A generalized Newton iteration for computing the solution of the inverse Henderson problem

TL;DR

This paper introduces a generalized Newton iteration method, IHNC, for efficiently computing effective pair potentials that match a target radial distribution function, reducing computational cost compared to existing methods.

Contribution

The paper presents the IHNC algorithm, a new Newton-based scheme that requires fewer computations and can incorporate thermodynamical constraints, improving efficiency over traditional inverse Monte Carlo methods.

Findings

IHNC matches the efficiency of IMC in numerical experiments.

IHNC requires only one molecular dynamics simulation per iteration.

The method allows easy incorporation of thermodynamical constraints.

Abstract

We develop a generalized Newton scheme IHNC for the construction of effective pair potentials for systems of interacting point-like particles.The construction is made in such a way that the distribution of the particles matches a given radial distribution function. The IHNC iteration uses the hypernetted-chain integral equation for an approximate evaluation of the inverse of the Jacobian of the forward operator. In contrast to the full Newton method realized in the Inverse Monte Carlo (IMC) scheme, the IHNC algorithm requires only a single molecular dynamics computation of the radial distribution function per iteration step, and no further expensive cross-correlations. Numerical experiments are shown to demonstrate that the method is as efficient as the IMC scheme, and that it easily allows to incorporate thermodynamical constraints.