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Michael Baer, Gert D.Billing — Advances in Chemical Physics, The Role of Degenerate States in Chemistry, Vol. 124
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Íàçâàíèå: Advances in Chemical Physics, The Role of Degenerate States in Chemistry, Vol. 124
Àâòîðû: Michael Baer, Gert D.Billing
Àííîòàöèÿ: Edited by Nobel Prize-winner Ilya Prigogine and renowned authority Stuart A. Rice, the Advances in Chemical Physics series provides a forum for critical, authoritative evaluations in every area of the discipline. In a format that encourages the expression of individual points of view, experts in the field present comprehensive analyses of subjects of interest.
This stand-alone, special topics volume, edited by Gert D. Billing of the University of Copenhagen and Michael Baer of the Soreq Nuclear Research Center in Yavne, Israel, reports recent advances on the role of degenerate states in chemistry.
Volume 124 collects innovative papers on "Complex States of Simple Molecular Systems," "Electron Nuclear Dynamics," "Conical Intersections and the Spin-Orbit Interaction," and many more related topics. Advances in Chemical Physics remains the premier venue for presentations of new findings in its field.
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Ãîä èçäàíèÿ: 2002
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Äîáàâëåíà â êàòàëîã: 05.08.2009
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Ïðåäìåòíûé óêàçàòåëü
Electronic states, three-state molecular system, non-adiabatic coupling, strongly coupled (2, 3) and (3, 4) conical intersections, “real” three-state systems 113—117
Electronic states, three-state molecular system, non-adiabatic coupling, theoretical-numeric approach 101—103
Electronic states, three-state molecular system, non-adiabatic coupling, Wigner rotation/adiabatic-to-diabatic transformation matrices 92
Electronic states, two-state molecular system, non-adiabatic coupling, Herzberg — Longuet — Higgins phase 185
Electronic states, two-state molecular system, non-adiabatic coupling, quantization 58—59
Electronic states, two-state molecular system, single conical intersection solution 97— 101
Electronic states, two-state molecular system, Wigner rotation/adiabatic-to-diabatic transformation matrices 92
Electronic states, two-state molecular system, “real” system properties 104—112
Electronic states, two-state molecular system, “real” system properties, -molecule: (1, 2) and (2, 3) conical intersections 109—112
Electronic states, two-state molecular system, “real” system properties, -molecule: (1, 2) and (2, 3) conical intersections, “real” two-state systems 109—112
Electronic states, two-state molecular system, “real” system properties, system and isotopic analogues 103—109
Electronic structure theory, electron nuclear dynamics (END), structure and properties 326—327
Electronic structure theory, electron nuclear dynamics (END), theoretical background 324—325
Electronic structure theory, electron nuclear dynamics (END), time-dependent variational principle (TDVP), general nuclear dynamics 334—337
Electronic wave function, permutational symmetry 680—682
Elhanine, M. 434(5) 500
Elizaga, D. 67(91) 141
Ellison, F.O. 345(49) 353
Elran, Y. 380(154—155) 428
Emile, O. 213(230) 279
Empirical valence bond (EVB), direct molecular dynamics, theoretical background 359—361
Energy format, permutational symmetry 737—738
Engels, B. 586(17) 610(17) 620(17) 622(17) 624(123—124) 625(142—145) 626(142—145 149 151 153) 627(144) 628(153) 630(144) 631(145 149 153) 634(153) 638(144) 641(153) 646(153) 647(149) 654 656—657
