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We discuss the calculation of collective excitations in atomic clusters usingthe time-dependent local density approximation. In principle there are manyformulations of the TDLDA, but we have found that a particularly efficientmethod for large clusters is to use a coordinate space mesh and the algorithmsfor the operators and the evolution equations that had been developed for thenuclear time-dependent Hartree-Fock theory. The TDLDA works remarkably well todescribe the strong excitations in alkali metal clusters and in carbonclusters. We show as an example the benzene molecule, which has two strongfeatures in its spectrum. The systematics of the linear carbon chains is wellreproduced, and may be understood in rather simple terms.Comment: 12 pages in Postscrip

The time-dependent local density approximation for collective excitations of atomic clusters