Essentials of Computational Chemistry

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E rel (kcal mol −1 ) 10 8 6 4 2 0 7 w O 5 O 4 6 1 2 3 ORBITAL LOCALIZATION 579 H w OCH3 C3H7 H −4 −8 −12 −16 −20 0 60 120 180 240 300 360 wO(2)C(3)O(4)C(5) (°) Figure D.2 The torsional potential for 2,4-dioxaheptane ( , left ordinate) exhibits a two-fold periodicity suggesting a large influence from hyperconjugative effects. The sum of the NBO interaction energies for the two O(4) lone pairs delocalizing into the C(3)–O(2) σ ∗ orbital(------,rightordinate) shows the same periodicity, with an amplitude of about 11 kcal mol −1 . The smaller amplitude of the full torsional potential reflects primarily the presence of other influences as well as the approximate nature of the NBO analysis. See Cramer, Kelterer, and French 2001 deriving from hyperconjugation. Figure D.2 illustrates how the minima in the torsional potential energy curve for 2,4-dioxaheptane are influenced by the changes in hyperconjugation between the O(4) lone pairs and the C(3)–O(2) antibonding σ ∗ orbital as quantified by NBO analysis (a similar analysis may be carried out for filled-orbital–filled-orbital repulsive interactions, which are the electronic component of steric interactions). This approach is a nice energetic complement to other analyses focusing on structural changes or changes in partial atomic charges (cf. Figure 9.3) in the investigation of hyperconjugative effects. Nevertheless, it must be stressed that the NBO procedure is only a conceptual model, since it is based on orbitals, and limitations in its utility may be expected in cases where chemical species are poorly represented as Lewis structures. References Cramer, C. J., Kelterer, A.-M., and French, A. D. 2001. J. Comput. Chem., 22, 1194. Reed, A. E., Curtiss, L. A., and Weinhold, F. 1988. Chem. Rev., 88, 899. E NBO (kcal mol −1 )
Index Ab initio, (see Molecular orbital theory) Acidity, 11, 176, 194, 410–413, 415, 469, 481 Activated complex, 523–527, 531, 535, 538 Activation energy, 62, 132, 149–150, 267, 285–288, 300, 349, 378, 390, 422, 440–442, 483–484, 527–539, 543–545 Active space, (see Orbital) Adiabatic connection, 264–268, 273, 278–300, 340, 371 Adiabatic process, 331, 489–490, 497, 505, 519 Alkane solvation, 388, 407 Allyl system, 116–119, 234 Alq3, 513–515 AM1, 145–156, 193, 281, 287, 313, 319–323, 338, 340, 375, 381–382, 459, 465, 476 AM1*, 154 AM1/d, 154 AM1/OPLS and AM1/TIP3P, (see QM/MM) AMBER, 51, 59, 99 AMBER*, 51, 60 Amine basicity, 91 Amsterdam Density Functional, 273 Analytic derivatives, (see Gradient) Anions, 119, 148, 176, 182, 244–246, 414 Anomeric effect, 23, 469, 578 Antisymmetry, 122–126, 190, 265 AOC, (see QM/MM) Aqueous solvation, (see Water, as solvent) Arrhenius equation, 528, 545 Atom types, 31, 38, 40, 48–49, 310, 356, 404, 408 Atomic partial charge, (see also Population analysis) 31–32, 100, 135, 151–152, 171, 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) 270, 309–324, 402–404, 411, 443, 446, 458, 462, 474–476, 480, 579 atoms-in-molecules, 309, 315–318 classes, 310–324 CMn, (n = 1–3), 319–324, 404, 459–461 conformational dependence, 313, 319 discretization, 399 electronegativity equalization, 54, 310–312 ESP, 318–319, 322–323, 449 GAPT, 315 Löwdin, 314–315, 320 Mulliken, 312–314, 320, 322–323, 404 NPA, 314–315, 322–323, 578 SCRF calculations, 404 Atomic radii, 27, 403 Atomic units, 15 Atomization energy, 111, 192, 267, 280–284, 367, 375, 381–382 Atoms-in-molecules, 315–318 Autocorrelation function, 86–88 Avidin, 452–454 Avogadro’s number, 359 Avoided crossing, 499, 540–541 B exchange, 263, 266–267, 295 B1B95, 267–268, 287, 290, 295 B1LYP, 267, 283, 292, 295, 339 B1PW91, 267, 283, 292, 295, 339 B3LYP, 241, 267–268, 271, 278–279, 284–286, 290–292, 294–295, 298–299, 330, 339–340, 347, 350, 381–382, 414, 544–545 B3LYP*, 268, 295 B3P86, 284, 290–291, 330
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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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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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Page 542 and 543: 526 15 ADIABATIC REACTION DYNAMICS
Page 564 and 565: Appendix A Acronym Glossary Note: B
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Page 578 and 579: Appendix C Spin Algebra C.1 Spin Op
Page 580 and 581: function we have SPIN ALGEBRA 567
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Page 584 and 585: C.3 UHF Wave Functions SPIN ALGEBRA
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Page 588 and 589: Appendix D Orbital Localization D.1
Page 590 and 591: ORBITAL LOCALIZATION 577 〈|H |〉
Page 594 and 595: 582 INDEX B3PW91, 266-267, 284, 288
Page 596 and 597: 584 INDEX Convergence (continued) f
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Page 600 and 601: Matrix diagonalization, (see also S
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Page 604 and 605: Reductive dechlorination, 422-424 R
Page 606 and 607: SYBYL, 58 Symmetry, 182-188, 209, 2
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