Semiclassical initial value treatments of atoms and molecules.

This review describes some developments in the theory and application of the semiclassical initial representation for the treatment of the dynamical and static properties of atoms and molecules. The theoretical basis of initial value treatments for the propagator is discussed. A variety of useful alternative initial value expressions for the propagator and other quantities are presented as generalizations of the well-known Herman-Kluk approximation. Special emphasis is given to treatments that involve integration over only half the phase space variables. The recent development of semiclassical initial value expressions that are exact for specific, desired systems is reviewed and some of the implications are described.

[1]  J. Bowman,et al.  Comparison of classical, new corrected-classical, and semiclassical IR spectra of non-rotating H2O with quantum calculations , 2004 .

[2]  B. Jackson,et al.  Guiding paths and time-dependent basis sets for wavefunction propagation , 2000 .

[3]  Haobin Wang,et al.  Semiclassical study of electronically nonadiabatic dynamics in the condensed-phase: Spin-boson problem with Debye spectral density , 1999 .

[4]  K. Kay.  Exact wave functions from classical orbits. II. The Coulomb, Morse, Rosen-Morse, and Eckart systems , 2002 .

[5]  M. Baranger,et al.  Reply to ‘Comment on ‘‘Semiclassical approximations in phase space with coherent states’’’ , 2002 .

[6]  J. Klauder,et al.  COHERENT STATES: APPLICATIONS IN PHYSICS AND MATHEMATICAL PHYSICS , 1985 .

[7]  D. Shalashilin,et al.  Locally coupled coherent states and Herman–Kluk dynamics , 2003 .

[8]  H. Meyer,et al.  Benchmark calculations on high-dimensional Henon–Heiles potentials with the multi-configuration time dependent Hartree (MCTDH) method , 2002 .

[9]  Eric J. Heller,et al.  Cellular dynamics: A new semiclassical approach to time‐dependent quantum mechanics , 1991 .

[10]  Gerhard Stock,et al.  Mapping approach to the semiclassical description of nonadiabatic quantum dynamics , 1999 .

[11]  J. Rost,et al.  Irregular orbits generate higher harmonics. , 1999, physics/9903036.

[12]  D. Shalashilin,et al.  Multidimensional quantum propagation with the help of coupled coherent states , 2001 .

[13]  William H. Miller,et al.  On the semiclassical description of quantum coherence in thermal rate constants , 1998 .

[14]  William H. Miller,et al.  The Semiclassical Initial Value Representation: A Potentially Practical Way for Adding Quantum Effects to Classical Molecular Dynamics Simulations , 2001 .

[15]  A. L. Xavier,et al.  Phase-Space Approach to the Tunnel Effect: A New Semiclassical Traversal Time , 1997 .

[16]  Raibatak Das,et al.  Real-time semiclassical initial value method and threshold tunneling probabilities , 2000 .

[17]  E. Heller,et al.  Generalized Gaussian wave packet dynamics , 1987 .

[18]  P. Brumer,et al.  Semiclassical collision theory in the initial value representation: Efficient numerics and reactive formalism , 1992 .

[19]  Some new classical and semiclassical models for describing tunneling processes with real-valued classical trajectories , 2001 .

[20]  Bambi Hu,et al.  General initial value form of the semiclassical propagator , 2001 .

[21]  D. Manolopoulos,et al.  APPLICATION OF THE FROZEN GAUSSIAN APPROXIMATION TO THE PHOTODISSOCIATION OF CO2 , 1995 .

[22]  R. Baer,et al.  Trajectory-dependent cellularized frozen Gaussians, a new approach for semiclassical dynamics: Theory and application to He–naphtalene eigenvalues , 2003, The Journal of Chemical Physics.

[23]  E. Pollak,et al.  Optimization of the semiclassical initial value representation of the exact quantum-mechanical real time propagator , 2003 .

[24]  William H. Miller,et al.  Classical S Matrix: Numerical Application to Inelastic Collisions , 1970 .

[25]  V. Filinov,et al.  Calculation of the feynman integrals by means of the Monte Carlo method , 1986 .

[26]  V. A. Apkarian,et al.  Semiclassical molecular dynamics computation of spontaneous light emission in the condensed phase: Resonance Raman spectra , 2001 .

[27]  W. Miller,et al.  Semiclassical initial value representation for rotational degrees of freedom: The tunneling dynamics of HCl dimer , 1998 .

[28]  William H. Miller,et al.  Semiclassical approximations for the calculation of thermal rate constants for chemical reactions in complex molecular systems , 1998 .

