Can molecular hydrogen form hydrogen bonds?

Basically, I want to know if molecular hydrogen (H$\_2$) can form hydrogen bonds with other molecules (CH$\_4$, CO$\_2$, N$\_2$). I'm trying to model the mixture of these molecules with [SAFT](https://en.wikipedia.org/wiki/Statistical_associating_fluid_theory) equations of state, and I want to know if I'll have to add the effects of associating fluids (capable of forming H-bonds).




Something like hydrogen bonding with $\ce{H2}$ molecules appears to occur in [hydrogen ion clusters](https://en.wikipedia.org/wiki/Hydrogen_ion_cluster). [Clampitt and Gowland[1]](https://doi.org/10.1038/223815a0) study these clusters in connection with stellar nebulae and report that the $\ce{H\_{15}^+}$ ion is especially stable; this likely has a $\ce{H3^+}$ core (which acts as the protic hydrogen) surrounded by six associated $\ce{H2}$ molecules.


Other nonpolar molecules, with lower ionization energies and greater polarizability, may form weak hydrogen bonds in more ordinary chemical environments. Such an interaction between methane and water, which may occur in methane clathrate-hydrates, is reported by [Isaev[2]](https://doi.org/10.1134/S0036024416100150).


All such hydrogen-bonding interactions with nonpolar molecules require a strongly protic hydrogen source with which the electrons of the nonpolar molecules can overlap. A simple mixture of low-polarity, nonprotic gases would not of itself generate any hydrogen bonding.


1. CLAMPITT, R., GOWLAND, L. (1969) "Clustering of Cold Hydrogen Gas on Protons". *Nature* **223**, 815–816. <https://doi.org/10.1038/223815a0>
2. Isaev, A.N. (2016) "O–H···C hydrogen bond in the methane–water complex". *Russ. J. Phys. Chem.* **90**, 1978–1985. <https://doi.org/10.1134/S0036024416100150>


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By definition, no, they can't. According to IUPAC's definition of a hydrogen bond:$^1$



> 
> The hydrogen bond is an attractive interaction between a hydrogen atom
> from a molecule or a molecular fragment X–H **in which X is more
> electronegative than H**, and an atom or a group of atoms in the same or
> a different molecule, in which there is evidence of bond formation.
> 
> 
> 


That isn't to say that you could not get dispersion interactions forming due to the instantaneous changes in electron distributions, but they will probably be negligible. There is also the possibility of other types of non covalent bonding (e.g. halogen [F, Cl, Br,...], chalcogen [O, S, Se,...], pnicogen [N, P, As,...], tetrel [C, Si,...], etc. bonding),$^2$ but be careful when you use the term 'hydrogen bond'.


1. Arunan, E.; Desiraju, G. R.; Klein, R. A.; Sadlej, J.; Scheiner, S.; Alkorta, I.; Clary, D. C.; Crabtree, R. H.; Dannenberg, J. J.; Hobza, P.; et al. Definition of the hydrogen bond (IUPAC Recommendations 2011). *Pure Appl. Chem.* **2011**, *83* (8), 1637-1641. DOI: 10.1351/PAC-REC-10-01-02
2. Alkorta, I.; Elguero, J.; Frontera, A. Not Only Hydrogen Bonds: Other Noncovalent Interactions. *Crystals* **2020**, *10* (3), 180. DOI: 10.3390/cryst10030180.


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