V pln     V ang Vpln/Vdih Vang/Vih\par 
 0.00     0.000     0.000    0.0000    0.0000    0.0000   -1.0000   -1.0000\par 
 0.10     2.334     2.341    0.0066    0.0017    0.0017    0.2516    0.2501\par 
 0.20     4.626     4.673    0.0260    0.0067    0.0065    0.2557    0.2505\par 
\par 
# C1A- NA - CHA- C2A with  NA === Ca pucker           ratios\par 
#   z     angle    anglep     V dih     V pln     V ang Vpln/Vdih Vang/Vih\par 
 0.00     0.020     0.000    0.0000    0.0000    0.0000    0.0000    0.2499\par 
 0.10     2.911     2.341    0.0103    0.0017    0.0026    0.1618    0.2502\par 
 0.20     5.756     4.673    0.0402    0.0067    0.0101    0.1653    0.2508\par 
}\pard \qc {\f22\fs18  }\page {\v\fs28 {\tc\tcl1\pard\plain \qc \f20 {\b\fs28 Appendix D\: Obs Files}}}{\b\fs28 \par 
}\pard \par 
\pard {\v {\tc\tcl2\pard\plain \f20 {\b Benzene Obs File}}}{\b \par 
}\pard \par 
\pard {\f22\fs18 benzene frequencies taken from the Scherer paper. \par 
Symmetry classification done here,charac added 01/15/97\par 
 13,'???','a1g','a2g','a1u','a2u','b1g','b2g','b1u','b2u','e1g','e1u','e2g','e2u'\par 
\tab none\tab \tab  \par 
 20  1 1  992.0   1.0 \par 
 20  1 2 3062.0   1.0\par 
 30  2 1 1326.0   1.0\par 
 40  4 1  673.0   1.0\par 
 40  6 1  703.0   1.0\par 
 40  6 2  995.0   1.0\par 
 30  7 1 1010.0   1.0\par 
 20  7 2 3068.0   1.0\par 
 0   8 1 1150.0   1.0\par 
 0   8 2 1310.0   0.0 \par 
 40  9 1  849.0   1.0\par 
 40  9 2  849.0   1.0\par 
 20 10 1 1038.0   1.0 \par 
 20 10 2 1038.0   1.0 \par 
 30 10 3 1486.0   1.0\par 
 30 10 4 1486.0   1.0\par 
 20 10 5 3063.0   1.0\par 
 20 10 6 3063.0   1.0\par 
 60 11 1  606.0   1.0\par 
 60 11 2  606.0   1.0\par 
 60 11 3 1178.0   1.0\par 
 60 11 4 1178.0   1.0\par 
 60 11 5 1596.0   1.0 \par 
 60 11 6 1596.0   1.0 \par 
 20 11 7 3047.0   1.0\par 
 20 11 8 3047.0   1.0\par 
 40 12 1  410.0   1.0\par 
 40 12 2  410.0   1.0\par 
 40 12 3  975.0   1.0\par 
 40 12 4  975.0   1.0\par 
200  0 1 1596.0   0.0\par 
300  0 2 1486.0   0.0\par 
400  0 3  995.0   0.0\par 
}\pard \par 
\pard {\v {\tc\tcl2\pard\plain \f20 {\b Ethyl Benzene Obs File}}}{\b \par 
}\pard \par 
\pard {\f22\fs18  Ethylbenzene (Cs sym) with the methyl group version 0\par 
 new file taken from ref# \par 
 3 "???" "a1 " "a2 "\par 
\tab none\tab \tab  \par 
200 0 1\tab 1712.0  0.0\par 
300 0 2 1530.0  0.0\par 
400 0 3  982.0  0.0\par 
  0 1 1  152.0  1.0\par 
  0 1 2  308.0  1.0\par 
  0 1 3  493.0  1.0\par 
  0 1 4  557.0  1.0\par 
  0 1 5  700.0  1.0\par 
  0 1 6  749.0  1.0\par 
  0 1 7  771.0  1.0\par 
  0 1 8  903.0  1.0\par 
  0 1 9  962.0  1.0\par 
 40 1 10 990.0  1.0\par 
 60 1 11 1005.0 1.0\par 
 60 1 12 1021.0 1.0\par 
 60 1 13 1065.0 1.0\par 
 60 1 14 1183.0 1.0\par 
 60 1 15 1207.0 1.0\par 
 60 1 16 1321.0 1.0\par 
 60 1 17 1378.0 1.0\par 
 60 1 18 1455.0 1.0\par 
 60 1 19 1467.0 1.0\par 
 60 1 20 1500.0 1.0\par 
 60 1 21 1606.0 1.0\par 
 60 1 22 2900.0 0.0\par 
 60 1 23 2949.0 0.0\par 
 60 1 24 3055.0 0.0\par 
 60 1 25 3056.0 0.0\par 
 60 1 26 3056.0 0.0\par 
 60 1 27 3057.0 0.0\par 
  0 2 1  45.0   0.3\par 
  0 2 2  190.0  0.3\par 
  0 2 3  360.0  1.0\par 
  0 2 4  415.0  1.0\par 
  0 2 5  618.0  1.0\par 
  0 2 6  787.0  1.0\par 
  0 2 7  856.0  1.0\par 
 40 2 8  975.0  0.5\par 
 60 2 9  1033.0 1.0\par 
 60 2 10 1098.0 1.0\par 
 60 2 11 1157.0 1.0\par 
 60 2 12 1245.0 1.0\par 
 60 2 13 1300.0 1.0\par 
 60 2 14 1332.0 1.0\par 
 60 2 15 1453.0 0.1\par 
 60 2 16 1459.0 0.1\par 
 60 2 17 1589.0 0.1\par 
 60 2 18 2951.0 0.0\par 
 60 2 19 3055.0 0.0\par 
 60 2 20 3055.0 0.0\par 
 60 2 21 3055.0 0.0\par 
}\pard \par 
\pard {\v {\tc\tcl2\pard\plain \f20 {\b Nickel Octa Ethyl Porphine Obs File}}}{\b \par 
}\pard \par 
\pard {\f22\fs18  nioepun with non-united methyl atoms, freq ordering changed\par 
 modified obsfull20\par 
 6 "???" "a1 "  "a2 "  "b1 "  "b2 "  "e  "\par 
           none            N15          Meso D\par 
   40     1     1    30.0  0.00     1    30.0  0.50     1    30.0  0.50\par 
   90     1     2   127.0  1.00     2   127.0  1.00     2   127.0  1.00\par 
   40     1     3   139.0  0.00     3   139.0  0.00     3   139.0  0.00\par 
    0     1     4   200.0  0.00     4   200.0  0.00     4   200.0  0.00\par 
   60     1     5   263.0  0.01     5   261.0  0.01     5   262.0  0.01\par 
    0     1     6   270.0  0.50     6   268.0  0.50     6   270.0  0.50\par 
   60     1     7   360.0  0.01     7   358.0  0.01     7   353.0  0.01\par 
   60     1     8   477.0  0.50     8   475.0  0.50     8   477.0  0.50\par 
   60     1     9   674.0  1.00     9   671.0  1.00     9   663.0  1.00\par 
   40     1    11   704.0  1.00    11   700.0  1.00    11   704.0  1.00\par 
   60     1    10   770.0  1.00    10   769.0  1.00    10   776.0  1.00\par 
   60     1    12   804.0  1.00    12   799.0  1.00    12   799.0  1.00\par 
    0     1    13   927.0  0.00    13   927.0  0.00    13   927.0  0.00\par 
   60     1    14   979.0  0.00    14   979.0  0.00    14   979.0  0.00\par 
   60     1    15  1024.0 10.00    15  1021.0  1.00    15  1024.0  1.00\par 
   60     1    16  1138.0  1.00    16  1131.0  1.00    16  1138.0  1.00\par 
   60     1    17  1258.0  1.00    17  1257.0  1.00    17  1258.0  1.00\par 
   60     1    18  1316.0  1.00    18  1316.0  1.00    18  1316.0  1.00\par 
   60     1    19  1378.0  0.00    19  1378.0  0.00    19  1378.0  0.00\par 
   60     1    20  1383.0  1.00    20  1376.0  1.00    20  1382.0  1.00\par 
    0     1    21  1400.0  0.00    21  1400.0  0.00    21  1400.0  0.00\par 
   60     1    22  1464.0  1.00    22  1464.0  1.00    22  1464.0  1.00\par 
   60     1    23  1520.0  1.00    23  1519.0  1.00    23  1512.0  1.00\par 
   60     1    24  1602.0  1.00    24  1601.0  1.00    24  1601.0  1.00\par 
   60     1    27  2941.0  0.00    27  2941.0  0.00    27  2941.0  0.00\par 
   60     1    28  2941.0  0.00    28  2941.0  0.00    28  2941.0  0.00\par 
   60     1    31  3041.0  0.50    31  3041.0  0.50    31  2263.0  0.50\par 
   40     2     1    44.0  0.00     1    44.0  0.00     1    43.0  0.00\par 
   40     2     2    60.0  0.00     2    60.0  0.00     2    60.0  0.00\par 
   90     2     3   130.0  0.00     3   130.0  0.00     3   125.0  0.50\par 
    0     2     4   200.0  0.00     4   200.0  0.00     4   200.0  0.00\par 
   60     2     5   243.0  0.00     5   243.0  0.00     5   243.0  0.00\par 
   60     2     6   392.0  0.01     6   392.0  0.01     6   392.0  0.01\par 
   60     2     7   551.0  1.00     7   551.0  1.00     7   545.0  1.00\par 
   60     2     9   597.0  0.50     9   594.0  0.50     9   582.0  0.50\par 
   40     2     8   612.0 25.00     8   612.0 25.00     8   652.0 25.00\par 
   40     2    10   732.0  0.25    10   732.0  0.25    10   790.0  0.25\par 
   60     2    11   842.0  0.00    11   842.0  0.00    11   842.0  0.00\par 
   40     2    12   853.0  0.04    12   853.0  0.04    12   501.0  0.04\par 
    0     2    13   931.0  0.00    13   931.0  0.00    13   931.0  0.00\par 
    0     2    14   957.0  0.00    14   957.0  0.00    14   957.0  0.00\par 
   60     2    15  1014.0  0.00    15  1014.0  0.00    15  1016.0  0.10\par 
   60     2    16  1058.0  1.00    16  1058.0  1.00    16  1058.0  1.00\par 
   60     2    17  1121.0  1.00    17  1106.0  1.00    17  1202.0  1.00\par 
   60     2    18  1252.0  1.00    18  1252.0  1.00    18  1260.0  1.00\par 
   60     2    19  1307.0  0.50    19  1303.0  0.50    19   887.0  0.50\par 
   60     2    20  1351.0  0.00    20  1351.0  0.00    20  1309.0  0.50\par 
