Use of Auxiliary Functions for Construction of Series Expansion Relations of Noninteger Slater Functions in Standard Convention

Abstract

Using complete orthonormal sets of y a ( *) -self-frictional exponential type orbitals (y a ( *) -SFETOs) and Q q -noninteger auxiliary functions (Q q -NIAFs) introduced by the author, the combined formulas for the one-and two-center one-range addition theorems of c-noninteger Slater type orbitals (c-NISTOs) with arbitrary values of distances between centers R ab (for R ab = 0 and R ab ¹ 0), and of integer (for a * = a, -¥ < a £ 2) and noninteger (for a * ¹ a, -¥ < a* < 3) self-frictional (SF) quantum numbers are suggested. The presented relations for the one-range addition theorems can be useful tools especially in the electronic structure studies of atoms, molecules and solids when c-NISTOs are employed as basis functions.