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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
Pfelzer, C. 624(125) 656
Phase factors see also "Modulus-phase formalism"
Phase factors, canonical intersection, historical background 144—148
Phase factors, geometric phase theory, eigenvector evolution 13—17
Phase factors, molecular systems 205—214
Phase factors, molecular systems, experimental probing 248—249
Phase factors, non-adiabatic coupling, Longuet — Higgins phase-based treatment, three-particle reactive system 157—168
Phase factors, non-adiabatic coupling, theoretical background 43—44
Phase factors, observability 208
Phase factors, quantum theory 200
Phase-change rule see "Longuet — Higgins phase-change rule"
Phase-inverting reactions, molecular model 496—499
Phase-inverting reactions, phase-change rule, pericyclic reactions 449—450
Phase-preserving reactions, phase-change rule, pericyclic reactions 449—450
Phillips, D.F. 249(316) 282
Phillips, J. 411(243) 431
Photochemistry, direct molecular dynamics, vibronic coupling 381—382
Photochemistry, future research issues 493—496
Photochemistry, loop construction 453—460
Photochemistry, loop construction, four-electron systems 455—458
Photochemistry, loop construction, larger four-electron systems 458—459
Photochemistry, loop construction, multielectron systems 459—460
Photochemistry, loop construction, qualitative analysis 472—482
Photochemistry, loop construction, qualitative analysis, ammonia 480—481
Photochemistry, loop construction, qualitative analysis, benzene derivatives 479—480
Photochemistry, loop construction, qualitative analysis, butadiene 474—479
Photochemistry, loop construction, qualitative analysis, cyclooctatetraene (COT) 482
Photochemistry, loop construction, qualitative analysis, cyclooctene isomerization 473—474
Photochemistry, loop construction, qualitative analysis, ethylene 472—473
Photochemistry, loop construction, qualitative analysis, inorganic complexes 481—482
Photochemistry, loop construction, quantitative analysis 482—487
Photochemistry, loop construction, three-electron systems 455
Photodissociation, direct molecular dynamics, nuclear motion Schroedinger equation 365—373
Photoelectron spectroscopy (PES), non-adiabatic coupling, Born — Oppenheimer — Huang equation 45
Photon capture, direct molecular dynamics, adiabatic systems, initial conditions 373—377
Piel, J. 410(240) 430
Pines, A. 3(13) 37 248(307) 281
Pires, M.V. 290(64) 321
Piskorz, P. 363(95) 426
Pistolesi, F. 210(168) 277
Pittner, J. 415(249) 431
Pitzer, R. 41(6) 138
Planar molecules, permutational symmetry, electronic wave function 681—682
Planar molecules, permutational symmetry, rotational wave function 685—687
Planar molecules, permutational symmetry, vibrational wave function 687—692
Ploehn, H. 506(4) 555
Podolsky method, Renner — Teller effect, triatomic molecules, Hamiltonian equations 612—615
Podolsky, B. 612(54) 655
Pogrebnya, S.K. 285(32) 320
Poincare sphere, phase properties 206
Point group symmetry, conical intersections, geometric phase theory 5—8
Point group symmetry, permutational symmetry, electronic wave function 681—682
Point group symmetry, permutational symmetry, group theoretical properties 669—674
Poisson equations, electronic states, adiabatic-to-diabatic transformation 296—300
Poisson equations, electronic states, adiabatic-to-diabatic transformation, two-state system 303—309
Poisson equations, permutational symmetry, dynamic Jahn — Teller and geometric phase effects 708—711
Poizat, J.-P. 207(126) 276
Polanyi, M. 692(63) 740
Polar coordinates, electronic states, adiabatic-to-diabatic transformation, two-state system 303—309
Polar coordinates, non-adiabatic coupling, Jahn — Teller systems, Longuet — Higgins phase 119—122
