  Microscopic energy density functionals (EDF) have become a standard tool for
nuclear structure calculations, providing an accurate global description of
nuclear ground states and collective excitations. For spectroscopic
applications this framework has to be extended to account for collective
correlations related to restoration of symmetries broken by the static mean
field, and for fluctuations of collective variables. In this work we compare
two approaches to five-dimensional quadrupole dynamics: the collective
Hamiltonian for quadrupole vibrations and rotations, and the Interacting Boson
Model. The two models are compared in a study of the evolution of non-axial
shapes in Pt isotopes. Starting from the binding energy surfaces of
$^{192,194,196}$Pt, calculated with a microscopic energy density functional, we
analyze the resulting low-energy collective spectra obtained from the
collective Hamiltonian, and the corresponding IBM-2 Hamiltonian. The calculated
excitation spectra and transition probabilities for the ground-state bands and
the $\gamma$-vibration bands are compared to the corresponding sequences of
experimental states.
