It is well known among spectroscopists that hydrogen has two modifications: para-H
2 and ortho-H
2. Pure para-H
2 can be produced by leading "normal" H
2, a 3:1 ortho:para mixture, over a catalyst at low temperature. It is perhaps less well known that para-ortho H
2 conversion is also catalyzed by collisions with paramagnetic molecules, such as O
2.
Almost ninety years ago Farkas and Sachsse measured the rate coefficient of para-ortho H
2 conversion in gas mixtures with O
2.[1] In the same year, 1933, it was proposed by Wigner [2] that it is the magnetic dipole-dipole coupling between the electron spin of O
2 and the nuclear spins of the two protons in H
2 that is responsible for the conversion. In asymmetric collisions this coupling makes the two H-nuclei inequivalent and mixes the nuclear spin functions of para- and ortho-H
2, as well as their rotational states with even and odd j values. Another mechanism, suggested to be much more effective, was proposed later: the exchange interaction with the open-shell O
2 induces spin density into the electronic wavefunction of H
2. In most collisions the spin density is different at the two H-nuclei, which makes them inequivalent by different hyperfine interactions through the Fermi contact term.
An important application of para-H
2 is in NMR spectroscopy and its imaging variant, MRI. By adding para-H
2 to the sample the sensitivity of NMR can be increased by four orders of magnitude by a phenomenon called para-hydrogen induced polarization (PHIP). Para-ortho H
2 conversion by O
2 in the gas phase was remeasured in 2014 in view of this application. A detailed and quantitative understanding of the conversion process was still lacking, however.
We theoretically investigated the para-ortho H
2 conversion by collisions with O
2 in a first principles approach.[3] Both mechanisms were taken into account and the corresponding coupling terms were quantitatively evaluated as functions of the geometry of the O
2-H
2 collision complex by means of
ab initio electronic structure calculations. Then they were included in nearly exact quantum mechanical coupled-channels scattering calculations for the collisions between O
2 and H
2, which yielded the para-ortho H
2 conversion cross sections and the rate coefficients for temperatures up to 400 K. The conversion rate and its temperature dependence are in good agreement with the values measured in H
2-O
2 gas mixtures. The calculations provide detailed insight into the conversion process.
[1] L. Farkas and H. Sachsse, Z. Phys. Chem. B
23, 1 (1933). [2] E. Wigner, Z. Phys. Chem. B
23, 28 (1933). [3] X. Zhang, T. Karman, G. C. Groenenboom, and A. van der Avoird, Nat. Sci. (2021); https://doi.org/10.1002/ntls.10002.