Polar coordinates, non-adiabatic coupling, Longuet — Higgins phase-based treatment, two-dimensional two-surface system, scattering calculation 154—155
Polar coordinates, non-adiabatic coupling, three-state molecular system 134—137
Polar coordinates, non-adiabatic coupling, two-state molecular system, single conical intersection solution 98—101
Polar coordinates, permutational symmetry, degenerate/near-degenerate vibrational levels 730—733
Polinger, V.Z. 33(45) 38 201(47) 209(47) 233(47 275—276) 247(47) 274 280 666(41) 739
Pollak, E. 213(225—226) 279
Pollard, J.E. 625(136) 657
Pollinger, V.Z. 461(71) 502
Poluyanov, L. 640—641(169) 658
Polyene molecules, direct molecular dynamics, complete active space self-consistent field (CASSCF) technique 409—410
Polyene molecules, direct molecular dynamics, semiempirical studies 414—415
Polyene molecules, phase-change rule, pericyclic reactions 448—450
Pomelli, C. 363(95) 426
Popescu, S. 4(18) 16(18) 27—28(18) 37 42(63) 122(63) 140 204(81) 232(264) 275 280
Pople — Longuet — Higgins model, Renner — Teller effect, tetraatomic molecules 629—631
Pople — Longuet — Higgins model, Renner — Teller effect, tetraatomic molecules, electronic states 633
Pople — Longuet — Higgins model, Renner — Teller effect, triatomic molecules 616—618
Pople, J.A. 41(5) 138 349(54) 353 363(95) 381(169) 426 429 615—616(69) 617(71) 629(69) 633(69) 655
Popper, K.R. 212(212) 279
Porter, R.N. 144(11) 194 728(94) 741
Poshusta, R.D. 439(34) 446(34) 474(43) 501
Potential energy surface (PES), conical intersection, nonadiabatic coupling 148
Potential energy surface (PES), crude Born — Oppenheimer approximation, angular-momentum-adopted Gaussian matrix elements 517—542
Potential energy surface (PES), crude Born — Oppenheimer approximation, angular-momentum-adopted Gaussian matrix elements, Coulomb potential derivatives 527—542
Potential energy surface (PES), crude Born — Oppenheimer approximation, angular-momentum-adopted Gaussian matrix elements, Coulomb potential derivatives, first-order derivatives 529—535
Potential energy surface (PES), crude Born — Oppenheimer approximation, angular-momentum-adopted Gaussian matrix elements, Coulomb potential derivatives, second-order derivatives 535—542
Potential energy surface (PES), crude Born — Oppenheimer approximation, angular-momentum-adopted Gaussian matrix elements, normalization factor 517
Potential energy surface (PES), crude Born — Oppenheimer approximation, angular-momentum-adopted Gaussian matrix elements, nuclei interaction terms 519—527
Potential energy surface (PES), crude Born — Oppenheimer approximation, angular-momentum-adopted Gaussian matrix elements, overlap integrals 518—519
Potential energy surface (PES), crude Born — Oppenheimer approximation, hydrogen molecule, minimum basis set calculation 542—550
Potential energy surface (PES), crude Born — Oppenheimer approximation, theoretical background 506—507
Potential energy surface (PES), direct molecular dynamics, adiabatic systems 362—381
Potential energy surface (PES), direct molecular dynamics, adiabatic systems, Gaussian wavepacket propagation 377—381
Potential energy surface (PES), direct molecular dynamics, adiabatic systems, initial condition selection 373—377
Potential energy surface (PES), direct molecular dynamics, adiabatic systems, nuclear Schroedinger equation 363—373
Potential energy surface (PES), direct molecular dynamics, Gaussian wavepackets and multiple spawning 399—402
Potential energy surface (PES), direct molecular dynamics, molecular mechanics valence bond (MMVB) 408—411
Potential energy surface (PES), direct molecular dynamics, nuclear motion Schroedinger equation 419—420
Potential energy surface (PES), direct molecular dynamics, theoretical background 356—362
Potential energy surface (PES), direct molecular dynamics, trajectory surface hopping 397—399
