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. [S0031-9007(99)09245-5].
Gonze, X., & Scheffler, M. (1999). Exchange and correlation kernels at the resonance frequency: Implications for excitation energies in density-functional theory. Physical Review Letters, 82(22), 4416-4419. https://doi.org/10.1103/PhysRevLett.82.4416 (Original work published 1999)