Excitation energies from density functional perturbation theory

We consider two perturbative schemes to calculate excitation energies, each employing the Kohn-Sham Hamiltonian as the unperturbed system. Using accurate exchange-correlation potentials generated from essentially exact densities and their exchange components determined by a recently proposed method, we evaluate energy differences between the groundstate and excited states in first-order perturbation theory for the helium, ionized lithium and beryllium atoms. It was recently observed that the zeroth-order excitations energies, simply given by the difference of the Kohn-Sham eigenvalues, almost always lie between the singlet and triplet experimental excitations energies, corrected for relativistic and finite nuclear mass effects. The first-order corrections provide about a factor of two improvement in one of the perturbative schemes but not in the other. The excitation energies within perturbation theory are found to be more accurate than the excitations obtained within Delta SCF while, for a two-electron system, they coincide with the ones obtained in time-dependent density functional theory within the single-pole approximation using our accurate static exchange-correlation potential and the time-dependent optimized effective potential kernel. We find that the agreement between the experimental and the perturbative excitation energies deteriorates significantly if potentials from approximate functionals such as the local density approximation and the optimized effective potential method are employed instead of the true Kohn-Sham potential. (C) 1997 American Institute of Physics. [S0021-9606(97)03147-4].