  Methods which aim at universal applicability must be able to describe both
weak and strong electronic correlation with equal facility. Such methods are in
short supply. The combination of symmetry projection for strong correlation and
coupled cluster theory for weak correlation offers tantalizing promise to
account for both on an equal footing. In order to do so, however, the coupled
cluster portion of the wave function must be optimized in the presence of the
symmetry projection. This paper discusses how this may be accomplished, and
shows the importance of doing so for both the Hubbard model Hamiltonian and the
molecular Hamiltonian, all with a computational scaling comparable to that of
traditional coupled cluster theory.
