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

Abstract

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.

Subspace effective potential theory for configuration interaction

“…This method was applied successfully for the ground state calculations of atoms and molecules, excited state exchange‐only OEP calculations as well as for incorporating static correlation effects . It was also appropriate for core hole excited and ionized states . In the present implementation of the CI subspace theory, we shall use the above potential and the parameters of will be chosen so that the functional defined earlier, takes its minimum value for the eigenstates produced by the one particle Schroedinger equation …”

Orthogonality of determinant functions in the Hartree-Fock method for highly excited electronic states

“…The experience of such calculations shows that the minimum is provided by the choice = ; i.e., all occupied molecular orbitals (MO) of the αcluster for the ES should be orthogonal to the α-spin highest occupied molecular orbital (HOMO) of the ground state. Therefore, we make the replacement and orthogonality requirement (11) becomes (12) Note that the requirements are easily generalized to the case of doubly excited states [28] and the "hole" states obtained by exciting (removing) electrons from inner shells (for example, the K-shell [29][30][31]). Requirement (12) can also be extended to higher ESs.…”

Toward the understanding of the environmental effects on core ionizations

“…In concluding this subsection, it is worth noting that the LSCF method is closely related to the projection operator technique (e.g., Ref. [46]). This technique deals with the modified operator F mod 5 I2P ð ÞF I2P ð Þ and can be considered as well as the LSCF approach as a benchmark for solving orthogonality constraint problems.…”