A periodic genetic algorithm with real-space representation for crystal structure and polymorph prediction

A genetic algorithm is described that is suitable for determining the global minimum energy configurations of crystal structures and which can also be used as a polymorph search technique. This algorithm requires no prior assumptions about unit cell size, shape, or symmetry, nor about the ionic configuration within the unit cell. This therefore enables true ab initio crystal structure and polymorph prediction. Our algorithm uses a real-space representation of the population members, and makes use of a periodic cut for the crossover operation. Results on large Lennard-Jones systems with fcc- and hcp-commensurate cells show robust convergence to the bulk structure from a random initial assignment and an ability to successfully discriminate between competing low enthalpy configurations. Results from an ab initio carbon polymorph search show the spontaneous emergence of both Lonsdaleite and graphite-like structures.