Calculation of 3-Center One-Electron Integrals \left\langle {AB|r_c^{ - 1} } \right\rangle and Coulomb Repulsion Matrix Elements \left\langle {AB|CC'} \right\rangle in an Exponential Type Spherical AO Basis

A new method for calculating 3-center one-electron integrals and matrix elements of electron interaction of $\left\langle {AB|CC'} \right\rangle $ type in MO LCAO theory, where A, B, and C are the centers of exponential type AO including Slater and hydrogen-like basis functions, has been developed. Integrals of this type are reduced to double integrals over the square with edge 1. This provides the grounds for effective calculation of quantum-chemical 3-center integrals in a basis of exponential type spherical functions.