Efficient Band Gap Prediction for Solids

An efficient method for the prediction of fundamental band gaps in solids using density functional theory (DFT) is proposed. Generalizing the Delta self-consistent-field ($\Delta \mathrm{SCF}$) method to infinite solids, the $\Delta$-sol method is based on total-energy differences and derived from dielectric screening properties of electrons. Using local and semilocal exchange-correlation functionals (local density and generalized gradient approximations), we demonstrate a 70% reduction of mean absolute errors compared to Kohn-Sham gaps on over 100 compounds with experimental gaps of 0.5–4 eV, at computational costs similar to typical DFT calculations.

Figure 1

Kohn-Sham (dots) and $\Delta$-sol (crosses) vs experimental [5] gaps. Cross sizes represent uncertainties.

Figure 2

Integrated screening charge $N_s$ for a unit charge in a homogeneous electron gas (HEG) and selected semiconductors (inset), vs the dimensionless distance $r{k}_f$. Different HEG curves correspond to different values of the density parameter $r_s$, in a range (1.5–3.5) typical for solids.

Figure 3

The calculated $E_{\mathrm{FG}}$ (PBE) as a function of $N$ for several compounds.

Figure 4

$E_{\mathrm{FG}}$ ($\Delta$-sol) and $E_{\mathrm{KS}}$ using PBE vs $E_{\mathrm{Exp}}$ for 74 compounds with only $s$ and $p$ valence electrons. Select compounds are highlighted with bolder symbols.

Figure 5

A comparison of $E_{\mathrm{FG}}$ computed with $\Delta$-sol (PBE) and $E_{\mathrm{KS}}$ (HSE06) vs $E_{\mathrm{Exp}}$ for 95 compounds.