Systematic convergence in the dynamical hybrid approach for complex systems: A numerically exact methodology

An efficient method, the self-consistent hybrid method, is proposed for accurately simulating time-dependent quantum dynamics in complex systems. The method is based on an iterative convergence procedure for a dynamical hybrid approach. In this approach, the overall system is first partitioned into a “core” and a “reservoir” (an initial guess). The former is treated via an accurate quantum mechanical method, namely, the time-dependent multiconfiguration self-consistent field or multiconfiguration time-dependent Hartree approach, and the latter is treated via a more approximate method, e.g., classical mechanics, semiclassical initial value representations, quantum perturbation theories, etc. Next, the number of “core” degrees of freedom, as well as other variational parameters, is systematically increased to achieve numerical convergence for the overall quantum dynamics. The method is applied to two examples of quantum dissipative dynamics in the condensed phase: the spin-boson problem and the electronic r...

[1]  A. Leggett,et al.  Dynamics of the dissipative two-state system , 1987 .

[2]  Gerhard Stock,et al.  A semiclassical self‐consistent‐field approach to dissipative dynamics: The spin–boson problem , 1995 .

[3]  E. Wigner.  On the Behavior of Cross Sections Near Thresholds , 1948 .

[4]  Richard A. Friesner,et al.  Nonadiabatic processes in condensed matter: semi-classical theory and implementation , 1991 .

[5]  M. Grifoni,et al.  Dissipation, decoherence and preparation effects in the spin-boson system , 1999 .

[6]  G. Worth,et al.  Molecular dynamics of pyrazine after excitation to the S2 electronic state using a realistic 24-mode model Hamiltonian , 1999 .

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

[8]  Nancy Makri,et al.  Path integrals for dissipative systems by tensor multiplication. Condensed phase quantum dynamics for arbitrarily long time , 1994 .

[9]  J. Gauyacq.  Model study of vibrational excitation in electron-polyatomic molecule collisions , 1990 .

[10]  EFFECT OF A THERMAL BATH ON ELECTRONIC RESONANCE DECAY : A NUMERICAL PATH-INTEGRAL STUDY , 1998 .

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

[12]  N. Mott.  On the Theory of Excitation by Collision with Heavy Particles , 1931, Mathematical Proceedings of the Cambridge Philosophical Society.

[13]  R. Feynman,et al.  The Theory of a general quantum system interacting with a linear dissipative system , 1963 .

[14]  T. Holstein,et al.  Studies of polaron motion: Part II. The “small” polaron , 1959 .

[15]  W. Domcke.  Theory of resonance and threshold effects in electron-molecule collisions: The projection-operator approach , 1991 .

[16]  Lorenz S. Cederbaum,et al.  Approaches to the approximate treatment of complex molecular systems by the multiconfiguration time-dependent Hartree method , 1999 .

[17]  David A. Micha,et al.  A self‐consistent eikonal treatment of electronic transitions in molecular collisions , 1983 .

[18]  U. Manthe,et al.  Wave‐packet dynamics within the multiconfiguration Hartree framework: General aspects and application to NOCl , 1992 .

[19]  H. Tachikawa.  Dynamics of Electron Attachment and Ionization Processes in the CCl4 Molecule: An ab Initio MO and Direct Dynamics Study , 1997 .

[20]  U. Weiss.  Quantum Dissipative Systems , 1993 .

[21]  Herman Feshbach,et al.  A Unified Theory of Nuclear Reactions, II , 1962 .

[22]  N. Makri,et al.  TENSOR PROPAGATOR FOR ITERATIVE QUANTUM TIME EVOLUTION OF REDUCED DENSITY MATRICES. I: THEORY , 1995 .

[23]  J. Light,et al.  Highly excited vibrational levels of "floppy" triatomic molecules: A discrete variable representation - Distributed Gaussian basis approach , 1986 .

[24]  M. Thoss,et al.  Theory of vibrational relaxation processes in resonant collisions of low-energy electrons with large molecules , 1998 .

[25]  Haobin Wang,et al.  Basis set approach to the quantum dissipative dynamics: Application of the multiconfiguration time-dependent Hartree method to the spin-boson problem , 2000 .

[26]  Mark A. Ratner,et al.  Time‐dependent self‐consistent field approximation for intramolecular energy transfer. I. Formulation and application to dissociation of van der Waals molecules , 1982 .

[27]  R. Friesner,et al.  Reduced dynamics in spin-boson models: A method for both slow and fast bath , 2000 .

[28]  G. Schulz.  Resonances in electron impact on atoms , 1973 .

[29]  R. Graham,et al.  Two-state system coupled to a boson mode: Quantum dynamics and classical approximations , 1984 .

[30]  Domcke,et al.  Path-integral approach to resonant electron-molecule scattering. II. Second-order cumulant approximation and multimode applications. , 1993, Physical review. A, Atomic, molecular, and optical physics.

[31]  William H. Miller,et al.  Self-consistent hybrid approach for complex systems: Application to the spin-boson model with Debye spectral density , 2001 .

[32]  Michael F. Herman.  Generalization of the geometric optical series approach for nonadiabatic scattering problems , 1982 .

[33]  G. D. Billing.  Quantum corrections to the classical path theory , 1993 .

[34]  M. Beck,et al.  The multiconfiguration time-dependent Hartree (MCTDH) method: A highly efficient algorithm for propa , 1999 .

[35]  N. F. Lane.  The theory of electron-molecule collisions , 1980 .

[36]  J. Tully,et al.  Trajectory Surface Hopping Approach to Nonadiabatic Molecular Collisions: The Reaction of H+ with D2 , 1971 .