Transition Metal Oxide Thermochemistry
The relative stabilities of transition metal oxides, expressed as formation energies or as oxidation energies between oxides of the same metal (for example MO to M3O4 to M2O3), set which phases exist under given conditions and underpin their use in catalysis, electrochemistry, photocatalysis and sensors. Computing these energies with plain GGA gives large errors, partly from the self-interaction error of d electrons, so practitioners turn to empirical DFT + U, hybrid functionals such as HSE06, or other corrections. Errors are usually reported per metal atom so that reactions of different stoichiometry can be compared. See DFT + U and the Hubbard U.
Oxygen transfer between titania and molybdenum (2003)
Kitchin, Barteau and Chen used NIST-JANAF heats of formation to compute heats of reaction per mole of O for reducing TiO2 to lower Ti oxides (roughly 84 to 94 kcal/mol O) and compared them with the heats released on forming MoO2 (about 70 kcal/mol O) and MoO3 (about 59 kcal/mol O). Bulk oxidation of Mo by titania is therefore unfavorable, but at a clean interface the relevant quantity is argued to be the initial heat of oxygen adsorption on Mo (about 86 kcal/mol O up to O/Mo of one), which roughly matches the cost of reducing TiO2, so partial interfacial oxidation of Mo is feasible. The same comparison rationalizes literature reports that metals with high oxygen adsorption heats reduce TiO2(110) while Rh, Ni, Pd, Pt and Cu do not (Kitchin et al. 2003). Summary: kitchin2003a.
Oxidation energies from calculated U values (2015)
Xu, Joshi, Raman and Kitchin computed 14 oxidation reactions among V, Cr, Mn, Fe and Co oxides by referencing each oxide’s energy to isolated metal atoms and O2 at U = 0, then using a semi-empirical DFT + U(V) cohesive energy built from linear response U values. With a single fitted weighting parameter, the mean absolute error was 0.14 eV per metal (Quantum ESPRESSO pseudopotentials) or 0.20 eV per metal (GBRV), compared with about 0.96 to 0.98 eV per metal for PBE and literature values of 0.23 eV for empirical DFT + U and 0.40 eV for HSE06. Formation energies computed the same way gave mixed results (Xu et al. 2015). Summary: xu2015c.