Test of the Inverse Monte Carlo Method for the Calculation of Interatomic Potential Energies in Atomic Liquids

Abstract

The principle purpose of this paper is to demonstrate the use of the Inverse Monte Carlo technique for calculating pair interaction energies in monoatomic liquids from a given equilibrium property. This method is based on the mathematical relation between transition probability and pair potential given by the fundamental equation of the “importance sampling” Monte Carlo method. In order to have well defined conditions for the test of the Inverse Monte Carlo method a Metropolis Monte Carlo simulation of a Lennard Jones liquid is carried out to give the equilibrium pair correlation function determined by the assumed potential. Because an equilibrium configuration is prerequisite for an Inverse Monte Carlo simulation a model system is generated reproducing the pair correlation function, which has been calculated by the Metropolis Monte Carlo simulation and therefore representing the system in thermal equilibrium. This configuration is used to simulate virtual atom displacements. The resulting changes in atom distribution for each single simulation step are inserted in a set of non-linear equations defining the transition probability for the virtual change of configuration. The solution of the set of equations for pair interaction energies yields the Lennard Jones potential by which the equilibrium configuration has been determined.     

On the Bond-angle Distributions in Liquids and Liquid Solutions

Bond-angle distributions are used for the study of local orientational order in liquid systems. Bond-angles between a central particle and particles in both the first and second coordination shells are considered. Molecular dynamics calculations are carried out for determining the bond-angle distributions in a Lennard Jones liquid. The resulting distributions are compared with those obtained from stochastic simulations of a subset of atoms (solute) of the same system (solution). Although the radial distribution functions from the two simulations are in agreement, the bond-angle distributions show noticeable difference. Computer simulation findings are compared with results obtained by using both the superposition and convolution approximations. The reliability of the generalized Langevin dynamics simulation method is discussed.