Exact-exchange time-dependent density-functional theory with the frequency-dependent kernel

The effects of the adiabatic approximation in time-dependent density-functional theory (TDDFT) on dynamic polarizabilities and van der Waals C6 coefficients have been analyzed quantitatively. These effects are shown to be small in the off-resonance region of the perturbation frequencies by comparing the results from the exact-exchange TDDFT employing the optimized effective potentials and the corresponding frequency-dependent kernel [time-dependent optimized effective potentials (TDOEP)] and those from the frequency-independent kernel [adiabatic TDOEP (ATDOEP)]. The magnitude of the computed dynamic polarizabilities near the static limit is found to be in the order: time-dependent Hartree-Fock (TDHF) >ATDOEP>TDOEP, whereas that of C6 is: TDHF>TDOEP>ATDOEP.