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| '''Reverse Monte Carlo''' (RMC) <ref>[http://dx.doi.org/10.1080/08927028808080958 R. L. McGreevy and L. Pusztai, "Reverse Monte Carlo Simulation: A New Technique for the Determination of Disordered Structures", Molecular Simulation, '''1''' pp. 359-367 (1988)]</ref> is a variation of the standard [[Metropolis Monte Carlo]] method. It is used to produce a 3 dimensional atomic [[models |model]] that fits a set of measurements (neutron diffraction, X-ray-diffraction, EXAFS etc.).
| | Reverse Monte Carlo (RMC) 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 (for example, chemical bonding etc.) can be applied. Some examples are:
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| *Closest approach between atoms ([[hard sphere model |hard sphere potential]])
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| *Coordination numbers.
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| *Angles in triplets of atoms.
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| 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.
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| The algorithm for reverse Monte Carlo can be written as follows:
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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.
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| #Calculate the total [[radial distribution function]] <math>g_o^C(r)</math> for this old configuration (''C''=Calculated, ''o''=Old).
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| #Transform to the total [[Structure factor | structure factor]]:
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| #:<math>S_o^C (Q)-1=\frac{4\pi\rho}{Q}\int\limits_{0}^{\infty} r(g_o^C(r)-1)\sin(Qr)\, dr</math>
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| #:where ''Q'' is the momentum transfer and <math>\rho</math> the number density.
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| #Calculate the difference between the measured structure factor <math>S^E(Q)</math> (''E''=Experimental) and the one calculated from the configuration <math>S_o^C(Q)</math>:
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| #:<math>\chi_o^2=\sum_i(S_o^C(Q_i)-S^E(Q_i))^2/\sigma(Q_i)^2</math>
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| #:this sum is taken over all experimental points <math>\sigma</math> is the experimental error.
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| #Select and move one atom at random and calculate the new (''n''=New) distribution function, structure factor and:
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| #:<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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| #If <math>\chi_n^2<\chi_o^2</math> accept the move and let the new configuration become the old. If <math>\chi_n^2 \geq \chi_o^2</math> then the move is accepted with probability <math>\exp(-(\chi_n^2-\chi_0^2)/2)</math> otherwise it is rejected.
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| #repeat from step 5.
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| When <math>\chi^2</math> have reached an equilibrium the configuration is saved and can be analysed.
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| == References == | | == References == |
| <references/>
| | R.L.McGreevy and L. Pusztai, ''Mol. Simulation,'' '''1''' 359-367 (1988) |
| ;Related reading
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| *[http://dx.doi.org/10.1088/0953-8984/13/46/201 R. L. McGreevy, "Reverse Monte Carlo modelling", Journal of Physics: Condensed Matter '''13''' pp. R877-R913 (2001)]
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| *[http://dx.doi.org/10.1016/S1359-0286(03)00015-9 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)]
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| *[http://dx.doi.org/10.1088/0953-8984/17/5/001 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)]
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| *[http://dx.doi.org/10.1016/j.molliq.2015.02.044 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)]
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| [[Category:Monte Carlo]]
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