   60     2    21  1374.0  0.50    21  1351.0  0.50    21  1309.0  0.50\par 
   60     2    22  1393.0  1.00    22  1393.0  1.00    22  1393.0  1.00\par 
    0     2    23  1410.0  0.00    23  1410.0  0.00    23  1410.0  0.00\par 
   60     2    24  1462.0  1.00    24  1462.0  1.00    24  1461.0  1.00\par 
    0     2    25  1562.0  0.00    25  1562.0  0.00    25  1562.0  0.00\par 
   60     2    26  1603.0  1.00    26  1602.0  1.00    26  1602.0  1.00\par 
   60     2    29  2941.0  0.00    29  2941.0  0.00    29  2965.0  0.00\par 
   60     2    31  2941.0  0.00    31  2941.0  0.00    31  2941.0  0.00\par 
   40     3     1    74.0  0.00     1    74.0  0.00     1    74.0  0.00\par 
   40     3     2    60.0  0.00     2    60.0  0.00     2    60.0  0.00\par 
   40     3     3   144.0  0.50     3   144.0  0.50     3   141.0  0.50\par 
   60     3     4   197.0  0.50     4   197.0  0.50     4   197.0  0.50\par 
    0     3     5   250.0  0.00     5   250.0  0.00     5   250.0  0.00\par 
   60     3     6   445.0  5.00     6   445.0  1.00     6   445.0  1.00\par 
   40     3     7   346.0  0.00     7   346.0  0.00     7   346.0  0.50\par 
   60     3     8   493.0  1.00     8   492.0  1.00     8   490.0  1.00\par 
   60     3     9   657.0  0.00     9   657.0  0.00     9   657.0  1.00\par 
   60     3    11   938.0  0.50    11   938.0  0.50    11   934.0  0.50\par 
   90     3    10   750.0  1.00    10   750.0  1.00    10   750.0  1.00\par 
    0     3    12   910.0  0.00    12   910.0  0.00    12   910.0  0.00\par 
   60     3    13  1015.0  1.00    13  1006.0  1.00    13  1003.0  1.00\par 
   60     3    14  1024.0  0.00    14  1021.0  0.00    14  1031.0  0.00\par 
    0     3    15  1100.0  0.00    15  1100.0  0.00    15  1100.0  0.00\par 
   60     3    16  1159.0  1.00    16  1149.0  1.00    16  1159.0  1.00\par 
   60     3    17  1269.0  0.00    17  1269.0  0.00    17  1269.0  0.00\par 
   60     3    18  1350.0  0.00    18  1350.0  0.00    18  1350.0  0.00\par 
    0     3    19  1360.0  0.00    19  1360.0  0.00    19  1360.0  0.00\par 
   60     3    20  1370.0  0.00    20  1370.0  0.00    20  1370.0  0.00\par 
   60     3    21  1407.0  1.00    21  1406.0  1.00    21  1405.0  1.00\par 
   60     3    22  1459.0  0.00    22  1459.0  0.00    22  1459.0  0.00\par 
   60     3    23  1483.0  1.00    23  1480.0  1.00    23  1478.0  1.00\par 
    0     3    24  1583.0  0.00    24  1583.0  0.00    24  1583.0  0.00\par 
   60     3    27  2941.0  0.00    27  2941.0  0.00    27  2941.0  0.00\par 
   60     3    28  2941.0  0.00    28  2941.0  0.00    28  2941.0  0.00\par 
   60     3    30  3041.0  0.50    30  3041.0  0.50    30  2261.0  0.50\par 
   40     4     1    32.0  0.00     1    32.0  0.00     1    32.0  0.00\par 
   40     4     2    90.0  0.00     2    90.0  0.00     2    90.0  0.00\par 
   60     4     3   168.0  1.00     3   168.0  1.00     3   168.0  1.00\par 
   90     4     4   108.0  0.00     4   108.0  0.00     4   107.0  0.50\par 
    0     4     5   200.0  0.00     5   200.0  0.00     5   200.0  0.00\par 
   46     4     6   284.0  1.00     6   284.0  1.00     6   277.0  1.00\par 
   60     4     7   305.0  1.00     7   305.0  1.00     7   305.0  1.00\par 
   40     4     8   360.0 25.00     8   355.0 25.00     8   337.0 25.00\par 
   60     4     9   525.0 10.00     9   525.0  1.00     9   525.0  1.00\par 
   60     4    10   740.0  0.01    10   740.0  0.01    10   762.0  0.01\par 
   60     4    11   751.0  0.10    11   748.0  0.10    11   683.0  0.10\par 
   40     4    12   739.0  4.00    12   733.0  4.00    12   760.0  4.00\par 
   60     4    14   781.0  1.00    14   781.0  1.00    14   781.0  1.00\par 
   40     4    13   844.0  4.00    13   844.0  4.00    13   681.0  4.00\par 
    0     4    15   900.0  0.00    15   900.0  0.00    15   900.0  0.00\par 
   60     4    17  1023.0 10.00    17  1021.0  1.00    17  1021.0  1.00\par 
   60     4    18  1131.0  1.00    18  1119.0  1.00    18  1186.0  1.00\par 
   60     4    19  1220.0  1.00    19  1218.0  1.00    19   948.0  1.00\par 
   60     4    20  1276.0  1.00    20  1276.0  1.00    20  1270.0  1.00\par 
   60     4    21  1312.0  1.00    21  1312.0  1.00    21  1312.0  1.00\par 
   60     4    22  1330.0  0.00    22  1330.0  0.00    22  1331.0  0.10\par 
    0     4    23  1340.0  0.00    23  1340.0  0.00    23  1331.0  0.00\par 
    0     4    24  1380.0  0.00    24  1380.0  0.00    24  1380.0  0.00\par 
   60     4    25  1463.0  1.00    25  1463.0  1.00    25  1463.0  1.00\par 
   60     4    26  1463.0  0.00    26  1463.0  0.00    26  1463.0  0.00\par 
   60     4    27  1577.0  1.00    27  1576.0  1.00    27  1576.0  1.00\par 
   60     4    28  1655.0  1.00    28  1655.0  1.00    28  1645.0  1.00\par 
    0     4    29  2941.0  0.00    29  2941.0  0.00    29  2941.0  0.00\par 
    0     4    30  2941.0  0.00    30  2941.0  0.00    30  2941.0  0.00\par 
    0     4    31  2941.0  0.00    31  2941.0  0.00    31  2941.0  0.00\par 
   60     4    32  2941.0  0.00    32  2941.0  0.00    32  2941.0  0.00\par 
   60     4    33  2941.0  0.00    33  2941.0  0.00    33  2941.0  0.00\par 
   40     5     2    63.0  0.00     2    63.0  0.00     2    63.0  0.00\par 
    0     5     4    60.0  0.00     4    60.0  0.00     4    60.0  0.00\par 
    0     5     6    60.0  0.00     6    60.0  0.00     6    60.0  0.00\par 
   60     5     8    90.0  0.10     8    90.0  0.10     8    90.0  0.10\par 
   90     5    10    91.0  0.00    10    90.0  0.00    10    91.0  0.00\par 
   40     5    12   200.0  0.00    12   200.0  0.00    12   200.0  0.10\par 
   40     5    14   200.0  0.00    14   200.0  0.00    14   200.0  0.10\par 
    0     5    16   230.0  0.04    16   228.0  0.04    16   227.0  0.04\par 
   40     5    20   254.0  1.00    20   251.0  1.00    20   253.0  1.00\par 
   60     5    18   263.0  1.00    18   261.0  1.00    18   260.0  1.00\par 
   60     5    22   328.0  0.10    22   328.0  0.10    22   322.0  0.10\par 
   60     5    24   358.0  0.10    24   357.0  0.10    24   357.0  0.10\par 
   60     5    26   382.0  0.00    26   382.0  1.00    26   382.0  0.00\par 
   40     5    28   494.0  1.00    28   492.0  1.00    28   483.0  1.00\par 
   60     5    30   544.0  1.00    30   544.0  1.00    30   543.0  1.00\par 
   60     5    32   552.0  1.00    32   549.0  1.00    32   552.0  1.00\par 
   60     5    36   605.0  0.10    36   605.0  0.10    36   600.0  0.10\par 
   40     5    34   656.0  0.04    34   656.0  0.04    34   627.0  0.04\par 
   60     5    38   726.0  0.50    38   722.0  0.50    38   726.0  0.50\par 
   40     5    40   731.0  0.00    40   731.0  0.00    40   712.0  0.50\par 
   60     5    42   754.0  0.50    42   754.0  0.50    42   754.0  0.50\par 
   60     5    46   791.0  0.00    46   786.0  0.10    46   766.0  0.10\par 
   40     5    44   841.0  0.01    44   841.0  0.01    44   773.0  0.01\par 
   60     5    48   927.0  1.00    48   924.0  1.00    48   919.0  1.00\par 
   60     5    50   996.0  0.10    50   991.0  0.10    50   996.0  0.10\par 
    0     5    52   996.0  0.00    52   991.0  0.00    52   996.0  0.00\par 
    0     5    54   996.0  0.00    54   991.0  0.00    54   996.0  0.00\par 
    0     5    56   996.0  0.00    56   991.0  0.00    56   996.0  0.00\par 
    0     5    58   996.0  0.00    58   991.0  0.00    58   996.0  0.00\par 
   60     5    60  1021.0  0.50    60  1021.0  0.50    60  1015.0  0.50\par 
