  The generator coordinate method (GCM) casts the wavefunction as an integral
over a weighted set of non-orthogonal single determinantal states. In principle
this representation can be used like the configuration interaction (CI) or
shell model to systematically improve the approximate wavefunction towards an
exact solution. In practice applications have generally been limited to systems
with less than three degrees of freedom. This bottleneck is directly linked to
the exponential computational expense associated with the numerical projection
of broken symmetry Hartree-Fock (HF) or Hartree-Fock-Bogoliubov (HFB)
wavefunctions and to the use of a variational rather than a bi-variational
expression for the energy. We circumvent these issues by choosing a
hole-particle representation for the generator and applying algebraic symmetry
projection, via the use of tensor operators and the invariant mean (operator
average). The resulting GCM formulation can be mapped directly to the coupled
cluster (CC) approach, leading to a significantly more efficient approach than
the conventional GCM route.
