# Reverse Monte Carlo

**Reverse Monte Carlo** (RMC) ^{[1]} is a variation of the standard Metropolis Monte Carlo method. It is used to produce a 3 dimensional atomic model that fits a set of measurements (neutron diffraction, X-ray-diffraction, EXAFS etc.).
In addition to measured data a number of constraints based on prior knowledge of the system (for example, chemical bonding etc.) can be applied. Some examples are:

- Closest approach between atoms (hard sphere potential)
- Coordination numbers.
- Angles in triplets of atoms.

The 3 dimensional structure that is produced by reverse Monte Carlo is not unique; it is a model consistent with the data and constraints provided.

The algorithm for reverse Monte Carlo can be written as follows:

- Start with a configuration of atoms with periodic boundary conditions. This can be a random or a crystalline configuration from a different simulation or model.
- Calculate the total radial distribution function for this old configuration (
*C*=Calculated,*o*=Old). - Transform to the total structure factor:
- where
*Q*is the momentum transfer and the number density.

- Calculate the difference between the measured structure factor (
*E*=Experimental) and the one calculated from the configuration :- this sum is taken over all experimental points is the experimental error.

- Select and move one atom at random and calculate the new (
*n*=New) distribution function, structure factor and: - If accept the move and let the new configuration become the old. If then the move is accepted with probability otherwise it is rejected.
- repeat from step 5.

When have reached an equilibrium the configuration is saved and can be analysed.

## References[edit]

- Related reading

- R. L. McGreevy, "Reverse Monte Carlo modelling", Journal of Physics: Condensed Matter
**13**pp. R877-R913 (2001) - R. L. McGreevy and P. Zetterström, "To RMC or not to RMC? The use of reverse Monte Carlo modelling", Current Opinion in Solid State and Materials Science.
**7**pp. 41-47 (2003) - G. Evrard, L. Pusztai, "Reverse Monte Carlo modelling of the structure of disordered materials with RMC++: a new implementation of the algorithm in C++", Journal of Physics: Condensed Matter
**17**pp. S1-S13 (2005) - V. Sánchez-Gil, E. G. Noya, L. Temleitner, L. Pusztai "Reverse Monte Carlo modeling: The two distinct routes of calculating the experimental structure factor", Journal of Molecular Liquids
**207**pp. 211-215 (2015)