Fourier transform infrared spectroscopy (FTIR) experiments together with interaction potential calculations are performed to interpret the adsorption-desorption properties of para and ortho H2 molecules physisorbed on the (001) faces of NaCl crystallites. Isotherms of the adsorption process show preferential adsorption of para-H2 from gaseous normal-H2 at surface temperature around 10 K. Isobars of the desorption process show preferential desorption of para-H2 from a mixed ortho-H2 and para-H2 adsorbate. A quantum description of the molecular motions corroborates preferential adsorption of p- and (M=±1) o-H2 on the cation sites, as proposed in previous classical studies. It is shown that the adsorption energy is smaller for the para than for the (M=±1) ortho species in agreement with experimental measurement of desorption energy, while (M=0) o-H2 is only slightly bound to the substrate. This indicates that the ionic surface can discriminate all the H2 species. The determination of the bar spectrum for a set of independently adsorbed H2 species can interpret most of the infrared signals assigned to adsorption on the terrace sites. More specially the experimental behavior, with temperature and coverage, of the frequencies and relative intensities of the pure vibrational peaks and of the translation-vibration combination bands is very well explained in terms of hindered external motions of the admolecule.