A new algorithm of two-electron repulsion integral calculations: a combination of Pople-Hehre and McMurchie-Davidson methods

A new algorithm of two-electron repulsion integral (ERI) calculations has been developed. In this algorithm, Cartesian axes are rotated to make several coordinate components zero or constant using the Pople-Hehre algorithm, and ERIs are evaluated at the rotated coordinate by the McMurchie-Davidson algorithm. The new algorithm applicable to(ss vertical bar ss) to (dd vertical bar dd) ERIs is implemented in the quantum chemistry program GAMESS. Test calculations show that the new algorithm reduces the computational times by 10-40%, as compared with the Pople-Hehre and the Rys quadrature algorithms.