Potential energy surface (PES), direct molecular dynamics, vibronic coupling 382—393
Potential energy surface (PES), electron nuclear dynamics (END), structure and properties 325—327
Potential energy surface (PES), electron nuclear dynamics (END), theoretical background 324—325
Potential energy surface (PES), electronic states, adiabatic representation, Born — Huang expansion 286—289
Potential energy surface (PES), electronic states, adiabatic representation, first-derivative coupling matrix 290—291
Potential energy surface (PES), electronic states, adiabatic representation, nuclear motion Schroedinger equation 289—290
Potential energy surface (PES), electronic states, adiabatic representation, second-derivative coupling matrix 291—292
Potential energy surface (PES), electronic states, adiabatic-to-diabatic transformation, diabatic nuclear motion Schroedinger equation 293—295
Potential energy surface (PES), electronic states, adiabatic-to-diabatic transformation, diabatization matrix 295—300
Potential energy surface (PES), electronic states, adiabatic-to-diabatic transformation, electronically diabatic representation 292—293
Potential energy surface (PES), electronic states, adiabatic-to-diabatic transformation, two-state application 300—309
Potential energy surface (PES), electronic states, theoretical background 283—286
Potential energy surface (PES), electronic states, triatomic reactions, two-state formalism 309—319
Potential energy surface (PES), electronic states, triatomic reactions, two-state formalism, partial wave expansion 312—317
Potential energy surface (PES), electronic states, triatomic reactions, two-state formalism, propagation scheme and asymptotic analysis 317—318
Potential energy surface (PES), electronic states, triatomic reactions, two-state formalism, symmetrized hyperspherical coordinates 310—312
Potential energy surface (PES), non-adiabatic coupling, extended Born — Oppenheimer equations 170—171
Potential energy surface (PES), non-adiabatic coupling, Longuet — Higgins phase-based treatment 155—157
Potential energy surface (PES), permutational symmetry, systems 692—694
Potential energy surface (PES), permutational symmetry, format 737—738
Potential energy surface (PES), Renner — Teller effect, theoretical principles 585—586
Potential fluid dynamics, molecular systems, modulus-phase formalism, quantum mechanics and 265—266
Pothier, H. 248(314) 282
Poutsma, J.C. 341(41) 353
Pragmatic models, Renner — Teller effect, triatomic molecules 618—621
Pratt, S.T. 625(137—138) 657
Press, W.H. 330(22) 352
Preston, R.K. 41(3) 49(3) 82(3) 104(3) 134(3) 138 147(61) 195 326(10) 345(10) 352 397(201) 429 719(89) 741
Probability densities, permutational symmetry, dynamic Jahn — Teller and geometric phase effects 705—711
Projection operators, geometric phase theory, eigenvector evolution 16—17
Projective Hilbert space, Berry’s phase 209—210
Prony analysis, electron nuclear dynamics (END), molecular systems 344—349
Propagation techniques, electronic states, triatomic quantum reaction dynamics 317—318
Pryce, M.H.L. 2—3(2) 9(2) 18—20(2) 31(2) 36 41—42(14) 53(14) 106(14) 121(14) 139 145(36) 195
Pseudomagnetic fields, degenerate states chemistry x—xiii
Pseudomagnetic fields, non-adiabatic coupling, curl equation 95—96
Pseudomagnetic fields, non-adiabatic coupling, vector potential, Yang — Mills field 94—95
Pseudoparticles, direct molecular dynamics, nuclear motion Schroedinger equation 371—373
Pseudoparticles, direct molecular dynamics, trajectory “swarms” 421—422
Pseudorotation, electronic states, quantum reaction dynamics 284—286
Pseudorotation, permutational symmetry, dynamic Jahn — Teller and geometric phase effects 702—711
Pseudoscalar term, multidegenerate nonlinearity, off-diagonal elements, squaring-off 246
