Excitation Energies from Time-Dependent Density-Functional Theory

A new density-functional approach to calculate the excitation spectrum of many-electron systems is proposed. It is shown that the full linear density response of the interacting system, which has poles at the exact excitation energies, can rigorously be expressed in terms of the response function of the noninteracting (Kohn-Sham) system and a frequency-dependent exchange-correlation kernel. Using this expression, the poles of the full response function are obtained by systematic improvement upon the poles of the Kohn-Sham response function. Numerical results are presented for atoms.