[29]  K. Kay,et al.  Globally uniform semiclassical wave functions for multidimensional systems , 1998 .

[30]  E. Heller,et al.  Hybrid mechanics. II , 1989 .

[31]  M. Thoss,et al.  Semiclassical Description of Nonadiabatic Quantum Dynamics , 1997 .

[32]  J. Bowman,et al.  A method to constrain vibrational energy in quasiclassical trajectory calculations , 1989 .

[33]  Yi Zhao,et al.  Quasiclassical dynamics methods from semiclassical approximations , 2002 .

[34]  E. Kluk,et al.  A semiclasical justification for the use of non-spreading wavepackets in dynamics calculations , 1984 .

[35]  Todd J. Martínez,et al.  Ab Initio Quantum Molecular Dynamics , 2002 .

[36]  E. Pollak,et al.  A prefactor free semiclassical initial value series representation of the propagator. , 2004, The Journal of chemical physics.

[37]  Michael J. Davis,et al.  Multidimensional wave functions from classical trajectories , 1981 .

[38]  P. Brumer,et al.  Decoherence in an anharmonic oscillator coupled to a thermal environment: a semiclassical forward-backward approach. , 2004, The Journal of chemical physics.

[39]  K. Kay,et al.  Semiclassical initial value representation propagation of vibrational wave functions , 2002 .

[40]  D. Manolopoulos,et al.  Semiclassical dynamics in up to 15 coupled vibrational degrees of freedom , 1997 .

[41]  K. Kay,et al.  Semiclassical IVR treatment of reactive collisions , 2002 .

[42]  J. C. Burant,et al.  Real time path integrals using the Herman–Kluk propagator , 2002 .

[43]  D. Coker,et al.  A semiclassical limit for the mapping Hamiltonian approach to electronically nonadiabatic dynamics , 2001 .

[44]  D. Truhlar,et al.  Classical S matrix: numerical applications to classically allowed chemical reactions , 1974 .

[45]  M. Brewer.  ON THE SCALING OF SEMICLASSICAL INITIAL VALUE METHODS , 1999 .

[46]  Michael F. Herman.  Dynamics by Semiclassical Methods , 1994 .

[47]  Brumer,et al.  Generalized semiclassical-phase-index formulas via sequential stationary phase. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[48]  M. Gutzwiller.  Phase-Integral Approximation in Momentum Space and the Bound States of an Atom , 1967 .

[49]  V. Mandelshtam,et al.  Extraction of tunneling splittings from a real time semiclassical propagation , 1998 .

[50]  Kay,et al.  Globally uniform semiclassical expressions for time-independent wave functions. , 1996, Physical review letters.

[51]  W. Miller,et al.  A simple model for correcting the zero point energy problem in classical trajectory simulations of polyatomic molecules , 1989 .

[52]  Brumer,et al.  Semiclassical propagation: Phase indices and the initial-value formalism. , 1994, Physical review. A, Atomic, molecular, and optical physics.

[53]  A. Perelomov.  Generalized Coherent States and Their Applications , 1986 .

[54]  F. Grossmann,et al.  COMMENT: Comment on 'Semiclassical approximations in phase space with coherent states' , 2002 .

[55]  F. Grossmann.  TIME-DEPENDENT SEMICLASSICAL CALCULATION OF RESONANCE LIFETIMES , 1996 .

[56]  E. Pollak,et al.  Monte Carlo method for evaluating the quantum real time propagator. , 2003, Physical review letters.

[57]  P. Brumer,et al.  Semiclassical initial value representation techniques for chaotic systems , 2000 .

[58]  Long-time and unitary properties of semiclassical initial value representations. , 2003, The Journal of chemical physics.

[59]  Michael F. Herman.  IMPROVING THE ACCURACY OF SEMICLASSICAL WAVEPACKET PROPAGATION USING INTEGRAL CONDITIONING TECHNIQUES , 1997 .

[60]  K. Kay,et al.  Uniform semiclassical IVR treatment of the S-matrix , 2001 .

[61]  Victor S Batista,et al.  Coherent control in the presence of intrinsic decoherence: proton transfer in large molecular systems. , 2002, Physical review letters.

[62]  Michael Thoss,et al.  Semiclassical description of molecular dynamics based on initial-value representation methods. , 2004, Annual review of physical chemistry.

[63]  Haobin Wang,et al.  Semiclassical description of quantum coherence effects and their quenching: A forward–backward initial value representation study , 2001 .

