An Attractive Way to Correct for Missing Singles Excitations in Unitary Coupled Cluster Doubles Theory

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 dynamic 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 T2 operators to define two flavors of unitary
coupled cluster doubles (UCCD) methods, we investigate the extent
to 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 single 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.