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A new estimator for three-center two-particle Coulomb integrals is presented.Our estimator is exact for some classes of integrals and is much more efficientthan the standard Schwartz counterpart due to the proper account of distancedecay. Although it is not a rigorous upper bound, the maximum degree ofunderestimation can be controlled by two adjustable parameters. We also givenumerical evidence of the excellent tightness of the estimator. The use of theestimator will lead to increased efficiency in reduced-scaling one- andmany-body electronic structure theories.

A tight distance-dependent estimator for screening three-center Coulomb integrals over Gaussian basis functions