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

The availability of quantitatively accurate total energies (Eₜₒₜ) 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 (ΔHf). Still, the ability to compute Eₜₒₜ and ΔHf values does not, necessarily, provide insights into the physical mechanisms behind their magnitudes or chemical trends. Here, we examine a large set of calculated Eₜₒₜ and ΔHf values obtained from the DFT+U-based fitted elemental-phase reference energies (FERE) approach [V. Stevanovi {c} \'{c}{}, S. Lany, X. Zhang, and A. Zunger, Phys. Rev. B 85, 115104 (2012)] to probe relationships between the Eₜₒₜ/ΔHf 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 Eₜₒₜ, and consequently ΔHf, that reproduces calculated FERE values with a mean absolute error of {~}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 O₂), 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 Eₜₒₜ/ΔHf model can be directly extended to predict the Eₜₒₜ and ΔHf of compounds outside the set used to develop the model.