Exchange and Correlation Kernels at the Resonance Frequency: Implications for Excitation Energies in Density-Functional Theory

Specific matrix elements of exchange and correlation kernels in time-dependent density-functional theory are computed. The knowledge of these matrix elements not only constrains approximate time-dependent functionals. It also allows one to link different practical approaches to excited states, based either on density-functional theory or on many-body perturbation theory, despite the approximations that have been performed to derive them.