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Symmetry and random sampling of symmetry independent configurations for the simulation of disordered solids

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Authors
D'Arco, P.
Mustapha, S.
Ferrabone, M.
Noël, Y.
De La Pierre, Marco
Dovesi, R.
Date
2013
Type
Journal Article

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D'Arco, P. and Mustapha, S. and Ferrabone, M. and Noël, Y. and De La Pierre, M. and Dovesi, R. 2013. Symmetry and random sampling of symmetry independent configurations for the simulation of disordered solids. Journal of Physics: Condensed Matter. 25 (35): Article ID 355401.
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Journal of Physics: Condensed Matter
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Department of Applied Chemistry
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This is an author-created, un-copy edited version of an article accepted for publication in Journal of Physics: Condensed Matter. The publisher is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at http://doi.org/10.1088/0953-8984/25/35/355401

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Abstract

A symmetry-adapted algorithm producing uniformly at random the set of symmetry independent configurations (SICs) in disordered crystalline systems or solid solutions is presented here. Starting from Pólya's formula, the role of the conjugacy classes of the symmetry group in uniform random sampling is shown. SICs can be obtained for all the possible compositions or for a chosen one, and symmetry constraints can be applied. The approach yields the multiplicity of the SICs and allows us to operate configurational statistics in the reduced space of the SICs. The present low-memory demanding implementation is briefly sketched. The probability of finding a given SIC or a subset of SICs is discussed as a function of the number of draws and their precise estimate is given. The method is illustrated by application to a binary series of carbonates and to the binary spinel solid solution Mg(Al,Fe)2O4.