  The generator-coordinate method is a flexible and powerful reformulation of
the variational principle. Here we show that by introducing a generator
coordinate in the Kohn-Sham equation of density-functional theory, excitation
energies can be obtained from ground-state density functionals. As a viability
test, the method is applied to ground-state energies and various types of
excited-state energies of atoms and ions from the He and the Li isoelectronic
series. Results are compared to a variety of alternative DFT-based approaches
to excited states, in particular time-dependent density-functional theory with
exact and approximate potentials.
