Improved tight-binding charge transfer model and calculations of energetics of a step on the rutile TiO₂(110) surface

A second-moment, tight-binding charge equilibration (SMTB-Q) model for the atomic interactions in TiO₂ is refined by comparison with results of density functional theory (DFT) calculations within the generalized gradient approximation and used to study the atomic structure of the <11¯1> step on the rutile (110) surface. The model is parametrized to reproduce the structure and energetics of a rutile crystal and its low index surfaces but also reproduces well anatase crystal and its surfaces. The application to a stepped surface represents an extrapolation to lower coordinated atoms, and two extensions of the model were made. First, a continuous dependence of the effective radius of the O atoms on atom coordination was introduced, and second, a covalent O-O interaction was added. The revised SMTB-Q model is then found to reproduce well the relative energy of local minima on the DFT energy surface. In particular, we demonstrate that the refined model is useful in global optimization studies by using it to search for reconstructions of the <11¯1> step on the rutile (110) surface. The low energy configurations generated with the model were used as input in subsequent DFT calculations. A low energy reconstruction involving a large corrugation along the step edge is found in this manner. When additional TiO₂ units are introduced, a reconstruction previously found by Martinez et al. (U. Martinez et al. Phys. Rev. B 2011, 84, 205434) is also successfully reproduced. However, in the present model the atomic forces are not reproduced accurately as compared to DFT, which shows that additional terms such as angular-dependent terms may be needed to improve the accuracy.