Symplectic Multiple-Time-Stepping Integrators for Quantum-Classical Molecular Dynamics

The overall Hamiltonian structure of the Quantum-Classical Molecular Dynamics model makes — analogously to classical molecular dynamics - symplectic integration schemes the methods of choice for long-term simulations. This has already been demonstrated by the symplectic PICKABACK method [19]. However, this method requires a relatively small step-size due to the high-frequency quantum modes. Therefore, following related ideas from classical molecular dynamics, we investigate symplectic multiple-time-stepping methods and indicate various possibilities to overcome the step-size limitation of PICKABACK.

[1]  D. G. Imre,et al.  Mixed quantum wave packet/classical trajectory treatment of the photodissociation process ArHCl→Ar+H+Cl , 1992 .

[2]  D. Manolopoulos,et al.  Symplectic integrators tailored to the time‐dependent Schrödinger equation , 1996 .

[3]  Herman J. C. Berendsen,et al.  QUANTUM SIMULATION OF REACTION DYNAMICS BY DENSITY-MATRIX EVOLUTION , 1993 .

[4]  S. Reich.  Preservation of adiabitic invariants under symplectic discretization , 1999 .

[5]  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 .

[6]  Mark E. Tuckerman,et al.  Reversible multiple time scale molecular dynamics , 1992 .

[7]  Robert D. Skeel,et al.  Dangers of multiple time step methods , 1993 .

[8]  C. Schütte,et al.  Quantum‐classical molecular dynamics as an approximation to full quantum dynamics , 1996 .

[9]  Christof Schütte,et al.  Numerical Integrators for Quantum-Classical Molecular Dynamics , 1999, Computational Molecular Dynamics.

[10]  G. Benettin,et al.  On the Hamiltonian interpolation of near-to-the identity symplectic mappings with application to symplectic integration algorithms , 1994 .

[11]  V. Arnold.  Mathematical Methods of Classical Mechanics , 1974 .

[12]  Marlis Hochbruck,et al.  A Bunch of Time Integrators for Quantum/Classical Molecular Dynamics , 1999, Computational Molecular Dynamics.

[13]  Ernst Hairer,et al.  The life-span of backward error analysis for numerical integrators , 1997 .

[14]  S. Reich.  Backward Error Analysis for Numerical Integrators , 1999 .

[15]  Christof Schütte,et al.  An explicit and symplectic integrator for quantum-classical molecular dynamics , 1996 .

[16]  Folkmar A. Bornemann,et al.  On the Singular Limit of the Quantum-Classical Molecular Dynamics Model , 1999, SIAM J. Appl. Math..