Approaching chemical accuracy with density functional calculations: Diatomic energy corrections

Density functional theory (DFT) is widely used to predict materials properties, but the local density approximation (LDA) and generalized gradient approximation (GGA) exchange-correlation functionals are known to poorly predict the energetics of reactions involving molecular species. In this paper, we obtain corrections for the O${}_2$, H${}_2$, N${}_2$, F${}_2$, and Cl${}_2$ molecules within the Perdew-Burke-Enzerhof GGA, Perdew-Wang GGA, and Perdew-Zunger LDA exchange-correlation functionals by comparing DFT-calculated formation energies of oxides, hydrides, nitrides, fluorides, and chlorides to experimental values. We also show that the choice of compounds used to obtain the correction is significant, and we use a leave-one-out cross-validation approach to rigorously determine the proper fit set. We report confidence intervals with our correction values, which quantifies the variation caused by the choice of fit set after outlier removal. The remaining variation in the correction values is of the order of 1 kcal/mol, which indicates that chemical accuracy is a realistic goal for these systems.

Figure 1

Cross-validation scores for each set of compounds, in units of eV. Higher CV scores indicate outlier compounds, which we then remove from the fitting sets via the LOOCV process described in Sec. 2b. Tl${}_2$O${}_3$, RbH (PW91, LDA), SrH${}_2$ (PW91, LDA), InN, InF${}_3$ (PW91, LDA), PbF${}_2$, and PbCl${}_2$ were removed from the fitting sets.

Figure 2

Plots for fitting diatomic energy corrections $C$ for the O${}_2$ molecule across the three exchange-correlation potentials, as indicated. The solid line represents a least-squares fit to Eq. (2). Applying the diatomic energy correction $C$ in Eq. (2), shown here in blue, would improve the agreement between the DFT-calculated and experimental formation enthalpies. The dotted line represents $y=x$, or perfect agreement between DFT calculations and experimental values.

Figure 3

The diatomic energy corrections for the H${}_2$ molecule across the three $\mathit{xc}$ functionals. Contrasting the behavior between the two GGA functionals and the LDA functional is consistent with the results of Wolverton et al.[13] and Hector et al.[28]

Figure 4

The diatomic energy corrections for the N${}_2$ molecule across the three $\mathit{xc}$ functionals. These figures show that the diatomic energy correction procedure may be less accurate for nitrides, which is also reflected in the 95$\%$ confidence intervals reported in Table .

Figure 5

The diatomic energy corrections for the F${}_2$ molecule across the three $\mathit{xc}$ functionals. All three $\mathit{xc}$ functionals predict fluorides to be less stable than experiment, in contrast to the predicted stability of oxides and hydrides.

Figure 6

The diatomic energy corrections for the Cl${}_2$ molecule across the three $\mathit{xc}$ functionals. Similar to the fluorides, all three $\mathit{xc}$ functionals predict chlorides to be less stable than experiment.