Pulay, P. 372(123 127) 427
Pump-probe techniques, molecular systems 211
Puzzarini, C. 624(130) 657
Quadratic coupling, geometric phase theory, Jahn — Teller effect 22—23
Quantal adiabatic phase, geometric phase theory 2
Quantal adiabatic phase, quantum theory 199—200
Quantization, degenerate states chemistry x—xiii
Quantization, non-adiabatic coupling, curl condition, pseudomagnetic field 96
Quantization, non-adiabatic coupling, extended Born — Oppenheimer equations 171—173
Quantization, non-adiabatic coupling, extended Born — Oppenheimer equations, three-state systems 173—174
Quantization, non-adiabatic coupling, future research applications 118—119
Quantization, non-adiabatic coupling, general case techniques 63—67
Quantization, non-adiabatic coupling, model systems 57—63
Quantization, non-adiabatic coupling, model systems, extensions 62—63
Quantization, non-adiabatic coupling, model systems, four-state case 60—62
Quantization, non-adiabatic coupling, model systems, three-state case 59—60
Quantization, non-adiabatic coupling, model systems, two-state system 58—59
Quantization, non-adiabatic coupling, theoretical background 41—44
Quantum chemistry, direct molecular dynamics 416
Quantum correction, molecular systems, modulus-phase formalism 264—265
Quantum dressed classical mechanics, non-adiabatic coupling 177—183
Quantum dressed classical mechanics, non-adiabatic coupling, geometric phase effect 180—183
Quantum dressed classical mechanics, non-adiabatic coupling, theoretical background 177—180
Quantum measurements, component amplitude analysis, phase-modulus relations, phase losses 218
Quantum mechanics, adiabatic molecular dynamics, theoretical background 362—363
Quantum mechanics, molecular systems, modulus-phase formalism, potential fluid dynamics and 265—266
Quantum numbers, permutational symmetry, dynamic Jahn — Teller and geometric phase effects 702—711
Quantum numbers, Renner — Teller effect, nonlinear molecules 607—610
Quantum numbers, Renner — Teller effect, triatomic molecules 592—598
Quantum reaction dynamics, electronic states, adiabatic representation, Born — Huang expansion 286—289
Quantum reaction dynamics, electronic states, adiabatic representation, first-derivative coupling matrix 290—291
Quantum reaction dynamics, electronic states, adiabatic representation, nuclear motion Schroedinger equation 289—290
Quantum reaction dynamics, electronic states, adiabatic representation, second-derivative coupling matrix 291—292
Quantum reaction dynamics, electronic states, adiabatic-to-diabatic transformation, diabatic nuclear motion Schroedinger equation 293—295
Quantum reaction dynamics, electronic states, adiabatic-to-diabatic transformation, diabatization matrix 295—300
Quantum reaction dynamics, electronic states, adiabatic-to-diabatic transformation, electronically diabatic representation 292—293
Quantum reaction dynamics, electronic states, adiabatic-to-diabatic transformation, two-state application 300—309
Quantum reaction dynamics, electronic states, theoretical background 283—286
Quantum reaction dynamics, electronic states, triatomic reactions, two-state formalism 309—319
Quantum reaction dynamics, electronic states, triatomic reactions, two-state formalism, partial wave expansion 312—317
Quantum reaction dynamics, electronic states, triatomic reactions, two-state formalism, propagation scheme and asymptotic analysis 317—318
Quantum reaction dynamics, electronic states, triatomic reactions, two-state formalism, symmetrized hyperspherical coordinates 310—312
Quantum theory, molecular systems 198—205
Quasi — Jahn — Teller model, non-adiabatic coupling, Longuet — Higgins phase-based treatment, two-dimensional two-surface system, scattering calculation 150—155
