Crystal structure optimisation using an auxiliary equation of state

Abstract

Standard procedures for local crystal-structure optimisation involve numerous energy and force calculations. It is common to calculate an energy-volume curve, fitting an equation of state around the equilibrium cell volume. This is a computationally intensive process, in particular for low-symmetry crystal structures where each isochoric optimisation involves energy minimisation over many degrees of freedom. Such procedures can be prohibitive for non-local exchange-correlation functionals or other 'beyond' density functional theory electronic structure techniques, particularly where analytical gradients are not available. We present a simple approach for efficient optimisation of crystal structures based on a known equation of state. The equilibrium volume can be predicted from one single-point calculation, and refined with successive calculations if required. The approach is validated for PbS, PbTe, ZnS and ZnTe using nine density functionals, and applied to the quaternary semiconductor Cu${}_2$ZnSnS${}_4$ and the magnetic metal-organic framework HKUST-1.

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• Projected gradient descent algorithm for $\text{ab initio}$ crystal structure relaxation under a fixed unit cell volume