Englman, R. 3(14) 10(22) 13(26) 28(26 36) 33(14) 37 41(12 21 24 27—28 55—56) 42(12 55—56) 43(12) 54(81) 68(21) 70(81) 71(12) 73(12) 80(24) 99(12) 102(12) 104(12) 109(12) 111(12) 115(81) 116(21) 117(12) 118(126) 122(55—56) 139—140 142 144(5) 145(5 42) 146(57) 194—195 200(29—38) 201(40) 202(59—61) 203(36 73) 204(34 100) 206(30—32 108—109) 209(157) 210(30—32) 213(34) 222(29) 229(29) 233(157) 238—240(157) 242(29—32 108) 243—245(157) 248(36 59 61) 264(31 33) 271(33) 274—277 285(47 49 52) 297(47) 301(47 49 52) 321 357(14) 359(57) 381—382(14) 424—425 668(53) 713(53) 719—720(53) 740
Entangled states, molecular systems, Yang — Mills fields 261
Enthalpy properties, molecular systems, modulus-phase formalism 265—266
Epling, G.A. 458(60) 487(60) 501
Errea, L.F. 67(91) 141
ESAB effect, phase properties 209
Estes, D. 611(45) 654
Esteve, D. 248(314) 282
Ethylene direct molecular dynamics, ab initio multiple spawning 414
Ethylene, loop construction, qualitative photochemistry 472—473
Euler angles, adiabatic-to-diabatic transformation matrix, quantization 66—67
Euler angles, electronic state adiabatic representation, Born — Huang expansion 287—289
Euler angles, electronic states, adiabatic-to-diabatic transformation, two-state system 302—309
Euler angles, electronic states, triatomic quantum reaction dynamics 311—312
Euler angles, non-adiabatic coupling, three-state molecular system 134—137
Euler angles, non-adiabatic coupling, Wigner rotation matrices 90
Euler angles, permutational symmetry, rotational wave function 685—687
Euler-Lagrange equations, electron nuclear dynamics (END), time-dependent variational principle (TDVP), basic ansatz 330—333
Euler-Lagrange equations, electron nuclear dynamics (END), time-dependent variational principle (TDVP), free electrons 333—334
Evans — Dewar — Zimmerman approach, phase-change rule 435
Evans, M.G. 435(17—18) 447(17—18) 494(17—18) 500
EWW Hamiltonian, Renner — Teller effect, triatomic molecules 610—615
Expanding potential, molecular systems, component amplitude analysis 230—232
Expectation value, crude Born — Oppenheimer approximation, nuclei interaction integrals 519—527
Extended Born — Oppenheimer equations, non-adiabatic coupling, closed path matrix quantization 171—173
Extended Born — Oppenheimer equations, non-adiabatic coupling, theoretical principles 144—148
Extended Born — Oppenheimer equations, non-adiabatic coupling, three-state matrix quantization 173—174
Extended Born — Oppenheimer equations, non-adiabatic coupling, three-state system analysis 174—175
Extended molecular systems, component amplitude analysis, phase-modulus relations 218
Eyring, H. 443(36) 499(140) 501 504 692(63) 740
Ezra, G. 381(162) 428
Fabris, A.R. 624(106) 656
Faraday, S.K. 411(243) 431
Farantos, S.C 676(57) 740
Farkas, O. 363(95) 426
Fast Fourier transformation (FFT), direct molecular dynamics, nuclear motion Schroedinger equation 364—373
Fast Fourier transformation (FFT), non-adiabatic coupling, Longuet — Higgins phase-based treatment, semiclassical calculation, reaction 164—167
Fast Fourier transformation (FFT), non-adiabatic coupling, Longuet — Higgins phase-based treatment, two-dimensional two-surface system 150—157
Fato, M. 359(50) 425
Feautrier, N. 622(92) 656
Fedoriuk, M.V. 212(209) 279
Feit, M.D. 364(105) 427
Felker, P.M. 211(179) 278
Feller, D. 33(42) 38
Femtosecond laser pulses, molecular systems 211
Feng, D.H. 212(207) 279
Fermi resonance, permutational symmetry, dynamic Jahn — Teller and geometric phase effects 710—711
Fermic-Dirac statistics, permutational symmetry, total molecular wave function 676—678
Fermi’s Golden Rule, direct molecular dynamics, adiabatic systems, initial conditions 373—377
Fermi’s Golden Rule, electron nuclear dynamics (END), molecular systems 340—342
Ferretti, A. 403(226) 430 491(120) 503
Feshbach projection operator, non-adiabatic coupling, analycity properties 124—126
Feshbach projection operator, non-adiabatic coupling, Born — Oppenheimer — Huang equation, sub-Hilbert space 46—47
Feshbach, H. 46(79) 140 204(98) 276 291(70) 321
Feuchtwang, T.E. 213(233) 279