[64]  William H. Miller,et al.  Spiers Memorial Lecture Quantum and semiclassical theory of chemical reaction rates , 1998 .

[65]  Eric J. Heller,et al.  Frozen Gaussians: A very simple semiclassical approximation , 1981 .

[66]  M. Alonso,et al.  New approach to semiclassical analysis in mechanics , 1999 .

[67]  Eric J. Heller,et al.  Semiclassical analysis of hierarchical spectra , 1994 .

[68]  A. Messiah.  Quantum Mechanics , 1961 .

[69]  E. Heller,et al.  A semiclassical correlation function approach to barrier tunneling , 1995 .

[70]  Haobin Wang,et al.  Generalized Filinov transformation of the semiclassical initial value representation , 2001 .

[71]  W. Miller,et al.  Time averaging the semiclassical initial value representation for the calculation of vibrational energy levels. II. Application to H2CO, NH3, CH4, CH2D2 , 2003 .

[72]  W. Miller,et al.  Forward-backward initial value representation for semiclassical time correlation functions , 1999 .

[73]  W. Miller,et al.  Monte carlo integration with oscillatory integrands: implications for feynman path integration in real time , 1987 .

[74]  K. Kay.  Classical representation of wave functions for integrable systems (15 pages) , 2004 .

[75]  E. Coronado,et al.  Nonadiabatic photodissociation dynamics of ICN in the à continuum: A semiclassical initial value representation study , 2000 .

[76]  W. Miller.  An alternate derivation of the Herman—Kluk (coherent state) semiclassical initial value representation of the time evolution operator , 2002 .

[77]  W. Miller.  On the Relation between the Semiclassical Initial Value Representation and an Exact Quantum Expansion in Time-Dependent Coherent States † , 2002 .

[78]  W. Miller,et al.  Semiclassical calculation of cumulative reaction probabilities , 1996 .

[79]  K. Kay,et al.  Integral expressions for the semiclassical time‐dependent propagator , 1994 .

[80]  K. Kay.  Semiclassical propagation for multidimensional systems by an initial value method , 1994 .

[81]  William H. Miller,et al.  Semiclassical calculation of thermal rate constants in full Cartesian space: The benchmark reaction D+H2→DH+H , 2003 .

[82]  E. Heller.  Reply to Comment on: Semiclassical time evolution without root searches: Comments and perspective , 1991 .

[83]  V. Guallar,et al.  Semiclassical molecular dynamics simulations of intramolecular proton transfer in photoexcited 2-(2′-hydroxyphenyl)–oxazole , 2000 .

[84]  W. Miller,et al.  Semiclassical molecular dynamics simulations of ultrafast photodissociation dynamics associated with the Chappuis band of ozone , 1998 .

[85]  F. Grossmann,et al.  From the coherent state path integral to a semiclassical initial value representation of the quantum mechanical propagator , 1998 .

[86]  V. Guallar,et al.  Semiclassical molecular dynamics simulations of excited state double-proton transfer in 7-azaindole dimers , 1999 .

[87]  S. Garashchuk,et al.  Semiclassical calculation of chemical reaction dynamics via wavepacket correlation functions. , 2000, Annual review of physical chemistry.

[88]  R. Marcus.  Theory of Semiclassical Transition Probabilities (S Matrix) for Inelastic and Reactive Collisions , 1971 .

[89]  W. Miller,et al.  Semiclassical initial value representation for electronically nonadiabatic molecular dynamics , 1997 .

[90]  J. Shao,et al.  Forward-Backward Semiclassical Dynamics without Prefactors , 1999 .

[91]  E. Heller,et al.  Generalized Gaussian wave packet dynamics, Schrödinger equation, and stationary phase approximation , 1988 .

[92]  J. Main,et al.  An application of error reduction and harmonic inversion schemes to the semiclassical calculation of molecular vibrational energy levels. , 2004, The Journal of chemical physics.

[93]  E. Pollak,et al.  A study of the semiclassical initial value representation at short times , 2002 .

[94]  Michael F. Herman,et al.  A numerical test of different integral conditioning approximations for a semiclassical initial value representation for wavepacket propagation , 1998 .

[95]  William H. Miller,et al.  Semiclassical theory of electronically nonadiabatic dynamics: results of a linearized approximation to the initial value representation , 1998 .

[96]  E. Kluk,et al.  Comparison of the propagation of semiclassical frozen Gaussian wave functions with quantum propagation for a highly excited anharmonic oscillator , 1986 .

