Compression of the electron repulsion integral tensor in tensor hypercontraction format with cubic scaling cost

TL;DR

This paper introduces a new algorithm that efficiently compresses the electron repulsion integral tensor into tensor hypercontraction format with cubic scaling cost, enabling faster quantum chemistry calculations.

Contribution

The work presents a novel density fitting algorithm that reduces computational complexity for tensor compression in quantum chemistry.

Findings

Achieves $ ext{O}(n N^2 ext{log} N)$ computational cost.

Uses a subset of spatial grid points for density fitting.

Enables efficient tensor compression in quantum chemistry applications.

Abstract

Electron repulsion integral tensor has ubiquitous applications in quantum chemistry calculations. In this work, we propose an algorithm which compresses the electron repulsion tensor into the tensor hypercontraction format with $\mathcal{O}(n N^2 \log N)$ computational cost, where $N$ is the number of orbital functions and $n$ is the number of spatial grid points that the discretization of each orbital function has. The algorithm is based on a novel strategy of density fitting using a selection of a subset of spatial grid points to approximate the pair products of orbital functions on the whole domain.