Feynman, R.P. 95(111) 118(111) 141 373(129) 427 435(16) 463(16) 456(16) 500
Fiddy, M.A. 208(150) 277
Field intensity tensor, molecular systems, Yang — Mills fields 254—255
Field intensity tensor, molecular systems, Yang — Mills fields, vanishing of, sufficiency criterion 257—259
Filtering techniques, phase interference 207
Final-state analysis, electron nuclear dynamics (END), molecular systems 342—349
First-derivative coupling matrix, crude Born — Oppenheimer approximation, Coulomb potential derivatives 529—535
First-derivative coupling matrix, electronic states, adiabatic representation 290—291
First-derivative coupling matrix, electronic states, adiabatic-to-diabatic transformation, two- state systems 300—309
First-derivative coupling matrix, electronic states, diabatic nuclear motion Schroedinger equation 293—295
Fischer, H. 464(75) 468(75) 502
Fischer, P. 207(123) 248(123) 276
Flannery, B.P. 330(22) 352
Fleischhauer, A. 249(316) 282
Fleming, G.R. 211(184) 278
Flesch, G.D. 82(96) 118(96) 141
Floethmann, H. 285(38) 321
Floissart, M. 208(147) 277
Floppy molecules, permutational symmetry, dynamic Jahn — Teller and geometric phase effects 701—711
Floquet theory, geometric phase theory, principles of 33—36
Floquet theory, geometric phase theory, single-surface nuclear dynamics, vibronic multiplet ordering 25—26
Fock, V. 223(250) 280
Fois, E. 360(71) 425
Follmeg, B. 621—622(88) 655
Force constants, crude Born — Oppenheimer approximation, hydrogen molecule, minimum basis set calculation 545—550
Ford, K.W. 339(32) 352
Foresman, J.B. 363(95) 426
Forney, D. 624(129) 657
Forward peak scattering, electron nuclear dynamics (END), molecular systems 339—342
Fougeres, A. 207(130) 276
Four-state system, loop construction, ammonia and chiral systems 456—458
Four-state system, loop construction, cis-trans isomerization, pi and sigma electrons 456
Four-state system, loop construction, larger systems 458—459
Four-state system, loop construction, photochemical reactions 455—458
Four-state system, loop construction, pi-electrons, butadiane ring closure 455— 456
Four-state system, loop construction, qualitative photochemistry 472—482
Four-state system, non-adiabatic coupling, quantization 60—62
Four-state system, non-adiabatic coupling, Wigner rotation/adiabatic-to-diabatic transformation matrices 92
Fourier transform, molecular systems, component amplitude analysis, cyclic wave functions 224—228
Fourier transform, molecular systems, component amplitude analysis, reciprocal relations 216—217
Fox, D.J. 363(95) 426
Franck — Condon factor, direct molecular dynamics, adiabatic systems 374—377
Franck — Condon factor, direct molecular dynamics, complete active space self-consistent field (CASSCF) technique, non-adiabatic systems 408—411
Frank, I. 360(76) 426
Free and Lombardi (FL) models, Renner — Teller effect, triatomic molecules 618—621
Free electrons, electron nuclear dynamics (END), time-dependent variational principle (TDVP) 333—334
Freed, K.F. 618(75) 655
Frenkel, E. 144(15) 194
Freund, I. 232(266) 280
Frey, S. 211(183) 278
Friedrich, B. 346—347(50) 353
Friesner, R. 364(105) 427
Frisch, M. 41(5) 138 326(9) 352 360(75) 363(95) 406(233) 426 430
Frishman, E. 204(93) 275
Frozen Gaussian approximation, direct molecular dynamics, Gaussian wavepackets, multiple spawning 402
Frozen Gaussian approximation, direct molecular dynamics, Gaussian wavepackets, propagation 380—381
Frozen Gaussian approximation, molecular systems, component amplitude analysis, wave packet construction 229—230
Fubini — Study metric, projective Hilbert space 209—210
Fuelscher, M. 363(97) 427
Fuentes-Guri, I. 248(312) 281
Fujii, M. 625(134) 657
Full Hilbert space, electron nuclear dynamics (END), time-dependent variational principle (TDVP) 328—330
Full Hilbert space, non-adiabatic coupling, analycity properties 124—126
Full Hilbert space, non-adiabatic coupling, theoretical background 42—44
