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A Smolyak algorithm adapted to system-bath separation is proposed forrigorous quantum simulations. This technique combines a sparse grid method withthe system-bath concept in a specific configuration without limitations on theform of the Hamiltonian, thus achieving a highly efficient convergence of theexcitation transitions for the "system" part. Our approach provides a generalway to overcome the perennial convergence problem for the standard Smolyakalgorithm and enables the simulation of floppy molecules with more than ahundred degrees of freedom.The efficiency of the present method is illustratedon the simulation of H$_2$ caged in an sII clathrate hydrate including twokinds of cage modes. The transition energies are converged by increasing thenumber of normal modes of water molecules. Our results confirm the tripletsplittings of both translational and rotational ($j=1$) transitions of theH$_2$ molecule. Furthermore, they show a slight increase of the translationaltransitions with respect to the ones in a rigid cage.

A Smolyak algorithm adapted to a system-bath separation: application to an encapsulated molecule with large amplitude motions