Quasiclassical trajectory (QCT) calculation, non-adiabatic coupling, Longuet — Higgins phase-based treatment, three-particle reactive system, reaction 160—163
Quasiclassical trajectory (QCT) calculation, non-adiabatic coupling, Longuet — Higgins phase-based treatment, three-particle reactive system, reaction 167—168
Quasidiabatic framework, non-adiabatic coupling, adiabatic-to-diabatic transformation matrix, line integral approach 53—57
Quenneville, J. 361(88) 414(88) 426 491(123) 503
Raab, A. 365(109) 381(109) 390(109) 393(109) 427
Rabitz, H. 211(182) 278 326(8) 352
Rabuck, A.D. 363(95) 426
Racah coefficients, multidegenerate nonlinear coupling, higher order coupling 243
Radazos, I.N. 234(279) 281
Radic-Peric, J. 586(18) 590(28) 599—600(28) 602(28) 604(28) 621(18) 626(18) 628(18) 631(18) 634(18) 646(18 173) 654
Radom, L. 381(169) 429
Ragazos, I. 358(42) 408(237) 425 430 479—480(92) 491(117) 502—503
Raghavachari, K. 363(95) 426
Raimond, J.M. 200(20) 273
Raimondi, M. 448(50) 501
Rakhecha, V.C. 207(123—124) 208(124) 248(123) 276
Ramachandran, G.N. 206(114) 276
Ramanujam, P.S. 208(139) 277
Ramaseshan, S. 206(114) 276
Ramsay, D.A. 585(9—10) 615(9—10) 624(107) 633(162) 653 656—657
Ramsey, N.F. 200(24) 273
Rao, K.V.S.R. 458(63) 487(63) 501
Raseev, G. 41(51) 140 242(295) 281
Rauch, M. 210(170) 278
Rauschenbeutel, A. 200(20) 273
Rayleigh, J.W.S. 206(111) 276
Reactive collisions, electron nuclear dynamics (END), molecular systems 338—342
Reactive collisions, electron nuclear dynamics (END), molecular systems, final-state analysis 343—349
Reactive double-slit model (RDSM), non-adiabatic coupling, Longuet — Higgins phase-based treatment, two-dimensional two-surface system, scattering calculation 150—155
Reactive transitions, non-adiabatic coupling, extended Born — Oppenheimer equations 175—177
Rechenberg, H. 199(2) 215(2) 217(2) 263(2) 273
Reciprocal relations, molecular systems, component amplitude analysis, cyclic wave functions 225—228
Reciprocal relations, molecular systems, component amplitude analysis, modulus-phase formalism 215
Reciprocal relations, molecular systems, component amplitude analysis, origins 215—217
Reciprocal relations, molecular systems, component amplitude analysis, theoretical consequences 232—233
Reciprocal relations, wave function analycity 201—205
Reck, M. 207(129) 276
Reference configuration, permutational symmetry 737—738
Reference configuration, Renner — Teller effect, triatomic molecules 614—615
Regge poles, molecular systems, phase properties 214
Rehfuss, B.D. 625(147) 657
Reinsch, E.-A. 622(92) 656
Relativistic states, conical intersections, spin-orbit interaction, future research issues 578—580
Relativistic states, conical intersections, spin-orbit interaction, seam loci 573—574
Relativistic states, molecular systems, modulus-phase formalism 262—263
Rembovsky, Yu.A. 208(140 142) 277
Remler, D. 360(73) 425
Renner effect, historical background 584—585
Renner parameter, Renner — Teller effect, tetraatomic molecules, electronic states 632—633 635—640
Renner parameter, Renner — Teller effect, tetraatomic molecules, perturbative handling 642—646
Renner parameter, Renner — Teller effect, triatomic molecules, vibronic/spin-orbit coupling 600—605
Renner — Teller effect, degenerate states chemistry xiii
Renner — Teller effect, historical background 584—585
Renner — Teller effect, multidegenerate nonlinear coupling, higher order coupling 243—248
Renner — Teller effect, multidegenerate nonlinear coupling, higher order coupling, complex representation 243—244
Renner — Teller effect, multidegenerate nonlinear coupling, higher order coupling, generalized coupling 247
Renner — Teller effect, multidegenerate nonlinear coupling, higher order coupling, interpretation 248
