Prediction of crystal structures from crystal chemistry rules by simulated annealing

Abstract

THE prediction of the structure of inorganic crystalline solids from the knowledge of their chemical composition is still a largely unresolved problem^1–3. The usual approach to this problem is to minimize, for a selection of candidate models, the potential energy of the system with respect to the structural parameters of these models: the solution is the arrangement that comes out lowest in energy. Methods using this procedure may differ in the origin (ab initio or empirical) of the interatomic potentials used, but they usually restrict themselves to optimizing a structural arrangement within the constraints of given symmetry and bond topology. As a result, they do not truly address the problem of predicting the unknown structure of a real compound. The method we describe here is an attempt at solving the following problem: given the chemical composition of a crystalline compound and the values of its unit-cell parameters, find its structure (topology and bond distances) by optimizing the arrangement of ions, atoms or molecules in accordance with a set of prescribed rules. The procedure uses simple, empirical crystal chemistry arguments (Pauling's principles for ionic compounds⁴) and a powerful stochastic search procedure, known as simulated annealing⁵ to identify the best atomic model or models. We discuss the potential of the method for structure determination and refinement, using results obtained for several known inorganic structures, and by the determination of a previously unknown structure. Although the approach is limited to the case of inorganic compounds, it is nevertheless very general, and would apply to any crystalline structure provided that the principles governing the architecture of the solid can be properly described.