Tensor-Structured Coupled Cluster Theory

TL;DR

This paper introduces a tensor-structured approach to coupled cluster theory that significantly reduces computational scaling from $O(N^6)$ to approximately $O(N^4)$, enabling more efficient quantum chemistry calculations.

Contribution

The authors develop a novel tensor decomposition method combining hypercontraction and CP decomposition to lower the computational cost of coupled cluster equations.

Findings

Achieves sub-millihartree accuracy compared to original theory.

Reduces computational scaling from $O(N^6)$ to about $O(N^4)$.

Method is general and extendable to other many-body techniques.

Abstract

We derive and implement a new way of solving coupled cluster equations with lower computational scaling. Our method is based on decomposition of both amplitudes and two electron integrals, using a combination of tensor hypercontraction and canonical polyadic decomposition. While the original theory scales as $O(N^6)$ with respect to the number of basis functions, we demonstrate numerically that we achieve sub-millihartree difference from the original theory with $O(N^4)$ scaling. This is accomplished by solving directly for the factors that decompose the cluster operator. The proposed scheme is quite general and can be easily extended to other many-body methods.