Full multiple spawning (FMS), direct molecular dynamics, non-adiabatic coupling 402
Fulvene molecule, direct molecular dynamics, complete active space self-consistent field (CASSCF) technique 408—410
Fung, P.C.W. 200(12) 208(12) 273
Fuss, W. 434(3) 448(48) 479(3) 500—501
Gabriel, W. 622(97) 656
Gabrys, C.M. 625(147) 657
Gadea, F.X. 82(107) 141 385(186) 429
Gale, W. 206(106) 276
Galloy, C. 41(51) 140 242(295) 281 290(64) 321
Garavelli, M. 359(49—50 83 86) 405(230) 409(83) 410(86 230) 425—426 430 446(37—38) 489(37) 490(37—38) 501
Garrison, J.G 210(171) 214(171) 278
Gaspard, P. 211(180) 278
Gauge fields, molecular systems, Yang — Mills fields, pure vs. tensorial gauge fields 250—253
Gauge invariant geometric phase, properties 3—4
Gauge theories, Yang — Mills field 204—205
Gauge transformation, molecular systems, Yang — Mills fields 254—255
Gauge transformation, wave functions 213—214
Gauss — Hermite basis set, non-adiabatic coupling, quantum dressed classical mechanics 178—179
Gauss — Hermite basis set, non-adiabatic coupling, quantum dressed classical mechanics, discrete variable representation (DVR) 181—183
Gauss — Hermite basis set, non-adiabatic coupling, quantum dressed classical mechanics, geometric phase effect 180
Gaussian basis sets, crude Born — Oppenheimer approximation, angular-momentum-adopted Gaussian matrix elements 517—542
Gaussian basis sets, crude Born — Oppenheimer approximation, angular-momentum-adopted Gaussian matrix elements, Coulomb potential derivatives 527—542
Gaussian basis sets, crude Born — Oppenheimer approximation, angular-momentum-adopted Gaussian matrix elements, Coulomb potential derivatives, first-order derivatives 529—535
Gaussian basis sets, crude Born — Oppenheimer approximation, angular-momentum-adopted Gaussian matrix elements, Coulomb potential derivatives, second-order derivatives 535—542
Gaussian basis sets, crude Born — Oppenheimer approximation, angular-momentum-adopted Gaussian matrix elements, normalization factor 517
Gaussian basis sets, crude Born — Oppenheimer approximation, angular-momentum-adopted Gaussian matrix elements, nuclei interaction terms 519—527
Gaussian basis sets, crude Born — Oppenheimer approximation, angular-momentum-adopted Gaussian matrix elements, overlap integrals 518—519
Gaussian basis sets, crude Born — Oppenheimer approximation, Coulomb potential derivatives, first-order derivatives 529—535
Gaussian basis sets, crude Born — Oppenheimer approximation, hydrogen molecule, minimum basis set calculation 542—550
Gaussian basis sets, crude Born — Oppenheimer approximation, theoretical background 507
Gaussian wavepacket calculations, direct molecular dynamics, adiabatic systems, propagation techniques 377—381
Gaussian wavepacket calculations, direct molecular dynamics, non-adiabatic coupling 399—402
Gaussian wavepacket calculations, direct molecular dynamics, theoretical background 358—361
Gaussian wavepacket calculations, non-adiabatic coupling, Longuet — Higgins phase-based treatment, semiclassical calculation, reaction 166—167
Gaussian wavepacket calculations, non-adiabatic coupling, Longuet — Higgins phase-based treatment, two-dimensional two-surface system, scattering calculation 151—155
Gaussian wavepacket calculations, non-adiabatic coupling, semiclassical calculation, reaction 164—167
Gaussorgues, C 284(18—19) 320
Ge, M.-L. 210(175) 278
Ge, Y.C 210(173—174) 278
Gefen, Y. 210(176) 278
Geometric phase effect (GPE), conical intersections 4—8
Geometric phase effect (GPE), conical intersections, adiabatic eigenstates 8—11
Geometric phase effect (GPE), conical intersections, topographical energy 568—569
Geometric phase effect (GPE), curl equations 11—17
Geometric phase effect (GPE), degenerate states chemistry x—xiii
Geometric phase effect (GPE), electron nuclear dynamics (END), time-dependent variational principle (TDVP), general nuclear dynamics 334—337
