The observed H2 level population distribution of the rotational levels J = 5, 6 and 7 in the ground electronic and vibrational state X(v = 0) is analysed using available Copernicus data (Spitzer and Morton, 1976) for the diffuse clouds toward the stars ζ Oph, δ Per and ξ Per. The abundances of H2 in these high purely rotationally excited energy levels are due to the influence of one or more of three possible excitation mechanisms: collisions with abundant particles (e.g. H atoms and H2 molecules), UV-photoexcitation and H2 formation.