Calculated formation and reaction energies of 3d transition metal oxides using a hierachy of exchange-correlation functionals

The formation and oxidation reaction energies of 16 transition metal oxides (TMOs) are benchmarked against experiments with an increasing complexity of the exchange-correlation (xc) functionals: PBE, PBE + U with a single U for each transition metal element, PBE0 (25% exact exchange included), EXX (100% exact exchange), and EXX + RPA (random phase approximation for the correlation energy). Although rather challenging on standard CPU computing facilities, the RPA calculations were performed efficiently on graphic processing units (GPUs). For the formation energies, the PBE + U, PBE0, EXX + RPA improves significantly over PBE with mean absolute errors (MAE) of 0.83 (PBE), 0.39 (PBE + U), 0.34 (PBE0), and 0.39 (EXX + RPA) eV per oxygen. In addition, EXX + RPA improves over the other xc functionals on the oxidation reaction energies, with MAE of 0.27 (PBE), 0.28 (PBE + U), 0.30 (PBE0), to 0.13 (EXX + RPA) eV per oxygen. The distinct trend observed for the calculated oxidation reaction energies compared to the formation energies is due to that the errors in formation energies for PBE and EXX + RPA are systematic; while for PBE + U and PBE0 the deviations have both signs, so that the error cancellations between different valence states work better for PBE and EXX + RPA. Finally, we compared the performance of the EXX + RPA for total energies and G₀W₀, which uses the random phase approximation in constructing the W kernel, for band gaps, and discuss a few challenges for the EXX + RPA method on TMOs.