Tensor Decomposed Distinguishable Cluster. I. Triples Decomposition

TL;DR

This paper introduces a tensor decomposition approach for coupled cluster calculations that significantly reduces computational scaling while maintaining high accuracy, enabling efficient treatment of larger molecular systems.

Contribution

The authors develop a cost-effective tensor decomposition method for DC-CCSDT using SVD basis truncation, improving efficiency and accuracy over previous approaches.

Findings

The method reduces scaling to N^6 without significant loss of accuracy.

SVD truncation errors are small with moderate thresholds.

The approach is size-extensive and effective for large molecules.

Abstract

We present a cost-reduced approach for the distinguishable cluster approximation to coupled cluster with singles, doubles and iterative triples (DC-CCSDT) based on a tensor decomposition of the triples amplitudes. The triples amplitudes and residuals are processed in the singular-value-decomposition (SVD) basis. Truncation of the SVD basis according to the values of the singular values together with the density fitting (or Cholesky) factorization of the electron repulsion integrals reduces the scaling of the method to $N^6$, and the DC approximation removes the most expensive terms of the SVD triples residuals and at the same time improves the accuracy of the method. The SVD basis vectors for the triples are obtained from the approximate CC3 triples density matrices constructed in an intermediate SVD basis of doubles amplitudes. This allows us to avoid steps that scale higher than $N^6$ altogether. Tests against DC-CCSDT and CCSDT(Q) on a benchmark set of chemical reactions with closed-shell molecules demonstrate that the SVD-error is very small already with moderate truncation thresholds, especially so when using a CCSD(T) energy correction. Tests on alkane chains demonstrated that the SVD-error grows linearly with system size confirming the size extensivity of SVD-DC-CCSDT within a chosen truncation threshold.