It is well known among spectroscopists that two modifications of hydrogen exist: para-H
2 and ortho-H
2. Pure para-H
2 can be produced by leading `normal' H
2, a 1:3 para:ortho mixture, over an iron-containing catalyst at low temperature, and can be kept for a long time also at higher temperature in specially prepared gas cylinders. It is perhaps less well known that para-ortho H
2 conversion is also accelerated by interactions with paramagnetic molecules, such as O
2.
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 through a phenomenon called para-hydrogen induced polarization (PHIP). The para-ortho H
2 conversion by O
2 was recently measured in view of this application.[1]
Two mechanisms have been suggested for the para-ortho H
2 conversion by collisions with O
2. The first one, proposed in 1933 by Eugene Wigner,[2] is the magnetic dipole-dipole coupling between the electron spin of O
2 and the nuclear spins of the two protons in H
2. 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, proposed by Minaev and Ågren[3] in 1995, is that the overlap of the O
2 and H
2 wavefunctions in a collision complex transfers some of the spin density of O
2 to the wavefunction of H
2. The spin densities induced at the two H-nuclei may be different, which causes a different hyperfine interaction through the Fermi contact term. Wigner made a crude estimate of the para-ortho H
2 conversion rate with the use of some kinetic gas data. Minaev and Ågren suggested, however, that the second mechanism is much more effective.
We investigated the para-ortho H
2 conversion by collisions with O
2 by a first principles approach. Both mechanisms are included: the corresponding coupling terms are quantitatively evaluated as a function of the geometry of the O
2-H
2 collision complex by means of
ab initio electronic structure calculations. Then they are included in nearly exact quantum mechanical coupled-channels scattering calculations for the collisions between O
2 and H
2, which yield the para-ortho H
2 conversion cross sections and the rate coefficients for a range of temperatures. The conversion rate at room temperature is compared with the value measured in H
2-O
2 gas mixtures.[1]
[1] S. Wagner, Magn. Reson. Mater. Phys., Biol. Med.
27, 195 (2014). [2] E. Wigner, Z. Phys. Chem. B
23, 28 (1933).
[3] B. F. Minaev and H. Ågren, J. Phys. Chem
99, 8936 (1995).