Modified linear response for time-dependent density-functional theory: Application to Rydberg and charge-transfer excitations

We present an improved ab initio time-dependent density-functional theory (TDDFT) approach to electronic excitations. A conventional TDDFT scheme within the local-density approximation (LDA) inaccurately predicts Rydberg and charge-transfer excitation energies, mainly because the electron-hole (e-h) interaction is inappropriately described in these excitations, as can be found by analyzing the linear response formula [M. Petersilka, U. J. Gossmann, and E. K. U. Gross, Phys. Rev. Lett. 76, 1212 (1996)]. When the formula is averaged over the electron occupation, the inappropriate e-h interaction within LDA is corrected to become explicitly similar to that of the exact exchange system. As anticipated from the similarity, our proposed scheme of modified linear response greatly improves the prediction of the problematic excitations, which are exemplified for typical molecules.