Double excitation effect in non-adiabatic time-dependent density functional theory with an analytic construction of the exchange-correlation kernel in the common energy denominator approximation

Time-dependent density functional (response) theory (TDDF(R)T) is applied almost exclusively in its adiabatic approximation (ATDDFT), which is restricted to predominantly single electronic excitations and neglects additional roots of the TDDFT eigenvalue problem stemming from the interaction between single and double excitations. We incorporate the effect of the latter interaction into a non-adiabatic frequency-dependent and spatially non-local Hartree-exchange- correlation (Hxc) kernel fCEDAHxc (