The tensor hypercontracted parametric reduced density matrix algorithm: coupled-cluster accuracy with O(r^4) scaling

TL;DR

This paper introduces a tensor hypercontraction-based algorithm for parametric reduced density matrices that achieves coupled-cluster accuracy with a reduced O(r^4) computational scaling, enabling efficient quantum chemistry calculations.

Contribution

The paper develops a novel tensor hypercontraction approach applied to pRDM, reducing the scaling to O(r^4) while maintaining high accuracy.

Findings

Achieves CC-level accuracy with O(r^4) scaling

Demonstrates effectiveness on small molecules and chains

Maintains accuracy between CCSD and CCSD(T)

Abstract

Tensor hypercontraction is a method that allows the representation of a high-rank tensor as a product of lower-rank tensors. In this paper, we show how tensor hypercontraction can be applied to both the electron repulsion integral (ERI) tensor and the two-particle excitation amplitudes used in the parametric reduced density matrix (pRDM) algorithm. Because only O(r) auxiliary functions are needed in both of these approximations, our overall algorithm can be shown to scale as O(r4), where r is the number of single-particle basis functions. We apply our algorithm to several small molecules, hydrogen chains, and alkanes to demonstrate its low formal scaling and practical utility. Provided we use enough auxiliary functions, we obtain accuracy similar to that of the traditional pRDM algorithm, somewhere between that of CCSD and CCSD(T).