By Baer M., Billing G.D. (eds.)

A distinct themes quantity at the position of degenerate states within the prime sequence on chemical physicsEdited through Nobel Prize-winner Ilya Prigogine and popular authority Stuart A. Rice, the Advances in Chemical Physics sequence offers a discussion board for serious, authoritative reviews in each zone of the self-discipline. In a structure that encourages the expression of person issues of view, specialists within the box current complete analyses of topics of curiosity. This stand-alone, certain themes quantity, edited by way of Gert D. Billing of the college of Copenhagen and Michael Baer of the Soreq Nuclear examine middle in Yavne, Israel, studies contemporary advances at the function of degenerate states in chemistry. quantity 124 collects cutting edge papers on "Complex States of easy Molecular Systems," "Electron Nuclear Dynamics," "Conical Intersections and the Spin-Orbit Interaction," and lots of extra comparable themes. Advances in Chemical Physics is still the most excellent venue for displays of latest findings in its box.

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See also Quantum reaction dynamics electron nuclear dynamics (END), timedependent variational principle (TDVP), general reactions, 334–337 geometric phase theory: quadratic Jahn-Teller effect, 22–23 single-surface nuclear dynamics, 23–31 molecular Aharonov-Bohm effect, vector-potential theory, 25–31 vibronic multiplet ordering, 24–25 permutational symmetry: adiabatic states, conical intersections: invariant operators, 735–737 Jahn-Teller theorem, 733–735 antilinear operator properties, 721–723 degenerate/near-degenerate vibration levels, 728–733 degenerate states chemistry, xiii electronic wave function, 680–682 energy functional form, 737–738 GBO approximation and geometric phase, two-dimensional Hilbert space model, 718–721 geometric phase theory, single-surface nuclear dynamics, 30–31 group theoretical issues, 668–674 nuclear spin function, 678–682 phase-change rule, 451–453 rotational wave function, 683–687 rovibronic/vibronic wave functions, 682– 683 2 S systems: alkali metal trimers, 712–713 dynamic Jahn-Teller and geometric phase effects, 698–711 electron/nuclear spin effects, 711–712 1 H3 isotopomers, 713–717 789 nonadiabatic coupling effects, 711 potential energy surfaces, 692–694 static Jahn-Teller effect, 694–698 theoretical background, 660–661 time-dependent Schro¨ dinger equation, 723–728 total molecular wave function, 661–668, 674–678 vibrational wave function, 687–692 Nuclear Lagrangean equation, molecular systems, Yang-Mills fields, 249–250, 255–257 Nuclear motion Schro¨ dinger equation: direct molecular dynamics, 363–373 vibronic coupling, adiabatic effects, 382–384 electronic states: adiabatic representation, 289–290 adiabatic-to-diabatic transformation, 293–295 diabatization matrix, 296–300 diabatic representation, 292–293 triatomic quantum reaction dynamics, partial wave expansion, 313–317 principles of, 417–420 Nuclear spin function, permutational symmetry, 678–680, 711–712 Nuclei subsystems, permutational symmetry, total molecular wave function, 677–678 Off-diagonal elements: adiabatic-to-diabatic transformation matrix, quantization, 67 conical intersection location, 488–489 multidegenerate nonlinearity: generalized coupling, 246–247 squaring-off method, 245–246 permutational symmetry, total molecular wave function, 666–668 One-dimensional representations: conical intersections, spin-orbit coupling, 558–559 Renner-Teller effect: theoretical principles, 585–586 triatomic molecules, pragmatic models, 620–621 On-the-fly molecular dynamics.

See also Quantum reaction dynamics electron nuclear dynamics (END), timedependent variational principle (TDVP), general reactions, 334–337 geometric phase theory: quadratic Jahn-Teller effect, 22–23 single-surface nuclear dynamics, 23–31 molecular Aharonov-Bohm effect, vector-potential theory, 25–31 vibronic multiplet ordering, 24–25 permutational symmetry: adiabatic states, conical intersections: invariant operators, 735–737 Jahn-Teller theorem, 733–735 antilinear operator properties, 721–723 degenerate/near-degenerate vibration levels, 728–733 degenerate states chemistry, xiii electronic wave function, 680–682 energy functional form, 737–738 GBO approximation and geometric phase, two-dimensional Hilbert space model, 718–721 geometric phase theory, single-surface nuclear dynamics, 30–31 group theoretical issues, 668–674 nuclear spin function, 678–682 phase-change rule, 451–453 rotational wave function, 683–687 rovibronic/vibronic wave functions, 682– 683 2 S systems: alkali metal trimers, 712–713 dynamic Jahn-Teller and geometric phase effects, 698–711 electron/nuclear spin effects, 711–712 1 H3 isotopomers, 713–717 789 nonadiabatic coupling effects, 711 potential energy surfaces, 692–694 static Jahn-Teller effect, 694–698 theoretical background, 660–661 time-dependent Schro¨ dinger equation, 723–728 total molecular wave function, 661–668, 674–678 vibrational wave function, 687–692 Nuclear Lagrangean equation, molecular systems, Yang-Mills fields, 249–250, 255–257 Nuclear motion Schro¨ dinger equation: direct molecular dynamics, 363–373 vibronic coupling, adiabatic effects, 382–384 electronic states: adiabatic representation, 289–290 adiabatic-to-diabatic transformation, 293–295 diabatization matrix, 296–300 diabatic representation, 292–293 triatomic quantum reaction dynamics, partial wave expansion, 313–317 principles of, 417–420 Nuclear spin function, permutational symmetry, 678–680, 711–712 Nuclei subsystems, permutational symmetry, total molecular wave function, 677–678 Off-diagonal elements: adiabatic-to-diabatic transformation matrix, quantization, 67 conical intersection location, 488–489 multidegenerate nonlinearity: generalized coupling, 246–247 squaring-off method, 245–246 permutational symmetry, total molecular wave function, 666–668 One-dimensional representations: conical intersections, spin-orbit coupling, 558–559 Renner-Teller effect: theoretical principles, 585–586 triatomic molecules, pragmatic models, 620–621 On-the-fly molecular dynamics.

