Use of auxiliary functions $${Q_{ns}^q}$$ and $${G_{-ns}^q}$$ in evaluation of multicenter integrals over integer and noninteger n-Slater type orbitals arising in Hartree–Fock–Roothaan equations for molecules

Abstract

With the help of expansion relations for the two-center Slater type orbitals (STOs) charge densities established by the author from the use of complete orthonormal sets of Ψα-exponential type orbitals (Ψα-ETOs), where α = 1, 0, − 1, − 2, . . . , a large number of series expansion formulas for the multicenter integrals of integer and noninteger n-STOs (ISTOs and NISTOs) occurring in Hartree–Fock–Roothaan (HFR) equations for molecules is derived through the auxiliary functions \({Q_{ns}^q}\) and \({G_{-ns}^q}\) , and one- and two-center basic integrals of ISTOs. The analytical relations for basic integrals are presented. As an example of application, the calculations have been performed for the ground state of electronic configuration of \({{\it CH}_4((1a_1)^{2}(2a_1)^{2}(1t_{2x})^{2} (1t_{2y})^{2} (1t_{2z})^{2},{}^1A_1)}\) using combined HFR theory suggested by the author.