[97]  N. Maitra.  Semiclassical maps: A study of classically forbidden transitions, sub-h structure, and dynamical localization , 2000 .

[98]  R. Littlejohn.  The Van Vleck formula, Maslov theory, and phase space geometry , 1992 .

[99]  W. Miller,et al.  Time averaging the semiclassical initial value representation for the calculation of vibrational energy levels , 2003 .

[100]  J. Shao,et al.  Systematic Improvement of Initial Value Representations of the Semiclassical Propagator , 2003 .

[101]  S. Garashchuk,et al.  Wave packet correlation function approach to H2(ν)+H→H+H2(ν′): semiclassical implementation , 1996 .

[102]  Nancy Makri,et al.  Semiclassical influence functionals for quantum systems in anharmonic environments 1 Presented at th , 1998 .

[103]  Y. Weissman.  Semiclassical approximation in the coherent states representation , 1982 .

[104]  P. Brumer,et al.  SEMICLASSICAL INITIAL VALUE THEORY FOR DISSOCIATION DYNAMICS , 1997 .

[105]  T. Voorhis,et al.  Similarity transformed semiclassical dynamics , 2003 .

[106]  William H. Miller,et al.  Application of the semiclassical initial value representation and its linearized approximation to inelastic scattering , 1999 .

[107]  D. McCormack.  An evaluation of the semiclassical Herman–Kluk (HK) propagator for molecule–surface reactive scattering , 2000 .

[108]  William H. Miller,et al.  Comment on: Semiclassical time evolution without root searches , 1991 .

[109]  K. Kay,et al.  Improving the efficiency of the Herman–Kluk propagator by time integration , 1999 .

[110]  Michael F. Herman,et al.  Globally uniform semiclassical surface-hopping wave function for nonadiabatic scattering. , 2004, The Journal of chemical physics.

[111]  Semiclassical real-time tunneling by multiple spawning of classical trajectories , 2000, Physical review letters.

[112]  K. Kay,et al.  Semiclassical initial value treatment of correlation functions. , 2004, The Journal of chemical physics.

[113]  John R. Klauder,et al.  Path integrals and stationary-phase approximations , 1979 .

[114]  Haobin Wang,et al.  Generalized forward–backward initial value representation for the calculation of correlation functions in complex systems , 2001 .

[115]  K. Kay,et al.  Time-integrated form of the semiclassical initial value method , 1999 .

[116]  P. Brumer,et al.  Semiclassical initial value approach for chaotic long-lived dynamics , 1998 .

[117]  Sophya Garashchuk,et al.  Semiclassical application of the Mo/ller operators in reactive scattering , 2001 .

[118]  E. Heller.  Time‐dependent approach to semiclassical dynamics , 1975 .

[119]  M. Thoss,et al.  Semiclassical description of nonadiabatic quantum dynamics: Application to the S1–S2 conical intersection in pyrazine , 2000 .

[120]  Heller,et al.  Long-time semiclassical dynamics of chaos: The stadium billiard. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[121]  M. Baranger,et al.  Semiclassical approximations in phase space with coherent states , 2001, quant-ph/0105153.

[122]  K. Kay.  Exact wave functions from classical orbits: The isotropic harmonic oscillator and semiclassical applications , 2001 .

[123]  K. Kay.  SEMICLASSICAL TUNNELING IN THE INITIAL VALUE REPRESENTATION , 1997 .

[124]  D. Secrest,et al.  Exact Quantum‐Mechanical Calculation of a Collinear Collision of a Particle with a Harmonic Oscillator , 1966 .

[125]  J. Ankerhold,et al.  Semiclassical tunneling in real time: Wave-packet dynamics in static and driven barrier potentials , 2003 .

[126]  O. Kuhn,et al.  Semiclassical tunneling splittings from short time dynamics: Herman-Kluk-propagation and harmonic inversion. , 2004, The Journal of chemical physics.

[127]  R. Levine,et al.  Conservation of zero‐point energy in classical trajectory computations by a simple semiclassical correspondence , 1994 .

[128]  A. Ravishankara,et al.  Absorption Cross Sections and Self-Reaction Kinetics of the IO Radical , 1997 .

[129]  W. Miller,et al.  Semi-classical correction for quantum-mechanical scattering , 1994 .

[130]  J. H. Van Vleck,et al.  The Correspondence Principle in the Statistical Interpretation of Quantum Mechanics , 1928 .