Julian,

Para-hydrogen (spin singlet) is much more stable than orto-hydrogen (spin triplet). The reason is that the spatial part of the wave function is antisymmetric for orto-, and symmetric for para-hydrogen. The two electrons forming a chemical bond must "escape each other" in orto configuration, thus making chemical bonding weaker.

Yes, it does influence on the hydrogen storage, yet, it in terms of kinetics. As example, here is a paper on the difference in difusion between models of para-hydrogen and classical hydrogen Article Quantum fluctuations increase the self-diffusive motion of p...