Assessment of the accuracy of coupled cluster perturbation theory for open-shell systems. I. Triples expansions

TL;DR

This study evaluates the accuracy of various coupled cluster perturbation theories for open-shell systems, demonstrating that higher-order CCSD(T-n) models improve precision over CCSD(T) across different reference determinants.

Contribution

It introduces and assesses higher-order CCSD(T-n) triples models, showing their consistent accuracy improvements for open-shell systems compared to the traditional CCSD(T) method.

Findings

Higher-order CCSD(T-n) models outperform CCSD(T) in accuracy.

Convergence towards CCSDT is similar for UHF and ROHF references.

CCSD(T) accuracy deteriorates when applied to open-shell systems.

Abstract

The accuracy at which total energies of open-shell atoms and organic radicals may be calculated is assessed for selected coupled cluster perturbative triples expansions, all of which augment the coupled cluster singles and doubles (CCSD) energy by a non-iterative correction for the effect of triple excitations. Namely, the second- through sixth-order models of the recently proposed CCSD(T-n) triples series [J. Chem. Phys. 140, 064108 (2014)] are compared to the acclaimed CCSD(T) model for both unrestricted as well as restricted open-shell Hartree-Fock (UHF/ROHF) reference determinants. By comparing UHF- and ROHF-based statistical results for a test set of 18 modest-sized open-shell species with comparable RHF-based results, no behavioral differences are observed for the higher-order models of the CCSD(T-n) series in their correlated descriptions of closed- and open-shell species. In particular, we find that the convergence rate throughout the series towards the coupled cluster singles, doubles, and triples (CCSDT) solution is identical for the two cases. For the CCSD(T) model, on the other hand, not only its numerical consistency, but also its established, yet fortuitous cancellation of errors breaks down in the transition from closed- to open-shell systems. The higher-order CCSD(T-n) models (orders n>3) thus offer a consistent and significant improvement in accuracy relative to CCSDT over the CCSD(T) model, equally for RHF, UHF, and ROHF reference determinants, albeit at an increased computational cost.