  The Hamiltonian action of a Lie group on a symplectic manifold induces a
momentum map generalizing Noether's conserved quantity occurring in the case of
a symmetry group. Then, when a Hamiltonian function can be written in terms of
this momentum map, the Hamiltonian is called `collective'. Here, we derive
collective Hamiltonians for a series of models in quantum molecular dynamics
for which the Lie group is the composition of smooth invertible maps and
unitary transformations. In this process, different fluid descriptions emerge
from different factorization schemes for either the wavefunction or the density
operator. After deriving this series of quantum fluid models, we regularize
their Hamiltonians for finite $\hbar$ by introducing local spatial smoothing.
In the case of standard quantum hydrodynamics, the $\hbar\ne0$ dynamics of the
Lagrangian path can be derived as a finite-dimensional canonical Hamiltonian
system for the evolution of singular solutions called `Bohmions', which follow
Bohmian trajectories in configuration space. For molecular dynamics models,
application of the smoothing process to a new factorization of the density
operator leads to a finite-dimensional Hamiltonian system for the interaction
of multiple (nuclear) Bohmions and a sequence of electronic quantum states.
