The global space-group optimization approach to crystal structure prediction

We present the global space-group optimization (GSGO) approach to the prediction of both the lattice structure and the atomic configuration of a crystalline solid. The GSGO method is based on an evolutionary algorithm within which a population of crystal structures is evolved substituting the highest total-energy structures with new ones. The search is performed directly on the atomic positions and the unit-cell vectors, after a similarity transformation is applied to bring structures of different unit-cell shapes to a common basis. Following this transformation, we can define a crossover operation that treats on the same footing structures with different unit-cell shapes. Newly generated structures are fully relaxed to the closest local total-energy minimum. Starting from random unit-cell vectors and atomic positions, and using the VASP code, the GSGO procedure found for Si, GaAs, SiC the correct lattice structure and configuration. In the case of Au$_{8}$Pd$_{4}$, the search retrieved the correct underlying lattice type (fcc), but energetically closely spaced ($\sim 2$ meV/atom) alloy configurations were not resolved. The GSGO approach opens the way to predicting unsuspected structures, using, in the cases noted above, an order of $\leq 100$ total-energy {\em ab initio} calculations.