An analytic method for three-center nuclear attraction integrals: A generalization of the Gegenbauer addition theorem

A completely analytic method for evaluating three-center nuclear attraction integrals for STOS is presented. The method exploits a separation of the STO into an ‘evenly loaded’ solid harmonic and a OS STO . The harmonics are translated to the molecular center of mass in closed finite terms. The OS STO is translated using the Gegenbauer addition theorem; 1s STOS are translated using a single parametric differentiation of the OS formula. Explicit formulas for the integrals are presented for arbitrarily located atoms. A numerical example is given to illustrate the method.