Computation of the Kohn-Sham orbital kinetic energy density in the full-potential linearized augmented plane-wave method

The Kohn-Sham orbital kinetic energy density ${\tau }_{\sigma }\left(\mathbf{r}\right)={\sum }_i{w}_{i\sigma }{\left|\nabla {\psi }_{i\sigma }\left(\mathbf{r}\right)\right|}^2$ is one fundamental quantity for constructing metageneralized gradient approximations (meta-GGAs) for use by density functional theory. We present a computational scheme of ${\tau }_{\sigma }\left(\mathbf{r}\right)$ for the full-potential linearized augmented plane-wave (FLAPW) method. Our scheme is highly accurate and efficient and easy to implement with existing computer codes. To illustrate its performance, we construct the Becke-Johnson meta-GGA exchange potentials for Be, Ne, Mg, Ar, Ca, Zn, Kr, and Cd atoms, which are in very good agreement with the original results. For bulk solids, we construct the Tran-Blaha modified Becke-Johnson potential (mBJ) and confirm its capability to calculate band gaps with the reported bad convergence of the mBJ potential being substantially improved. The present computational scheme of ${\tau }_{\sigma }\left(\mathbf{r}\right)$ should also be valuable for developing other meta-GGAs in the FLAPW as well as in similar methods utilizing atom centered basis functions.

Figure 1

Becke-Johnson exchange potential for Be, Ne, Mg, Ar, Ca, Zn, Kr, and Cd atoms calculated by the FLAPW method with the implementation of ${\tau }_{\sigma }\left(\mathbf{r}\right)$ of this paper.

Figure 2

(a) BJ06 potentials of Zn calculated by Eq. (1) or (3) with the Kohn-Sham or Dirac-Kohn-Sham core states. (b) Difference on the potentials by Eqs. (1) and (3) with the core states being solved by the Kohn-Sham equation.

Figure 3

Rubber-sheet plot of the up-spin kinetic energy density ${log}_{10}{\tau }_{\uparrow }$ of the NiO (001) plane. Atomic positions are illustrated at the bottom left of the plot.

Figure 4

Rubber-sheet plot of the up-spin mBJ potential $v_{\uparrow }^{\mathrm{mBJ}}$ of the NiO (001) plane. Atomic positions are illustrated at the bottom left of the plot.

Figure 5

Comparison among the mBJ band gaps, the LDA band gaps, and the experimental band gaps for the 40 semiconductors of the SC40 test set.