Spin-multiplet electronic transition energies in NaF:Cu+by the self-interaction-corrected local-spin-density approximation

We bring together several theoretical and computational techniques to perform a unified, ab initio calculation of the optical-absorption spectrum for the NaF:${\mathrm{Cu}}^{+}$ impurity system. First, the spurious self-energy terms in the local-spin-density approximation are removed by a variationally based method, known as the self-interaction correction, which has had much success when applied to atoms and solids; here, the method is applied both to the impurity and host-crystal states. Second, a fractional-occupation-parameter technique is used in order to account rigorously for both orbital-relaxation and spin-polarization effects in the excited states. Third, the spin-orbit interaction is included in a treatment that uses the full impurity wave function, and that fully accounts for impurity-ligand covalency effects. We have used this approach to calculate the energy levels of the eight spin-orbit terms belonging to the impurity ${\mathrm{Cu}}^{+}$ 3$d^9$4s manifold. All eight energy levels are in excellent agreement with recent laser-spectroscopy absorption results, and the relative ordering of the levels is correctly predicted. The 3d→4p excitation energy has also been calculated and is in good agreement with the broad peak observed in ultraviolet absorption.