## Introduction

The

**Reverse Monte Carlo** (RMC) modelling method is a variation of the standard

Metropolis-Hastings algorithm to solve an

inverse problem whereby a model is adjusted until its parameters have the greatest consistency with experimental data.

Inverse problems are found in many branches of

science and

mathematics, but this approach is probably best known for its applications in

condensed matter physics and

solid state chemistry.

## Applications in Condensed Matter Sciences

### Basic method

This method is often used in

condensed matter sciences to produce atom-based structural models that are consistent with

experimental data and subject to a set of constraints.

An initial configuration is constructed by placing atoms in a

periodic boundary cell, and one or more

measurable quantities are calculated based on the current configuration. Commonly used data include the

pair distribution function and its

Fourier transform, the latter of which is derived directly from neutron or x-ray

total scattering data. Other data that are used included

Bragg diffraction data for crystalline materials, and

EXAFS data. The comparison with experiment is quantified using a function of the form

where and are the observed (measured) and calculated quantities respectively, and is a measure of the accuracy of the measurement. The sum is over all independent measurements, which will include the sum over all points in a function such as the pair distribution function.

An iterative procedure is...

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