Microfaceting of Cu$_2$O and its implications in photochemistry

The high Miller-index microfacets e.g. \{211\}, \{311\}, and \{522\} have been proposed to play a key role in shape-controlled crystal engineering of Cu$_2$O polyhedrons for various clean energy applications. These Cu$_2$O microcrystals with high Miller-index microfacets are found to have a higher photocatalytic activity than those with octahedra and cube morphologies, and thus suggesting that the catalytically active sites are more abundant on the high Miller-index surfaces. Although much effort has been devoted to the actual synthesis and characterizations of these shaped Cu$_2$O nanocrystals with various morphologies, a firm theoretical understanding of these system are currently limited to low Miller-index facets of Cu$_2$O. Here, we perform first-principles density-functional theory (DFT) calculations to study the surface energetics and electronic structure of these high Miller-index Cu$_2$O surfaces, and evaluate their overpotential for water redox reactions on Cu$_2$O, in comparison with that for the low Miller-index surfaces.