Algorithm for generating irreducible site-occupancy configurations

Generating irreducible site-occupancy configurations by taking advantage of crystal symmetry is a ubiquitous method for the acceleration of disordered structure prediction, which plays an important role in condensed matter physics and material science. Here, we present an algorithm for generating irreducible site-occupancy configurations, which works for arbitrary parent cells with any supercell expansion matrix, and for any number of atom types with arbitrary stoichiometry. The algorithm identifies the symmetrically equivalent configurations by searching the space group operations of the underlying lattice and building the equivalent atomic matrix based on it. Importantly, an integer representation of configurations can greatly accelerate the speed of elimination of duplicate configurations, resulting in a linear scale of run time with the number of irreducible configurations that are finally found. Moreover, based on our algorithm, we write the corresponding code named disorder in fortran programming language, and the performance test results show that the time efficiency of our disorder code is superior to that of other related codes (supercell, enumlib, and SOD).