   60     5    62  1021.0  0.50    62  1021.0  0.50    62  1015.0  0.50\par 
   60     5    64  1133.0  1.00    64  1121.0  1.00    64  1151.0  1.00\par 
   60     5    66  1153.0  1.00    66  1145.0  1.00    66  1185.0  1.00\par 
   60     5    68  1231.0  0.10    68  1228.0  0.10    68   948.0  0.10\par 
   60     5    70  1275.0  0.10    70  1275.0  0.10    70  1267.0  0.10\par 
   60     5    72  1307.0  0.00    72  1307.0  0.00    72  1307.0  0.00\par 
   60     5    74  1323.0  0.10    74  1323.0  0.10    74  1322.0  0.10\par 
    0     5    76  1323.0  0.00    76  1323.0  0.00    76  1322.0  0.00\par 
   60     5    78  1346.0  0.00    78  1341.0  0.00    78  1342.0  0.00\par 
    0     5    80  1346.0  0.00    80  1341.0  0.00    80  1342.0  1.00\par 
   60     5    82  1378.0  1.00    82  1378.0  1.00    82  1380.0  0.00\par 
    0     5    84  1378.0  0.00    84  1378.0  0.00    84  1380.0  0.00\par 
   60     5    86  1396.0  1.00    86  1396.0  1.00    86  1392.0  1.00\par 
   60     5    88  1440.0  1.00    88  1440.0  1.00    88  1440.0  1.00\par 
   60     5    90  1456.0  1.00    90  1456.0  1.00    90  1454.0  1.00\par 
    0     5    92  1456.0  0.00    92  1456.0  0.00    92  1454.0  0.00\par 
   60     5    94  1501.0  1.00    94  1501.0  1.00    94  1494.0  1.00\par 
    0     5    96  1501.0  0.00    96  1501.0  0.00    96  1494.0  0.00\par 
    0     5    98  1501.0  0.00    98  1501.0  0.00    98  1494.0  0.00\par 
   60     5   100  1604.0  1.00   100  1604.0  1.00   100  1604.0  1.00\par 
   60     5   102  1637.0  0.00   102  1637.0  0.10   102  1620.0  0.10\par 
   60     5   112  2941.0  0.00   112  2941.0  0.00   112  2941.0  0.00\par 
   60     5   114  2941.0  0.00   114  2941.0  0.00   114  2941.0  0.00\par 
   60     5   116  2941.0  0.00   116  2941.0  0.00   116  2941.0  0.00\par 
   60     5   118  2941.0  0.00   118  2941.0  0.00   118  2941.0  0.00\par 
   60     5   124  3041.0  0.50   124  3041.0  0.50   124  2262.0  0.50\par 
  400     0     3   844.0  4.00     3   844.0  4.00     3   681.0  4.00\par 
}\pard \par 
\pard {\v {\tc\tcl2\pard\plain \f20 {\b Nickel Octa Ethyl Porphine D4h Obs File}}}{\b \par 
}\pard \par 
\pard {\f22\fs18  nipor observed freq weighted shifts no weights no order change 1/31 \par 
 1=mass 2=bond 3= angle 4=dihed 5= maxbond 6=maxangle 7=maxdih\par 
 1=a1g  2=a2g  3=b1g  4=b2g  5=eg 6=a1u  7=a2u  8=b1u  9=b2u 10=eu\par 
           none       Meso D               N15          NI62 \par 
 60  1  1  369.0  1.0  1  367.0 0.0  1   367.0  0.0  1   369.0  0.0   \par 
 60  1  2  732.0  1.0  2  711.0 0.0  2   732.0  0.0  2   732.0  0.0\par 
 60  1  3  995.0  1.0  3  992.0 0.0  3   975.0  0.0  3   995.0  0.0\par 
 60  1  4 1066.0  1.0  4 1065.0 0.0  4  1065.0  0.0  4  1066.0  0.0\par 
 60  1  5 1376.0  1.0  5 1374.0 0.0  5  1374.0  0.0  5  1376.0  0.0\par 
 60  1  6 1459.0  1.0  6 1456.0 0.0  6  1459.0  0.0  6  1459.0  0.0\par 
 60  1  7 1574.0  1.0  7 1566.0 0.0  7  1574.0  0.0  7  1574.0  0.0\par 
 60  1  8 3042.0  1.0  8 2272.0 0.0  8  3042.0  0.0  8  3042.0  0.0\par 
 60  1  9 3097.0  1.0  9 3097.0 0.0  9  3097.0  0.0  9  3097.0  0.0\par 
 60  4  1  197.0  1.0  1  197.0 0.0  1   195.0  0.0  1   197.0  0.0\par 
 60  4  2  435.0  1.0  2  432.0 0.0  2   435.0  0.0  2   435.0  0.0\par 
 60  4  3  819.0  1.0  3  815.0 0.0  3   819.0  0.0  3   819.0  0.0\par 
 60  4  4 1036.0  1.0  4 1020.0 0.0  4  1017.0  0.0  4  1036.0  0.0\par 
 60  4  5 1193.0  1.0  5 1193.0 0.0  5  1193.0  0.0  5  1193.0  0.0\par 
 60  4  6 1368.0  1.0  6 1368.0 0.0  6  1368.0  0.0  6  1368.0  0.0\par 
 60  4  7 1505.0  1.0  7 1477.0 0.0  7  1499.0  0.0  7  1505.0  0.0\par 
 60  4  8 3041.0  1.0  8 2269.0 0.0  8  3041.0  0.0  8  3041.0  0.0\par 
 20  4  9 3088.0  1.0  9 3088.0 0.0  9  3088.0  0.0  9  3088.0  0.0\par 
 60  3  1  237.0  1.0  1  237.0 0.0  1   236.0  0.0  1   237.0  0.0\par 
 60  3  2  732.0  1.0  2  665.0 0.0  2   729.0  0.0  2   732.0  0.0\par 
 60  3  3 1003.0  1.0  3 1020.0 0.0  3   989.0  0.0  3  1003.0  0.0\par 
 60  3  4 1060.0  1.0  4 1066.0 0.0  4  1060.0  0.0  4  1060.0  0.0\par 
 60  3  5 1185.0  1.0  5  938.0 0.0  5  1184.0  0.0  5  1185.0  0.0\par 
 60  3  6 1319.0  1.0  6 1321.0 0.0  6  1308.0  0.0  6  1319.0  0.0\par 
 60  3  7 1505.0  1.0  7 1504.0 0.0  7  1505.0  0.0  7  1505.0  0.0\par 
 60  3  8 1650.0  1.0  8 1642.0 0.0  8  1650.0  0.0  8  1650.0  0.0\par 
 60  3  9 3097.0  1.0  9 3097.0 0.0  9  3097.0  0.0  9  3097.0  0.0\par 
 60  2  1  429.0  1.0  1  419.0 0.0  1   428.0  0.0  1   429.0  0.0\par 
 60  2  2  806.0  1.0  2  783.0 0.0  2   806.0  0.0  2   806.0  0.0\par 
 60  2  3 1005.0  1.0  3 1012.0 0.0  3  1001.0  0.0  3  1005.0  0.0\par 
 60  2  4 1139.0  1.0  4  910.0 0.0  4  1138.0  0.0  4  1139.0  0.0\par 
 60  2  5 1317.0  1.0  5 1249.0 0.0  5  1309.0  0.0  5  1317.0  0.0\par 
 60  2  6 1354.0  1.0  6 1347.0 0.0  6  1353.0  0.0  6  1354.0  0.0\par 
 60  2  7 1611.0  1.0  7 1598.0 0.0  7  1609.0  0.0  7  1611.0  0.0\par 
 60  2  9 3087.0  1.0  8 3087.0 0.0  8  3087.0  0.0  8  3087.0  0.0\par 
 60 10  2  282.0  1.0  2  280.0 0.0  2   282.0  0.0  2   277.2  0.0\par 
 60 10  4  366.0  1.0  4  349.0 0.0  4   363.0  0.0  4   366.0  0.0\par 
 60 10  6  420.0  1.0  6  411.0 0.0  6   418.0  0.0  6   417.8  0.0\par 
 60 10  8  745.0  1.0  8  648.0 0.0  8   744.0  0.0  8   745.0  0.0\par 
 60 10 10  806.0  1.0 10  807.0 0.0 10   805.0  0.0 10   806.0  0.0\par 
 60 10 12  995.0  1.0 12  999.0 0.0 12   975.0  0.0 12   995.0  0.0\par 
 60 10 14 1033.0  1.0 14 1026.0 0.0 14  1020.0  0.0 14  1033.0  0.0\par 
 60 10 16 1064.0  1.0 16 1068.0 0.0 16  1063.0  0.0 16  1064.0  0.0\par 
 60 10 18 1150.0  1.0 18 1261.0 0.0 18  1148.0  0.0 18  1150.0  0.0\par 
 60 10 20 1250.0  1.0 20  910.0 0.0 20  1248.0  0.0 20  1250.0  0.0\par 
 60 10 22 1319.0  1.0 22 1315.0 0.0 22  1309.0  0.0 22  1319.0  0.0\par 
 60 10 24 1385.0  1.0 24 1373.0 0.0 24  1373.0  0.0 24  1385.0  0.0\par 
 60 10 26 1462.0  1.0 26 1458.0 0.0 26  1457.0  0.0 26  1462.0  0.0\par 
 60 10 28 1547.0  1.0 28 1543.0 0.0 28  1546.0  0.0 28  1547.0  0.0\par 
 60 10 30 1624.0  1.0 30 1620.0 0.0 30  1623.0  0.0 30  1624.0  0.0\par 
 60 10 32 3042.0  1.0 32 2270.0 0.0 32  3042.0  0.0 32  3042.0  0.0\par 
 60 10 34 3088.0  1.0 34 3088.0 0.0 34  3088.0  0.0 34  3088.0  0.0\par 
 20 10 36 3097.0  1.0 36 3097.0 0.0 36  3097.0  0.0 36  3097.0  0.0\par 
 40  6  1   74.0  0.0  1   74.0 0.0  1    74.0  0.0  1    74.0  0.0\par 
 40  6  2  346.0  0.0  2  346.0 0.0  2   346.0  0.0  2   346.0  0.0\par 
 40  6  3  750.0  0.0  3  750.0 0.0  3   750.0  0.0  3   750.0  0.0\par 
 40  7  1   32.0  0.0  1   32.0 0.0  1    32.0  0.0  1    31.2  0.0\par 
 40  7  2  108.0  0.0  2  108.0 0.0  2   108.0  0.0  2   106.4  0.0\par 
 40  7  3  284.0  0.0  3  284.0 0.0  3   284.0  0.0  3   283.7  0.0\par 
 40  7  4  360.0  0.0  4  360.0 0.0  4   355.0  0.0  4   359.2  0.0\par 
 40  7  5  739.0  0.0  5  739.0 0.0  5   733.0  0.0  5   739.0  0.0\par 
 40  7  6  844.0  0.0  6  844.0 0.0  6   844.0  0.0  6   844.0  0.0\par 
 40  8  1   44.0  0.0  1   44.0 0.0  1    44.0  0.0  1    44.0  0.0\par 
 40  8  2  130.0  0.0  2  130.0 0.0  2   130.0  0.0  2   130.0  0.0\par 
 40  8  3  612.0  0.0  3  612.0 0.0  3   612.0  0.0  3   612.0  0.0\par 
 40  8  4  732.0  0.0  4  732.0 0.0  4   732.0  0.0  4   732.0  0.0\par 
 40  8  5  853.0  0.0  5  853.0 0.0  5   853.0  0.0  5   853.0  0.0\par 
 40  9  1   30.0  0.0  1   30.0 0.0  1    30.0  0.0  1    30.0  0.0\par 
 40  9  2  127.0  0.0  2  127.0 0.0  2   127.0  0.0  2   127.0  0.0\par 
