H₂ column density as a function of the total column density of protons N_H. Open circles correspond to detections of H₂ while arrows correspond to upper limits (see Table A.1). The blue dashed line indicates the maximum value of N(H₂) derived from a purely molecular medium with an integrated molecular fraction (Eq. (2)). The red dashed-dotted line indicates the theoretical molecular fraction derived in an unshielded WNM-type environment with a density of 0.5 cm⁻³ and a temperature of 8000 K, illuminated by a UV photon flux of 10⁸ cm⁻² s⁻¹ (see Eqs. (13) and (15)). The regions A, B, C, D, and E defined in Table 1 correspond to an arbitrary separation of the observational sample used for quantitative comparisons with the results of simulations (see Sect. 4).