Charge-transfer excitation energies with a time-dependent density-functional method suitable for orbital-dependent exchange-correlation kernels

A time-dependent density-functional (TDDFT) response equation for the effective Kohn-Sham potential instead of the electron densities is presented that enables the use of orbital-dependent exchange-correlation kernels. In combination with the frequency-dependent exact-exchange kernel the present approach describes long-range charge-transfer excitations qualitatively correct in contrast to standard TDDFT methods, as shown by formal analysis and applications to molecular systems. Even charge-transfer excitations obtained with the adiabatic frequency-independent exact-exchange kernel exhibit a long-range dependence with the distance of the charge transfer, which, however, is too weak by a factor of 2. This indicates that it is not the frequency dependence of the kernel alone that leads to a correct description of charge-transfer excitations.