First-Principles Cluster Expansions for Predicting Missing-row Surface Reconstructions

It is well-known that the (110) surfaces of late 5d transition metals (e.g. Au, Pt) undergo a (1$\times $2) missing-row reconstruction, while clean surfaces of 3d and 4d metals (e.g. Cu, Ag) do not. Here, we report the use of a cluster expansion (CE) approach to study this particular class of ``missing-row'' surface reconstructions of some transition metals.~We have used first-principles density functional calculations along with a CE to study the (110) surface of late transition metals by considering the reconstructed surface as a 2D binary system of metal atoms and vacancies. Without any experimental input or intuition-based ``guessing'', the CE results demonstrate the (1$\times $2) missing-row structure is the T=0K ground state for the (110) surface of Au and Pt, but not for Cu and Ag. The finite temperature properties of the missing-row surfaces were also studied by a CE+Monte Carlo approach, and we find a (1x2) to (1x1) transition temperature in good agreement with experimental results.