How to predict very large and complex crystal structures

Abstract

Evolutionary crystal structure prediction proved to be a powerful approach in discovering new materials. Certain limitations are encountered for systems with a large number of degrees of freedom (“large systems”) and complex energy landscapes (“complex systems”). We explore the nature of these limitations and address them with a number of newly developed tools. For large systems a major problem is the lack of diversity: any randomly produced population consists predominantly of high-energy disordered structures, offering virtually no routes toward the ordered ground state. We offer two solutions: first, modified variation operators that favor atoms with higher local order (a function we introduce here), and, second, construction of the first generation non-randomly, using pseudo-subcells with, in general, fractional atomic occupancies. This enhances order and diversity and improves energies of the structures. We introduce an additional variation operator, coordinate mutation, which applies preferentially to low-order (“badly placed”) atoms. Biasing other variation operators by local order is also found to produce improved results. One promising version of coordinate mutation, explored here, displaces atoms along the eigenvector of the lowest-frequency vibrational mode. For complex energy landscapes, the key problem is the possible existence of several energy funnels – in this situation it is possible to get trapped in one funnel (not necessarily containing the ground state). To address this problem, we develop an algorithm incorporating the ideas of abstract “distance” between structures. These new ingredients improve the performance of the evolutionary algorithm USPEX, in terms of efficiency and reliability, for large and complex systems.