Maximum-entropy Monte Carlo method for the inversion of the structure factor in simple classical systems

TL;DR

This paper introduces a maximum-entropy Monte Carlo approach to derive interaction potentials from structure factor data in classical systems, validated on Lennard-Jones fluids and liquid sodium.

Contribution

It presents a novel two-phase maximum entropy method for inverting structure factors to obtain interaction potentials in classical systems.

Findings

Successfully applied to Lennard-Jones fluid data

Reliable in extracting potentials despite incomplete data

Extended to experimental liquid sodium data

Abstract

We present a method for the evaluation of the interaction potential of an equilibrium classical system starting from the (partial) knowledge of its structure factor. The procedure is divided into two phases both of which are based on the maximum entropy principle of information theory. First we determine the maximum entropy estimate of the radial distribution function constrained by the information contained in the structure factor. Next we invert the pair function and extract the interaction potential. The method is tested on a Lennard-Jones fluid at high density and the reliability of its results with respect to the missing information in the structure factor data are discussed. Finally, it is applied to the experimental data of liquid sodium at 100$^{\circ}$C.