Essentials of Computational Chemistry

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xii CONTENTS 11.4 Strengths and Weaknesses of Continuum Solvation Models 410 11.4.1 General Performance for Solvation Free Energies 410 11.4.2 Partitioning 416 11.4.3 Non-isotropic Media 416 11.4.4 Potentials of Mean Force and Solvent Structure 419 11.4.5 Molecular Dynamics with Implicit Solvent 420 11.4.6 Equilibrium vs. Non-equilibrium Solvation 421 11.5 Case Study: Aqueous Reductive Dechlorination of Hexachloroethane 422 Bibliography and Suggested Additional Reading 424 References 425 12 Explicit Models for Condensed Phases 429 12.1 Motivation 429 12.2 Computing Free-energy Differences 429 12.2.1 Raw Differences 430 12.2.2 Free-energy Perturbation 432 12.2.3 Slow Growth and Thermodynamic Integration 435 12.2.4 Free-energy Cycles 437 12.2.5 Potentials of Mean Force 439 12.2.6 Technical Issues and Error Analysis 443 12.3 Other Thermodynamic Properties 444 12.4 Solvent Models 445 12.4.1 Classical Models 445 12.4.2 Quantal Models 447 12.5 Relative Merits of Explicit and Implicit Solvent Models 448 12.5.1 Analysis of Solvation Shell Structure and Energetics 448 12.5.2 Speed/Efficiency 450 12.5.3 Non-equilibrium Solvation 450 12.5.4 Mixed Explicit/Implicit Models 451 12.6 Case Study: Binding of Biotin Analogs to Avidin 452 Bibliography and Suggested Additional Reading 454 References 455 13 Hybrid Quantal/Classical Models 457 13.1 Motivation 457 13.2 Boundaries Through Space 458 13.2.1 Unpolarized Interactions 459 13.2.2 Polarized QM/Unpolarized MM 461 13.2.3 Fully Polarized Interactions 466 13.3 Boundaries Through Bonds 467 13.3.1 Linear Combinations of Model Compounds 467 13.3.2 Link Atoms 473 13.3.3 Frozen Orbitals 475 13.4 Empirical Valence Bond Methods 477 13.4.1 Potential Energy Surfaces 478 13.4.2 Following Reaction Paths 480 13.4.3 Generalization to QM/MM 481 13.5 Case Study: Catalytic Mechanism of Yeast Enolase 482 Bibliography and Suggested Additional Reading 484 References 485 14 Excited Electronic States 487 14.1 Determinantal/Configurational Representation of Excited States 487
CONTENTS xiii 14.2 Singly Excited States 492 14.2.1 SCF Applicability 493 14.2.2 CI Singles 496 14.2.3 Rydberg States 498 14.3 General Excited State Methods 499 14.3.1 Higher Roots in MCSCF and CI Calculations 499 14.3.2 Propagator Methods and Time-dependent DFT 501 14.4 Sum and Projection Methods 504 14.5 Transition Probabilities 507 14.6 Solvatochromism 511 14.7 Case Study: Organic Light Emitting Diode Alq3 513 Bibliography and Suggested Additional Reading 515 References 516 15 Adiabatic Reaction Dynamics 519 15.1 Reaction Kinetics and Rate Constants 519 15.1.1 Unimolecular Reactions 520 15.1.2 Bimolecular Reactions 521 15.2 Reaction Paths and Transition States 522 15.3 Transition-state Theory 524 15.3.1 Canonical Equation 524 15.3.2 Variational Transition-state Theory 531 15.3.3 Quantum Effects on the Rate Constant 533 15.4 Condensed-phase Dynamics 538 15.5 Non-adiabatic Dynamics 539 15.5.1 General Surface Crossings 539 15.5.2 Marcus Theory 541 15.6 Case Study: Isomerization of Propylene Oxide 544 Bibliography and Suggested Additional Reading 546 References 546 Appendix A Acronym Glossary 549 Appendix B Symmetry and Group Theory 557 B.1 Symmetry Elements 557 B.2 Molecular Point Groups and Irreducible Representations 559 B.3 Assigning Electronic State Symmetries 561 B.4 Symmetry in the Evaluation of Integrals and Partition Functions 562 Appendix C Spin Algebra 565 C.1 Spin Operators 565 C.2 Pure- and Mixed-spin Wave Functions 566 C.3 UHF Wave Functions 571 C.4 Spin Projection/Annihilation 571 Reference 574 Appendix D Orbital Localization 575 D.1 Orbitals as Empirical Constructs 575 D.2 Natural Bond Orbital Analysis 578 References 579 Index 581
Page 2 and 3: Essentials of Computational Chemist
Page 4 and 5: Essentials of Computational Chemist
Page 6 and 7: For Katherine
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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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266 8 DENSITY FUNCTIONAL THEORY som
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268 8 DENSITY FUNCTIONAL THEORY for
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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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302 8 DENSITY FUNCTIONAL THEORY Cho
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9 Charge Distribution and Spectrosc
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9.1 PROPERTIES RELATED TO CHARGE DI
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H H P O H H H F Cl Cl P P F H F F P
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9.3 SPECTROSCOPY OF NUCLEAR MOTION
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Energy hn 0→1 9.3 SPECTROSCOPY OF
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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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