Reverse Monte Carlo

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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