The electronic and atomic structure of SrTiO₃, BaTiO ₃, and PbTiO₃(0 0 1) surfaces: Ab initio DFT/HF hybrid calculations

In our first-principles study, the electronic properties of the (0 0 1) surfaces of three key perovskite crystals, namely SrTiO₃ (STO), BaTiO₃ (BTO), and PbTiO₃ (PTO), have been calculated by means of the density functional theory (DFT) using the exchange-correlation functional containing "hybrid" of the non-local Hartree-Fock (HF) exchange, DFT exchange, and Generalized Gradient Approximation (GGA) correlation functionals, commonly known as B3PW. Such a technique allows us to get the optical bulk band gap very close to experiment unlike previous calculations of perovskites. Special attention is paid to careful calculations of the surface rumpling and change of the distances between three near-surface planes. We compare results with available experimental data. The calculated electronic band structures for relaxed surfaces show no splitting of surface electronic states from the upper valence bands for the AO-terminated (0 0 1) surfaces (consisting of Ti 4d and O 2p orbitals) and the presence of Pb 6s orbitals in the top of the PbTiO₃ valence band. This is important for the treatment of the electronic structure of surface defects on ABO ₃ perovskite surfaces as well as for adsorption and surface diffusion of atoms and small molecules (e.g. O, O₂), relevant for catalysis and fuel cell applications.