Molecular excitation spectra by TDDFT with the nonadiabatic exact exchange kernel

A time‐dependent density functional theory (TDDFT) method using the nonadiabatic exact‐exchange kernel is discussed. Compared to previous TDDFT methods with orbital‐dependent kernels, the presented time‐dependent exact exchange (TDEXX) approach avoids a numerical unstable inversion of the Kohn–Sham response function. If the complete frequency dependency of the exact‐exchange kernel is taken into account, then the proposed method yields the long‐range distance behavior of charge‐transfer (CT) excitation energies qualitatively correctly. The relation between time‐dependent Hartree–Fock and TDEXX approaches is analyzed. This analysis shows by formal arguments why the TDEXX method is capable to correctly treat CT excitations and conversely shows that the problems to describe CT excitations with conventional TDDFT methods based on generalized gradient approximations (GGAs) has its origin in the shortcomings of the GGA exchange functionals.