 40  9  3  270.0  0.0  3  270.0 0.0  3   268.0  0.0  3   270.0  0.0\par 
 40  9  4  704.0  0.0  4  704.0 0.0  4   700.0  0.0  4   704.0  0.0\par 
 40  5  2   63.0  0.0  2   63.0 0.0  2    63.0  0.0  2    63.0  0.0\par 
 40  5  4   91.0  0.0  4   91.0 0.0  4    90.0  0.0  4    91.0  0.0\par 
 40  5  6  230.0  0.0  6  230.0 0.0  6   228.0  0.0  6   230.0  0.0\par 
 40  5  8  254.0  0.0  8  254.0 0.0  8   251.0  0.0  8   254.0  0.0\par 
 40  5 10  494.0  0.0 10  494.0 0.0 10   492.0  0.0 10   494.0  0.0\par 
 40  5 12  656.0  0.0  2  656.0 0.0 12   656.0  0.0 12   656.0  0.0\par 
 40  5 14  731.0  0.0  4  731.0 0.0 14   731.0  0.0 14   731.0  0.0\par 
 40  5 16  841.0  0.0  6  841.0 0.0 16   841.0  0.0 16   841.0  0.0\par 
200  0  1 1650.0  0.0  1 1650.0 0.0  1  1650.0  0.0  1  1650.0  0.0 \par 
300  0  2 1317.0  0.0  2 1317.0 0.0  2  1250.0  0.0  2  1250.0  0.0\par 
400  0  3  880.0  0.0  3  880.0 0.0  3   850.0  0.0  3   850.0  0.0\par 
500  0  4 1354.0  0.0  4 1354.0 0.0  4  1350.0  0.0  4  1350.0  0.0\par 
}\pard \par 
\pard {\v {\tc\tcl2\pard\plain \f20 {\b Toluene Obs File}}}{\b \par 
}\pard \par 
\pard {\f22\fs18  toluene (Cs sym) with the methyl group version 0\par 
 new file taken from ref# \par 
 3 "???" "a1 " "a2 "\par 
\tab none\tab \tab  \par 
 200 0 1 1712.0 0.0\par 
 300 0 2 1530.0 0.0\par 
 400 0 3  992.0 5.0\par 
  0 1 1  220.0  1.0\par 
  0 1 2  467.0  1.0\par 
  0 1 3  522.0  1.0\par 
  0 1 4  698.0  1.0\par 
  0 1 5  732.0  1.0\par 
  0 1 6  788.0  1.0\par 
 40 1 7  898.0  1.0\par 
 40 1 8  991.0  1.0\par 
 60 1 9  1005.0 1.0\par 
 60 1 10 1030.0 1.0\par 
 60 1 11 1041.0 1.0\par 
 60 1 12 1182.0 1.0\par 
 60 1 13 1211.0 1.0\par 
 60 1 14 1380.0 1.0\par 
 60 1 15 1450.0 1.0\par 
 60 1 16 1497.0 1.0\par 
 60 1 17 1606.0 1.0\par 
 60 1 18 2900.0 1.0\par 
 60 1 19 2949.0 1.0\par 
 60 1 20 3055.0 1.0\par 
 60 1 21 3056.0 1.0\par 
 60 1 22 3057.0 1.0\par 
  0 2 1  44.0   0.2\par 
  0 2 2  348.0  1.0\par 
  0 2 3  407.0  1.0\par 
  0 2 4  622.0  1.0\par 
  0 2 5  841.0  1.0\par 
 40 2 6  967.0  1.0\par 
 40 2 7  975.0  0.5\par 
 60 2 8  1084.0 1.0\par 
 60 2 9  1157.0 1.0\par 
 60 2 10 1286.0 1.0\par 
 60 2 11 1316.0 1.0\par 
 60 2 12 1445.0 1.0\par 
 60 2 13 1468.0 1.0\par 
 60 2 14 1587.0 1.0\par 
 60 2 15 2951.0 1.0\par 
 60 2 16 3054.0 1.0\par 
 60 2 17 3055.0 1.0\par 
}\pard \par 
\pard {\v {\tc\tcl2\pard\plain \f20 {\b Sample Run Nmode Script}}}{\b \par 
}\pard \par 
\pard {\f22\fs18 #! /bin/csh \par 
/bin/rm nmode.in\par 
/bin/rm nmode.out\par 
/bin/rm heme.vecs \par 
set DIR=$AMBER1\par 
#\par 
cat << eof > nmode.in\par 
Test of normal modes on heme\par 
 &data ntrun=1, cut=12.0 , drms=12.0, nvect =255, &end\par 
eof\par 
#\par 
$DIR/exe/nmode -O  \\\par 
         -i nmode.in \\\par 
         -o nmode.out \\\par 
         -c min2.xyz \\\par 
\tab  -v heme.vecs \tab \tab || goto error\par 
\par 
/bin/rm -f \tab nmanal.out \par 
cat << eof > nmanal.in\par 
  normal mode analysis, rms fluctuations\par 
 &data\par 
     ntrun = 1, nvect=255, iend=255, \par 
     pcut = 1e-3, \par 
 &end\par 
\par 
eof\par 
\par 
$DIR/exe/nmanal -O -i nmanal.in \\\par 
\tab \tab  -v heme.vecs \\\par 
\tab \tab  -o nmanal.out \tab \tab || goto error\par 
\par 
exit(0)\par 
\par 
error:\par 
echo "Failure: run.nmode check .out and retry"\par 
exit(1)\par 
\par 
}\pard \qc \page {\v\fs28 {\tc\tcl1\pard\plain \qc \f20 {\b\fs28 Appendix E\: Symmetry Files}}}{\b\fs28 \par 
}\pard \par 
\pard {\v {\tc\tcl2\pard\plain \f20 {\b Benzene Symmetry File}}}{\b \par 
}\pard \par 
\pard {\f22\fs18  &symmetry\par 
 symtitle='Toluene all atoms c2v symmetry file'\par 
 thresh=0.01\par 
 iprnt=5,\par 
 nrep=13,\par 
 kgen= 4,\par 
 idgen= 9, 10, 11, 12,\par 
 termsym( 1)='???',itable(1,1 )=    9, 9, 9, 9,\par 
 termsym( 2)='A1g',itable(1,2 )=    1, 1, 1, 1,\par 
 termsym( 3)='A2g',itable(1,3 )=    1, 1,-1, 1,\par 
 termsym( 4)='A1u',itable(1,4 )=    1, 1,-1,-1,\par 
 termsym( 5)='A2u',itable(1,5 )=    1, 1, 1,-1,\par 
 termsym( 6)='B1g',itable(1,6 )=   -1, 1,-1, 1,\par 
 termsym( 7)='B2g',itable(1,7 )=   -1, 1, 1, 1,\par 
 termsym( 8)='B1u',itable(1,8 )=   -1, 1, 1,-1,\par 
 termsym( 9)='B2u',itable(1,9 )=   -1, 1,-1,-1,\par 
 termsym(10)='E1g',itable(1,10)=    1,-1, 9, 1,\par 
 termsym(11)='E1u',itable(1,11)=    1,-1, 9,-1,\par 
 termsym(12)='E2g',itable(1,12)=   -1,-1, 9, 1,\par 
 termsym(13)='E2u',itable(1,13)=   -1,-1, 9,-1,\par 
 numrep= 0, 2, 1, 0, 1, 0, 2, 2, 2, 2, 6, 8, 4,\par 
 nsym=          12\par 
 nasym=  1,  2,  3,  4,  5,  6,  7,  8,  9, 10,\par 
         11, 12,\par 
 t_op( 1)="C6 ",\par 
 r_op(1, 1)=   0.500,   0.866,   0.000,\par 
              -0.866,   0.500,   0.000,\par 
               0.000,   0.000,   1.000,\par 
 n_op(1, 1)= 11, 12,  1,  2,  3,  4,  5,  6,  7,  8,\par 
              9, 10,\par 
 t_op( 2)="C3 ",\par 
 r_op(1, 2)=  -0.500,   0.866,   0.000,\par 
              -0.866,  -0.500,   0.000,\par 
               0.000,   0.000,   1.000,\par 
 n_op(1, 2)=  9, 10, 11, 12,  1,  2,  3,  4,  5,  6,\par 
              7,  8,\par 
 t_op( 3)="sxz",\par 
 r_op(1, 3)=   1.000,   0.000,   0.000,\par 
               0.000,  -1.000,   0.000,\par 
               0.000,   0.000,   1.000,\par 
 n_op(1, 3)=  9, 10,  7,  8,  5,  6,  3,  4,  1,  2,\par 
             11, 12,\par 
 t_op( 4)="i  ",\par 
 r_op(1, 4)=  -1.000,   0.000,   0.000,\par 
               0.000,  -1.000,   0.000,\par 
               0.000,   0.000,  -1.000,\par 
 n_op(1, 4)=  7,  8,  9, 10, 11, 12,  1,  2,  3,  4,\par 
              5,  6,\par 
\par 
 &end\par 
}\pard \par 
\pard {\v {\tc\tcl2\pard\plain \f20 {\b Ethyl Benzene Symmetry File}}}{\b \par 
}\pard {\b \par 
}\pard {\f22\fs18  &symmetry\par 
 symtitle='Toluene all atoms c2v symmetry file'\par 
 thresh=0.01,\par 
 iprnt=0,\par 
 nrep=3,\par 
 kgen= 0,\par 
 termsym( 1)='???',itable(1,1 )=    9, 9, 9, 9,\par 
 termsym( 2)='A1 ',itable(1,2 )=    1, 1, 1, 1,\par 
 termsym( 3)='A2 ',itable(1,3 )=    1,-1, 1,-1,\par 
 numrep= 0, 27, 21,\par 
 nsym=          18,\par 
 thresh= 0.01, \par 
  nasym=  1,  2,  3,  4,  5,  6,  7,  8,  9, 10,\par 
         11, 12, 13, 14, 15, 16, 17, 18,\par 
 t_op( 1)="E  ",\par 
 r_op(1, 1)=   1.000,   0.000,   0.000,\par 
               0.000,   1.000,   0.000,\par 
               0.000,   0.000,   1.000,\par 
 n_op(1, 1)=  1,  2,  3,  4,  5,  6,  7,  8,  9, 10,\par 
             11, 12, 13, 14, 15, 16, 17, 18,\par 
 t_op( 2)="sxz",\par 
 r_op(1, 2)=   1.000,   0.000,   0.000,\par 
               0.000,  -1.000,   0.000,\par 
               0.000,   0.000,   1.000,\par 
 n_op(1, 2)=  9, 10,  7,  8,  5,  6,  3,  4,  1,  2,\par 
             11, 12, 13, 15, 14, 16, 18, 17,\par 
 t_op( 3)="E  ",\par 
 r_op(1, 3)=   1.000,   0.000,   0.000,\par 
               0.000,   1.000,   0.000,\par 
               0.000,   0.000,   1.000,\par 
 n_op(1, 3)=  1,  2,  3,  4,  5,  6,  7,  8,  9, 10,\par 
             11, 12, 13, 14, 15, 16, 17, 18,\par 
 t_op( 4)="sxz",\par 
 r_op(1, 4)=   1.000,   0.000,   0.000,\par 
               0.000,  -1.000,   0.000,\par 
               0.000,   0.000,   1.000,\par 
 n_op(1, 4)=  9, 10,  7,  8,  5,  6,  3,  4,  1,  2,\par 
             11, 12, 13, 15, 14, 16, 18, 17,\par 
\par 
&end\par 
}\pard \par 
\pard {\v {\tc\tcl2\pard\plain \f20 {\b Nickel Octa Ethyl Porphine Symmetry File}}}{\b \par 
}\pard \par 
\pard {\f22\fs18  &symmetry\par 
 symtitle='Nioepy all atom d2d symmetry file'\par 
 thresh=  9.9999998E-03\par 
 nsym=85,\par 
 iprnt=1,\par 
 nrep=6,\par 
 termsym(1)='???',itable(1,1)=    9, 9, 9, 9\par 