Geometric phase effect (GPE), electronic states, adiabatic-to-diabatic transformation, two-state system 301—309
Geometric phase effect (GPE), electronic states, quantum reaction dynamics 284—286
Geometric phase effect (GPE), Floquet theory principles 33—36
Geometric phase effect (GPE), historical background 1—4 3—4
Geometric phase effect (GPE), Jahn — Teller problem 17—23
Geometric phase effect (GPE), Jahn — Teller problem, linear Jahn — Teller effect 18—20
Geometric phase effect (GPE), Jahn — Teller problem, quadratic Jahn — Teller effect 22—23
Geometric phase effect (GPE), Jahn — Teller problem, spin-orbit coupling, state 20—22
Geometric phase effect (GPE), molecular systems, electronic states 202—205
Geometric phase effect (GPE), molecular systems, modulus-phase formalism, Dirac electrons 270—272
Geometric phase effect (GPE), molecular systems, multidegenerate nonlinear coupling, continuous tracing, component phase 237—241
Geometric phase effect (GPE), molecular systems, multidegenerate nonlinear coupling, off-diagonal elements, squaring-off 246
Geometric phase effect (GPE), molecular systems, multidegenerate nonlinear coupling, research background 234
Geometric phase effect (GPE), non-adiabatic coupling, Longuet — Higgins phase-based treatment, quasi-Jahn — Teller model, scattering calculation 150—155
Geometric phase effect (GPE), non-adiabatic coupling, Longuet — Higgins phase-based treatment, two-dimensional two-surface system 148—157
Geometric phase effect (GPE), non-adiabatic coupling, quantum dressed classical mechanics 180
Geometric phase effect (GPE), non-adiabatic coupling, quantum dressed classical mechanics, discrete variable representation (DVR) 181—183
Geometric phase effect (GPE), non-adiabatic coupling, quasiclassical trajectory (QCT) calculation, three-particle reactive system, reaction 160—163
Geometric phase effect (GPE), non-adiabatic coupling, sign flip interpretation 77—80
Geometric phase effect (GPE), non-adiabatic coupling, theoretical background 42—44
Geometric phase effect (GPE), non-adiabatic coupling, two-state molecular system, molecule 105—109
Geometric phase effect (GPE), non-adiabatic coupling, vector potential, Yang — Mills field 95
Geometric phase effect (GPE), permutational symmetry, systems, isotopomers 713—717
Geometric phase effect (GPE), permutational symmetry, systems, alkali metal trimers 712—713
Geometric phase effect (GPE), permutational symmetry, systems, dynamic Jahn — Teller and geometric phase effects 698—711
Geometric phase effect (GPE), permutational symmetry, systems, electron/nuclear spin effects 711—712
Geometric phase effect (GPE), permutational symmetry, systems, nonadiabatic coupling effects 711
Geometric phase effect (GPE), permutational symmetry, systems, potential energy surfaces 692—694
Geometric phase effect (GPE), permutational symmetry, systems, static Jahn — Teller effect 694—698
Geometric phase effect (GPE), permutational symmetry, adiabatic states, conical intersections, invariant operators 735—737
Geometric phase effect (GPE), permutational symmetry, adiabatic states, conical intersections, Jahn — Teller theorem 733—735
Geometric phase effect (GPE), permutational symmetry, antilinear operator properties 721—723
Geometric phase effect (GPE), permutational symmetry, degenerate states chemistry xiii
Geometric phase effect (GPE), permutational symmetry, degenerate/near-degenerate vibration levels 728—733
Geometric phase effect (GPE), permutational symmetry, electronic wave function 680—682
Geometric phase effect (GPE), permutational symmetry, energy functional form 737—738
Geometric phase effect (GPE), permutational symmetry, GBO approximation and geometric phase, two-dimensional Hilbert space model 718—721
Geometric phase effect (GPE), permutational symmetry, group theoretical issues 668—674
