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Hubbard-corrected oxide formation enthalpies without adjustable parameters

A density functional theory (DFT) approach to computing transition metal oxide heat of formation without adjustable parameters is presented. Different degrees of $d$-electron localization in oxides are treated within the DFT+$U$ approach with site-dependent, first-principles Hubbard $U$-parameters obtained from linear response theory, and delocalized states in the metallic phases are treated without Hubbard corrections. Comparison of relative stabilities of these differently treated phases is enabled by a local $d$-electron density matrix-dependent model, which was found by genetic programming against experimental reference formation enthalpies. This mathematically simple model does not explicitly depend on the Hubbard-corrected ionic species and is shown to reproduce the heats of formation of the Mott insulators Ca$_2$RuO$_4$ and Y$_2$Ru$_2$O$_7$ within $\sim$3% of experimental results, where the experimental training data did not contain Ru oxides. This newly developed method thus absolves from the need for element-specific corrections fitted to experiments in existing Hubbard-corrected approaches to the prediction of reaction energies of transition metal oxides and metals. The absence of fitting parameters opens up here the possibility to predict relative thermodynamic stabilities and reaction energies involving $d$-states of varying degree of localization at transition metal oxide interfaces and defects, where site-dependent $U$-parameters will be particularly important and devising a fitting scheme against experimental data with predictive power would be exceedingly difficult.