 termsym(2)='A1 ',itable(1,2)=    1, 1, 1, 9\par 
 termsym(3)='A2 ',itable(1,3)=    1,-1, 1, 9\par 
 termsym(4)='B1 ',itable(1,4)=   -1, 1, 1, 9\par 
 termsym(5)='B2 ',itable(1,5)=   -1,-1, 1, 9\par 
 termsym(6)='E  ',itable(1,6)=    9, 9, 1,-1\par 
 numrep=0,31, 31, 30, 33, 124,\par 
 nsym=         85 \par 
  nasym=  1,  2,  3,  4,  5,  6,  7,  8,  9, 10,\par 
         11, 12, 13, 14, 15, 16, 17, 18, 19, 20,\par 
         21, 22, 23, 24, 25, 26, 27, 28, 29, 30,\par 
         31, 32, 33, 34, 35, 36, 37, 38, 39, 40,\par 
         41, 42, 43, 44, 45, 46, 47, 48, 49, 50,\par 
         51, 52, 53, 54, 55, 56, 57, 58, 59, 60,\par 
         61, 62, 63, 64, 65, 66, 67, 68, 69, 70,\par 
         71, 72, 73, 74, 75, 76, 77, 78, 79, 80,\par 
         81, 82, 83, 84, 85,\par 
\par 
 t_op( 1)="S14",\par 
 r_op(1, 1)=   0.000,  -1.000,   0.000,\par 
               1.000,   0.000,   0.000,\par 
               0.000,   0.000,  -1.000,\par 
 n_op(1, 1)=  1, 23, 24, 25, 26, 27, 28, 29, 30, 32,\par 
             31, 33, 34, 35, 36, 37, 38, 40, 39, 41,\par 
             42, 43, 44, 45, 46, 47, 48, 49, 50, 51,\par 
             53, 52, 54, 55, 56, 57, 58, 59, 61, 60,\par 
             62, 63, 64, 65, 66, 67, 68, 69, 70, 71,\par 
             72, 74, 73, 75, 76, 77, 78, 79, 80, 82,\par 
             81, 83, 84, 85,  2,  3,  4,  5,  6,  7,\par 
              8,  9, 11, 10, 12, 13, 14, 15, 16, 17,\par 
             19, 18, 20, 21, 22,\par 
\par 
 t_op( 2)="C_2",\par 
 r_op(1, 2)=   0.000,   1.000,   0.000,\par 
               1.000,   0.000,   0.000,\par 
               0.000,   0.000,  -1.000,\par 
 n_op(1, 2)=  1, 23, 41, 33, 34, 36, 35, 37, 38, 39,\par 
             40, 25, 26, 28, 27, 29, 30, 31, 32, 24,\par 
             21, 22,  2, 20, 12, 13, 15, 14, 16, 17,\par 
             18, 19,  4,  5,  7,  6,  8,  9, 10, 11,\par 
              3, 84, 85, 65, 83, 75, 76, 78, 77, 79,\par 
             80, 81, 82, 67, 68, 70, 69, 71, 72, 73,\par 
             74, 66, 63, 64, 44, 62, 54, 55, 57, 56,\par 
             58, 59, 60, 61, 46, 47, 49, 48, 50, 51,\par 
             52, 53, 45, 42, 43,\par 
\par 
 t_op( 3)="  E",\par 
 r_op(1, 3)=   1.000,   0.000,   0.000,\par 
               0.000,   1.000,   0.000,\par 
               0.000,   0.000,   1.000,\par 
 n_op(1, 3)=  1,  2,  3,  4,  5,  6,  7,  8,  9, 10,\par 
             11, 12, 13, 14, 15, 16, 17, 18, 19, 20,\par 
             21, 22, 23, 24, 25, 26, 27, 28, 29, 30,\par 
             31, 32, 33, 34, 35, 36, 37, 38, 39, 40,\par 
             41, 42, 43, 44, 45, 46, 47, 48, 49, 50,\par 
             51, 52, 53, 54, 55, 56, 57, 58, 59, 60,\par 
             61, 62, 63, 64, 65, 66, 67, 68, 69, 70,\par 
             71, 72, 73, 74, 75, 76, 77, 78, 79, 80,\par 
             81, 82, 83, 84, 85,\par 
\par 
 t_op( 4)="C2p",\par 
 r_op(1, 4)=  -1.000,   0.000,   0.000,\par 
               0.000,  -1.000,   0.000,\par 
               0.000,   0.000,   1.000,\par 
 n_op(1, 4)=  1, 44, 45, 46, 47, 48, 49, 50, 51, 52,\par 
             53, 54, 55, 56, 57, 58, 59, 60, 61, 62,\par 
             63, 64, 65, 66, 67, 68, 69, 70, 71, 72,\par 
             73, 74, 75, 76, 77, 78, 79, 80, 81, 82,\par 
             83, 84, 85,  2,  3,  4,  5,  6,  7,  8,\par 
              9, 10, 11, 12, 13, 14, 15, 16, 17, 18,\par 
             19, 20, 21, 22, 23, 24, 25, 26, 27, 28,\par 
             29, 30, 31, 32, 33, 34, 35, 36, 37, 38,\par 
             39, 40, 41, 42, 43,\par 
\par 
 &end\par 
}\pard \par 
\pard {\v {\tc\tcl2\pard\plain \f20 {\b Nickel Octa Ethyl Porphine D4h Symmetry File}}}{\b \par 
}\pard \par 
\pard {\f22\fs18  &symmetry\par 
 thresh=0.01,\par 
 nsym=37,\par 
 iprnt=1,\par 
 nrep=11,\par 
 termsym(1)='???',itable(1,1)=    9, 9, 9, 9,\par 
 termsym(2)='A1g',itable(1,2)=    1, 1, 1, 9\par 
 termsym(3)='A2g',itable(1,3)=    1,-1, 1, 9\par 
 termsym(4)='B1g',itable(1,4)=   -1, 1, 1, 9\par 
 termsym(5)='B2g',itable(1,5)=   -1, 9, 1, 9\par 
 termsym(6)='E g',itable(1,6)=    0, 9, 1,-1\par 
 termsym(7)='A1u',itable(1,7)=    1, 1,-1, 9\par 
 termsym(8)='A2u',itable(1,8)=    1,-1,-1, 9\par 
 termsym(9)='B1u',itable(1,9)=   -1, 1,-1, 9\par 
 termsym(10)='B2u',itable(1,10)= -1,-1,-1, 9\par 
 termsym(11)='E u',itable(1,11)=  0, 9,-1,-1\par 
 numrep=0,9,8,9,9,16,3,6,5,4,36\par 
 nsym=          37\par 
  nasym=  1,  2,  3,  4,  5,  6,  7,  8,  9, 10,\par 
         11, 12, 13, 14, 15, 16, 17, 18, 19, 20,\par 
         21, 22, 23, 24, 25, 26, 27, 28, 29, 30,\par 
         31, 32, 33, 34, 35, 36, 37,\par 
 t_op( 1)="C14",\par 
 r_op(1, 1)=   0.000,   1.000,   0.000,\par 
              -1.000,   0.000,   0.000,\par 
               0.000,   0.000,   1.000,\par 
 n_op(1, 1)=  1, 29, 30, 31, 32, 33, 34, 35, 36, 37,\par 
              2,  3,  4,  5,  6,  7,  8,  9, 10, 11,\par 
             12, 13, 14, 15, 16, 17, 18, 19, 20, 21,\par 
             22, 23, 24, 25, 26, 27, 28,\par 
 t_op( 2)="C2p",\par 
 r_op(1, 2)=   1.000,   0.000,   0.000,\par 
               0.000,  -1.000,   0.000,\par 
               0.000,   0.000,  -1.000,\par 
 n_op(1, 2)=  1,  2,  8,  6,  7,  4,  5,  3, 36, 37,\par 
             29, 35, 33, 34, 31, 32, 30, 27, 28, 20,\par 
             26, 24, 25, 22, 23, 21, 18, 19, 11, 17,\par 
             15, 16, 13, 14, 12,  9, 10,\par 
 t_op( 3)="  i",\par 
 r_op(1, 3)=  -1.000,   0.000,   0.000,\par 
               0.000,  -1.000,   0.000,\par 
               0.000,   0.000,  -1.000,\par 
 n_op(1, 3)=  1, 20, 21, 22, 23, 24, 25, 26, 27, 28,\par 
             29, 30, 31, 32, 33, 34, 35, 36, 37,  2,\par 
              3,  4,  5,  6,  7,  8,  9, 10, 11, 12,\par 
             13, 14, 15, 16, 17, 18, 19,\par 
 t_op( 4)="C2n",\par 
 r_op(1, 4)=  -1.000,   0.000,   0.000,\par 
               0.000,  -1.000,   0.000,\par 
               0.000,   0.000,   1.000,\par 
 n_op(1, 4)=  1, 20, 21, 22, 23, 24, 25, 26, 27, 28,\par 
             29, 30, 31, 32, 33, 34, 35, 36, 37,  2,\par 
              3,  4,  5,  6,  7,  8,  9, 10, 11, 12,\par 
             13, 14, 15, 16, 17, 18, 19,\par 
\par 
 &end\par 
}\pard \par 
\pard {\v {\tc\tcl2\pard\plain \f20 {\b Toluene Symmetry File}}}{\b \par 
}\pard \par 
\pard {\f22\fs18  &symmetry\par 
 symtitle='Toluene all atoms c2v symmetry file'\par 
 thresh=0.01,\par 
 iprnt=0,\par 
 nrep=3,\par 
 kgen= 0,\par 
 termsym( 1)='???',itable(1,1 )=    9, 9, 9, 9,\par 
 termsym( 2)='A1 ',itable(1,2 )=    1, 1, 1, 1,\par 
 termsym( 2)='A2 ',itable(1,3 )=    1,-1, 1,-1,\par 
 numrep= 0, 22, 17,\par 
 nsym=          15,\par 
 thresh= 0.01, \par 
  nasym=  1,  2,  3,  4,  5,  6,  7,  8,  9, 10,\par 
         11, 12, 13, 14, 15,\par 
 t_op( 1)="E  ",\par 
 r_op(1, 1)=   1.000,   0.000,   0.000,\par 
               0.000,   1.000,   0.000,\par 
               0.000,   0.000,   1.000,\par 
 n_op(1, 1)=  1,  2,  3,  4,  5,  6,  7,  8,  9, 10,\par 
             11, 12, 13, 14, 15,\par 
 t_op( 2)="sxz",\par 
 r_op(1, 2)=   1.000,   0.000,   0.000,\par 
               0.000,  -1.000,   0.000,\par 
               0.000,   0.000,   1.000,\par 
 n_op(1, 2)=  9, 10,  7,  8,  5,  6,  3,  4,  1,  2,\par 
             11, 12, 13, 15, 14,\par 
 t_op( 3)="E  ",\par 
 r_op(1, 3)=   1.000,   0.000,   0.000,\par 
               0.000,   1.000,   0.000,\par 
               0.000,   0.000,   1.000,\par 
 n_op(1, 3)=  1,  2,  3,  4,  5,  6,  7,  8,  9, 10,\par 
             11, 12, 13, 14, 15,\par 
 t_op( 4)="sxz",\par 
 r_op(1, 4)=   1.000,   0.000,   0.000,\par 
               0.000,  -1.000,   0.000,\par 
               0.000,   0.000,   1.000,\par 
