Non-Negative Least Squares Reweighting and Pruning of Quadrature Grids for Tensor Hypercontraction

Abstract

Tensor hypercontraction provides an attractive four-center two-electron repulsion integral format that can lower the scaling of many electronic structure methods while only requiring O(N^2) memory. However, in its grid-based least-squares incarnation, tensor hypercontraction requires the tedious design of compact spatial quadrature grids to achieve efficiency and accuracy, representing a bottleneck for widespread application. To simplify grid generation, we devise a reweighting scheme in which the grid weights are optimized to ensure accurate reproduction of the atomic orbital overlap matrix by numerical integration. By casting this fitting task as a non-negative least-squares problem, we obtain a black-box methodology that not only yields robust grids for tensor hypercontraction as well as numerical integration of other integrals but also prunes the grids by zeroing quadrature weights for insignificant points.