Targeting high symmetry in structure predictions by biasing the potential energy surface

TL;DR

This paper introduces a biasing scheme for potential energy surfaces that accelerates the discovery of high symmetry structures in crystal predictions without prior symmetry group specification.

Contribution

A novel potential energy biasing method that efficiently finds high symmetry structures without needing to specify symmetry groups beforehand.

Findings

Speedups of 25 and 63 times in test cases

High symmetry structures are found faster on biased surfaces

Similarity of atomic environments correlates with low energy

Abstract

Ground state structures found in nature are in many cases of high symmetry. But structure prediction methods typically render only a small fraction of high symmetry structures. Especially for large crystalline unit cells there are many low energy defect structures. For this reason methods have been developed where either preferentially high symmetry structures are used as input or where the whole structural search is done within a certain symmetry group. In both cases it is necessary to specify the correct symmetry group beforehand. However it can in general not be predicted which symmetry group is the correct one leading to the ground state. For this reason we introduce a potential energy biasing scheme that favors symmetry and where it is not necessary to specify any symmetry group beforehand. On this biased potential energy surface, high symmetry structures will be found much faster than on an unbiased surface and independently of the symmetry group to which they belong. For our two test cases, a $C_{60}$ fullerene and bulk silicon carbide, we get a speedups of 25 and 63. In our data we also find a clear correlation between the similarity of the atomic environments and the energy. In low energy structures all the atoms of a species tend to have similar environments.