A method for two-electron Gaussian integral and integral derivative evaluation using recurrence relations

An efficient method is presented for evaluating two-electron Cartesian Gaussian integrals, and their first derivatives with respect to nuclear coordinates. It is based on the recurrence relation (RR) of Obara and Saika J. Chem. Phys. 84, 3963 (1986), and an additional new RR, which are combined together in a general algorithm applicable to any angular momenta. This algorithm exploits the fact that the new RR can be applied outside contraction loops. It is shown, by floating point operation counts and comparative timings, to be generally superior to existing methods, particularly for basis sets containing d functions.