  We discuss the calculation of collective excitations in atomic clusters using
the time-dependent local density approximation. In principle there are many
formulations of the TDLDA, but we have found that a particularly efficient
method for large clusters is to use a coordinate space mesh and the algorithms
for the operators and the evolution equations that had been developed for the
nuclear time-dependent Hartree-Fock theory. The TDLDA works remarkably well to
describe the strong excitations in alkali metal clusters and in carbon
clusters. We show as an example the benzene molecule, which has two strong
features in its spectrum. The systematics of the linear carbon chains is well
reproduced, and may be understood in rather simple terms.