See Direct molecular dynamics Oosterhoff correlation diagram, conical intersection research, 494–496 790 subject index Open-path phase: molecular systems, multidegenerate nonlinear coupling, 242–243 properties, 210 Operator definitions, phase properties, 206–207 Optical phases, properties, 206–207 Orbital overlap mechanism, phase-change rule, chemical reactions, 450–453 Orthogonal transformation matrix: conical intersections, spin-orbit interaction: invariant parameters, 574–576 seam loci, 576–578 molecular systems, 204–205 non-adiabatic coupling: adiabatic-to-diabatic transformation, 122–123 Longuet-Higgins phase-based treatment, two-dimensional two-surface system, scattering calculation, 151–155 two-state molecular system, H3 molecule, 104–109 Orthonormalization: electron nuclear dynamics (END), molecular systems, final-state analysis, 343–349 permutational symmetry, GBO approximation/geometric phase, Hilbert space model, 719–721 Out-of-phase states: conical intersection, two-state systems, 438 loop construction, benzene molecules, 479–481 phase-change rule, pericyclic reactions, 448– 450 phase inverting reactions, 496–499 quantitative photochemical analysis, 485–487 Overlap integrals, crude Born-Oppenheimer approximation, angular-momentumadopted Gaussian matrix elements, 518–519 Pairing approximation, phase inverting reactions, 499 Pancharatnam phase, properties, 206 Parabolical insertions, non-adiabatic coupling, topological spin, 70–73 Parallel transported eigenstates, geometric phase theory, 10–11 Partial wave expansion, electronic states, triatomic quantum reaction dynamics, 312–317 Pauli principle: conical intersections: phase-change rule, chemical reaction, 446–453 pericyclic reactions, 447–450 pi-bond reactions, 452–453 sigma bond reactions, 452 two-state chemical reactions, 436–438 degenerate states chemistry, xii–xiii loop construction, coodinate properties, 443–446 permutational symmetry, rotational wave function, 685–687 Pauli spin matrices, geometric phase theory, eigenvector evolution, 14–17 Pegg-Barnett operators, phase properties, 207–208 Pericyclic reactions, phase-change rule, 447–450 Permutational symmetry: adiabatic states, conical intersections: invariant operators, 735–737 Jahn-Teller theorem, 733–735 antilinear operator properties, 721–723 degenerate/near-degenerate vibration levels, 728–733 degenerate states chemistry, xiii electronic wave function, 680–682 energy functional form, 737–738 GBO approximation and geometric phase, two-dimensional Hilbert space model, 718–721 geometric phase theory, single-surface nuclear dynamics, 30–31 group theoretical issues, 668–674 nuclear spin function, 678–680 phase-change rule, 451–453 rotational wave function, 683–687 rovibronic/vibronic wave functions, 682–683 2 S systems: alkali metal trimers, 712–713 dynamic Jahn-Teller and geometric phase effects, 698–711 electron/nuclear spin effects, 711–712 1 H3 isotopomers, 713–717 nonadiabatic coupling effects, 711 potential energy surfaces, 692–694 static Jahn-Teller effect, 694–698 theoretical background, 660–661 subject index time-dependent Schro¨ dinger equation, 723–728 total molecular wave function, 661–668, 674–678 vibrational wave function, 687–692 Perturbation theory: conical intersections: location, 488–489 spin-orbit interaction, 559, 561–563 time-reversal symmetry, 563–564 crude Born-Oppenheimer approximation, basic principles, 510–512 electronic states, quantum reaction dynamics, 285–286 non-adiabatic coupling, two-state molecular system, single conical intersection solution, 97–101 permutational symmetry, total molecular wave function, 665–668 Renner-Teller effect: tetraatomic molecules: Á electronic states, 647–653 Å electronic states, 641–646 triatomic molecules, minimal models, 615–618 Petelin-Kiselev (PK) model, Renner-Teller effect, tetraatomic molecules, 625–633 Å electronic states, 634–640 Phase-change rule.