) where f s is the occupation and ϵ s is the Kohn-Sham energy corresponding to ψ s . Here, we have suppressed the crystal momentum index k, where s = nk Application of the Sokhotski-Plemelj formula to Eq.13 yields (14) Note that at T = 0, the two pole terms in Eq. 14 collapse into a single term dictated by sgn(E f -ϵ s ), or in other words, whether or not the band is valence or conduction: