We demonstrate a model for stoichiometric and reduced titanium dioxide intended for use in molecular dynamics and other atomistic simulations and based in the polarizable ion tight binding theory. This extends the model introduced in two previous papers from molecular and liquid applications into the solid state, thus completing the task of providing a comprehensive and unified scheme for studying chemical reactions, particularly aimed at problems in catalysis and electrochemistry. As before, experimental results are given priority over theoretical ones in selecting targets for model fitting, for which we used crystal parameters and band gaps of titania bulk polymorphs, rutile and anatase. The model is applied to six low index titania surfaces, with and without oxygen vacancies and adsorbed water molecules, both in dissociated and non-dissociated states. Finally, we present the results of molecular dynamics simulation of an anatase cluster with a number of adsorbed water molecules and discuss the role of edge and corner atoms of the cluster.