On the use of the symmetry-adapted Monte Carlo for an effective sampling of large configuration spaces. The test cases of calcite structured carbonates and melilites - Université Pierre et Marie Curie Accéder directement au contenu
Article Dans Une Revue Computational Materials Science Année : 2017

On the use of the symmetry-adapted Monte Carlo for an effective sampling of large configuration spaces. The test cases of calcite structured carbonates and melilites

Résumé

The symmetry-adapted Monte Carlo sampling scheme is applied for the ab initio study of two mineral systems, namely the calcite structured compound Ca0.75Mg0.25CO3 and soda-melilite (Na,Ca)AlSi2O7. It is shown how an extensive use of symmetry, from the sampling of atomic configurations up to the quantum-mechanical calculation, makes feasible the investigation of large configuration spaces. As for the sampling, we describe an effective procedure to specifically target low-energy configurations on the potential energy surface of supercells of virtually any size. It is based on the suggestion that a correlation between symmetry and energy of the configurations exists according to which atomic distributions of minimum and maximum energy are likely to have some spatial symmetry. This hypothesis is verified empirically and leads to a significant alleviation of the original problem by virtue of the possibility of tailoring the symmetry-adapted Monte Carlo to select only symmetric configurations. The latter are also found to display a probability distribution similar to that of the entire set of configurations, thus providing, eventually, a suitable ab initio reference for the parameterization of model Hamiltonians. The most stable configuration so identified is used as pivot for the selection of new configurations having the same atomic distribution but for the exchange of a couple of atoms. These are called ‘‘neighbors” to highlight both their structural and energetic proximity to the pivot. We illustrate how, by collecting neighbors of configurations of increasing energy, the description of the system can be progressively and deterministically improved up to convergence of the calculated average properties, whatever the temperature. The same scheme works when moving to a supercell larger than the initial one (but of equivalent symmetry) since it is shown that stable structures remain so at any volume.
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hal-01377748 , version 1 (07-10-2016)

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Valentina Lacivita, Philippe d'Arco, Sami Mustapha, Daniel Faria Bernardes. On the use of the symmetry-adapted Monte Carlo for an effective sampling of large configuration spaces. The test cases of calcite structured carbonates and melilites. Computational Materials Science, 2017, 126, pp.217-227. ⟨10.1016/j.commatsci.2016.09.037⟩. ⟨hal-01377748⟩
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