  We develop and test efficient approximations to estimate ground state
correlations associated with low- and zero-energy modes. The scheme is an
extension of the generator-coordinate-method (GCM) within Gaussian overlap
approximation (GOA). We show that GOA fails in non-Cartesian topologies and
present a topologically correct generalization of GOA (topGOA). An RPA-like
correction is derived as the small amplitude limit of topGOA, called topRPA.
Using exactly solvable models, the topGOA and topRPA schemes are compared with
conventional approaches (GCM-GOA, RPA, Lipkin-Nogami projection) for
rotational-vibrational motion and for particle number projection. The results
shows that the new schemes perform very well in all regimes of coupling.
