Predicting density functional theory total energies and enthalpies of formation of metal-nonmetal compounds by linear regression

The availability of quantitatively accurate total energies $({E}_{\mathrm{tot}})$ of atoms, molecules, and solids, enabled by the development of density functional theory (DFT), has transformed solid state physics, quantum chemistry, and materials science by allowing direct calculations of measureable quantities, such as enthalpies of formation $(\mathrm{\ensuremath{\Delta}}{H}_{f})$. Still, the ability to compute ${E}_{\mathrm{tot}}$ and $\mathrm{\ensuremath{\Delta}}{H}_{f}$ values does not, necessarily, provide insights into the physical mechanisms behind their magnitudes or chemical trends. Here, we examine a large set of calculated ${E}_{\mathrm{tot}}$ and $\mathrm{\ensuremath{\Delta}}{H}_{f}$ values obtained from the DFT+$U$-based fitted elemental-phase reference energies (FERE) approach [V. Stevanovi\ifmmode \acute{c}\else \'{c}\fi{}, S. Lany, X. Zhang, and A. Zunger, Phys. Rev. B 85, 115104 (2012)] to probe relationships between the ${E}_{\mathrm{tot}}/\mathrm{\ensuremath{\Delta}}{H}_{f}$ of metal-nonmetal compounds in their ground-state crystal structures and properties describing the compound compositions and their elemental constituents. From a stepwise linear regression, we develop a linear model for ${E}_{\mathrm{tot}}$, and consequently $\mathrm{\ensuremath{\Delta}}{H}_{f}$, that reproduces calculated FERE values with a mean absolute error of \ensuremath{\sim}80 meV/atom. The most significant contributions to the model include calculated total energies of the constituent elements in their reference phases (e.g., metallic iron or gas phase ${\mathrm{O}}_{2}$), atomic ionization energies and electron affinities, Pauling electronegativity differences, and atomic electric polarizabilities. These contributions are discussed in the context of their connection to the underlying physics. We also demonstrate that our ${E}_{\mathrm{tot}}/\mathrm{\ensuremath{\Delta}}{H}_{f}$ model can be directly extended to predict the ${E}_{\mathrm{tot}}$ and $\mathrm{\ensuremath{\Delta}}{H}_{f}$ of compounds outside the set used to develop the model.