Essentials of Computational Chemistry

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288 8 DENSITY FUNCTIONAL THEORY Table 8.3 (continued) Level of theory Activation Reaction Mean Maximum Mean Maximum B3PW91 4.4 5.8 O3LYP Reaction set 3 4.7 5.8 b,e HF 18.7 26.7 3.8 6.5 CASSCF 16.0 34.6 14.7 20.6 MP2 4.6 7.6 6.0 9.6 CASPT2//CASSCF 2.4 5.7 1.6 4.5 CBS-QB3 1.9 4.3 1.6 2.5 BPW91 3.7 6.9 3.4 7.4 KMLYP 3.2 10.3 12.7 19.8 OLYP 3.4 9.0 6.2 12.9 OLYP/6-311+G(2d,p) 4.4 13.0 9.8 20.5 MPW1K/6-31+G(d,p) 2.2 6.9 6.2 10.0 B3LYP 1.7 6.0 4.1 8.6 B3LYP/6-31+G(d,p) 2.4 8.1 7.0 13.6 B3LYP/6-311+G(2d,p) 2.9 10.1 8.2 15.9 O3LYP//OLYP 3.0 9.0 3.9 8.3 a See Baker, Muir, and Andzelm (1995). b 6-31G(d) basis set unless otherwise indicated. c Using five spherical d functions instead of the usual six Cartesian functions implied by this basis set name. d See Lynch and Truhlar (2003a) and Zhao et al. (2004); 6-31+G(d,p) basis set; the Reaction column refers to the atomization enthalpies for six molecules chosen to be representative of a larger set in a fashion analogous to the H-atom transfer reactions, namely, SiO, S2, silane, propyne, glyoxal, and cyclobutane. e See Guner et al. (2003, 2004). functional to become systematically worse with increasing basis-set size, so some cancellation of errors appears to be responsible for the excellent performance of this functional when used with the 6-31G(d) basis set. This analysis is supported as well by the relatively poor performance of B3LYP for the forward reaction enthalpies. Indeed, although the best MO methods continue to perform well for this latter test, the best DFT functional was found to be BPW91, which was the worst for the activation enthalpies. St-Amant et al. (1995) have analyzed the utility of HF, MP2, LSDA, and BP86, using basis sets of DZP to TZP quality, for the prediction of 35 conformational energy differences in small to medium-sized organic molecules (e.g., axial–equatorial disposition of substituents on cyclohexanes, E vs. Z amide rotamers, s-cis vs. s-trans rotamers of carboxylic acids and conjugated systems, etc.) The mean unsigned errors over the data for these four methods are 0.5, 0.4, 0.6, and 0.3 kcal mol −1 , respectively; the average conformational energy difference is 1.6 kcal mol −1 . A substantial body of data exists evaluating the utility of DFT (and other methods) for computing ionization potentials and electron affinities following a SCF approach. These data are summarized over four different test sets in Table 8.4. The conclusions one may
8.6 GENERAL PERFORMANCE OVERVIEW OF DFT 289 Table 8.4 Mean absolute errors and maximum errors, where available, in IPs and EAs for different methods over several different test sets (eV) Level of theory IP test sets EA test sets G2 a G2/97 b G2 G2/97 MO theoretical methods HF 1.03c 1.10c (2.60) (2.21) G2(MP2) 0.1 0.1 G2 0.06 0.06 0.06 0.06 (0.19) (0.19) (0.14) (0.17) CBS-QB3 0.05 0.05 (0.12) (0.12) G3 0.04 0.04 0.05 0.04 (0.18) (0.18) (0.18) (0.18) W1 0.01 0.02 0.02 0.02 (0.06) (0.13) (0.05) (0.08) W2 0.01 0.01 LSDA functionals (0.05) (0.04) SVWN/6-311+G(2df,p) 0.7 0.6 0.7 0.7 (1.2) (1.7) (1.2) (1.3) SVWN/aug-cc-pVTZ 0.7 0.8 SVWN5/6-311+G(2df,p) 0.2 0.23c 0.3 0.24c GGA and MGGA functionals (0.6) (1.18) (0.7) (0.88) BB95/numeric 0.2 (0.5) BLYP/6-311+G(3df,2p) 0.19 0.29c 0.11 0.12c (0.6) (1.06) (0.4) (0.70) BLYP/aug-cc-pVTZ 0.2 0.1 BP86/6-311+G(3df,2p) 0.18 0.22c 0.21 0.19c (1.21) (0.89) BP86/aug-cc-pVTZ 0.2 0.2 BPW91/6-311+G(3df,2p) 0.16 0.24c 0.09 0.12c (1.14) (0.78) HCTH/6-311++G(3df,3pd) 0.23c (1.34) OLYP/6-311++G(3df,3pd) 0.29c 0.15c (1.11) (0.60) PBE/6-311+G(3df,2p) 0.16 0.24c 0.12 0.12c (0.5) (1.11) (0.3) (0.78) PKZB/6-311++G(3df,3pd) 0.31c 0.15c (1.31) (0.57) PWPW91/6-311++G(3df,3pd) 0.16 0.22c (1.19) 0.14 (continued overleaf )
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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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Page 324 and 325: 9 Charge Distribution and Spectrosc
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9.3 SPECTROSCOPY OF NUCLEAR MOTION
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9.4 NMR SPECTRAL PROPERTIES 345 The
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9.4 NMR SPECTRAL PROPERTIES 347 Tab
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9.5 CASE STUDY: MATRIX ISOLATION OF
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REFERENCES 351 The use of computed
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REFERENCES 353 Rablen, P. R., Pearl
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356 10 THERMODYNAMIC PROPERTIES of
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358 10 THERMODYNAMIC PROPERTIES whe
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360 10 THERMODYNAMIC PROPERTIES tha
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362 10 THERMODYNAMIC PROPERTIES (Th
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364 10 THERMODYNAMIC PROPERTIES the
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368 10 THERMODYNAMIC PROPERTIES Ene
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372 10 THERMODYNAMIC PROPERTIES 10.
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374 10 THERMODYNAMIC PROPERTIES gen
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382 10 THERMODYNAMIC PROPERTIES Tab
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384 10 THERMODYNAMIC PROPERTIES Clo
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386 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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