An approximate solution to the time-dependent density functional theory
(TDDFT) response equations for finite systems is developed, yielding
corrections to the single-pole approximation. These explain why allowed
Kohn-Sham transition frequencies and oscillator strengths are usually good
approximations to the true values, and why sometimes they are not. The
approximation yields simple expressions for G\"orling-Levy perturbation theory
results, and a method for estimating expectation values of the unknown
exchange-correlation kernel.Comment: 4 pages, 1 tabl