Rank-reduced coupled-cluster III. Tensor hypercontraction of the doubles amplitudes

TL;DR

This paper introduces a GPU-accelerated, tensor hypercontraction-based implementation of coupled-cluster singles and doubles (CCSD) that significantly reduces computational cost while maintaining accuracy, enabling large-scale molecular calculations.

Contribution

The authors develop a quartic-scaling, tensor hypercontraction approach for CCSD that extends previous methods and is efficiently implemented on GPUs for large molecular systems.

Findings

Enables CCSD calculations for molecules with 250 atoms and 2500 basis functions.

Achieves computational efficiency comparable to existing RR-CCSD methods.

Maintains accuracy of correlation energies despite tensor hypercontraction approximations.

Abstract

We develop a quartic-scaling implementation of coupled-cluster singles and doubles based on low-rank tensor hypercontraction (THC) factorizations of both the electron repulsion integrals (ERIs) and the doubles amplitudes. This extends our rank-reduced coupled-cluster method to incorporate higher-order tensor factorizations. The THC factorization of the doubles amplitudes accounts for most of the gain in computational efficiency as it is sufficient, in conjunction with a Cholesky decomposition of the ERIs, to reduce the computational complexity of most contributions to the CCSD amplitude equations. Further THC factorization of the ERIs reduces the complexity of certain terms arising from nested commutators between the doubles excitation operator and the two-electron operator. We implement this new algorithm using graphical processing units (GPUs) and demonstrate that it enables CCSD calculations for molecules with 250 atoms and 2500 basis functions using a single computer node. Further, we show that the new method computes correlation energies with comparable accuracy to the underlying RR-CCSD method.