Oxidation energies of transition metal oxides within the GGA + U framework

The energy of a large number of oxidation reactions of $3d$ transition metal oxides is computed using the generalized gradient approach (GGA) and $mathrm{GGA}+mathrm{U}$ methods. Two substantial contributions to the error in GGA oxidation energies are identified. The first contribution originates from the overbinding of GGA in the ${mathrm{O}}_{2}$ molecule and only occurs when the oxidant is ${mathrm{O}}_{2}$. The second error occurs in all oxidation reactions and is related to the correlation error in $3d$ orbitals in GGA. Strong self-interaction in GGA systematically penalizes a reduced state (with more $d$ electrons) over an oxidized state, resulting in an overestimation of oxidation energies. The constant error in the oxidation energy from the ${mathrm{O}}_{2}$ binding error can be corrected by fitting the formation enthalpy of simple nontransition metal oxides. Removal of the ${mathrm{O}}_{2}$ binding error makes it possible to address the correlation effects in $3d$ transition metal oxides with the $mathrm{GGA}+mathrm{U}$ method. Calculated oxidation energies agree well with experimental data for reasonable and consistent values of U.