Many-Body Diagrammatic Expansion in a Kohn-Sham Basis: Implications for Time-Dependent Density Functional Theory of Excited States

We formulate diagrammatic rules for many-body perturbation theory which uses Kohn-Sham Green's functions as basic propagators. The diagram technique allows one to study the properties of the dynamic nonlocal exchange-correlation (xc) kernel $f_{\mathrm{xc}}$. We show that the spatial nonlocality of $f_{\mathrm{xc}}$ is strongly frequency dependent. In particular, in extended systems the nonlocality range diverges at the excitation energies. This divergency is related to the discontinuity of the xc potential.