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. U sing accurate exchange-correlation potentials generated from essential ly exact densities and their exchange components determined by a recen tly proposed method, we evaluate energy differences between the ground state and excited states in first-order perturbation theory for the he lium, ionized lithium and beryllium atoms. It was recently observed th at the zeroth-order excitations energies, simply given by the differen ce of the Kohn-Sham eigenvalues, almost always lie between the singlet and triplet experimental excitations energies, corrected for relativi stic and finite nuclear mass effects. The first-order corrections prov ide about a factor of two improvement in one of the perturbative schem es but not in the other. The excitation energies within perturbation t heory are found to be more accurate than the excitations obtained with in Delta SCF while, for a two-electron system, they coincide with the ones obtained in time-dependent density functional theory within the s ingle-pole approximation using our accurate static exchange-correlatio n potential and the time-dependent optimized effective potential kerne l. We find that the agreement between the experimental and the perturb ative excitation energies deteriorates significantly if potentials fro m approximate functionals such as the local density approximation and the optimized effective potential method are employed instead of the t rue Kohn-Sham potential. (C) 1997 American Institute of Physics. [S002 1-9606(97)03147-4].