The chemistry in the diffuse interstellar medium initiates the gradual increase of molecular complexity during the life cycle of matter. A key molecule that enables build-up of new molecular bonds and new molecules via proton-donation is H3+. Its evolution is tightly related to molecular hydrogen and thought to be well understood. However, recent observations of ortho and para lines of H2 and H3+ in the diffuse ISM showed a puzzling discrepancy in nuclear spin excitation temperatures and populations between these two key species. H3+, unlike H2, seems to be out of thermal equilibrium, contrary to the predictions of modern astrochemical models. We conduct the first time-dependent modeling of the para-fractions of H2 and H3+ in the diffuse ISM and compare our results to a set of line-of-sight observations, including new measurements presented in this study. We isolate a set of key reactions for H3+ and find that the destruction of the lowest rotational states of H3+ by dissociative recombination largely control its ortho/para ratio. A plausible agreement with observations cannot be achieved unless a ratio larger than 1:5 for the destruction of (1,1)- and (1,0)-states of H3+ is assumed. Additionally, an increased CR ionization rate to 10(-15) 1/s further improves the fit whereas variations of other individual physical parameters, such as density and chemical age, have only a minor effect on the predicted ortho/para ratios. Thus our study calls for new laboratory measurements of the dissociative recombination rate and branching ratio of the key ion H3+ under interstellar conditions.
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