Essentials of Computational Chemistry

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SYBYL, 58 Symmetry, 182–188, 209, 215, 275–276, 279, 335, 490–491, 498–500, 510, 557–562 number, 362–364, 377 τ1 correlation, 264, 298 τHCTH, 264, 285, 298 T1 diagnostic, 226 TDDFT, (see Density Functional Theory) Temperature, 28, 61, 69–71, 75, 77–78, 82, 91–92, 97, 336, 356–357, 360, 362–363, 369–370, 372, 377, 380, 438, 442, 444, 447, 519, 523, 527–528, 531–533, 535–538, 542, 544, 546 Tetramethylsilane, 346 Theory, (definition), 1 Thermal electron convention, 378 Thermodynamic integration, 435–437, 443, 454 Thermodynamics, 11, 39–40, 355–380, 429–445 Thomas-Fermi functional, 251 Thomas-Fermi-Dirac functional, 252 TIPnP, (n = 3, 4; see Water) Torsions, (see also Potential Energy Functions), 22, 27, 356, 376–377, 469, 578–579 TPSS, 264, 279, 283, 290, 292, 298 TPSSh, 283, 290, 292, 298 Trajectory, (see also Propagation), 70–80, 482–484, 522, 541 Transition dipole moment, 501–502, 510, 563 Transition metal, (see also Metal), 58, 140–141, 154, 179, 268, 275, 285–286, 291, 299, 345, 504 Transition probability, 272, 305, 507–511 Transition state, (see also Geometry), 7, 9, 11, 46, 48–50, 62, 133, 159–162, 185–186, 208, 235, 279, 293, 300, 338, 378, 390–93, 421–422, 440, 450–452, 463–464, 468, 482–484, 507, 522–533, 536, 538–539, 544–546 Transition-state theory, 160, 524–537 microcanonical, 536 variational, 531–533, 536, 538 Translation, 6, 327, 361–362, 378, 386 Transmission coefficient, 535–537 Trichloroacetic acid, 422–424 Trimethylenemethane, 204–209, 277, 504 INDEX 595 Tunneling, 482, 530, 533–538, 544 Turning point, 511 Two-electron integral, 127–129, 132, 136–140, 143–144, 154, 158, 166, 169, 191, 221, 251, 257, 273, 462, 475 Coulomb, 122, 125–127, 138, 189–191, 273–274, 402 exchange, 125–127, 189, 191, 214, 261 symmetry, 186 UFF, 38, 58, 60, 469 Umbrella potential, 99, 440–441, 451, 481 Uncertainty principle, 334 Uniform electron gas, 250–252, 259–260, 262 United-atom model, 38, 51, 446 Universal gas constant, 359, 542 Urey-Bradley term, 26, 100 UV-Vis spectroscopy, 135–136, 139–141, 393, 411, 507–508, 511–515 effect <strong>of</strong> solvation, (see Solvatochromism) VALBOND, 38, 58 Valence angle bending, (see Potential Energy Functions) Valence bond, (see also Empirical valence bond), 49 van der Waals, interaction, (see Potential Energy Functions) radius, 311, 399, 401, 408 surface, 308, 318, 400, 408 van’t H<strong>of</strong>f plot, 444 Vapor pressure, 152, 405 Variational principle, 108–110, 172, 203, 212, 215, 222, 251, 253–254, 257, 490–491, 499 Verlet algorithm, 77–79 Vertical process, 331, 423, 489–490, 505–506, 511–513 Vibrational averaging, 61, 342–344 Vibrational frequency, (see Frequency) Vibrational motion, 76, 334–336, 356 Vibrational spectroscopy, 17, 21, 35, 88, 101, 332, 334–342, 349–351, 411, 514 Voronoi cell, 318 VSXC, 264, 283, 285, 287, 290, 292, 298, 340 VTST, (see Transition-state theory) VWN, 259–260, 298 VX, 177–178
596 INDEX Wn, (n = 1–4; see Multilevel methods) Water, 2, 82–83, 85, 91, 151, 172–173, 184, 230, 236, 291, 294, 306–307, 309, 315, 347–348, 559 acidity, 477–481 as solvent, 385–387, 390, 392, 407–408, 422–424, 429–433, 437–438, 445, 449, 452, 460, 462–464, 480–481 density anomaly, 447 polarizable models, 90, 446–447 SPC, 446 TIPnP, (n = 3, 4), 446, 449, 462 Water dimer, 149–151 Wave function, 4, 105–129, 166, 181, 186–190, 230, 244, 249, 312, 324, 326, 411, 459–466, 561–562, 575–577 adiabatic, 478, 539–540 CIS, 214, 496–498 determination from electron density, 253–254 excited-state, 487–494, 497–501, 504–507 harmonic oscillator, 335–337, 510–511 Kohn-Sham, 271–273, 448, 506 mixed-spin state, 504–507, 566–570 multideterminantal, 190, 203–216, 230–235, 274–277, 324, 487–488, 562 nuclear, 111, 331–333, 335–337, 342–343, 539–541 rigid-rotor, 332–333, 510 single-determinantal, 203–205, 222, 226, 230–232, 271–273, 487–488, 493 stability, 187, 192, 234, 275, 475, 498 VB, 477–479 vibrational, 61, 334–337, 342–343, 510–511 Weighted histogram analysis method, 441–442 Wigner correction, 535 X exchange, 263, 298 Xα method, 252, 259 X-ray crystallography, 3, 61–62, 84, 315, 470–471 X3LYP, 267, 279, 284, 290, 298 XLYP, 283, 290 XSOL, (see QM/MM) Zeolite, 99–101, 312 Zero-flux surface, 316–317 Zero-point vibrational energy, 62, 69, 356–357, 364–365, 368–369, 375, 484, 490, 495, 511, 525, 529–532, 545 Zwitterion, 392, 465
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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 556 and 557: 540 15 ADIABATIC REACTION DYNAMICS
Page 564 and 565: Appendix A Acronym Glossary Note: B
Page 566 and 567: ACRONYM GLOSSARY 551 ECP Effective
Page 568 and 569: ACRONYM GLOSSARY 553 mPW1S mPW1PW91
Page 570 and 571: ACRONYM GLOSSARY 555 SF-CISD Spin-f
Page 572 and 573: 558 APPENDIX B H 3 C CH 3 H H H a
Page 574 and 575: 560 APPENDIX B Linear molecule? no
Page 576 and 577: 562 APPENDIX B Table B.5 Product ru
Page 578 and 579: Appendix C Spin Algebra C.1 Spin Op
Page 580 and 581: function we have SPIN ALGEBRA 567
Page 582 and 583: SPIN ALGEBRA 569 + = 1 1 ( 2 2 α(
Page 584 and 585: C.3 UHF Wave Functions SPIN ALGEBRA
Page 586 and 587: SPIN ALGEBRA 573 = 〈cs s |H |cs s
Page 588 and 589: Appendix D Orbital Localization D.1
Page 590 and 591: ORBITAL LOCALIZATION 577 〈|H |〉
Page 592 and 593: E rel (kcal mol −1 ) 10 8 6 4 2 0
Page 594 and 595: 582 INDEX B3PW91, 266-267, 284, 288
Page 596 and 597: 584 INDEX Convergence (continued) f
Page 598 and 599: Global minimum, 23, 46, 97, 146, 38
Page 600 and 601: Matrix diagonalization, (see also S
Page 602 and 603: primitive, 168-173 Slater-type, 134
Page 604 and 605: Reductive dechlorination, 422-424 R
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