Reverse Monte Carlo: Difference between revisions

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#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.
#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 partial radial distribution functions <math> g_{\alpha \beta} (r) </math> for this configuration.
#Calculate the total radial distribution function <math>g_o^C(r)</math> for this old configuration.
#Transform to the total structure factor:
#Transform to the total structure factor:
<math>S_o^2 (Q)-1=4\pi over Q\int</math>
<math>S_o^2 (Q)-1=\frac{4\pi\rho}{Q}\int\limits_{0}^{\inf} r(g_o^C(r)-1)sin(Qr)\, dr</math>
 
where ''Q'' is the momentum transfer <math>\rho</math> and the number density.
#Calculate the difference between the measured structure factor <math>S^E(Q)</math> and the one calculated from the configuration <math>S_o^C(Q)</math>:
<math>\chi_o^2=\sum_i(S_o^C(Q_i)-S^E(Q_i))^2/\sigma(Q_i)^2</math>
 
this sum is taken over all experimental points <math>\sigma</math> is the experimental error.
#Select and move one atom at random and calculate the new distribution function, structure factor and:
<math>\chi_n^2=\sum_i(S_n^C(Q_i)-S^E(Q_i))^2/\sigma(Q_i)^2</math>
 
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== References ==
== References ==
#R.L.McGreevy and L. Pusztai, ''Mol. Simulation,'' '''1''' 359-367 (1988)
#R.L.McGreevy and L. Pusztai, ''Mol. Simulation,'' '''1''' 359-367 (1988)

Revision as of 18:24, 19 February 2007

Reverse Monte Carlo (RMC) [1] is a variation of the standard Metropolis Monte Carlo (MMC) method. It is used to produce a 3 dimensional atomic model that fits a set of measurements (Neutron-, X-ray-diffraction, EXAFS etc.). In addition to measured data a number of constraints based on prior knowledge of the system (like chemocal bonds etc.) can be applied. Some examples are:

  1. Closest approach between atoms (hard sphere potential)
  2. Coordination numbers.
  3. Angels in triplets of atoms.

The algorithm for RMC can be written:

  1. 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.
  2. Calculate the total radial distribution function for this old configuration.
  3. Transform to the total structure factor:

where Q is the momentum transfer and the number density.

  1. Calculate the difference between the measured structure factor and the one calculated from the configuration :

this sum is taken over all experimental points is the experimental error.

  1. Select and move one atom at random and calculate the new distribution function, structure factor and:


References

  1. R.L.McGreevy and L. Pusztai, Mol. Simulation, 1 359-367 (1988)