On orthogonality constrained multiple core-hole states and optimized effective potential method.

An attempt to construct a multiple core-hole state within the optimized effective potential (OEP) methodology is presented. In contrast to the conventional Δ-self-consistent field method for hole states, the effects of removing an electron is achieved using some orthogonality constraints imposed on the orbitals so that a Slater determinant describing a hole state is constrained to be orthogonal to that of a neutral system. It is shown that single, double, and multiple core-hole states can be treated within a unified framework and can be easily implemented for atoms and molecules. For this purpose, a constrained OEP method proposed earlier for excited states (Glushkov and Levy, J. Chem. Phys. 2007, 126, 174106) is further developed to calculate single and double core ionization energies using a local effective potential expressed as a direct mapping of the external potential. The corresponding equations, determining core-hole orbitals from a one-particle Schrödinger equation with a local potential as well as correlation corrections derived from the second-order many-body perturbation theory are given. One of the advantages of the present direct mapping formulation is that the effective potential, which plays the role of the Kohn-Sham potential, has the symmetry of the external potential. Single and double core ionization potentials computed with the presented scheme were found to be in agreement with data available from experiment and other calculations. We also discuss core-hole state local potentials for the systems studied.