Many post Hartree-Fock calculations requires the use of molecular orbital electron repulsion integrals (MO ERIs), which are calculated using atomic orbital electron repulsion integrals (AO ERIs) in an algorithm with fifth order scaling in the number of basis functions (N). Resolution of the identity approximation (RI) reduces the scaling factor to fourth order, but involves many temporary matrices, which have to be computed for each molecular orbital using the AO ERIs. Conventional algorithms take advantage of RAM memory to save AO ERIs values once they have been computed in order to use them in the future. In this way, AO ERIs are calculated just once and N2Naux RAM elements are accessed each time a temporary matrix is required to be computed, with a total of N3Naux memory accesses. In our algorithm, integrals are not saved in memory, but computed just once and immediately used in the elements of all temporary matrices they contribute to. RAM is used to save all the temporary matrices instead of the AO ERIs, which are computed on the fly. Because integrals are computed just once, the algorithm keeps the advantage of conventional algorithms without saving integrals in RAM, and because RI temporary matrices are accessed one time in the iteration, only N2Naux memory accesses are needed and the amount of RAM accesses is reduced. If there is not enough memory to save temporary matrices, the algorithm is done in batches, and the AO ERIs are calculated as many times as the number of batches, which usually is less than the number of basis functions. This algorithm has been tested in electron propagator calculations, and has shown to be 10 times faster than conventional algorithms and 40 times faster than direct algorithms.

Reduced RAM access algorithm for molecular orbital electron repulsion integrals with resolution of the identity applied in post Hartree-Fock methods

2019 Fall National Meeting

The official archive and repository for all ACS Meetings & Expositions abstracts and select posters or presentations.