Essentials of Computational Chemistry

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Reductive dechlorination, 422–424 Reference interaction site model, 465–467 Relativistic effects, 107, 140, 179, 223–224, 345, 368, 565 Relativity, 123, 129, 565 Renner-Teller, 244 Reorganization energy, 454, 542–543 Resolution <strong>of</strong> the identity, 573 Resonance energy, 118–119 Resonance integral, 114, 134, 144 Rice-Ramsperger-Kassel-Marcus theory, 536 Rigid-rotor approximation, 332–334, 362, 527, 531 Ring critical point, 316 RNA, (see Nucleic acids) Root switching, 499–500 Roothaan, 126–128 Root-mean-square deviation, 94 Rotation, 23, 97, 119, 150, 194, 280, 332–335, 363, 370, 439, 557–558 barriers about bonds, 150, 158, 194 spectroscopy, 332–334 RPA, (see Propagator method) RRKM theory, (see Rice-Ramsperger-Kassel-Marcus theory) Runge-Kutta integration, 78 Rydberg states, 113, 141, 498 Saddle point, (see also Transition state), 6, 9, 522–523, 531, 533–534, 539 SAM1, 154–155 Sampling, (see also Metropolis sampling), 72, 75, 82, 93, 95, 98, 415, 420, 432–445, 448, 450–451, 463 Scaling behavior, 46–48, 128, 190 CCSD, 225, 237 CCSD(T), 237 CCSDT, 225, 237 CISD, 214, 237 DFT, 262, 273–274 Ewald summation, 47 fast multipole methods, 48 Hartree-Fock theory, 128, 178, 190, 237, 262 linear, 14, 48, 157, 191, 222, 237, 274 matrix inversion/diagonalization, 14, 45, 185, 262, 274 molecular mechanics, 29, 47–48 MP2, 221, 237 INDEX 593 MP4, 222, 237 QCISD, 237 Schrödinger equation, 106, 539 electronic, 110, 120, 122, 128–129, 134, 165, 167, 170, 211, 225, 228, 237, 246, 250, 254–255, 278, 332–333, 507 non-linear, 225, 396–397, 400 nuclear, 331, 540 one-dimensional, 334–335, 536 rigid-rotor, 332–333, 362–363 time-dependent, 507, 532, 536 SCIPCM, (see Solvation) Second derivatives, (see Hessian) Secular equation, 113–115, 134–136, 212, 256 Selection rules, 332–333, 336, 341, 510 Self-consistent field, (see also Density functional, Hartree-Fock, and Kohn-Sham theories), 121–122, 126–129, 448, 475, 482, 493–496, 505, 514, 577 localized, 475–477 multiconfiguration, 205–211, 233–235, 246, 336, 349–350, 495, 499–501, 574 reaction field, (see Reaction field, self-consistent) Self-interaction error, 251, 263, 278, 280 Semiempirical, (see Molecular orbital theory) SHAKE, 79 SHAPES, 26, 58 Shear viscosity, 88 Simulated annealing, 97 Simulation, 38, 69–99, 319–320, 357, 429–454, 459, 462–465, 475–477, 513 SINDO1, 141–143, 153 Single-point calculation, 129, 192, 345, 473 Single topology, 443 Singlet-triplet splitting, 138, 216, 232–234, 275–277, 350, 493–495 Size-consistency, 215, 221, 225–226, 241, 257 Slater determinant, 124–126, 166, 203, 255–256, 265, 272, 274, 328, 396, 400, 461, 487–488, 493, 504, 573 Slater exchange, 252, 258, 260 Slater-type orbitals, (see Orbital) Slow growth, 435–437, 443 SMx model, (see Solvation) SN2 reaction, 185–186, 198, 293, 390, 440 S<strong>of</strong>tware, 12–15
594 INDEX Soil, 418 Solid, (see also Metal), 9, 49, 89, 99–101, 136, 186, 192, 252, 269, 273, 366, 418, 470, 498, 559 Solubility, 418 Solvation, (see also Condensed-phase effects and Reaction Field), continuum, 385–386, 393–424, 448–454, 460, 462, 467, 469, 473, 513, 538 convergence, 401 COSMO and COSMO-RS, 404–406 effect on UV/Vis spectroscopy, (see Solvatochromism) effective coordinate, 539, 542–544 electrostatic component, 397–410, 449 explicit modeling, 91, 429–454, 459–460, 462 explicit/implicit hybrid models, 421, 451–452 free energy, 386–424, 429, 437–439, 458, 463–466 generalized Born, (see Born equation) GB/SA, 408–409 IEF-PCM, 401 ions, 90, 447 IPCM, 401 MST-ST, 408–410, 416–417 non-electrostatic component, (see also Cavitation and Dispersion), 406–410, 421 non-equilibrium, 421–422, 450–451, 538, 542–543 non-isotropic, 418 PCM, 400–401, 405, 417, 473 proton, 410, 412 SCIPCM, 401 separable equilibrium, 538 shell, 86, 385–386, 410, 420, 449–452, 512–513 SMx, 387–388, 404, 409, 411, 416–418, 422–424, 438, 448, 460, 462 supermolecule, 415–416, 450–451 time scale, 421–422 Solvatochromism, 393, 511–5133 Solvent-accessible surface area, (see Surface area) Solvent model, 400–403 Solvent-separated pair, 419–420 Solvent-solvent interaction, 432, 436 Space group, 559 SPC, (see Water) Spherical harmonics, 134, 332–333 Spin, 122–124, 136, 258, 324–325, 360, 487–488, 492, 565–574 contamination, 190, 234, 272–273, 275–276, 324–325, 328–330, 494–495, 506–507, 571–574 degeneracy, 360 density, 189, 199, 330 polarization, 188–190, 199, 258–259, 328 projection, 234, 325, 328–329, 506–507, 571–574 Spin-orbit coupling, 107, 129, 242, 361, 368–369 Spin-orbital, (see Orbital) Spin-spin coupling constant, 305, 345–349 SRP, 155–156 Standard state, 361–362, 366–375, 386, 526 conversion, 378–379, 386, 423 elemental, 366–372 State-averaging, 500 Stationary point, 24–25, 45–46, 133, 135, 183, 185, 192, 262, 300, 338, 356, 389–393, 423, 511, 523, 527, 529, 531, 545 Statistical mechanics, 357–366, 377, 386 Steepest descent minimization, 44 Steric interaction, 19, 24, 27–30, 452–454, 467, 579 Stirling’s approximation, 359, 362 STO-3G, (see Basis set) Stochastic dynamics, 79–80 Stokes shift, 489, 515 Strain energy, 21, 40–41, 355–356 Structure-activity relationship, 152–153, 418 Structure prediction, 19, 61 Sublimation, 418 Sucrose, 469–472 Sum method, 494–495, 504–507, 570 Supercritical fluid, 417 Surface area, 47, 152, 386, 400, 407 solvent-accessible, 407–409 Surface hopping, 540–541 Surface tension, 407–410, 452, 467 SVWN, 260, 282, 286, 289, 291, 294, 339 Switching function, 47, 100, 394 Switching parameter, (see Coupling parameter)
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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 554 and 555: 538 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
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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 600 and 601: Matrix diagonalization, (see also S
Page 602 and 603: primitive, 168-173 Slater-type, 134
Page 606 and 607: SYBYL, 58 Symmetry, 182-188, 209, 2
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