Rigorous bounds to molecular electron repulsion and electrostatic potential integrals

Abstract

Novel rigorous upper and lower bounds, at primitive level, to general electron-repulsion integrals (ERIs) involving Gaussian basis sets have been derived and interconnections with the earlier works in the literature are brought out. New optimal strategies for a preemptive elimination of insignificant ERIs at atom and contraction levels are discussed and tested, resulting in a significant reduction in CPU time. Similar analysis is carried out for the computation of the molecular electrostatic potential for the first time in the literature, leading to a marked savings in computer time.