First-order perturbation calculations for transition-metal atoms and ions

We have calculated the total energy and s-d promotion energies of 3d-transition-metal atoms using a common set of orbitals but various expressions for the energy. These include Hartree-Fock (HF), local-spin-density-approximation (LSDA), and self-interaction-corrected (SIC) LSDA expressions. The orbitals were generated from a self-consistent, spherically averaged, local-density calculation. The results using the HF expression are in remarkably good agreement with self-consistent Hartree-Fock calculations both for the total energy and for the HF eigenvalues. Further, the LSDA underestimates the total correlation energy by roughly 30 eV, while the SIC calculation overestimates the correlation energy in calcium by \ensuremath{\sim}15 eV.