Upper Bounds on Gaussian Geminal Integrals

We derive tight upper bounds on integrals involving contracted Gaussian one-electron basis functions and the Gaussian geminal (GG) two-electron operatorexp(-λr122). To accomplish this, we first derive a compact matrix recurrence relation between normalized primitive GG integrals and then use the Triangle Inequality to construct an analogous matrix recurrence relation between rigorous upper bounds on the largest GG integral associated with a contracted shell quartet. Numerical results obtained by applying our bounds to the more than 32000000 quartets that arise in the n-decane molecule with the pc-1 basis set lead us to conclude that the bounds successfully screen out almost all of the quartets that yield negligible integrals.