The Exact Evaluation of Basic Two-Center Coulomb Integrals Appearing in Intermolecular Electrostatic Interaction Energy in Molecular Coordinate System

We proposed a general and effective approach for accurate calculating method of the electron-electron, nuclear-electron and nuclear-nuclear Coulomb electrostatic interaction energies. It is well known that electron-electron, nuclear-electron and nuclear-nuclear Coulomb electrostatic interaction energies reduced to basic two-center Coulomb integrals. The analytical calculation of electrostatic interaction energies with respect to basic two-center Coulomb integrals over Slater type orbitals (STOs) in molecular coordinate systems allows us the routine evaluation of molecular structures and related properties. In this study we have introduced a new full analytical algorithm for calculation of the basic two-center Coulomb integrals over STOs by using Guseinov’s auxiliary functions especially interactions between electrons. The auxiliary functions has been calculated by using the exact recurrence relations which developed by Guseinov. The new approach is successfully tested on earlier published studies data and can be recommended for evaluation of related problems in atomic and molecular physics.

Self-friction power series and their use for evaluation of atomic nuclear attraction integrals with noninteger indices of Slater orbitals and Coulomb–Yukawa-like potentials

Using complete orthogonal [Formula: see text]-Self-Friction Polynomials ([Formula: see text]-SFPs) introduced by one of the authors, the analytical and power series formulas for SF atomic nuclear attraction integrals over [Formula: see text]-noninteger Slater type orbitals ([Formula: see text]-NISTOs) and [Formula: see text]-noninteger Coulomb–Yukawa-like potentials ([Formula: see text]-NICYPs) are presented, where [Formula: see text] are the integer ([Formula: see text] or noninteger ([Formula: see text] SF quantum numbers and [Formula: see text]. As an application, the computer calculations for dependence of the atomic nuclear attraction integrals over [Formula: see text]-NISTOs and [Formula: see text]-NICYPs functions are presented.