The structural and vibrational properties of the molecular units of sulfur hexafluoride crystal as a function of pressure have been studied by the Extreme Pressure Polarizable Continuum Model (XP-PCM) method. Within the XP-PCM model, single molecule calculations allow a consistent interpretation of the experimental measurements when considering the effect of pressure on both the molecular structure and the vibrational normal modes. This peculiar aspect of XP-PCM provides a detailed description of the electronic origin of normal modes variations with pressure, via the curvature of the potential energy surface and via the anharmonicity of the normal modes. When applied to the vibrational properties of the sulfur hexafluoride crystal, the XP-PCM method reveals a hitherto unknown interpretation of the effects of the pressure on the vibrational normal modes of the molecular units of this crystal.