 n_op(1, 4)=  9, 10,  7,  8,  5,  6,  3,  4,  1,  2,\par 
             11, 12, 13, 15, 14,\par 
\par 
&end\par 
}\pard \par 
\pard \qc \page {\v\fs28 {\tc\tcl1\pard\plain \qc \f20 {\b\fs28 Appendix F\: Potential Files}}}{\b\fs28 \par 
}\pard \par 
\pard {\v {\tc\tcl2\pard\plain \f20 {\b Benzene Potential File}}}{\b \par 
}\pard {\b \par 
}\pard {\f22\fs18  ethylbenzene in entirety \par 
\par 
BOND\par 
CA-CA   427.010     1.400\par 
CA-HA   366.200     1.080\par 
\par 
ANGLE\par 
CA-CA-CA    71.673   120.000\par 
CA-CA-HA    36.178   120.000\par 
\par 
DIHEDRAL\par 
CA-CA-CA-CA   1       4.178     180.000       2.000\par 
CA-CA-CA-HA   2       8.063     180.000       2.000\par 
HA-CA-CA-HA   1       2.292     180.000       2.000\par 
\par 
IMPROPER\par 
CA-CA-HA-CA   1       0.000     180.000       2.000\par 
CA-HA-CA-CA   1       0.000     180.000       2.000\par 
\par 
}\pard \par 
\pard {\v {\tc\tcl2\pard\plain \f20 {\b Ethyl Benzene Potential File}}}{\b \par 
}\pard \par 
\pard {\f22\fs18  ethylbenzene in entirety \par 
\par 
MASS\par 
HM   1.008\par 
HA   1.008\par 
CC  12.001\par 
\par 
BOND\par 
CA-CA   414.908     1.400\par 
CA-HA   366.200     1.080\par 
CA-CC   358.353     1.400\par 
CT-CT   337.148     1.526\par 
CT-HC   325.634     1.090\par 
CC-CT   313.846     1.510\par 
CT-HM   337.442     1.090\par 
\par 
ANGLE\par 
CA-CA-CA    77.041   120.000\par 
CA-CA-HA    35.348   120.000\par 
CC-CA-HA    35.348   120.000\par 
CC-CT-HC    50.290   109.500\par 
CA-CC-CA    68.932   120.000\par 
CA-CA-CC    78.335   120.000\par 
CA-CC-CT    42.863   120.000\par 
HM-CT-CT    49.415   109.500\par 
HC-CT-CT    47.204   109.500\par 
CC-CT-CT    58.916   109.500\par 
HM-CT-HM    31.286   109.500\par 
HC-CT-HC    31.286   109.500\par 
\par 
DIHEDRAL\par 
CA-CA-CA-CA   1       3.407     180.000       2.000\par 
CA-CA-CA-HA   2       8.330     180.000       2.000\par 
HA-CA-CA-HA   1       2.335     180.000       2.000\par 
CA-CA-CC-CT   1       3.475     180.000       2.000\par 
CA-CA-CC-CA   1       4.626     180.000       2.000\par 
HA-CA-CC-CT   1       2.100     180.000       2.000\par 
HA-CA-CC-CA   1       4.009     180.000       2.000\par 
CA-CC-CT-HC   4       0.600     180.000       3.000\par 
HM-CT-CT-HC   6       1.254       0.000       3.000\par 
HM-CT-CT-CC   3       0.000       0.000       3.000\par 
CA-CC-CT-CT   2       0.560     180.000      -4.000\par 
CA-CC-CT-CT   2       0.000     180.000      -3.000\par 
CA-CC-CT-CT   2       2.308     180.000       2.000\par 
\par 
IMPROPER\par 
CA-CC-CT-CA   1       4.143     180.000       2.000\par 
CA-CT-CC-CA   1       4.143     180.000       2.000\par 
X -HA-CA-X    1       0.000     180.000       2.000\par 
X -CA-HA-X    1       0.000     180.000       2.000\par 
\par 
\par 
HBOND\par 
  HW  OW   225.     0000.                                4.\par 
\par 
NONBON\par 
  HM         1.54      0.01      0.00000\par 
  HA         1.54      0.01      0.00000\par 
\par 
}\pard \par 
\pard {\v {\tc\tcl2\pard\plain \f20 {\b Heme Potential File}}}{\b \par 
}\pard \par 
\pard {\f22\fs18  Jason aveaged rest5.final\par 
HP  beta hydrogen\par 
HM  meso hydrogen\par 
w running a simplex routine with run.simple5 on correct sym\par 
CX  beta c1 of ethane\par 
CY  beta c2 of ethane  15.03 amu\par 
added imidazole atom types\par 
corrected LC-LO force constant\par 
united methyl atom (CX)\par 
\par 
MASS\par 
HM   1.008\par 
HI   1.008\par 
HE   1.008\par 
HN   1.008\par 
HQ   1.008\par 
NO   14.01\par 
NP   14.01\par 
CX   12.01\par 
CY   12.01\par 
CQ   12.01\par 
CD   12.01\par 
LC   12.01\par 
LO   16.01\par 
\par 
BOND\par 
FE-NP   110.308     1.930\par 
FE-NO   110.308     1.930\par 
NP-CC   335.936     1.380\par 
NO-CC   335.936     1.380\par 
CC-CB   330.655     1.440\par 
CC-CD   365.547     1.380\par 
CB-CB   460.380     1.350\par 
CD-HM   363.015     1.090\par 
CB-CX   316.227     1.501\par 
CX-CY   310.552     1.506\par 
CX-HE   337.442     1.100\par 
CY-HN   337.442     1.100\par 
CB-CQ   316.277     1.500\par 
CQ-CQ   549.000     1.313\par 
CQ-HQ   340.000     1.090\par 
CV-HC   367.000     1.090\par 
CR-HC   367.000     1.090\par 
CY-C    317.000     1.090\par 
LC-LO  1075.000     1.200\par 
FE-LC   140.000     2.110\par 
FE-NB   110.308     1.930\par 
\par 
\par 
\par 
ANGLE\par 
NP-FE-NP     0.000   180.000\par 
NO-FE-NO     0.000   180.000\par 
NO-FE-NP     9.981    90.000\par 
FE-NP-CC    80.289   120.000\par 
FE-NO-CC    80.289   120.000\par 
CB-CB-CX    26.414   120.000\par 
CC-CB-CX    26.414   120.000\par 
CB-CX-HE    39.778   109.500\par 
CY-CX-HE    53.997   109.500\par 
CB-CX-CY    65.618   109.500\par 
CB-CC-CD    49.662   120.000\par 
CC-NP-CC    62.010   120.000\par 
CC-NO-CC    62.010   120.000\par 
CC-CB-CB    72.582   120.000\par 
CC-CD-CC    92.601   120.000\par 
NO-CC-CD    43.773   120.000\par 
NP-CC-CD    43.773   120.000\par 
NO-CC-CB   101.511   120.000\par 
NP-CC-CB   101.511   120.000\par 
HN-CY-CX    43.457   109.500\par 
CC-CD-HM    31.413   120.000\par 
HE-CX-HE    32.614   109.500\par 
HN-CY-HN    32.614   109.500\par 
CQ-CB-CC    70.000   120.000 \par 
CQ-CB-CB    70.000   120.000\par 
CQ-CQ-CB    70.000   120.000 \par 
HQ-CQ-CB    35.000   120.000\par 
HQ-CQ-CQ    35.000   120.000\par 
HQ-CQ-HQ    35.000   120.000\par 
NB-FE-NO    50.000    90.000\par 
NB-FE-NP    50.000    90.000\par 
NB-FE-LC     0.000   180.000\par 
CV-NB-FE     0.000   110.000\par 
CR-NB-FE     0.000   110.000\par 
FE-LC-LO    65.000   180.000\par 
NP-FE-LC    45.000    90.000\par 
NO-FE-LC    45.000    90.000\par 
HC-CY-C     50.000   109.500\par 
CX-CY-C     63.000   110.100\par 
CY-C -O2    70.000   117.000\par 
N -CT-HC    50.000   109.500\par 
CC-CV-HC    50.000   120.000\par 
NA-CR-HC    35.000   109.500\par 
HC-CR-NB    35.000   109.500\par 
NB-CV-HC    50.000   120.000\par 
HN-CY-C     50.000   109.500\par 
\par 
DIHEDRAL\par 
CC-NO-FE-NP   4       7.122     180.000       2.000\par 
CC-NO-FE-NO   2       0.000     180.000       2.000\par 
CC-NO-FE-NB   2       0.000     180.000       2.000\par 
CC-NO-FE-LC   2       0.000     180.000       2.000\par 
CC-NP-FE-NO   4       7.222     180.000       2.000\par 
CC-NP-FE-NP   2       0.000     180.000       2.000\par 
CC-NP-FE-NB   2       0.000     180.000       2.000\par 
CC-NP-FE-LC   2       0.000     180.000       2.000\par 
X -NB-FE-X    8       0.000     180.000       2.000\par 
X -FE-NB-X    8       0.000     180.000       2.000\par 
CB-CB-CX-CY   1       0.280     180.000      -4.000\par 
CB-CB-CX-CY   1       0.000     180.000      -3.000\par 
CB-CB-CX-CY   1       1.154     180.000       2.000\par 
CC-CB-CX-CY   1       0.280     180.000      -4.000\par 
CC-CB-CX-CY   1       0.000     180.000      -3.000\par 
CC-CB-CX-CY   1       1.154     180.000       2.000\par 
CB-CB-CX-HE   2       0.300     180.000       2.000\par 
CC-CB-CX-HE   2       0.300     180.000       2.000\par 
HE-CX-CY-HN   6       1.254       0.000       3.000\par 
CB-CX-CY-HN   3       0.000       0.000       3.000\par 
CC-CB-CB-CC   1       7.759     180.000       2.000\par 
CX-CB-CB-CX   1       5.579     180.000       2.000\par 
CC-CB-CB-CX   2       3.475     180.000       2.000\par 
NO-CC-CB-CX   1       2.811     180.000       2.000\par 
NP-CC-CB-CX   1       2.811     180.000       2.000\par 
FE-NO-CC-CB   1       3.113     180.000       2.000\par 
FE-NP-CC-CB   1       3.113     180.000       2.000\par 
FE-NP-CC-CD   1       3.701     180.000       2.000\par 
FE-NO-CC-CD   1       3.701     180.000       2.000\par 
