Using genetic algorithms to find from first-principles the minimum-energy crystal structure starting from random cell vectors and random atomic positions.

We address the global space-group optimization problem in binary metallic A$_{q}$B$_{1-q}$ alloys using an evolutionary algorithm. A set of crystal structures with randomly-selected lattice vectors and atomic positions is evolved, replacing the highest energy structures with new ones generated through mating or mutation, as well as ab-initio structural relaxation to the nearest local minimum. This was applied to a few compounds whose lattice-type is difficult to guess because the constituent solids A and B have different lattice types (e.g., A is fcc and B is bcc): (i) compounds with the crystal lattice of either A or B constituents, i.e., CdPt$_{3}$, AlSc$_{3}$, Al$_{3}$Sc; (ii) compounds with a crystal lattice different than that of either constituents, i.e., AlSc and CuPd; (iii) compounds whose crystal lattice is not even of a Bravais type, e.g., PdTi$_{3}$. The optimization scheme retrieved the lowest energy structures within about 100 total-energy evaluations. Not all independent GA sequences end up giving the same final structure; we select the lowest energy structure from all sequences. Using a model calculation, we will discuss how many independent GA sequences are needed to find the lowest energy structure with given confidence.