  The convergence of a recently proposed coupled cluster (CC) family of
perturbation series [Eriksen, J. J. et al., J. Chem. Phys. 140, 064108 (2014)],
in which the energetic difference between two CC models - a low-level parent
and a high-level target model - is expanded in orders of the M{\o}ller-Plesset
(MP) fluctuation potential, is investigated for four prototypical closed-shell
systems (Ne, singlet methylene, distorted HF, and the fluoride anion) in
standard and augmented basis sets. In these investigations, energy corrections
of the various series have been calculated to high orders and their convergence
radii determined by probing for possible front- and back-door intruder states,
the existence of which would make the series divergent. In summary, we conclude
how it is primarily the choice of target state, and not the choice of parent
state, which ultimately governs the convergence behavior of a given series. For
example, restricting the target state to, say, triple or quadruple excitations
might remove intruders present in series that target the full configuration
interaction (FCI) limit, such as the standard MP series. Furthermore, we find
that whereas a CC perturbation series might converge within standard
correlation consistent basis sets, it may start to diverge whenever these
become augmented by diffuse functions, similar to the MP case. However, unlike
for the MP case, such potential divergences are not found to invalidate the
practical use of the low-order corrections of the CC perturbation series.
