A review of rigorous bounds to electron-repulsion integrals for atoms and molecules is presented. Inequalities involving direct (classical) as well as indirect (quantal) Coulomb energies are discussed. This is followed by an account of two-electron integrals in a Hartree Fock context over Gaussian basis-sets. Novel rigorous bounds to these integrals are derived and tested for some organic molecules. Connections are established with the density-based inequalities presented earlier. The present results are expected to enhance the efficiency of a generalab initio Gaussian program and yet have a sound theoretical footing.
