Self-friction power series and their use for evaluation of atomic nuclear attraction integrals with noninteger indices of Slater orbitals and Coulomb–Yukawa-like potentials

Using complete orthogonal [Formula: see text]-Self-Friction Polynomials ([Formula: see text]-SFPs) introduced by one of the authors, the analytical and power series formulas for SF atomic nuclear attraction integrals over [Formula: see text]-noninteger Slater type orbitals ([Formula: see text]-NISTOs) and [Formula: see text]-noninteger Coulomb–Yukawa-like potentials ([Formula: see text]-NICYPs) are presented, where [Formula: see text] are the integer ([Formula: see text] or noninteger ([Formula: see text] SF quantum numbers and [Formula: see text]. As an application, the computer calculations for dependence of the atomic nuclear attraction integrals over [Formula: see text]-NISTOs and [Formula: see text]-NICYPs functions are presented.

Evaluation of Self-Friction Three-Center Nuclear Attraction Integrals with Integer and Noninteger Principal Quantum Numbers n over Slater Type Orbitals

We have proposed a new approach to evaluate self-friction (SF) three-center nuclear attraction integrals over integer and noninteger Slater type orbitals (STOs) by using Guseinov one-range addition theorem in standard convention. A complete orthonormal set of Guseinov ψα exponential type orbitals (ψα-ETOs, α=2,1,0,-1,-2,…) has been used to obtain the analytical expressions. The overlap integrals with noninteger quantum numbers occurring in SF three-center nuclear attraction integrals have been evaluated using Qnsq auxiliary functions. The accuracy of obtained formulas is satisfactory for arbitrary integer and noninteger principal quantum numbers.