New Atomic Orbital Functions.Complete and Orthonormal Sets of ETOs with Non-integer Quantum Numbers.Results for He-like atoms

Abstract

The Hartree-Fock-Rothaan equations are solved for He-like ions using the iterative self-consistent method. New complete and orthonormal sets of exponential-type orbitals are employed as the basis. These orbitals satisfy the orthonormality condition for quantum numbers with fractional power. They are solutions of a Schrodinger-like differential equation derived by the authors. 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, which is the simplest system with electron correlation effects.