  The impact of beyond mean field effects on the ground state and fission
properties of superheavy nuclei has been investigated in a five-dimensional
collective Hamiltonian based on covariant density functional theory. The
inclusion of dynamical correlations reduces the impact of the $Z=120$ shell
closure and induces substantial collectivity for the majority of the $Z=120$
nuclei which otherwise are spherical at the mean field level (as seen in the
calculations with the PC-PK1 functional). Thus, they lead to a substantial
convergence of the predictions of the functionals DD-PC1 and PC-PK1 which are
different at the mean field level. On the contrary, the predictions of these
two functionals remain distinctly different for the $N=184$ nuclei even when
dynamical correlations are included. These nuclei are mostly spherical (oblate)
in the calculations with PC-PK1 (DD-PC1).
  Our calculations for the first time reveal significant impact of dynamical
correlations on the heights of inner fission barriers of superheavy nuclei with
soft potential energy surfaces, the minimum of which at the mean field level is
located at spherical shape. These correlations affect the fission barriers of
the nuclei, which are deformed in the ground state at the mean field level, to
a lesser degree.
