Response of finite many-electron systems beyond the time-dependent local density approximation: Application to small metal clusters

A linear response formalism is developed which is based on density functional theory within the local density approximation, but which is now corrected for its spurious self-interaction errors, in the way originally proposed by Perdew and Zunger for ground state calculations. The original formulation is extended to incorporate self-interaction corrections in the scrrening terms. The general formalism is then applied to the calculation of the static and dynamic response of the metal clusters {Na₈, Na₉⁺}, {Na₂₀, Na} and {Na₄₀ Na} within the jellium model. Comparison with experimental data and with other theoretical calculations indicates that the present formalism accounts for the overall (and most of the fine) features of the photoabsorption spectrum of these systems, providing a systematic improvement with respect to previous approaches. The remaining discrepancies are rationalized in terms of the effects to be expected by correctly accounting for the discrete structure of the ionic cores.