Essentials of Computational Chemistry

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primitive, 168–173 Slater-type, 134, 136–138, 141, 148, 155, 158, 167–172, 181–182, 270, 273, 328, 347–348 spin, 124–126, 188–190, 234, 324, 575 valence, 134, 140, 145, 155, 171–173, 328, 345, 498 virtual, 195, 205–212, 216, 221, 228–229, 272, 487–496 Orthogonality, 107, 126, 158, 177, 182, 206, 221, 314, 475–476, 491–492, 495–496, 501, 509 Orthonormality, 107, 218, 312, 314, 540, 565, 567, 569 Oscillator strength, 141 Overlap integral, 114, 134–138, 262, 312–314, 321, 325, 328, 571 Overtone, 341 Oxygen atom, 227–228 P exchange, 263, 297 P86 correlation, 263, 290, 297 Pairlist, 47, 90 Pairwise descreening, 404, 420 Parameterization, 36–39, 140–142, 145–147, 154, 172, 237–244, 266–271, 341–342, 410–411, 418, 445–447, 459–463, 477–482, 497, 514 Parameterized correlation methods, 237–244, 370–371 Pariser-Parr approximation, 137 Pariser-Parr-Pople model, 138, 502 Partial charge, (see Atomic partial charge) Particle in a box, 361 Particle-mesh Ewald, (see Ewald sum) Partition coefficient, 411, 416–419 Partition function, 71, 357–366, 429–432, 525–531, 562–563 activated complex, 525–532, 535 electronic, 359–361 molecular, 359–366 rotational, 359, 362–364, 528–529, 563 translational, 359, 361–362, 526–529 vibrational, 359, 364–366, 484, 528–529 Pauli exclusion principle, 123–124, 179, 251 PBE, 263, 283, 285, 287, 289, 292, 297 PBE1PBE, 267, 283, 285, 287, 290, 292, 298, 330, 347, 503–504 PCI-80, 238, 286, 370 INDEX 591 PCM, (see Solvation) PDDG, 158 PEF95SAC, 54 Penalty function, 36–37, 41, 146, 154 Perchloroethylene, 423–424, 460 Periodic boundary conditions, 86–89, 101, 273, 431, 448, 452, 459 Permutation operator, 123–124 Perturbation theory, 216–224, 226, 228–243, 336, 401, 469, 498, 573–574 convergence, 228–229 localized MP2, 222 multireference, 223, 233–234, 375, 495, 501 predictions from, 281, 287–289, 291–292, 294, 321–323, 327–330, 338–340, 343, 346–347, 366 spin-component-scaled, 239 spin-projected, 574 time-dependent, 507 Phase angle, 23, 25–26, 35, 40 Phase point, 70–72, 80–83, 448 Phase space, 70–82, 92–98, 420, 429–430, 439, 443–444, 448, 450–451, 538 Phenylnitrene, 276, 490–492, 494–496, 500–501, 504–505 Phenylnitrenium cation, 272 Pierotti’s formula, 406 pKa, (see Acidity) PKZB, 264, 283, 285, 289, 292, 298 Planck’s constant, 15, 107, 356, 489, 507 PM3, 146–156, 158, 160–162, 193, 281, 320–323, 338, 340, 469 PM3BP, 156 PM3(tm), 154 PM4 and PM5, 151, 155 Point group, 183–186, 232, 234, 254, 362–363, 490–492, 494, 514, 559–563, 577 Poisson equation, 394–402 Poisson-Boltzmann equation, 394–395, 399–400, 453 Polarizability, 33–34, 90–91, 155, 294, 325–327, 387, 407, 446–447, 451, 464, 466–467, 513 frequency-dependent, 502 Polarization, 90–91, 156, 173–175, 387, 411, 459, 462, 466–467, 512 free energy, 394–405, 449
592 INDEX Population analysis, (see also Atomic partial charge), 315, 476, 578 bond order, 320 Löwdin, 314–315, 320 Mulliken, 199, 270, 312–315, 319–323 natural, 314–315, 321–323, 578 Potential energy functions bond stretching, 18–21, 473 torsions, 22–27, 377, 474 valence angle bending, 21–22, 26, 473 van der Waals, 27–30, 46 Potential energy surface, 6–10, 17, 99, 111, 183–187, 216, 221, 238, 244–246, 331, 334–338, 356, 469, 511–512, 522–523, 535–536 electron-transfer, 542–543 EVB, 478–481 excited-state, 490, 500, 511–512, 539–544 solvated, 389–393, 409, 415, 380, 423, 511–512, 538–539 Potential <strong>of</strong> mean force, 146, 419–420, 439–442, 463–464 PPP, (see Pariser-Parr-Pople) Pressure, 92–93, 358–359, 380, 385, 430, 443 standard-state, 361–362 Principal components analysis, 95, 421 Probability, (see also Transition probability), 4, 12, 69, 81, 83, 85, 92–93, 98, 106, 112, 121, 125, 166, 262, 377, 430–432, 439–441, 541 Projection, (see Spin, projection) Prolate top, 333, 362 Propagation, 74–79 Propagator method, 497, 501–504 Propylene oxide, 544–546-497 Protein, (see also Enzyme-substrate binding), 31, 35, 38, 54, 56–59, 77, 96–97, 99, 157, 408, 421, 444, 452, 473, 475–476, 481–484, 538 Proton affinity, 148, 194, 291 Proton transfer, 442, 477–481 Pseudobond/pseudoangle, 35–36 Pseudohalogen, 474, 477 PW exchange, 263, 267, 298, 330 PW91 correlation, 263, 266, 291, 298 PWPW91, 283, 285, 287, 289, 339 QCISD, (see Configuration interaction, quadratic) QM/MM, 61, 157, 447, 457–484, 513, 532 AM1/OPLS, 465 AM1/TIP3P, 463–465 AOC, 459–460, 463 boundary, 458, 467–468, 473–476 HF/3–21G/OPLS, 465 IMOMM, 472 ONIOM, 473 XSOL, 465 QSAR and QSPR, (see Structure-activity relationship) Quadrature, 260, 338 Quadrupole, 31, 144, 154, 307, 398 Quantization, 105 Quantum mechanics, 1, 4–5, 28, 105–129, 309, 326, 357, 457–484, 575 Quantum numbers, 122–123, 134, 167, 229, 324, 333, 336, 361 R12 method, 229–230, 249 Radial distribution function, 84–86, 449, 465 Radical, 105, 117, 119, 148, 179, 185–190, 194–195, 199–200, 234, 244, 279, 329, 331, 349 Radical polymerization, 199–200 Radius, (see Born equation, Cavity, and van der Waals) Raman spectroscopy, 341 Random number, 82 Rare event, 440, 442 RASSCF, (see Self-consistent field, multiconfiguration) Rate constant, 12, 519–522, 532–538, 541–546 Rate-determining step, 481–482, 537 Reaction coordinate, 48–49, 207, 211, 241, 277, 391–392, 409, 419, 439–442, 449, 451, 457–458, 463–464, 479–484, 511, 522–526, 536–538, 542–546 intrinsic, (see Minimum-energy path) Reaction dynamics, (see Dynamics) Reaction field, (see also Solvation), 387, 394, 396, 400–401, 404, 513, 542 charge transfer, 415, 448 self-consistent, 393–406, 410–424, 449–450, 513 Reaction quotient, 379 Redox potential, (see Electrochemistry) Reduced mass, 17, 332, 336–337, 357, 535
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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 552 and 553: 536 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 604 and 605: Reductive dechlorination, 422-424 R
Page 606 and 607: SYBYL, 58 Symmetry, 182-188, 209, 2
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