On the rank-reduced relativistic coupled cluster method

TL;DR

This paper demonstrates that applying Tucker decomposition to amplitude tensors in relativistic CCSD calculations significantly reduces computational cost while maintaining high accuracy, enabling efficient modeling of large heavy-atom systems.

Contribution

The study introduces a rank reduction technique using Tucker decomposition in relativistic CCSD, improving efficiency without sacrificing accuracy for large systems.

Findings

Correlation energies within 1 kJ/mol accuracy achieved with high tensor compression.

Only about 3% of doubles amplitudes are significant in large YbCl7 cluster.

Rank reduction enhances computational scaling of relativistic CCSD.

Abstract

An efficiency of the Tucker decomposition of amplitude tensors within the single-reference relativistic coupled cluster method with single and double excitations (RCCSD) was studied in a series of benchmark calculations for (AuCl)$_n$ chains, Au$_n$ clusters, and the cluster model of solid YbCl$_2$. The 1 kJ/mol level of accuracy for correlation energy estimates of moderate-size systems and typical reaction energies can be achieved with relatively high compression rates of amplitude tensors via rejecting singular values smaller than $\sim 10^{-4}$. For the most extensive system studied (YbCl$_7$ cluster used for modeling of ytterbium center in ytterbium dichloride crystal), only $\sim 3$% of compressed doubles amplitudes were shown to be significant. Thus, the rank reduction for the relativistic CCSD theory improving its computational scaling is feasible. The advantage (if not necessity) of using the Goldstone diagrammatic technique rather than the "antisymmetrized" Brandow one is underlined. The proposed approach is promising for high-precision modeling of relatively large systems with heavy atoms.