  We present a spin-dependent localized Hartree-Fock (SLHF) density-functional
approach for the treatment of the inner-shell excited-state calculation of
atomic systems. In this approach, the electron spin-orbitals in an electronic
configuration are obtained first by solving Kohn-Sham (KS) equation with SLHF
exchange potential. Then a single-Slater-determinant energy of the electronic
configuration is calculated by using these electron spin-orbitals. Finally, a
multiplet energy of an inner-shell excited state is evaluated from the
single-Slater-determinant energies of the electronic configurations involved in
terms of Slater's diagonal sum rule. This procedure has been used to calculate
the total and excitation energies of inner-shell excited states of close-shell
atomic systems: Be, B^+, Ne, and Mg. The correlation effect is taken into
account by incorporating the correlation potentials and energy functionals of
Perdew and Wang's (PW) or Lee, Yang, and Parr's (LYP) into calculation. The
calculated results with the PW and LYP energy functionals are in overall good
agreement with each other and also with available experimental and other ab
initio theoretical data. In addition, we present some new results for highly
excited inner-shell states.
