Quantum corrections in the computer simulation of simple liquids and solids

Abstract

A number of methods for the inclusion of quantum effects in the computer simulation of simple systems have been studied. The systems principally studied are fluids such as neon or fluorine, (modelled by simple potentials such as the Lennard-Jones 12-6) , for which quantum effects are small, in some sense. These methods all follow the structure of classical Monte Carlo or molecular dynamics methods, to a greater or lesser extent. The Wigner expansion of the partition function in powers of Planck's constant allows quantum corrections to the free energy to be expressed in terms of classical ensemble averages, which (to order h2) can easily be estimated by classical simulation. The Wigner expansion can be derived from Feynman's path integral formulation of quantum mechanics, which also leads to a number of other methods, all resembling classical Monte Carlo methods. These range from effective, temperature dependent, potentials, to approximate schemes for estimating path integrals. Since Monte Carlo methods can give no dynamical data, an attempt has been made to represent the solids and liquids of interest as systems of wavepackets, and to derive equations of motion for these using the time-dependent Schrodinger equation. All of the Monte Carlo methods give results for neon that are in accord with all previous work, while attempts to simulate helium provide an insight into the range of validity of the methods. The wavepacket methods give excellent results for the solid and liquid states of neon.