Combined theory of two-electron nonrelativistic and quasirelativistic multicenter integrals over integer and noninteger n Slater type orbitals using auxiliary functions Qnsq and G-nsq

Using complete orthonormal sets of psi(alpha)-exponential type orbitals (alpha = 1, 0, -1, -2, ...) a large number of series expansion formulas for the two-electron nonrelativistic and quasirelativistic multicenter integrals over integer and noninteger n Slater type orbitals is obtained through the non- and quasi-relativistic basic functions. The non- and quasirelativistic basic functions are determined by the linear combinations of auxiliary functions Q(ns)(q) and G(-ns)(q) introduced by the author. The coefficients of series expansion relations are expressed in terms of two-center overlap integrals over integer n Slater functions. The relationships obtained are valid for the arbitrary location, quantum numbers and screening constants of orbitals.