  Projected Hartree-Fock theory provides an accurate description of many kinds
of strong correlation but does not properly describe weakly correlated systems.
Coupled cluster theory, in contrast, does the opposite. It therefore seems
natural to combine the two so as to describe both strong and weak correlations
with high accuracy in a relatively black-box manner. Combining the two
approaches, however, is made more difficult by the fact that the two techniques
are formulated very differently. In earlier work, we showed how to write
spin-projected Hartree-Fock in a coupled-cluster-like language. Here, we fill
in the gaps in that earlier work. Further, we combine projected Hartree-Fock
and coupled cluster theory in a variational formulation and show how the
combination performs for the description of the Hubbard Hamiltonian and for
several small molecular systems.
