Optimization of Coulomb Energies in Gigantic Configurational Spaces of Multi-Element Ionic Crystals

Most of the novel energy materials contain multiple elements occupying a single site in their lattice. The exceedingly large configurational space of these materials imposes challenges in determining their ground-state structures. Coulomb energies of possible configurations generally show a satisfactory correlation to computed energies at higher levels of theory and thus allow to screen for minimum-energy structures. Employing a second-order cluster expansion, we obtain an efficient Coulomb energy optimizer using Monte Carlo and Genetic Algorithms. The presented optimization package, GOAC (Global Optimization of Atomistic Configurations by Coulomb), can achieve a speed up of several orders of magnitude compared to existing software. Our code is able to find low-energy configurations of complex systems involving up to $10^{920}$ structural configurations. The GOAC package thus provides an efficient method for constructing ground-state atomistic models for multi-element materials with gigantic configurational spaces.