Calculating particle pair potentials from fluid-state pair correlations: Iterative Ornstein-Zernike Inversion

TL;DR

This paper introduces an improved iterative Monte Carlo method, called Iterative Ornstein-Zernike Inversion, for accurately deriving particle pair potentials from fluid pair correlations, enhancing reliability over previous techniques.

Contribution

It generalizes and improves the Iterative Boltzmann Inversion by incorporating a more accurate approximant based on the Ornstein-Zernike formalism and includes an accelerated iteration scheme.

Findings

The new method surpasses Iterative Boltzmann Inversion in reliability.

It effectively uses both real space and Fourier space correlations.

Accelerated iteration reduces computational effort.

Abstract

An iterative Monte Carlo inversion method for the calculation of particle pair potentials from given particle pair correlations is proposed in this paper. The new method, which is best referred to as Iterative Ornstein-Zernike Inversion, represents a generalization and an improvement of the established Iterative Boltzmann Inversion technique [Reith, P\"{u}tz \& M\"{u}ller-Plathe, J. Comput. Chem. 24, 1624 (2003)]. Our modification of Iterative Boltzmann Inversion consists of replacing the potential of mean force as an approximant for the pair potential with another, generally more accurate approximant that is based on a trial bridge function in the Ornstein-Zernike integral equation formalism. As an input, the new method requires the particle pair correlations both in real space and in the Fourier conjugate wavenumber space. An accelerated iteration method is included in the discussion, by which the required number of iterations can be greatly reduced below that of the simple Picard iteration that underlies most common implementations of Iterative Boltzmann Inversion. Comprehensive tests with various pair potentials show that the new method generally surpasses the Iterative Boltzmann Inversion method in terms of reliability of the numerical solution for the particle pair potential.