  Three fully variational formulations of the complete-active space
coupled-cluster (CASCC) method are derived. The formulations include the
ability to approximate the model vectors by smooth manifolds, thereby opening
up the possibility for overcoming the exponential wall of scaling for model
spaces of CAS type. In particular, model vectors of matrix-product states are
considered, and it is argued that the present variational formulation allows
not only favorably-scaling multireference coupled-cluster calculations, but
also systematic correction of tailored coupled-cluster calculation and of
quantum chemical density-matrix renormalization group methods, which are fast
and polynomial scaling, but lacks the ability to properly resolve dynamical
correlation at chemical accuracy. The extension of the variational formulations
to the time-domain is also discussed, with derivations of abstract evolution
equations.
