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-depend ent density-functional theory are computed. The knowledge of these matrix e lements 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, d espite the approximations that have been performed to derive them. [S0031-9 007(99)09245-5].