FE-CC-CB-CB   1       0.193     180.000       2.000\par 
NP-CC-CB-CB   1       0.193     180.000       2.000\par 
CC-NO-CC-CD   1       2.390     180.000       2.000\par 
CC-NP-CC-CD   1       2.390     180.000       2.000\par 
CD-CC-CB-CX   1       1.398     180.000       2.000\par 
CD-CC-CB-CB   1       6.699     180.000       2.000\par 
CC-NO-CC-CB   1       4.244     180.000       2.000\par 
CC-NP-CC-CB   1       4.244     180.000       2.000\par 
CC-CD-CC-NO   1       3.685     180.000       2.000\par 
CC-CD-CC-NP   1       3.685     180.000       2.000\par 
HM-CD-CC-CB   1       1.878     180.000       2.000\par 
CC-CD-CC-CB   1       1.106     180.000       2.000\par 
HM-CD-CC-NO   1       2.616     180.000       2.000\par 
HM-CD-CC-NP   1       2.616     180.000       2.000\par 
NO-CC-CB-CQ   1       6.547     180.000       2.000\par 
NP-CC-CB-CQ   1       6.547     180.000       2.000\par 
NO-CC-CB-CB   1       6.547     180.000       2.000\par 
NP-CC-CB-CB   1       6.547     180.000       2.000\par 
HQ-CQ-CB-CB   1       0.823     180.000       2.000\par 
HQ-CQ-CB-CC   1       0.823     180.000       2.000\par 
CQ-CQ-CB-CC   2       1.933     180.000       2.000\par 
CQ-CQ-CB-CB   2       1.933     180.000       2.000\par 
HQ-CQ-CQ-HQ   2      14.659     180.000       2.000\par 
CC-CQ-CQ-HQ   1      10.512     180.000       2.000\par 
CB-CQ-CQ-HQ   1      10.512     180.000       2.000\par 
CQ-CB-CC-CD   1       1.398     180.000       2.000\par 
X -FE-LC-X    4       0.000     180.000       2.000\par 
X -CX-CY-X    9       1.400       0.000       3.000\par 
X -C -CY-X    4       0.000       0.000       2.000\par 
\par 
\par 
IMPROPER\par 
X -CD-HM-X    0       0.000     180.000       2.000\par 
X -CB-CX-X    0       4.314     180.000       2.000\par 
CC-NO-FE-CC   0       3.600     180.000       2.000\par 
CC-NP-FE-CC   0       3.600     180.000       2.000\par 
CC-NO-CD-CB   0       1.108     180.000       2.000\par 
CC-NP-CD-CB   0       1.108     180.000       2.000\par 
X -CC-CC-X    0       0.000     180.000       2.000\par 
X -CC-CB-X    0       0.000     180.000       2.000\par 
X -CB-CC-X    0       0.000     180.000       2.000\par 
X -NP-CB-X    0       0.000     180.000       2.000\par 
X -NO-CB-X    0       0.000     180.000       2.000\par 
X -CB-NO-X    0       0.000     180.000       2.000\par 
X -CB-NP-X    0       0.000     180.000       2.000\par 
X -CB-CQ-X    0       4.314     180.000       2.000\par 
\par 
\par 
HBOND\par 
  HW  OW   225.     0000.                                4.\par 
\par 
NONBON\par 
  HW         1.00      0.020     0.0\par 
  CL         2.223     0.107     0.0\par 
  FE         1.20000   0.05000   0.00000\par 
  LO         1.60000   0.20000   0.00000\par 
  LC         1.85      0.12      0.00000\par 
  HM         1.54      0.01      0.00000\par 
  HP         1.54      0.01      0.00000\par 
  HE         1.54      0.01      0.00000\par 
  HI         1.54      0.01      0.00000\par 
  HN         1.54      0.01      0.00000\par 
  HQ         1.54      0.01      0.00000\par 
  CX         1.9080    0.1094    0.000\par 
  CY         1.80      0.06      0.00000\par 
  C9         1.80      0.06      0.000\par 
  C8         1.80      0.06      0.0000\par 
  CQ         1.80      0.06      0.0000\par 
\par 
}\pard \par 
\pard {\v {\tc\tcl2\pard\plain \f20 {\b Heme Sundar New Potential File}}}{\b \par 
}\pard \par 
\pard {\f22\fs18  Jason aveaged rest5.final\par 
HP  beta hydrogen\par 
HM  meso hydrogen\par 
w running a simplex routine with run.simple5 on correct sym\par 
CX  beta c1 of ethane\par 
CY  beta c2 of ethane  15.03 amu\par 
added imidazole atom types\par 
corrected LC-LO force constant\par 
united methyl atom (CX)\par 
\par 
MASS\par 
HM   1.008\par 
HI   1.008\par 
HE   1.008\par 
HN   1.008\par 
NI   58.69\par 
NO   14.01\par 
NP   14.01\par 
CX   12.01\par 
CY   12.01\par 
CD   12.01\par 
\par 
BOND\par 
NI-NP    80.308     1.860\par 
NI-NO    80.308     1.860\par 
NP-CC   335.936     1.380\par 
NO-CC   335.936     1.380\par 
CC-CB   330.655     1.440\par 
CC-CD   365.547     1.380\par 
CB-CB   460.380     1.350\par 
CD-HM   363.015     1.090\par 
CB-CX   316.227     1.495\par 
CX-CY   310.552     1.506\par 
CX-HE   337.462     1.100\par 
CY-HN   337.462     1.100\par 
\par 
ANGLE\par 
NP-NI-NP     0.000   180.000\par 
NO-NI-NO     0.000   180.000\par 
NO-NI-NP     9.981    90.000\par 
NI-NP-CC    80.289   120.000\par 
NI-NO-CC    80.289   120.000\par 
CB-CB-CX    26.414   120.000\par 
CC-CB-CX    26.414   120.000\par 
CB-CX-HE    39.778   109.500\par 
CY-CX-HE    53.997   109.500\par 
CB-CX-CY    65.618   109.500\par 
CB-CC-CD    49.662   120.000\par 
CC-NP-CC    62.010   120.000\par 
CC-NO-CC    62.010   120.000\par 
CC-CB-CB    72.582   120.000\par 
CC-CD-CC    92.601   120.000\par 
NO-CC-CD    43.773   120.000\par 
NP-CC-CD    43.773   120.000\par 
NO-CC-CB   101.511   120.000\par 
NP-CC-CB   101.511   120.000\par 
HN-CY-CX    43.457   109.500\par 
CC-CD-HM    31.413   120.000\par 
HE-CX-HE    32.614   109.500\par 
HN-CY-HN    32.614   109.500\par 
\par 
\par 
DIHEDRAL\par 
CC-NO-NI-NP   4       7.122     180.000       2.000\par 
CC-NO-NI-NO   2       0.000     180.000       2.000\par 
CC-NP-NI-NO   4       7.122     180.000       2.000\par 
CC-NP-NI-NP   2       0.000     180.000       2.000\par 
CB-CB-CX-CY   1       0.280     180.000      -4.000\par 
CB-CB-CX-CY   1       0.000     180.000      -3.000\par 
CB-CB-CX-CY   1       1.154     180.000       2.000\par 
CC-CB-CX-CY   1       0.280     180.000      -4.000\par 
CC-CB-CX-CY   1       0.000     180.000      -3.000\par 
CC-CB-CX-CY   1       1.154     180.000       2.000\par 
CB-CB-CX-HE   2       0.300     180.000       2.000\par 
CC-CB-CX-HE   2       0.300     180.000       2.000\par 
HE-CX-CY-HN   6       1.254       0.000       3.000\par 
CB-CX-CY-HN   3       0.000       0.000       3.000\par 
CC-CB-CB-CC   1       7.579     180.000       2.000\par 
CX-CB-CB-CX   1       5.579     180.000       2.000\par 
CC-CB-CB-CX   2       3.475     180.000       2.000\par 
NO-CC-CB-CX   1       2.811     180.000       2.000\par 
NP-CC-CB-CX   1       2.811     180.000       2.000\par 
NI-NO-CC-CB   1       3.113     180.000       2.000\par 
NI-NP-CC-CB   1       3.113     180.000       2.000\par 
NI-NP-CC-CD   1       3.701     180.000       2.000\par 
NI-NO-CC-CD   1       3.701     180.000       2.000\par 
NO-CC-CB-CB   1       0.193     180.000       2.000\par 
NP-CC-CB-CB   1       0.193     180.000       2.000\par 
CC-NO-CC-CD   1       2.390     180.000       2.000\par 
CC-NP-CC-CD   1       2.390     180.000       2.000\par 
CD-CC-CB-CX   1       1.398     180.000       2.000\par 
CD-CC-CB-CB   1       6.699     180.000       2.000\par 
CC-NO-CC-CB   1       4.244     180.000       2.000\par 
CC-NP-CC-CB   1       4.244     180.000       2.000\par 
CC-CD-CC-NO   1       3.685     180.000       2.000\par 
CC-CD-CC-NP   1       3.685     180.000       2.000\par 
HM-CD-CC-CB   1       1.878     180.000       2.000\par 
CC-CD-CC-CB   1       1.106     180.000       2.000\par 
HM-CD-CC-NO   1       2.616     180.000       2.000\par 
HM-CD-CC-NP   1       2.616     180.000       2.000\par 
\par 
IMPROPER\par 
X -CD-HM-X    0       0.000     180.000       2.000\par 
X -CB-CX-X    0       4.314     180.000       2.000\par 
CC-NO-NI-CC   0       3.600     180.000       2.000\par 
CC-NP-NI-CC   0       3.600     180.000       2.000\par 