Geometric phase effect (GPE), permutational symmetry, nuclear spin function 678—682
Geometric phase effect (GPE), permutational symmetry, phase-change rule 451—453
Geometric phase effect (GPE), permutational symmetry, rotational wave function 683—687
Geometric phase effect (GPE), permutational symmetry, rovibronic/vibronic wave functions 682—683
Geometric phase effect (GPE), permutational symmetry, single-surface nuclear dynamics 30—31
Geometric phase effect (GPE), permutational symmetry, theoretical background 660—661
Geometric phase effect (GPE), permutational symmetry, time-dependent Schroedinger equation 723—728
Geometric phase effect (GPE), permutational symmetry, total molecular wave function 661—668 674—678
Geometric phase effect (GPE), permutational symmetry, vibrational wave function 687—692
Geometric phase effect (GPE), research background 209—210
Geometric phase effect (GPE), single-surface nuclear dynamics 23—31
Geometric phase effect (GPE), single-surface nuclear dynamics, molecular Aharonov — Bohm effect, vector-potential theory 25—31
Geometric phase effect (GPE), single-surface nuclear dynamics, molecular Aharonov — Bohm effect, vector-potential theory, symmetry properties 28—31
Geometric phase effect (GPE), single-surface nuclear dynamics, vector-potential theory, molecular effects 25—31
Geometric phase effect (GPE), single-surface nuclear dynamics, vibronic multiplet ordering 23—24
George, S. 204(89) 208(89) 211(89) 275
George, T. 397(207) 430
Georghiu-Sviershevski, S. 212(220) 279
Gerber, W.H. 145(38) 195 660(9) 738
Gerhartz, W. 439(34) 446(34) 474(43) 501
Gerratt, J. 448(50) 501
Ghirardi, G.C. 200(21) 273
Gianturco, F. 719(91) 741
Giavarini, G. 206(117) 210(117) 276
Gilbert, A. 479—480(90) 502
Gilibert, M. 82(97) 118(97) 141
Gill, P.M.W. 363(95) 426
Gilmore, R. 212(207) 279
Girard, B. 204(94) 207(94) 275
Gislason, E.A. 162(78) 196
Glasstone, S. 443(36) 501
Glauber, R.J. 340(37) 352
Glogower, J. 208(137) 277
Glory scattering, electron nuclear dynamics (END), molecular systems 339—342
Goddard, J.D. 634(166) 658
Goddard, W.A. III 435(22—24) 436(24) 447(22 39) 453(22 39) 455(24) 474(23—24) 493(39) 500—501
Goff, W. 17(28) 37
Goldbart, P.M. 248(311) 281
Golden, S. 506(12) 555
Goldstein, H. 66(86) 90(86) 141 160(74) 196 200(26) 274
Gomperts, R. 363(95) 426
Gonzales, M. 640—641(169) 658
Gonzalez, C. 359(47—48) 363(95) 425—426
Gonzalez-Lafont, A. 326(6) 352
Gordon, M. 358(44—45) 363(96) 405(229) 425—426 430
Gordon, M.S. 42—43(65) 97(65) 104(65) 118(65) 140 236(285) 281 458(59) 501
Gordon, R.J. 144(6) 194
Gordon, W. 263(320 323) 267(323) 282
Gottlieb, C.A. 633—634(164) 658
Gottlieb, E.W. 633—634(164) 658
Gozzi, e. 206(117) 210(117) 276
Gradient difference (GD) vector, direct molecular dynamics, vibronic coupling, conical intersections 386—389
Grangier, P. 207(126) 276
Grant, E.R. 3(16) 20(16) 22(30) 32(16) 37 41(22) 68(22) 71(22) 117(22) 139 228(256) 233(256) 245(256) 280 381(162) 428 471(78) 502 625(135) 657
Granucci, G. 403(226) 430 491(119) 503
Gray, S. 371(122) 427
Green, W.H. 622(91) 626(157) 656—657
Greenaway, A.H. 208(150) 277
Gregory, T.J. 144(29) 195
Greiner, W. 263(321) 271(321) 282
Griffith, J.S. 33(43) 38 243(303—304) 244(303) 281
Grimbert, D. 719(90) 741
Gronbech-Jensen, N. 208(139) 277
Gronki, J. 386(188) 429
Grosche, C. 230(263) 280
Grossmann, F. 358(29) 424
Grotch, H. 213(233) 279
Ground-state wave function, conical intersection, anchors, molecules and independent quantum species 440—441
Ground-state wave function, geometric phase theory, adiabatic eigenstates 11
Ground-state wave function, permutational symmetry, static Jahn — Teller effect 696—698
Ground-state wave function, phase-change rule, loop construction 441—446
Ground-state wave function, phase-change rule, pericyclic reactions 448—450
Grover, L. 200(23) 273
Grozdanov, T.P. 660(16) 739
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