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

TL;DR

This paper introduces a new, efficient estimator for three-center Coulomb integrals over Gaussian basis functions that improves computational efficiency while maintaining controllable accuracy, benefiting electronic structure calculations.

Contribution

The paper presents a novel distance-dependent estimator that is exact for certain integrals and more efficient than traditional methods, with adjustable parameters to control underestimation.

Findings

Estimator is exact for some classes of integrals.

It is significantly more efficient than the Schwartz estimator.

Numerical evidence shows excellent tightness of the estimator.

Abstract

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 efficient than the standard Schwartz counterpart due to the proper account of distance decay. Although it is not a rigorous upper bound, the maximum degree of underestimation can be controlled by two adjustable parameters. We also give numerical evidence of the excellent tightness of the estimator. The use of the estimator will lead to increased efficiency in reduced-scaling one- and many-body electronic structure theories.