CC-NO-CD-CB   0       1.108     180.000       2.000\par 
CC-NP-CD-CB   0       1.108     180.000       2.000\par 
\par 
\par 
HBOND\par 
  HW  OW   225.     0000.                                4.\par 
\par 
NONBON\par 
  HW         1.00      0.020     0.0\par 
  CL         2.223     0.107     0.0\par 
  NI         1.20000   0.05000   0.00000\par 
  LO         1.60000   0.20000   0.00000\par 
  LC         1.85      0.12      0.00000\par 
  HM         1.54      0.01      0.00000\par 
  HP         1.54      0.01      0.00000\par 
  HE         1.54      0.01      0.00000\par 
  HI         1.54      0.01      0.00000\par 
  HN         1.54      0.01      0.00000\par 
  CX         1.9080    0.1094    0.000\par 
  CY         1.80      0.06      0.00000\par 
  C9         1.80      0.06      0.000\par 
  C8         1.80      0.06      0.0000\par 
\par 
}\pard \par 
\pard {\v {\tc\tcl2\pard\plain \f20 {\b Heme Sundar Old Potential File}}}{\b \par 
}\pard \par 
\pard {\f22\fs18  Jason aveaged rest5.final\par 
HP  beta hydrogen\par 
HM  meso hydrogen\par 
w running a simplex routine with run.simple5 on correct sym\par 
CX  beta c1 of ethane\par 
CY  beta c2 of ethane  15.03 amu\par 
added imidazole atom types\par 
corrected LC-LO force constant\par 
united methyl atom (CX)\par 
\par 
MASS\par 
HM   1.008\par 
HI   1.008\par 
HE   1.008\par 
HN   1.008\par 
NI   58.69\par 
NO   14.01\par 
NP   14.01\par 
CX   12.01\par 
CY   12.01\par 
CD   12.01\par 
\par 
BOND\par 
NI-NP   157.246     1.958\par 
NI-NO   157.246     1.958\par 
NP-CC   297.322     1.376\par 
NO-CC   297.322     1.376\par 
CC-CB   260.679     1.443\par 
CC-CD   327.507     1.371\par 
CB-CB   413.606     1.346\par 
CD-HM   356.593     1.090\par 
CB-CX   282.851     1.501\par 
CX-CY   329.418     1.506\par 
CX-HE   337.442     1.100\par 
CY-HN   337.442     1.100\par 
\par 
\par 
ANGLE\par 
NP-NI-NP     0.000   180.000\par 
NO-NI-NO     0.000   180.000\par 
NO-NI-NP     8.780    90.000\par 
NI-NP-CC    87.705   120.000\par 
NI-NO-CC    87.705   120.000\par 
NO-CC-CB   117.615   120.000\par 
NP-CC-CB   117.615   120.000\par 
NO-CC-CD    36.191   121.800\par 
NP-CC-CD    36.191   121.800\par 
CB-CC-CD    36.117   118.200\par 
CC-NP-CC   130.413   108.000\par 
CC-NO-CC   130.413   108.000\par 
CC-CB-CB    90.796   120.000\par 
CC-CD-CC   166.070   124.000\par 
CB-CX-HE    55.062   109.500\par 
CB-CX-CY    93.004   109.500\par 
CB-CB-CX    29.230   120.000\par 
CC-CB-CX    29.230   120.000\par 
CY-CX-HE    35.847   109.500\par 
HN-CY-CX    35.847   109.500\par 
CC-CD-HM    32.014   119.300\par 
HE-CX-HE    31.560   109.500\par 
HN-CY-HN    31.560   109.500\par 
\par 
\par 
DIHEDRAL\par 
CC-NO-NI-NP   4       7.122     180.000       2.000\par 
CC-NO-NI-NO   2       0.000     180.000       2.000\par 
CC-NP-NI-NO   4       7.122     180.000       2.000\par 
CC-NP-NI-NP   2       0.000     180.000       2.000\par 
CB-CB-CX-CY   1       0.280     180.000      -4.000\par 
CB-CB-CX-CY   1       0.000     180.000      -3.000\par 
CB-CB-CX-CY   1       1.154     180.000       2.000\par 
CC-CB-CX-CY   1       0.280     180.000      -4.000\par 
CC-CB-CX-CY   1       0.000     180.000      -3.000\par 
CC-CB-CX-CY   1       1.154     180.000       2.000\par 
CB-CB-CX-HE   2       0.300     180.000       2.000\par 
CC-CB-CX-HE   2       0.300     180.000       2.000\par 
HE-CX-CY-HN   6       1.254       0.000       3.000\par 
CB-CX-CY-HN   3       0.000       0.000       3.000\par 
CC-CB-CB-CC   1       7.579     180.000       2.000\par 
CX-CB-CB-CX   1       5.579     180.000       2.000\par 
CC-CB-CB-CX   2       3.475     180.000       2.000\par 
NO-CC-CB-CX   1       2.811     180.000       2.000\par 
NP-CC-CB-CX   1       2.811     180.000       2.000\par 
NI-NO-CC-CB   1       3.113     180.000       2.000\par 
NI-NP-CC-CB   1       3.113     180.000       2.000\par 
NI-NP-CC-CD   1       3.701     180.000       2.000\par 
NI-NO-CC-CD   1       3.701     180.000       2.000\par 
NO-CC-CB-CB   1       0.193     180.000       2.000\par 
NP-CC-CB-CB   1       0.193     180.000       2.000\par 
CC-NO-CC-CD   1       2.390     180.000       2.000\par 
CC-NP-CC-CD   1       2.390     180.000       2.000\par 
CD-CC-CB-CX   1       1.398     180.000       2.000\par 
CD-CC-CB-CB   1       6.699     180.000       2.000\par 
CC-NO-CC-CB   1       4.244     180.000       2.000\par 
CC-NP-CC-CB   1       4.244     180.000       2.000\par 
CC-CD-CC-NO   1       3.685     180.000       2.000\par 
CC-CD-CC-NP   1       3.685     180.000       2.000\par 
HM-CD-CC-CB   1       1.878     180.000       2.000\par 
CC-CD-CC-CB   1       1.106     180.000       2.000\par 
HM-CD-CC-NO   1       2.616     180.000       2.000\par 
HM-CD-CC-NP   1       2.616     180.000       2.000\par 
\par 
IMPROPER\par 
X -CD-HM-X    0       0.000     180.000       2.000\par 
X -CB-CX-X    0       2.314     180.000       2.000\par 
CC-NO-NI-CC   0       3.600     180.000       2.000\par 
CC-NP-NI-CC   0       3.600     180.000       2.000\par 
CC-NO-CD-CB   0       1.108     180.000       2.000\par 
CC-NP-CD-CB   0       1.108     180.000       2.000\par 
\par 
HBOND\par 
  HW  OW   225.     0000.                                4.\par 
\par 
NONBON\par 
  HW         1.00      0.020     0.0\par 
  CL         2.223     0.107     0.0\par 
  NI         1.20000   0.05000   0.00000\par 
  LO         1.60000   0.20000   0.00000\par 
  LC         1.85      0.12      0.00000\par 
  HM         1.54      0.01      0.00000\par 
  HP         1.54      0.01      0.00000\par 
  HE         1.54      0.01      0.00000\par 
  HI         1.54      0.01      0.00000\par 
  HN         1.54      0.01      0.00000\par 
  CX         1.9080    0.1094    0.000\par 
  CY         1.80      0.06      0.00000\par 
  C9         1.80      0.06      0.000\par 
  C8         1.80      0.06      0.0000\par 
\par 
}\pard \par 
\pard {\v {\tc\tcl2\pard\plain \f20 {\b Toluene Potential File}}}{\b \par 
}\pard \par 
\pard {\f22\fs18  Toluene with all same HC\par 
\par 
MASS\par 
HC   1.008\par 
HA   1.008\par 
CC  12.001\par 
\par 
BOND\par 
CA-CA   414.547     1.400\par 
CA-HA   366.200     1.080\par 
CT-HC   325.634     1.090\par 
CA-CC   357.966     1.400\par 
CC-CT   315.148     1.510\par 
\par 
ANGLE\par 
CA-CA-HA    35.348   120.000\par 
CA-CA-CA    74.538   120.000\par 
CC-CT-HC    50.290   109.500\par 
HC-CT-HC    31.869   109.500\par 
CC-CA-HA    31.041   120.000\par 
CA-CC-CA    69.231   120.000\par 
CA-CA-CC    78.657   120.000\par 
CA-CC-CT    51.857   120.000\par 
\par 
\par 
DIHEDRAL\par 
CA-CA-CA-CA   1       3.407     180.000       2.000\par 
CA-CA-CA-HA   2       8.330     180.000       2.000\par 
HA-CA-CA-HA   1       2.335     180.000       2.000\par 
CA-CA-CC-CT   1       3.475     180.000       2.000\par 
CA-CA-CC-CA   1       4.626     180.000       2.000\par 
HA-CA-CC-CT   1       2.100     180.000       2.000\par 
HA-CA-CC-CA   1       4.009     180.000       2.000\par 
CA-CC-CT-HC   6       0.900     180.000       3.000\par 
\par 
IMPROPER\par 
X -CA-HA-X    1       0.000     180.000       2.000\par 
X -HA-CA-X    1       0.000     180.000       2.000\par 
CA-CC-CT-CA   1       2.764     180.000       2.000\par 
CA-CT-CC-CA   1       2.764     180.000       2.000\par 
\par 
HBOND\par 
  HW  OW   225.     0000.                                4.\par 
\par 
NONBON\par 
  HC         1.54      0.01      0.00000\par 
  HA         1.54      0.01      0.00000\par 
\par 
}\pard \par 
\par 
}