  We present a variational many-body wave function for repelling bosons in
rotating traps, focusing on rotational frequencies that do not lead to
restriction to the lowest Landau level. This wave function incorporates
correlations beyond the Gross-Pitaevskii (GP) mean field approximation, and it
describes rotating boson molecules (RBMs) made of localized bosons that form
polygonal-ring-like crystalline patterns in their intrinsic frame of reference.
The RBMs exhibit characteristic periodic dependencies of the ground-state
angular momenta on the number of bosons in the polygonal rings. For small
numbers of neutral bosons, the RBM ground-state energies are found to be always
lower than those of the corresponding GP solutions, in particular in the regime
of GP vortex formation.
