  A Smolyak algorithm adapted to system-bath separation is proposed for
rigorous quantum simulations. This technique combines a sparse grid method with
the system-bath concept in a specific configuration without limitations on the
form of the Hamiltonian, thus achieving a highly efficient convergence of the
excitation transitions for the "system" part. Our approach provides a general
way to overcome the perennial convergence problem for the standard Smolyak
algorithm and enables the simulation of floppy molecules with more than a
hundred degrees of freedom.The efficiency of the present method is illustrated
on the simulation of H$_2$ caged in an sII clathrate hydrate including two
kinds of cage modes. The transition energies are converged by increasing the
number of normal modes of water molecules. Our results confirm the triplet
splittings of both translational and rotational ($j=1$) transitions of the
H$_2$ molecule. Furthermore, they show a slight increase of the translational
transitions with respect to the ones in a rigid cage.
