Inner-shell excitation of open-shell atoms: a spin-dependent localized Hartree–Fock density-functional approach

Abstract

The spin-dependent localized Hartree-Fock (SLHF) density-functional approach is extended to the treatment of the inner-shell excited-state calculation of open-shell atomic systems. In this approach, the electron spin-orbitals in an electronic configuration are obtained by solving Kohn-Sham (KS) equation with SLHF exchange potential and the Slater's diagonal sum rule is used to evaluate the multiplet energy of an inner-shell excited state from the single-Slater-determinant energies of the electronic configurations involved. This approach together with the correlation potentials and energy functionals proposed by Perdew and Wang's (PW) or Lee, Yang, and Parr's (LYP) have been used to calculate the total and excitation energies of inner-shell excited states of open-shell atomic systems: Li, B, Ne + , Ne 2+ , Ne 3+ , and Na. The 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. Some new results for highly excited inner-shell states are presented.

Time-dependent localized Hartree-Fock density-functional linear response approach for photoionization of atomic excited states

“…The electron spin-orbitals of an atomic system can be calculated by using the procedure previously developed in [21,24]. In spherical coordinates, the electron spin-orbital ϕ iσ (r) is expressed as a product of a radial spin-orbital R nlσ (r) and a spherical harmonic Y lm (θ, φ)…”

“…where, n is the principal quantum number, l is the orbital angular momentum quantum number, m is the azimuthal quantum number, and i is a set of quantum numbers except the spin σ. The radial spin-orbital R nlσ (r) is calculated from the radial KS equation [21,24] − 1 2…”

“…It allows for nonuniform and optimal spatial discretization with the use of only a modest number of grid points. It has been shown that the GPS method is a very effective and efficient numerical algorithm for the high-precision solution of KS equation [21,24,29,30].…”

“…To calculate the occupied electron spin-orbitals we use the SLHF density-functional approach [21,23,24]. In this approach, the electron spin-orbital ϕ iσ (r) and orbital energy ε iσ are calculated from the KS equation…”

“…More recently, a spin-dependent localized Hartree-Fock (SLHF) density-functional approach has been developed for the excited-state calculation of atomic and molecular systems [21]. This approach together with Slater's diagonal sum rule [22] have been successfully used to calculate the energies of multiply excited states of valence electrons of atomic systems [21] and the energies of inner-shell excited states of closed-shell [23] and open-shell [24] atomic systems.…”