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We calculate the excitation energies of small neutral sodium clusters in theframework of time-dependent density-functional theory. In the presentedcalculations, we extract these energies from the power spectra of the dipoleand quadrupole signals that result from a real-time and real-space propagation.For comparison with measured photoelectron spectra, we use the ionicconfigurations of the corresponding single-charged anions. Our calculationsclearly improve on earlier results for photoelectron spectra obtained fromstatic Kohn-Sham eigenvalues.

Photoelectron spectra of anionic sodium clusters from time-dependent density-functional theory in real-time