The vibrational spectroscopy and the matrix-site geometries of several novel rare-gas compounds in the matrix environment were computed theoretically, and compared with experiment. Ab initio calculations are used in the fitting of analytical potential surfaces for the HRgY molecules and for the interactions between HRgY and the matrix atoms Rg. With these potentials, matrix-site geometries for the molecule in the solid are computed. Finally, the vibrational spectroscopy of HRgY in the Rg matrix is computed using the vibrational self-consistent field (VSCF) method. The VSCF includes anharmonic effects, that are essential in this case. The version of VSCF used here includes coupling between HRgY and the vibrations of the solid atoms. The vibrations of 72 matrix atoms are treated. The main results are: (1) The matrix shifts are considerably greater than typically found for neutral, strongly bond molecules, but are much smaller than discrepancies between theory and experiment. This can be attributed to the insufficient accuracy of the potentials used for the HRgY molecules. This calls for better future description of the electronic structure of HRgY. (2) The matrix shifts and splitting effects are interpreted by the calculations in terms of the site geometries involved. These effects are very different for HArF, HKrF than for HXeCl, HXeI. (3) The computed matrix-site splittings are in semiquantitative accord with experiment. This supports the interaction potentials used between HRgY and the matrix. The results provide insights on the effects of the matrix on the rare-gas molecules.