Catalytic Properties of Selected Transition Metal Oxides—Computational Studies

This chapter is the review of the computational methods applied to the transition metal oxides most abundant in heterogeneous catalysis and is focused on the influence of the environment on the transition metal cation properties. The shortcomings of the most commonly used DFT level of theory are discussed, and its extensions towards more realistic environment are presented. The modern reactive force-field methods are also mentioned. The embedding schemes most commonly found in the quantum-chemical or classical description of the heterogeneous processes are discussed. The errors stemming from the non-completeness of the basis function, i.e. the basis set superposition error, found in the calculations with atomic basis, and the Pulay stress, occurring in the planewave calculations, together with remedies, are briefly described. It is shown that in all discussed systems, i.e. \( {\mathrm {CeO}}_{2}\), \({\mathrm {TiO}}_{2}\), \({\mathrm {ZrO}}_{2}\), zeolites, d-electron metal spinels, and \({\mathrm {V}}_{2}\mathrm{O}_{5}\), the appropriately applied Hubbard DFT GGA+U methods are successful for the compromise between computational cost and resultant accuracy. The much more time-consuming hybrid functionals give slightly more accurate results and, moreover, are more universal in the sense that they do not need calibration against experiment contrary to DFT+U where the Hubbard correction needs to be carefully selected for modelling particular properties.