Excitation energies from time-dependent density functional theory using exact and approximate functionals

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The role of the exchange-correlation potential and the exchange-correlation kernel in the calculation of excitation energues from time-dependent density functional theory is studied. Excitation energies of the He and Be atoms are calculated, both from the exact ground-state Kohn-Sham potential, and from two orbital-dependent approximations. These are exact exchange and self-interaction corrected local density approximation (SIC-LDA), both calculated using the Krieger-Li-Iafrate (KLI) approximation. For the exchange-correlation kernela, three adiabatic approximations were tested: The local density approximation, exact exchange, and SIC-LDA. The choice of the ground-state exchange-correlation potential has the largest impact on the absolute position of most excitation energies. In particular, orbital-dependent approximate potentials result in a uniform shift of the transition energies to the Rydberg states.