Analytical second derivatives of two electron integrals over s and p Cartesian Gaussians

An efficient algorithm for computing second derivatives of two electron integrals is outlined and has been coded for s- and p-type Cartesian Gaussians. This method is an extension of a previous algorithm for two electron integral first derivatives [H. B. Schlegel, J. Chem. Phys. 77, 3676 (1982)] and is suitable for scalar machines with modest memories. Timing data indicates that the present algorithm is 3–6 times faster than a scalar version of the Rys polynomial method. Furthermore, the computational time for the two electron integral second derivatives is only 2–3 times longer than for the integral first derivatives by the same approach. The code has been incorporated in the recently released version of gaussian 88.