Use of auxiliary functions in calculation of multicenter electronic attraction, electric field and electric field gradient integrals of screened and nonscreened Coulomb potentials over noninteger n Slater orbitals

By the use of complete orthonormal sets of Ψα - exponential type orbitals (Ψα - ETOs, α = 1,0,−1,−2,…) and auxiliary functions QNN′q introduced in our previous paper [I.I. Guseinov, J. Phys. B, 3 (1970) 1399] the multicenter electronic attraction, electric field and electric field gradient integrals of nonscreened and Yukawa-like screened Coulomb potentials over integer and noninteger n Slater type orbitals are evaluated. These integrals are expressed through the two-center overlap integrals with the same screening constants and the new central and noncentral potential functions depending upon the auxiliary functions QNN′q. The convergence of the series is tested by calculating concrete cases.