LOCAL PARABOLIC REFERENCE APPROXIMATION OF THERMAL FEYNMAN PATH INTEGRALS IN QUANTUM MONTE CARLO SIMULATIONS

摘要

We have developed a new propagator, called the local parabolic reference (LPR), for use in the numerical evaluation of discretized Feynman path integrals by Metropolis Monte Carlo simulations. The form of the propagator is motivated by fitting a local quadratic reference potential (with positive, negative or zero curvature) to the potential energy surface of interest, and constructing the exact propagator for this reference potential. The final form of the propagator contains adjustments designed to eliminate artifacts that can develop at very low temperatures. In the low temperature regime, the approximation accommodates tunneling and zero-point motion with a small number of discretization points in the path integral. In the limit of high temperature, the LPR propagator approaches the form of the standard high temperature propagator. Both the single- and multi-dimensional formulations are discussed in this paper. The accuracy of the Monte Carlo path integrals is demonstrated in the calculation of the equilibrium average potential energies for a set of model systems with one degree of freedom, and for a system of ten coupled double-well oscillators. Also, for a one-dimensional quartic oscillator system, the LPR approximation results are compared with those of the approximations of Messina, Garrett and Schenter [J. Chem. Phys. 100, 6570 (1994)], Mak and Andersen [J. Chem. Phys. 92, 2953 (1990)], and Zhang, Levy and Freisner [Chem. Phys. Lett. 144, 236 (1988)]. It is anticipated that this approach to constructing propagators will be useful for multi-dimensional barrier-crossing problems. (C) 1997 American Institute of Physics. [S0021-9606(97)50246-7]. [References: 29]