Inhomogeneous STLS theory and TDCDFT

We consider the inhomogeneous Singwi-Tosi-Land-Sjolander theory (ISTLS) of Dobson, Wang and Gould (Phys. Rev. B, 2002, 66, 081108(R)), and possible generalizations, in the context of time dependent current density functional theory (TDCDFT) and its tensor exchange correlation kernel f(xc). We show that ISTLS corresponds to an f(xc) that is nonlocal in space but has only a trivial frequency dependence, and only a very simple tensorial structure. We propose approaches that may obtain more realistic structure while retaining the positive ISTLS features, namely that strong spatial inhomogeneity is allowed, with a kernel that contains physics specific to the inhomogeneous system under study, rather than being based on uniform-gas data.