Importance of the Kinetic Energy Density for Band Gap Calculations in Solids with Density Functional Theory

Abstract

Recently, exchange-correlation potentials in density functional theory were developed with the goal of providing improved band gaps in solids. Among them, the semilocal potentials are particularly interesting for large systems since they lead to calculations that are much faster than with hybrid functionals or methods like GW. We present an exhaustive comparison of semilocal exchange-correlation potentials for band gap calculations on a large test set of solids, and particular attention is paid to the potential HLE16 proposed by Verma and Truhlar. It is shown that the most accurate potential is the modified Becke–Johnson potential, which, most noticeably, is much more accurate than all other semilocal potentials for strongly correlated systems. This can be attributed to its additional dependence on the kinetic energy density. It is also shown that the modified Becke–Johnson potential is at least as accurate as the hybrid functionals and more reliable for solids with large band gaps.

Rare earth doping and effective band-convergence in SnTe for improved thermoelectric performance

“…Here, Eb also decreases because of doping with other elements including alkaline or transition metal. Our ab-initio band-structure calculations (Fig.3) shows that the band-convergence effect is more prominent with rare earth (Yb) doping than transition metal doping (Mn as representative Fig.3 (a)) for the parent SnTe, which is consistent with earlier results, 39 while Eb at the L and Σ points is 0.256 eV. By substituting 1/27 Sn with Yb, we get Sn0.97Yb0.03Te and perform our calculations.…”

Semilocal exchange-correlation potentials for solid-state calculations: Current status and future directions

“…As illustrated and discussed in previous works, 29,32,48 the mBJLDA potential is, compared to the PBE potential, more negative around the nuclei (where the orbital of the VBM is usually located) and less negative in the interstitial region (where the orbital of the CBM is located). This enlarges the band gap.…”

Orbital-free approximations to the kinetic-energy density in exchange-correlation MGGA functionals: Tests on solids

“…The deterioration is the smallest when t KS is replaced by t PCopt , and in this case the MAE increases from 0.47 to 0.67 eV and the MARE from 15 to 16%. This increase in the MARE is clearly negligible, but also quite acceptable for the MAE considering that most other potentials lead to larger MAE for this test set 73,75. With mBJLDA(CRopt), a small increase of 4% for the MARE is obtained, while the MAE increases to 0.75 eV, which is now on the verge of being acceptable since other potentials, e.g., AK13, 100 B3PW91, 101 or HSE06 98,99 lead to similar MAE 73,75.…”

“…This increase in the MARE is clearly negligible, but also quite acceptable for the MAE considering that most other potentials lead to larger MAE for this test set 73,75. With mBJLDA(CRopt), a small increase of 4% for the MARE is obtained, while the MAE increases to 0.75 eV, which is now on the verge of being acceptable since other potentials, e.g., AK13, 100 B3PW91, 101 or HSE06 98,99 lead to similar MAE 73,75. Substituting t KS by any of the other OF KED leads to a clearly larger MAE (around 1 eV) and MARE (above 30%, except with t GEAloc ).…”