An attractive way to correct for missing singles excitations in unitary coupled cluster doubles theory

TL;DR

This paper introduces novel perturbative corrections to unitary coupled cluster doubles methods to effectively recover missing single excitations, achieving results comparable to UCCSD with reduced computational cost.

Contribution

The authors develop and analyze the UCCD[4S] and UCCD[6S] methods that incorporate low-order MBPT corrections for missing singles in UCCD, improving accuracy.

Findings

Augmenting UCCD with perturbative singles corrections yields UCCSD-like results.

The new methods show significant accuracy improvements over standard UCCD.

Marginal improvements observed with electron pair-restricted ansatz.

Abstract

Coupled cluster methods based exclusively on double excitations are comparatively "cheap" and interesting model chemistries, as they are typically able to capture the bulk of the dynamical electron correlation effects. The trade-off in such approximations is that the effect of neglected excitations, particularly single excitations, can be considerable. Using standard and electron pair-restricted $T_2$ operators to define two flavors of unitary coupled cluster doubles (UCCD) methods, we investigate the extent in which missing single excitations can be recovered from low-order corrections in many-body perturbation theory (MBPT) within the unitary coupled cluster (UCC) formalism. Our analysis includes the derivations of finite-order, UCC energy functionals which are used as a basis to define perturbative estimates of missed single excitations. This leads to the novel UCCD[4S] and UCCD[6S] methods, which consider energy corrections for missing singles excitations through fourth- and sixth-order in MBPT, respectively. We also apply the same methodology to the electron pair-restricted ansatz, but the improvements are only marginal. Our findings show that augmenting UCCD with these post hoc perturbative corrections can lead to UCCSD-quality results.