Effect of relaxation on the energetics and electronic structure of clean Ag₃PO₄(111) surface

The effect of relaxation on the energetics and electronic structure of clean Ag₃PO₄(111) surface has been studied, carried out using first-principles density functional theory (DFT) incorporating the GGA+U formalism. After atomic relaxation of the Ag₃PO₄(111) surface, it is found that O atoms are exposed to the outermost surface, due to an inward displacement of more than 0.06 nm for the two threefold-coordinated Ag atoms and an outward displacement of about 0.004 nm for three O atoms in the sublayer. The atomic relaxations result in a large transfer of surface charges from the outermost layer to the inner layer, and the surface bonds have a rehybridization, which makes the covalence increase and thus causes the surface bonds to shorten. The calculated energy band structures and density of states of the Ag₃PO₄(111) surface present that the atomic relaxation narrows the valence band width 0.15 eV and increases the band gap width 0.26 eV. Meantime, the two surface peaks for the unrelaxed structure disappear at the top of the valence band and the bottom of the conduction band after the relaxed structure, which induces the transformation from a metallic to a semi-conducting characteristic. (paper)