A theoretical study of the interstitial molecular hydrogen in the silicon single-crystal is reported. H2 and Si have been approximated as a rigid object and a static matrix, respectively. A five-dimensional numerical-analytical representation of an ab initio potential energy surface of the system has been constructed. This representation has been used to calculate rotational, translational, and roto-translational energy levels of the interstitial hydrogen, where three levels of theory, 2D, 3D, and 5D were considered. The potential energy surface, the band structure of energy levels, and the roto-translational states obtained are presented together with the symmetry analysis of the roto-translational wavefunctions.