Molecular one-electron integrals over slater-type atomic orbitals and irregular solid spherical harmonics

The one-electron integral over Slater-type atomic orbitals centered at A and B and irregular solid spherical harmonics as operator centered at C is evaluated analytically by using elliptical coordinates and translation of the solid spherical harmonics from center C to either focus A or B. A special case is the three-center nuclear attraction integral which is also evaluated by means of the Neumann expansion and expressed without associate Legendre functions of the second kind. The strict observation of the charge distribution concept leads to compact expressions for the integral. It has the further advantage that the charge density distributions which have been developed for the two-center cases and used in calculations for diatomic molecules can be utilized.