The rotational-vibrational correlations are important aspects of nuclear collective dynamics; they also contribute to nuclear binding through quantum zero-point corrections. To estimate the magnitude of the rotational-vibrational corrections, one usually applies RPA [70], GCM [63], or the Gaussian overlap approximation to GCM [71,72,73,74].
Regardless of the approach used, a key point
is the choice of collective
subspace. In the case of GCM and related methods, the collective
manifold is determined by the set of external fields associated
with the collective motion of the system.
In most practical applications, one considers five quadrupole
degrees of freedom that give rise to nuclear rotations and
quadrupole vibrations, octupole deformations,
and pairing vibrations [75,70].
An important step towards the microscopic description
of correlation energies are the recent large-scale benchmark calculations
of ground-state quadrupole correlations of binding energies
for all even-even nuclei, from 
O up to the superheavy
systems [63].