  The recent quantum information boom has effected a resurgence of interest in
unitary coupled cluster (UCC) theory. Our group's interest in local energy
landscapes of unitary ans\"atze prompted us to investigate the classical
approach of truncating the Taylor series expansion (instead of a perturbative
expansion) of UCCSD energy at second-order. This amounts to an approach where
electron correlation energy is estimated by taking a single Newton-Raphson step
from Hartree-Fock toward UCCSD. Such an approach has been explored previously,
but the accuracy was not extensively studied. In this paper, we investigate the
performance and observe similar pathologies to linearized coupled cluster with
singles and doubles. We introduce the use of derivatives of order three or
greater to help partially recover the variational lower bound of true UCCSD,
restricting these derivatives to those of the "unmixed" category in order to
simplify the model. By testing the approach on several potential energy
surfaces and reaction energies, we find this "diagonal" approximation to higher
order terms to be effective at reducing sensitivity near singularities for
strongly correlated regimes, while not significantly diminishing the accuracy
of weakly correlated systems.
