Essentials of Computational Chemistry

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REFERENCES 353 Rablen, P. R., Pearlman, S. A., and Finkbiner, J. 1999. J. Phys. Chem. A, 103, 7357. Rappé, A. K. and Goddard, W. A. 1991. J. Phys. Chem., 95, 358. Reed, A. E., Weinstock, R. B., and Weinhold, F. 1985. J. Chem. Phys., 83, 735. Sadlej, A. J. 1992. Theor. Chem. Acc., 79, 123. Schindler, M. and Kutzelnigg, W. 1982. J. Chem. Phys., 76, 1919. Schreckenbach G. and Ziegler, T. 1995. J. Phys. Chem., 99, 606. Schreckenbach, G., Dickson, R. M., Ruiz-Morales, Y., and Ziegler, T. 1996. In: Chemical Applications of Density-functional Theory, Laird, B. B., Ross, R. B., and Ziegler, T., Eds., ACS Symposium Series, Vol. 629, American Chemical Society: Washington, DC, 328. Scott, A. P. and Radom, L. 1996. J. Phys. Chem., 100, 16502. Sebag, A. B., Forsyth, D. A., and Plante, M. A. 2001 J. Org. Chem., 20, 91. Sefcik, J., Demiralp, E., Cagin, T., and Goddard, W. A., III, 2002. J. Comput. Chem., 23, 1507. Sherer, E. C., Kinsinger, C. R., Kormos, B. L., Thompson, J. D., and Cramer, C. J. 2002. Angew. Chem., Int. Ed. Engl., 41, 1953. Storer, J. W., Giesen, D. J., Cramer, C. J., and Truhlar, D. G. 1995. J. Comput.-Aid. Mol. Des., 9, 87. Sychrovsky, V., Gräfenstein, J., and Cremer, D. 2000. J. Chem. Phys., 113, 3530. Thompson, J. D., Xidos, J. D., Sonbuchner, T. M., Cramer, C. J., and Truhlar, D. G. 2002. Phys. Chem. Comm., 5, 117. Wang, B., Fleischer, U., Hinton, J. F., and Pulay, P. 2001. J. Comput. Chem., 22, 1987. Wang, B., Hinton, J. F., and Pulay, P. 2002. J. Comput. Chem., 23, 492. Wenk, H. H., Balster, A., Sander, W., Hrovat, D. A., and Borden, W. T. 2001. Angew. Chem., Int. Ed. Engl., 40, 2295. Williams, D. E. 1988. J. Comput. Chem., 9, 745. Wilson, P. J., Bradley, T. J., and Tozer, D. J. 2001. J. Chem. Phys., 115, 9233. Wilson, P. J. and Tozer, D. J. 2001. Chem. Phys. Lett., 337, 341. Winget, P., Thompson, J. D., Xidos, J. D., Cramer, C. J., Truhlar, D. G. 2002. J. Phys. Chem. A, 106, 10707. Wong, M. W. 1996. Chem. Phys. Lett., 256, 391. Yu, L., Srinivas, G. N., and Schwartz, M. 2003. J. Mol. Struct. Theochem, 625, 215.
10 Thermodynamic Properties 10.1 Microscopic–macroscopic Connection In the very recent past, it has become possible under certain circumstances to observe single molecules in the laboratory. Nevertheless, the vast majority of chemical research concerns itself not with individual molecules, but instead with macroscopic quantities of matter that are made up of unimaginably large numbers of molecules. The behavior of such ensembles of molecules is governed by the empirically determined laws of thermodynamics, and most chemical reactions and many chemical properties are defined in terms of some of the fundamental variables of thermodynamics, such as enthalpy, entropy, free energy, and others. Until now, we have for the most part concerned ourselves only with the potential and kinetic energies of individual electrons and nuclei in single molecules, and one of our rare connections to thermodynamics has been in some sense a misleading one, namely that we have often converted atomic units into other units more typically associated with macroscopic quantities, e.g., kcal mol −1 or kJ mol −1 . This sometimes leads newcomers to the field to think of the atomic unit of energy, the hartree, as being enormously large, since 1 Eh is equal to 627.51 kcal mol −1 . In reality, however, the hartree is a tremendously tiny unit, since ‘kcal mol −1 ’, as its name makes clear, refers to the energy associated with one mole (i.e., 6.0221 × 10 23 ) of molecules, not with the single molecule that is the typical subject of an electronic-structure calculation. Moreover, when we make comparisons between two different calculations, say to determine the relative energies of two isomers, and we carry out such simple unit conversions, we tacitly (and often incorrectly) assume that the potential energy difference determined from the calculation is all that matters when comparing to a measured energy difference, that is almost always in the form of some thermodynamic quantity, most typically enthalpy or free energy. In this chapter, the most common procedures for augmenting electronic-structure calculations in order to convert single-molecule potential energies to ensemble thermodynamic variables will be detailed, and key potential ambiguities and pitfalls described. Within the context of certain assumptions, this connection can be established in a rigorous way. Note that the situation is less clear-cut for molecular mechanics calculations. As already discussed in Chapter 2, the ‘strain energy’ from a typical MM calculation must be thought Essentials of Computational Chemistry, 2nd Edition Christopher J. Cramer © 2004 John Wiley & Sons, Ltd ISBNs: 0-470-09181-9 (cased); 0-470-09182-7 (pbk)
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Essentials of Computational Chemist
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Essentials of Computational Chemist
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For Katherine
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viii CONTENTS 2.5 Menagerie of Mode
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x CONTENTS 7 Including Electron Cor
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xii CONTENTS 11.4 Strengths and Wea
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Preface to the First Edition Comput
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PREFACE TO THE FIRST EDITION xvii d
