Abstract
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.
Highlights
A prerequisite for analyzing and understanding the electronic properties and the function of surfaces is the detailed knowledge of the surface composition and atomistic geometry under realistic conditions
By combining advantages of both GC and RE, our massively parallel algorithm requires no prior knowledge of the phase diagram and takes only the potential energy function together with the desired μ and T ranges as inputs
The range of chemical potentials is selected such that the lowest value of μ is comparable to and slightly lower than the adsorption energy of one B particle on A18, in order to assure that the sampling includes states where zero or few particles are adsorbed
Summary
A prerequisite for analyzing and understanding the electronic properties and the function of surfaces is the detailed knowledge of the surface composition and atomistic geometry under realistic conditions. The key assumption is, that all relevant local minima of the potential energy surface (PES) of a given system are enumerated, a (strong) limitation in case of unexpected surface stoichiometries or geometries. Such limitation can only be overcome by an unbiased sampling of configurational and compositional space. We will see below that this is not always justified
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