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.