Effects of semicore d-electrons in screened-exchange density functional methods

We report a theoretical study on the role of shallow $d$ states in the screened-exchange local density approximation (sX-LDA) band structure of binary semiconductor systems. We found that the inaccurate pseudo-wavefunctions can lead to 1) an overestimation of the screened-exchange interaction between the localized $d$ states and the delocalized higher energy $s$ and $p$ states and 2) an underestimation of the screened-exchange interaction between the $d$ states. The resulting sX-LDA band structures have substantially smaller band gaps compared with experiments. We correct the pseudo-wavefunctions of $d$ states by including the $s$ and $p$ states of the same shell in the valence states. The correction of pseudo-wavefunctions yields band gaps and the $d$ state binding energy in good agreement with experiments. Compared with the quasi-particle GW method, our sX-LDA results shows not only similar quality band gaps but also much better $d$ state binding energy. As an example, we present sX-LDA results of $s-d$ coupling in zinc-blende semiconductors and compare them with LDA+U results. We also present an efficient method to correct the pseudo-wavefunction exchange-integral error by using projection of wavefunctions onto atomic orbitals.