Local-resolvent formulation and assessment of linear-scaling Kohn-Sham calculations

Kohn-Sham density-functional theory is expensive because it needs orbitals that extend over the whole system. For insulators this can be avoided by using only the diagonal of the one-electron resolvent, $g(\mathbf{r},z)=\langle\mathbf{r}|(z-\hat h)^{-1}|\mathbf{r}\rangle$, at a few complex energies