Constructing convex energy landscapes for atomistic structure optimization

Abstract

We propose a global optimization strategy for atomistic structure determination based on two new concepts: a few-atom complementary energy landscape and atomic role models. Global optimization of costly energy expressions may be aided by performing some of the optimization on model energy landscapes. These are often based on a sum-of-atomic-contributions form that accurately reproduces every local energy minimum of the true energy expression. However, we propose that, by not including all atomic contributions, the resulting energy landscapes may become more convex, making the search for the global optimum more facile. A role model is someone we aspire to be more like; in the same vein we define the role model of an atom to be another atom whose local environment the first atom seeks to obtain itself. Basing a complementary energy landscape on the distance of some atoms from their role models in a feature space, we arrive at a useful few-atom complementary energy landscape. We show that relaxation in this landscape is an effective mutation when employed in an evolutionary algorithm used to identify the bulk cristobalite structure of ${\mathrm{SiO}}_{2}$ and the $(1\ifmmode\times\else\texttimes\fi{}4)$ surface reconstruction of anatase ${\mathrm{TiO}}_{2}$(001).