Determining Surface Phase Diagrams Including Anharmonic Effects

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 (PES) 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 Lennard-Jones system describing a surface in contact with a gas phase. Furthermore, the algorithm is applied to Si$_M$ clusters ($M=2, 4$) in contact with an H$_{2}$ atmosphere, with all interactions described at the \textit{ab initio} level, i.e., via density-functional theory, with the PBE gradient-corrected exchange-correlation functional. We identify the most thermodynamically stable phases at finite $T, p$(H$_{2}$) conditions.