Correcting density functional theory for accurate predictions of compound enthalpies of formation: Fitted elemental-phase reference energies

Despite the great success that theoretical approaches based on density functional theory have in describing properties of solid compounds, accurate predictions of the enthalpies of formation ($\ensuremath{\Delta}{H}_{f}$) of insulating and semiconducting solids still remain a challenge. This is mainly due to incomplete error cancellation when computing the total energy differences between the compound total energy and the total energies of its elemental constituents. In this paper we present an approach based on GGA $+$ $U$ calculations, including the spin-orbit coupling, which involves fitted elemental-phase reference energies (FERE) and which significantly improves the error cancellation resulting in accurate values for the compound enthalpies of formation. We use an extensive set of 252 binary compounds with measured $\ensuremath{\Delta}{H}_{f}$ values (pnictides, chalcogenides, and halides) to obtain FERE energies and show that after the fitting, the 252 enthalpies of formation are reproduced with the mean absolute error $\text{MAE}=0.054$ eV/atom instead of $\text{MAE}\ensuremath{\approx}0.250$ eV/atom resulting from pure GGA calculations. When applied to a set of 55 ternary compounds that were not part of the fitting set the FERE method reproduces their enthalpies of formation with $\text{MAE}=0.048$ eV/atom. Furthermore, we find that contributions to the total energy differences coming from the spin-orbit coupling can be, to a good approximation, separated into purely atomic contributions which do not affect $\ensuremath{\Delta}{H}_{f}$. The FERE method, hence, represents a simple and general approach, as it is computationally equivalent to the cost of pure GGA calculations and applies to virtually all insulating and semiconducting compounds, for predicting compound $\ensuremath{\Delta}{H}_{f}$ values with chemical accuracy. We also show that by providing accurate $\ensuremath{\Delta}{H}_{f}$ the FERE approach can be applied for accurate predictions of the compound thermodynamic stability or for predictions of Li-ion battery voltages.