An efficient algorithm for calculating a b i n i t i o energy gradients using s, p Cartesian Gaussians

A method is presented for the calculation of analytical first derivatives of the two electron integrals over s- and p-type Cartesian Gaussian basis functions. Formulas are developed for derivatives with respect to the positions of the nuclei and basis functions (for use in geometry optimization) and with respect to the exponents of the primitive Gaussians (for use in basis set optimization). Full use is made of the s = p constraint on the Gaussian exponents. Contributions from an entire shell block are computed together and added to the total energy derivative directly, avoiding the computation and storage of the individual integral derivatives. This algorithm is currently being used in the ab initio molecular orbital program gaussian 80.