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xx PREFACE TO THE SECOND EDITION to
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Known Typographical and Other Error
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1 What are Theory, Computation, and
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Activation free energy (kcal mol
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1.3 COMPUTABLE QUANTITIES 5 etc.) f
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a a r 1 1.3 COMPUTABLE QUANTITIES 7
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1.3 COMPUTABLE QUANTITIES 9 path is
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1.4 COST AND EFFICIENCY 11 this is
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1.4 COST AND EFFICIENCY 13 kinds of
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Physical quantity (unit name) BIBLI
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2 Molecular Mechanics 2.1 History a
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2.2 POTENTIAL ENERGY FUNCTIONAL FOR
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2.3 FORCE-FIELD ENERGIES AND THERMO
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Heat of formation A E nb (A) 2.4 GE
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gradient vector, g, which is define
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Eq. (2.38) as 2.4 GEOMETRY OPTIMIZA
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2.4 GEOMETRY OPTIMIZATION 47 that t
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2.4 GEOMETRY OPTIMIZATION 49 is opp
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Table 2.1 Force fields Name (if any
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12 Davies, E. K. and Murrall, N. W.
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5 (MM2(85), MM2(91), Chem-3D) Compr
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2.5 MENAGERIE OF MODERN FORCE FIELD
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2.6 FORCE FIELDS AND DOCKING 63 Fig
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2.7 CASE STUDY: (2R ∗ ,4S ∗ )-1
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REFERENCES 67 Cramer, C. J. 1994.
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3 Simulations of Molecular Ensemble
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3.2 PHASE SPACE AND TRAJECTORIES 71
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m −b r eq −b 3.3 MOLECULAR DYNA
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and 3.3 MOLECULAR DYNAMICS 75 p(t +
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3.3 MOLECULAR DYNAMICS 77 step mean
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3.3 MOLECULAR DYNAMICS 79 of course
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3.4 MONTE CARLO 81 One way to reduc
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3.5 ENSEMBLE AND DYNAMICAL PROPERTY
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3.6 KEY DETAILS IN FORMALISM 89 Fig
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3.6 KEY DETAILS IN FORMALISM 91 alc
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3.6 KEY DETAILS IN FORMALISM 93 mor
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3.6 KEY DETAILS IN FORMALISM 95 der
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3.6 KEY DETAILS IN FORMALISM 97 to
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3.8 CASE STUDY: SILICA SODALITE 99
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BIBLIOGRAPHY AND SUGGESTED ADDITION
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REFERENCES 103 Jaqaman, K. and Orto
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106 4 FOUNDATIONS OF MOLECULAR ORBI
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132 5 SEMIEMPIRICAL IMPLEMENTATIONS
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166 6 AB INITIO HARTREE-FOCK MO THE
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204 7 INCLUDING ELECTRON CORRELATIO
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250 8 DENSITY FUNCTIONAL THEORY num
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252 8 DENSITY FUNCTIONAL THEORY for
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254 8 DENSITY FUNCTIONAL THEORY fun
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256 8 DENSITY FUNCTIONAL THEORY Not
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258 8 DENSITY FUNCTIONAL THEORY emp
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260 8 DENSITY FUNCTIONAL THEORY whe
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264 8 DENSITY FUNCTIONAL THEORY [As
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272 8 DENSITY FUNCTIONAL THEORY Ano
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274 8 DENSITY FUNCTIONAL THEORY Eve
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276 8 DENSITY FUNCTIONAL THEORY val
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278 8 DENSITY FUNCTIONAL THEORY acc
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280 8 DENSITY FUNCTIONAL THEORY als
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282 8 DENSITY FUNCTIONAL THEORY Tab
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294 8 DENSITY FUNCTIONAL THEORY con
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300 8 DENSITY FUNCTIONAL THEORY dou
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404 11 IMPLICIT MODELS FOR CONDENSE
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12 Explicit Models for Condensed Ph
