Accurate evaluation of overlap integrals of Slater type orbitals with noninteger principal quantum numbers using complete orthonormal sets of $$\Psi^{\alpha}$$ - exponential type orbitals

Abstract

In this paper, by the use of complete orthonormal sets of $$\Psi^{\alpha}$$ exponential-type orbitals ( $$\Psi^{\alpha}$$ -ETOs, $$\alpha = 1, 0, -1, -2,\ldots$$ ), the series expansion formulas in line-up coordinate systems are established for the overlap integrals with noninteger n * Slater-type orbitals (NISTOs) in terms of overlap integrals over integer n Slater-type orbitals (ISTOs). The suggested approach guarantees a highly accurate calculation of the noninteger n * overlap integrals with arbitrary values of parameters. The results of computer calculations presented are in a complete agreement with those obtained in the literature using the alternative procedure.