Within the adiabatic approximation, time-dependent density functional theory yields only single excitations. Near states of double excitation character, the exact exchange–correlation kernel has a strong dependence on frequency. We derive the exact frequency-dependent kernel when a double excitation mixes with a single excitation, well separated from the other excitations, in the limit that the electron–electron interaction is weak. Building on this, we construct a nonempirical approximation for the general case, and illustrate our results on a simple model.
Double excitations within time-dependent density functional theory linear response. Neepa T. Maitra, Fan Zhang, Robert J. Cave, and Kieron Burke, J. Chem. Phys. 120, 5932 (2004), DOI:10.1063/1.1651060.