A shell model for atomistic simulation of charge transfer in titania

The derivation of atomistic potential parameters, based on electronic structure calculations, for modeling electron and hole polarons in titania polymorphs is presented. The potential model is a polarizable version of the Matsui and Akaogi model (Matsui, M.; Akaogi, M. Mol. Simul. 1901, 6, 239) that makes use of a shell model to account for the polarizability of oxygen ions. The -1 and +1 formal charges of the electron and hole polarons, respectively, are modeled by delocalizing the polaron's charge over a titanium or oxygen ion, respectively, and its first nearest-neighbors. The charge distributions and the oxygen polarizability were fitted to the reorganization energies of a series of electron and hole polaron transfers in rutile and anatase obtained from electronic structure calculations at zero Kelvin and validated against lattice deformation due to both types of polaron. Good agreement was achieved for both properties. In addition, the potential model yields an accurate representation of a range of bulk properties of several TiO2 polymorphs as well as Ti2O3. The model thus derived enables us to consider systems large enough to investigate how the charge transfer properties at titania surfaces and interfaces differ from those in the bulk. For example, reorganization energies and free energies of charge transfer were computed as a function of depth below vacuum-terminated rutile (110) and anatase (001) surfaces using a mapping approach first introduced by Warshel (Warshel, A. J. Phys. Chem. 1982, 86, 2218). These calculations indicate that deviations from bulk values at the surface are substantial but limited to the first couple of surface atomic layers and that polarons are generally repelled from the surface. Moreover, attractive subsurface sites may be found as is predicted for hole polarons at the rutile (I 10) surface. Finally, several charge transfers from under-coordinated surface sites were found to be in the so-called Marcus inverted-region.