Use of self-friction polynomials in standard convention and auxiliary functions for construction of One-Range addition theorems for noninteger slater type orbitals

Abstract

Using $ \mathcal{L}^{(p_l *)}$-self-friction polynomials ($ \mathcal{L}^{(p_l^ *)}$-SFPs), complete orthonormal sets of $\psi^{(p_l^*)}$-SF exponential type orbitals ( $\psi^{(p_l^*)}$-SFETOs) in standard convention and $Q^q$-integer auxiliary functions ($Q^q$-IAFs) introduced by the author, the combined one- and two-center one-range addition theorems for $ \chi $-noninteger Slater type orbitals ($ \chi $-NISTOs) are established, where $p_l^* =2l+2 - \alpha^*$ and $ \alpha^* $ is SF quantum number. As an application, the one-center atomic nuclear attraction integrals of $ \chi $-NISTOs and $V$-noninteger Coulombic potential ($V$-NICPs) are calculated. The obtained formulas can be useful especially in the electronic structure calculations of atoms, molecules and solids.