We introduce a massively parallel replica-exchange grand-canonical sampling algorithm to simulate materials at realistic conditions, in particular surfaces and clusters in reactive atmospheres. Its purpose is to determine in an automated fashion equilibrium phase diagrams for a given potential-energy surface and for any observable sampled in the grand-canonical ensemble. The approach enables an unbiased sampling of the phase space and is embarrassingly parallel. It is demonstrated for a model of the Lennard-Jones system describing a surface in contact with a gas phase. Furthermore, the algorithm is applied to ${\mathrm{Si}}_M$ clusters ($M=2,4$) in contact with an ${\mathrm{H}}_2$ atmosphere, with all interactions described at the ab initio level, i.e., via density-functional theory, with the Perdew-Burke-Ernzerhof gradient-corrected exchange-correlation functional. We identify the most thermodynamically stable phases at finite $T,p({\mathrm{H}}_2$) conditions.

• Received 27 August 2019

DOI:https://doi.org/10.1103/PhysRevB.100.174106