A spin-dependent density-functional approach for the calculation of highly and multiply excited state of atomic system is proposed based on the localized Hartree-Fock density-functional method and Slater’s diagonal sum rule. In this approach, electron spin orbitals in an electronic configuration are obtained first by solving the Kohn-Sham equation with an exact nonvariational spin-dependent localized Hartree-Fock 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 excited state is evaluated from the single-Slater-determinant energies of the electronic configurations involved in terms of Slater’s diagonal sum rule. This approach has been applied to the calculation of singly, doubly, and especially triply excited Rydberg states of He- and Li-like ions. The total energies obtained from the calculation with an exchange-only ($X$-only) potential are surprisingly close to those of Hartree-Fock method and the total energies from the calculation with exchange-correlation potential are in overall agreement with available theoretical and experimental data. The presented procedure provides a simple and computationally efficient scheme for the accurate calculation of highly and multiply excited Rydberg states of an atomic system within density-functional theory.

• Received 7 July 2004

DOI:https://doi.org/10.1103/PhysRevA.71.022513