Application of canonical augmentation to the atomic substitution problem

A common approach for studying a solid solution or disordered system within a periodic ab-initio framework is to create a supercell in which a certain amount of target elements is substituted with other ones. The key to generating supercells is determining how to eliminate symmetry-equivalent structures from the large number of substitution patterns. Although the total number of substitutions is on the order of trillions, only symmetry-inequivalent atomic substitution patterns need to be identified, and their number is far smaller than the total. A straightforward solution would be to classify them after determining all possible patterns, but it is redundant and practically unfeasible. Therefore, to alleviate this drawback, we developed a new formalism based on the it canonical augmentation, and successfully applied it to the atomic substitution problem. Our developed verb|python| software package, which is called textscSHRY (underlineSuite for underlineHigh-thunderlineroughput generation of models with atomic substitutions implemented by punderlineython), enables us to pick up only symmetry-inequivalent structures from the vast number of candidates very efficiently. We demonstrate that the computational time required by our algorithm to find N symmetry-inequivalent structures scales it linearly with N up to ~ 109. This is the best scaling for such problems.