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Semi-local DFT methods exhibit significant errors for the phase diagrams oftransition-metal oxides that are caused by an incorrect description ofmolecular oxygen and the large self-interaction error in materials withstrongly localized electronic orbitals. Empirical and semiempirical correctionsbased on the DFT+U method can reduce these errors, but the parameterization andvalidation of the correction terms remains an on-going challenge. We develop asystematic methodology to determine the parameters and to statistically assessthe results by considering thermochemical data across a set of transition metalcompounds. We consider three interconnected levels of correction terms: (1) aconstant oxygen binding correction, (2) Hubbard-U correction, and (3) DFT/DFT+Ucompatibility correction. The parameterization is expressed as a unifiedoptimization problem. We demonstrate this approach for 3d transition metaloxides, considering a target set of binary and ternary oxides. With a total of37 measured formation enthalpies taken from the literature, the dataset isaugmented by the reaction energies of 1,710 unique reactions that were derivedfrom the formation energies by systematic enumeration. To ensure a balanceddataset across the available data, the reactions were grouped by theirsimilarity using clustering and suitably weighted. The parameterization isvalidated using leave-one-out cross-validation (CV), a standard technique forthe validation of statistical models. We apply the methodology to the SCANdensity functional. Based on the CV score, the error of binary (ternary) oxideformation energies is reduced by 40% (75%) to 0.10 (0.03) eV/atom. The methodand tools demonstrated here can be applied to other classes of materials or toparameterize the corrections to optimize DFT+U performance for other targetphysical properties.

Data-driven Approach to Parameterize SCAN+U for an Accurate Description of 3d Transition Metal Oxide Thermochemistry