(189bg) Colloidal Crystal Structure Analysis Using Symmetry Groups and Stochastic Optimization

We present PACCS, a Python package for the analysis of colloidal crystal structures and prediction of the stability of such structures under various conditions. PACCS uses symmetry groups, specifically, the seventeen unique wallpaper groups in two-dimensional space, to generate various periodic arrangements of particles. These configurations are then used as inputs to a stochastic optimization algorithm such as differential evolution or basin-hopping to generate a library of distinct candidates from which a ground state (minimum energy) structure can be found. Free energy calculations can also be performed on these lattices to evaluate stability of phases at finite temperature. We discuss how the symmetries of a selected wallpaper group and the requirements of a given crystal stoichiometry can be cast as a constraint satisfaction problem for solution and generation of these initial inputs. We consider how this approach functions for a simple colloidal system in two dimensions, and also show how various complexities can be handled: size disparate systems, molecular systems, and three-dimensional systems. We demonstrate that this algorithm is amenable to parallelization and compare its performance to that of stochastic optimization alone, showings its usefulness for enumerating structures for multicomponent mixtures in a computationally efficient manner.