Hashing to detect identical ordering of species in a shared sublattice

Finding very low energy configurations of species on a shared sublattice is unavoidable in some problems governed by ground states of the sublattice, such as voltage curve estimation of battery cathode materials. Calculations of partial occupancy systems, most notably in first-principles calculations, require the atom species to be explicitly specified at partial occupancy sites. Brute-force calculations over all relevant configurations are becoming a realistic approach with the recent development in easily accessible universal neural network potential calculations, and detecting and removing duplicate configurations of species is critical to reduce computational cost. A digest calculation procedure inspired by hashing in computer cryptography is proposed that projects the local environments of atoms in a crystal into a scalar number ‘digest’. The digest can tolerate numerical precision errors to some extent, and configurations with the same local environments are identified by simply sorting the digest numbers and detecting crystals with very close digests.