Construction of Оne-Range Addition Theorems for Noninteger Slater Functions Using Self-Friction Exponential Type Orbitals and Polynomials

Abstract

The addition theorems of Slater type orbitals (STOs) presented in literature are generally complicated to theoretically examine the electronic structure of atoms and molecules. The computational deficiencies in use of these theorems arise from the separation of integral variables. In this work, to eliminate these calculation efforts, a large number of independent one-range addition theorems for $$\chi $$ -noninteger Slater type orbitals ( $$\chi $$ -NISTOs) in terms of $$\chi $$ -integer STOs ( $$\chi $$ -ISTOs) is presented by using complete orthogonal basis sets of $${{L}^{{(p_{l}^{*})}}}$$ -self-friction (SF) polynomials ( $${{L}^{{(p_{l}^{*})}}}$$ -SFPs), $${{\psi }^{{(p_{l}^{*})}}}$$ -SF exponential type orbitals ( $${{\psi }^{{(p_{l}^{*})}}}$$ -SFETOs), $${{L}^{{(\alpha \text{*})}}}$$ -modified SFPs ( $${{L}^{{(\alpha \text{*})}}}$$ -MSFPs), and $${{\psi }^{{(\alpha \text{*})}}}$$ -modified SFETOs ( $${{\psi }^{{(\alpha \text{*})}}}$$ -MSFETOs) introduced by one of the authors. Here, $$p_{l}^{*} = 2l + 2 - \alpha \text{*}$$ and $$\alpha \text{*}$$ are the integer $$(\alpha \text{*} = \alpha ,\; - {\kern 1pt} \infty < \alpha \leqslant 2)$$ or noninteger ( $$\alpha \text{*} \ne \alpha ,$$ $$ - \infty < \alpha < 3$$ ) SF quantum numbers based on the Lorentz damping theory. The expansion coefficients of series for the one-range addition theorems are expressed through the analytical relations for the overlap integrals of $$\chi $$ -NISTOs with the same screening parameters. As an application, the calculations of overlap integrals with the different screening constants of $$\chi $$ -NISTOs are performed.