  A simple and yet powerful approach for modeling the structure of endohedrally
confined diatomic molecules is introduced. The theory, based on a u(4)+u(3)
dynamical algebra, combines u(4), the vibron model dynamical algebra, with a
u(3) dynamical algebra that models a spherically symmetric three dimensional
potential. The first algebra encompasses the internal roto-vibrations degrees
of freedom of the molecule, while the second takes into account the confined
molecule center-of-mass degrees of freedom. A resulting subalgebra chain is
connected to the underlying physics and the model is applied to the
prototypical case of H2 caged in a fullerene molecule. The spectrum of the
supramolecular complex H2@C60 is described with a few parameters and
predictions for not yet detected levels are made. Our fits suggest that the
quantum numbers of a few lines should be reassigned to obtain better agreement
with data.