Renner — Teller effect, multidegenerate nonlinear coupling, higher order coupling, nonlinear diagonal elements 247
Renner — Teller effect, multidegenerate nonlinear coupling, higher order coupling, off-diagonal coupling 246—247
Renner — Teller effect, multidegenerate nonlinear coupling, higher order coupling, off-diagonal squaring 245—246
Renner — Teller effect, non-adiabatic coupling, topological spin insertion 70—73
Renner — Teller effect, nonadiabatic coupling, two-state molecular system 59
Renner — Teller effect, tetraatomic molecules, -electronic states, ABBA molecules 631—633
Renner — Teller effect, tetraatomic molecules, -electronic states, HCCS radical 633—640
Renner — Teller effect, tetraatomic molecules, -electronic states, perturbative handling 641—646
Renner — Teller effect, tetraatomic molecules, delta electronic states, perturbative handling 647—653
Renner — Teller effect, tetraatomic molecules, theoretical principles 625—633
Renner — Teller effect, tetraatomic molecules, theoretical principles, Hamiltonian equation 626—628
Renner — Teller effect, tetraatomic molecules, theoretical principles, vibronic problem 628—631
Renner — Teller effect, theoretical principles 585—586
Renner — Teller effect, triatomic molecules, benchmark handling 621—623
Renner — Teller effect, triatomic molecules, effective Hamiltonians 623—624
Renner — Teller effect, triatomic molecules, Hamiltonian equations 610—615
Renner — Teller effect, triatomic molecules, minimal models 615—618
Renner — Teller effect, triatomic molecules, multi-state effects 624
Renner — Teller effect, triatomic molecules, pragmatic models 618—621
Renner — Teller effect, triatomic molecules, spectroscopic properties 598—610
Renner — Teller effect, triatomic molecules, spectroscopic properties, linear molecules, singlet state vibronic coupling 598—600
Renner — Teller effect, triatomic molecules, spectroscopic properties, linear molecules, vibronic/spin-orbit coupling 600—605
Renner — Teller effect, triatomic molecules, spectroscopic properties, nonlinear molecules 606—610
Renner — Teller effect, triatomic molecules, theoretical principles 587—598
Renner, R. 2(9) 37 59(83) 68(83) 141 584(7) 597(7) 615(7) 653
Replogle, E.S. 363(95) 426
Requena, A. 661(35) 739
Resta, R. 215(240) 218(240 247) 280
Restricted open-shell Hartree-Fock (ROHF) procedure 415
Restriction equations, molecular systems, component amplitude analysis, reciprocal relations 215—217
Reuter, W. 621(87) 624(122) 655—656
Reutt, J.E. 625(136) 657
Reznik, B. 210(177) 232(264) 278 280
Richard, J.-M. 506(10) 555
Rico, R.J. 460(67) 502
Riedle, E. 410(240) 430
Rieke, C.A. 349(60) 353
Riera, A. 41(47—48) 67(91) 82(47—48) 140—141 284(18—19) 320 385(183) 429
Rimini, A. 200(21) 273
Rinen, K.D. 286(56) 321
Robb, Bernardi, and Olivucci (RBO) method, conical intersection location 489—490
Robb, M.A. 234(279) 281 357(6—7) 358(38 42—43) 359(49—52 63—64) 360(79—87) 363(95) 381(6—7) 405(230) 406(63—64 233) 407(79 237) 408(80—82) 409(83—84) 410(85—86 230) 411—412(87) 424—426 430 434(9) 446(37—38) 447(44) 450(44) 479(89 92) 480(92) 489(37 114—115) 490(9 37—38 116) 491(117) 494—496(44) 500—503 558(6) 580
Roesslein, M. 625(147) 657
Rohrlich, D. 4(18) 16(18) 27—28(18) 37 42(63) 122(63) 140 204(81) 206(117) 210(117) 275—276
Rojas, A. 67(91) 141
Romelt, J. 290(63) 321
Romero, T. 82(107) 141
Roncero, O. 364(105) 427
Roos, B. 358(37 39—41) 363(97) 424 427 472(80) 484(99) 502—503 622(98) 656
Rose, M.E. 89(109) 91—92(109) 141
Rosen, N. 284(7) 320
Rosmus, P. 481(93) 502 612(51) 621(88) 622(51 88 92—95 97 99—101) 623(94) 655—656
Ross, A.J. 624(111) 656
Ross, G. 208(150) 277
Ross, I.G. 381(172) 429
Rossi, A.R. 458(60) 487(60) 501
Rotational couplings, electron nuclear dynamics (END), final-state analysis 348—349
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