  We present an extension of the Hamiltonian of the two dimensional limit of
the vibron model encompassing all possible interactions up to four-body
operators. We apply this Hamiltonian to the modeling of the experimental
bending spectrum of fourteen molecules. The bending degrees of freedom of the
selected molecular species include all possible situations: linear, bent, and
nonrigid equilibrium structures; demonstrating the flexibility of the algebraic
approach, that allows for the consideration of utterly different physical cases
with a general formalism and a single Hamiltonian. For each case, we compute
predicted term values used to depict the quantum monodromy diagram, the
Birge-Sponer plot, the participation ratio. We also show the bending energy
functional obtained using the coherent --or intrinsic-- state formalism.
