Improving the modified Becke-Johnson exchange potential

The modified Becke-Johnson exchange potential [F. Tran and P. Blaha, Phys. Rev. Lett. 102, 226401 (2009)] (TB-mBJ) yields very accurate electronic band structures and gaps for various types of semiconductors and insulators (e.g., $sp$ semiconductors, noble-gas solids, and transition-metal oxides). However, the TB-mBJ potential has, for a few groups of solids, the tendency to underestimate the band gap. This has led us to examine the possibility to further improve over the original TB-mBJ potential by either reparametrizing its coefficients using a larger test set of solids or defining a parametrization for small-/medium-size band-gap semiconductors only. We also checked alternatives to the average of $\left|\nabla \rho \right|/\rho$ in the unit cell for the determination of parameter $c$, which determines the amount of the screening contribution. Among these different possibilities, the best one seems to be a reparametrization of the coefficients, which leads to a much more balanced description of the band gaps.

Figure 1

Plot of $c_{\mathrm{opt}}$ versus $\overline{g}$ (symbols) and several parametrizations of $c$ as a function of $\overline{g}$ (lines).

Figure 2

Difference between calculated and experimental band gaps for the different categories of solids and different parametrizations. Full symbols use $P$-original, open symbols use the new $P$-present parameters.

Figure 3

Difference between calculated and experimental band gaps for small-gap semiconductors and different parametrizations.

Figure 4

Plot of $c_{\mathrm{opt}}$ versus $\overline{s}$.

Figure 5

$g\left(\mathbf{r}\right)$ in the LiF-(001) plane. The numbers are given in ${\mathrm{bohr}}^{-1}$.

Figure 6

Comparison of band gaps predicted by the original TB-mBJ method and an approach, which includes a semilocal $c_{\mathrm{SL}}\left(\mathbf{r}\right)$ as described in Sec. 2c with experimental results (see Table ).