Unified Treatment of One-Range Addition Theorems for Complete Orthonormal Sets of Generalized Exponential-Type Orbitals and Noninteger n Slater Functions

摘要

By the use of L-(pl*())-generalized Laguerre polynomials (L-(pl*())-GLPs) introduced by the author, the combined formulas for the one- and two-center one-range addition theorems of complete orthonormal sets of phi((pl)*())-generalized exponential-type orbitals (phi((pl)*())-GETOs) and x-noninteger n Slater type orbitals (chi-NISTOs) in terms of chi-integer STOs (chi-ISTOs) are suggested, where pl* = 2l + 2 - alpha* and alpha* are the integer (alpha* = alpha, -infinity < alpha <= 2) or noninteger (alpha* not equal alpha, -infinity < alpha* < 3) self-frictional quantum numbers. The series expansion coefficients of these theorems are expressed through the overlap integrals over chi-NISTOs. As an application, the Combined Hartree-Fock-Roothaan (CHFR) total energy values for the ground states of some atoms obtained in the minimal basis set approximation are presented.