Bagci-Hoggan Complete and Orthonormal Sets of ETOs. Results for He-like atoms

• URL: http://arxiv.org/abs/2504.10086v1
• Date: Mon, 14 Apr 2025 10:42:04 GMT
• Title: Bagci-Hoggan Complete and Orthonormal Sets of ETOs. Results for He-like atoms
• Authors: A. Bagci, P. E. Hoggan,
• Abstract summary: Bagci-Hoggan complete and orthonormal sets of exponential-type orbitals are employed as the basis.<n>This study examines the effect of fractional values of the quantum numbers for two-electron systems, where electron correlation effects exist.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The Hartree-Fock-Rothaan equations are solved for He-like ions using the iterative self-consistent method. Bagci-Hoggan complete and orthonormal sets of exponential-type orbitals are employed as the basis. These orbitals satisfy the orthonormality relationship for quantum numbers with fractional order. They are solution of Schrodinger-like differential equation derived by the author. In a recent study conducted for the calculation of the hydrogen atom energy levels, it has been demonstrated that the fractional formalism of the principal and the angular momentum quantum numbers converges to the 1s level of the ground state energy of hydrogen atom, obtained from the solution of the standard Schrodinger equation. This study examines the effect of fractional values of the quantum numbers for two-electron systems, where electron correlation effects exist.

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