Reverse Monte Carlo
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Reverse Monte Carlo (RMC) is a variation of the standard Metropolis-Hastings algorithm to solve an inverse problem probing the configuration space though a random walk in search for set of parameters that is consistent with experimental data. An inverse problem is the task that often occurs in many branches of science and mathematics where the values of some model parameter(s) must be obtained from the observed data.
[edit] Applications
This method is used in condensed matter physics to produce structural models which are consistent with experimental data and subject to a set of constraints. A set of N atoms are randomly placed in a periodic boundary cell, and then a measurable quantity is calculated based on the current configuration. An iterative procedure is run where one randomly chosen atom is moved a random amount. The measurable quantity is recalculated. The move is rejected if the atom overlap with another atom or if the calculated quantity less similar to the experimental value than the previous configuration. Otherwise the move is accepted, and the procedure is executed again. As the number of accepted atom moves increases, the calculated quantity will get closer to the experimental value, until it reaches an equilibrium value, about which it will then oscillate. The resulting configuration should be a structure that is consistent with the experimental data within its errors.
Recently, Reverse Monte Carlo method (under the name of alternating least squares) was used to construct the mass spectrum of water isotopologue, HOD.[1]
[edit] References
- R L McGreevy 2001 J. Phys.: Condens. Matter 13 R877-R913 doi:10.1088/0953-8984/13/46/201
- Phys. Rev. B 69, 195207 (2004) doi:10.1103/PhysRevB.69.195207 (http://link.aps.org/abstract/PRB/v69/e195207)
- EMU Notes in Mineralogy, Vol. 4 (2002), Chapter 4, 59–82
