Beyond LDA calculations

We are also interested in beyond LDA calculations, by which we mean methods like GW or the screened exchange method. These can be used for electronic structure calculations alone (e.g., the GW method, and for nonselfconsistent electronic structure calculations), or also for total energy calculations (e.g., the screened exchange method, and for deep impurity level calculations). There are many reasons to believe that in order to get both the band structure and total energy correctly, one needs to go beyond the density functional theory. In other words, there should be some kind of geniune nonlocal potential for the single particle equation. The usual candidate for that is the nonlocal Hatree-Fock exchange potential, or some screened variation of it. At first step, one might still want to keep using a single slater determinate to represent the whole occupied electron space. Thus, a single particle Hamiltonian (with a nonlocal potential) can still be found. This Hamiltonian might not depend on the single particle energy (like in screened exchange method, but unlike the current GW formalism), so it is Hermissian. Further development might include energy dependent Hamiltonian (like in GW formalism, with dynamic screening), or even go beyond the single slater determinate. But how to express the total energy in such a formalism is still not clear. All these are very interesting research topics with great implications on material simulations.

The comparison between LDA band gaps and screened exchange (sX) band gaps.