Properties of rutile TiO 2 surfaces from a Tight-Binding Variable-Charge model. Comparison with ab initio calculations

Abstract

Up until now, variable charge models appeared to be inadequate for surface simulations of TiO 2. Particularly, the relative stability of the low-index surfaces was not well predicted, and the formation energy of the most stable (110) surface was far from recent ab initio predictions (Surf. Sci. 504, (2002) 115). In the present paper, low index (110), (100) and (001) surfaces of rutile TiO 2 have been successfully described at the atomic scale by means of a new variable-charge model. In this model, the iono-covalent metal–oxygen bond energy is calculated thanks to an analytical expression derived from a tight-binding description of the electronic structure of the oxide. This expression, which is a function of charge, is included in the charge equilibration procedure, which modifies the equilibrium state of the crystal with respect to previous models. Thus, the model becomes very stable with respect to charge transfers and leads to the stabilization of the (110), (100) and (001) surfaces of rutile TiO 2 with the right order in energy. Surface formation energies, atomic relaxations and charge transfers have been calculated and compared with density functional theory (DFT) calculations using the generalized gradient approximation (GGA) and the B3LYP hybrid functional with the CRYSTAL06 code. The surface energies calculated with the atomic model (0.42, 0.49 and 1.26 J m −2 respectively) are in very good agreement with our DFT calculations (0.48, 0.68 and 1.36 J m −2). Moreover, the atomic relaxations and the charge transfers at surfaces obtained with the model compare very reasonably both with the DFT results and the available experimental measurements. Our new model, whose transferability has been previously tested on different polymorphs of TiO 2, appears to be very useful in studying chemical properties of metal oxide surfaces.