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12.2 COMPUTING FREE-ENERGY DIFFEREN
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∆G 12.2 COMPUTING FREE-ENERGY DIF
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12.4 SOLVENT MODELS 445 In some cas
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12.4 SOLVENT MODELS 447 increases t
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12.5 RELATIVE MERITS OF EXPLICIT AN
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12.5 RELATIVE MERITS OF EXPLICIT AN
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12.6 CASE STUDY: BINDING OF BIOTIN
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REFERENCES 455 Levy, R. M. and Gall
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13 Hybrid Quantal/Classical Models
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13.2 BOUNDARIES THROUGH SPACE 459 a
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13.2 BOUNDARIES THROUGH SPACE 461 i
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13.2 BOUNDARIES THROUGH SPACE 463 T
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13.2 BOUNDARIES THROUGH SPACE 465 W
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13.3 BOUNDARIES THROUGH BONDS 467 t
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13.3 BOUNDARIES THROUGH BONDS 469 o
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180 180 4 10 15 15 20 150 6 8 150 8
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13.3 BOUNDARIES THROUGH BONDS 473 O
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13.3.3 Frozen Orbitals 13.3 BOUNDAR
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Link atom LSCF GHO 13.4 EMPIRICAL V
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13.4 EMPIRICAL VALENCE BOND METHODS
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13.4 EMPIRICAL VALENCE BOND METHODS
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13.5 CASE STUDY: CATALYTIC MECHANIS
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REFERENCES 485 Gao, J., Amara, P.,
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14 Excited Electronic States 14.1 D
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14.1 DETERMINANTAL/CONFIGURATIONAL
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14.1 DETERMINANTAL/CONFIGURATIONAL
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14.2 SINGLY EXCITED STATES 493 and
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14.2 SINGLY EXCITED STATES 495 Tabl
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14.2 SINGLY EXCITED STATES 497 wher
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14.3 GENERAL EXCITED STATE METHODS
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14.3 GENERAL EXCITED STATE METHODS
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14.4 SUM AND PROJECTION METHODS 503
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14.4 SUM AND PROJECTION METHODS 505
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14.5 TRANSITION PROBABILITIES 507 o
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14.5 TRANSITION PROBABILITIES 509 I
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14.6 SOLVATOCHROMISM 511 overlap) l
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14.7 CASE STUDY: ORGANIC LIGHT EMIT
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BIBLIOGRAPHY AND SUGGESTED ADDITION
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REFERENCES 517 Kim, K., Shavitt, I,
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520 15 ADIABATIC REACTION DYNAMICS
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Appendix A Acronym Glossary Note: B
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ACRONYM GLOSSARY 551 ECP Effective
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ACRONYM GLOSSARY 553 mPW1S mPW1PW91
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ACRONYM GLOSSARY 555 SF-CISD Spin-f
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558 APPENDIX B H 3 C CH 3 H H H a
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560 APPENDIX B Linear molecule? no
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562 APPENDIX B Table B.5 Product ru
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Appendix C Spin Algebra C.1 Spin Op
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function we have SPIN ALGEBRA 567
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SPIN ALGEBRA 569 + = 1 1 ( 2 2 α(
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C.3 UHF Wave Functions SPIN ALGEBRA
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SPIN ALGEBRA 573 = 〈cs s |H |cs s
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Appendix D Orbital Localization D.1
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ORBITAL LOCALIZATION 577 〈|H |〉
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E rel (kcal mol −1 ) 10 8 6 4 2 0
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582 INDEX B3PW91, 266-267, 284, 288
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584 INDEX Convergence (continued) f
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Global minimum, 23, 46, 97, 146, 38
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Matrix diagonalization, (see also S
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primitive, 168-173 Slater-type, 134
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Reductive dechlorination, 422-424 R
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SYBYL, 58 Symmetry, 182-188, 209, 2
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