Essentials of Computational Chemistry

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Matrix diagonalization, (see also Scaling behavior), 14, 212–214, 262, 274, 462, 480, 496, 522 Matrix elements, (see also Configuration interaction), 114, 116, 119, 127–128, 138, 184–185, 213, 222, 257, 269, 272, 345, 462, 496–497, 502, 510, 562, 573 Matrix isolation, 349–351 Mayer bond order, 320–321 MBPTn, (see Perturbation theory) MCG3, (see Multilevel methods, multicoefficient models) MCSCF, (see Self-consistent field, multiconfiguration) Membrane, 418, 421 Memory, 13, 191 Menschutkin reaction, 393 meta-Generalized gradient approximation, 264, 268, 278, 285 Metal, (see also Solid and Transition metal), 26, 38, 61, 141, 179, 275, 286, 291, 299, 328, 452, 542 Metastability, 96 Methanol, 100, 156, 208, 211, 299–300, 319, 347, 437–438 Methyl radical, 116, 188–189, 330, 343–344, 374 Methyldiazonium cation, 317 Metropolis sampling, 81–82, 451, 459 Microcanonical ensemble, 91 MINDO/3, 141–145 Minimum, (see Global and Local minima) Minimum-energy path, (see also Reaction coordinate), 7, 449, 522–523, 531–532, 538, 545 Missing parameters, 39–41 MM2, 38, 40, 50, 55, 59–60 MM2*, 50–51 MM3, 14, 20–21, 38, 50, 55, 59–60, 64–65, 341, 469–471 MM3*, 50–51 MM4, 55 MMFF, 38, 50, 56, 60, 341, 459 MMX, 56 MNDO, 143–156, 158, 193, 281, 287, 346–347 MNDO/d, 145, 153–155 MNDOC, 145 Model, (definition), 2 INDEX 589 Model chemistry, 180, 240 Mole, 355 Molecular dynamics, (see Dynamics) Molecular electrostatic potential, (see Electrostatic potential) Molecular mechanics, 17–66, 150, 264, 341, 445, 457–484, 532 Molecular orbital, (see Orbital) Molecular orbital theory, 105–129, 203–244, 271–280, 285, 575–579 ab initio, 129, 131, 133, 143, 165–246 semiempirical, 128, 131–162, 237, 260, 375 Molecular rotational constant, 333 Molecular weight, 100, 152, 362, 380, 450 Molecularity, 519 MOMEC, 56 Moment <strong>of</strong> inertia, 6, 94, 332–334, 362–364, 377 Monte Carlo, 64, 80–82, 90, 92–93, 259, 431–434, 438–440, 444, 447, 449, 451, 459, 463, 513 Morse potential, 20–21, 30, 311, 478 mPBE exchange, 263, 279, 297 MPn, (n = 2, 3, 4,... ; see Perturbation theory) mPW exchange, 263, 297 MPW1K, 267–268, 279, 283, 285–288, 297 mPW1N, 268, 297 MPW1S, 268, 297 mPW1PW91, 268, 283, 287, 290, 292, 297, 339 mPW3PW91, 284, 293, 339 mPWPW91, 283, 285, 287, 290, 292, 339, 503 MST, (see Solvation, PCM) Mulliken, (see Population analysis) Multiconfigurational molecular mechanics, 50, 532 Multilevel methods, 239–244, 260 CBS, 239, 242, 281, 286–289, 371, 382 Gn, (n = 1–3), 240–243, 281, 284, 289, 291, 371, 382 multicoefficient models, 242–243, 281, 287 Wn, (n = 1–4), 242, 282, 289 Multiple-minima problem, 96–98, 451 Multipole expansion, 154, 307–308, 397–398, 401, 416
590 INDEX Multipole moment, electric, 30–33, 144, 154, 305–308, 317–318, 387–388, 397–398 magnetic, 326, 344 NBO, (see Orbital, natural) NDDO, 143–158, 371, 476 Newton’s equations <strong>of</strong> motion, 74 Newton’s second law, 74 Newton’s third law, 79 Newton-Raphson minimization, 44–46 NHE, (see Hydrogen electrode) Non-classical reflection, 534–535 Non-crossing rule, 499 Non-local DFT, (see Generalized gradient approximation and Gradient, electron density) Nonbonded interaction, (see also Charge-charge, Dipole-dipole, and Steric interactions and Dispersion), 19, 27, 30, 33–35, 40, 47, 62–64, 88, 100, 149, 151, 157, 195, 271, 278–279, 293, 311, 371, 432–434, 443, 459, 461, 467, 480 Normal mode, 46, 337, 341–342, 356, 364–366, 376, 391, 452, 514–515, 523, 530–531, 535 Normalization, 71, 84–87, 107, 124, 168, 203, 206, 218, 321, 361, 418, 439, 462, 504, 572 Nosé-Hoover coupling, 92 Nuclear magnetic resonance, 10, 36, 64–66, 305, 344–349, 411 Nuclear motion spectroscopy, (see also Rotational and Vibrational spectroscopies), 331–344 Nuclear Overhauser effect, 35–36, 99 Nuclear repulsion energy, 106, 110–111, 145, 158 Nucleic acids, 35, 38, 47, 57, 99, 156, 279, 387, 408, 411, 416–417, 421, 462, 469, 472 O exchange, 263, 267, 297 O3LYP, 267, 284, 287–288, 290, 297 Occupation number, 206, 210, 489 Octanol solution, 409, 446 Octanol-water partitioning, 152, 416, 438 Odd function, 342 OMn, (n = 1, 2), 158 One-electron integral, 127, 137–138, 153, 184, 262 external potential, 262 symmetry, 184 Open-shell singlet, 136, 190, 208, 276–277, 505, 570 Operator, 4, 106, 216–221, 249, 271, 396, 463, 565–566 cluster, 224–226 Coulomb and exchange, 127, 220, 265, 273–274 Fock, (see Hartree-Fock theory and Reaction field) Hamiltonian, (see Hamiltonian) Kirkwood-Onsager, 396 Kohn-Sham, (see Kohn-Sham theory) one-electron, 120–122, 126–129, 203, 223, 253, 255–256, 462, 466, 475, 510 permutation, 123–124 S 2 , 188, 324–325, 328, 506, 565–572 spin-annihilation, 506, 571–573 Sz, 122, 272, 324–325, 327, 565–571 OPLS, 38, 56, 60, 98–99, 438, 446, 449, 459–460 OPLSA*, 51 Optical rotatory dispersion, 504 Orbital, (see also Basis set) active space, 207–210, 233–234, 239, 499–501 banana-bond, 576 complex, 234 contracted, 168–173, 180 core, 134, 171–172, 209, 215, 224, 328, 345 energy, 111, 115–119, 128, 195, 219, 230–231, 269, 498, 502, 577 floating, 173 frozen, 215, 475–476 gauge-including, 345 Gaussian-type, 155, 167–180, 273–274, 328 generalized hybrid, 476–477, 483 hydrogenic, 112, 128, 134, 167–168 Kohn-Sham, 256–257, 264, 272, 306, 448, 502 localized, 209, 221, 345, 475–476, 575–579 molecular, 39, 100, 105–129, 149, 158, 165–199, 203–244, 306, 324, 328, 343, 475, 487–500, 506, 559–562, 571, 573, 575–577 natural, 578
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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 550 and 551: 534 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
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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
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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 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 602 and 603: primitive, 168-173 Slater-type, 134
Page 604 and 605: Reductive dechlorination, 422-424 R
Page 606 and 607: SYBYL, 58 Symmetry, 182-188, 209, 2
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