Optimal Path Search for Recurrence Relation in Cartesian Gaussian Integrals

In quantum chemistry applications the computation of analytical integrals with Gaussian basis functions such as electron repulsion integrals is often the rate-determining step. In this work we developed a general search algorithm to find the optimal path for the recurrence relations in the integral evaluation. This optimal path uses the least amount of intermediate integrals for building the recurrence relations to improve the computational efficiency. We also developed a redundant integral removal technique, and an efficient hybrid scheme to compute incomplete Gamma functions. A software implementation of these algorithms is able to generate efficient integral code for electron repulsion integrals and other types of integrals used in quantum chemistry. Because the algorithms are independent of the details of the recurrence relations, the software can be easily modified to generate new types of analytical integrals.