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Nuclear Spin Conversion in Molecules

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Science  23 Dec 2005:
Vol. 310, Issue 5756, pp. 1913-1914
DOI: 10.1126/science.1122110

Molecules with identical nuclei having nonzero spin can exist in different states called nuclear spin modifications by most researchers and nuclear spin isomers by some. Once prepared in a particular state, the arrangement of spins can in principle convert to another arrangement. The concept of nuclear spin modifications in molecules (1) is intriguing to chemists because interconversion between different spin states is often slow enough to be considered negligible for many purposes. This in turn allows one to treat different spin modifications as though they were different molecules both in terms of spectroscopy and collision dynamics. In addition, these spin modifications are associated one-to-one with different rotational levels in the molecule. In fact, however, the interconversion rates are not zero, so the scientific questions become: How can these extremely slow rates be measured, and how can these rates be explained by theory? On page 1938 of this issue, Sun et al. (2) present answers to both of these questions in the case of the ethylene molecule.

In the case of hydrogen, it is well known that rotational levels with even and odd J quantum number belong to the para (where the nuclear spins are aligned in opposite directions and I = 0) and ortho (the spins are parallel and I = 1) nuclear spin modifications, respectively (I is the total nuclear spin angular momentum of the two H nuclei). Furthermore, nearly pure para-H2 can be readily prepared by cooling hydrogen to low temperature on a paramagnetic catalyst as initially shown by Bonhoeffer and Harteck in 1929 (3). Once prepared, a para-H2 sample can be preserved for months at room temperature in a glass container without converting to ortho-H2. This remarkable stability of a single spin modification was ascribed by Wigner to the smallness of the nuclear spin interaction term that mixes ortho and para states (4).

Spin modifications are relevant also for polyatomic molecules with two or more identical and equivalent nuclei. Thus, for example, H2O, H2CO, etc., have ortho (I = 1) and para (I = 0) species; NH3, CH3F, etc., have ortho (I = 3/2) and para (I = ½) species; and CH4 has ortho (I = 1), meta (I = 2), and para (I = 0) species. More complicated molecules such as C2H4 have more than three spin modifications, and their symmetry is used to label different spin modifications, as reported by Sun et al. (2). Polyatomic molecules have faster interconversion rates than H2, not because their magnetic interactions are larger but because their rotational levels are closer. This is particularly true for spherical-top molecules in which levels are clustered and some levels with different spin modifications are very close. Thus, Ozier et al. observed a spectrum between ortho and para CH4, by shifting an ortho level close to a para level with a magnetic field, and determined the small mixing term (5). For a heavy spherical top like SF6 with very high rotational level (J = 53), the levels are so close that Bordé and colleagues naturally observed transitions between different spin species (6).

Getting the drift.

Laser light tuned slightly below resonance excites a molecule moving away from the laser (red sphere on the right) and increases its size. The molecule is slowed down by collisions with buffer gas because of its larger size. A molecule in the same level moving toward the laser (red sphere on the left), however, is not excited and keeps moving with the normal speed. This causes a net drift toward the laser of molecules with selected spin modification. The increase of the molecular size is greatly exaggerated for clarity. [Adapted from (8)]

CREDIT: P. HUEY/SCIENCE

The theory for spin conversion in polyatomic molecules by collision was first formulated by Curl et al., who enumerated mixing terms in the spirit of Wigner's theory—that is, choosing those nuclear spin interaction terms that are invariant with respect to exchange of the entire sets of nuclear coordinates but are not invariant to exchange of spin coordinates alone (7). They identified levels belonging to different spin modifications that are accidentally close and surmised that interconversion occurs through those pairs of levels. The validity of the theory of Curl et al. has been demonstrated by a series of beautiful experiments by Chapovsky and his collaborators since 1980. They introduced the method of light-induced drift developed in the former Soviet Union (see the figure) and succeeded in separating ortho and para species of CH3F, the first such separation since H2 and D2 were separated several decades ago. [Readers are referred to an excellent review by Chapovsky and Hermans (8) for more details of history, experiments, and theory of the field.] This is the technique used by Sun et al. in their studies.

The exciting aspect of the experiment by Takagi and colleagues. (2) is that ethylene, C2H4, has symmetry with higher dimension than that of other molecules so far studied, and there are four nuclear spin modifications with different symmetry. This has allowed them to demonstrate yet another subtlety of the interconversion. Because the parity (the symmetry of the wave functions with respect to an inversion in space) is rigorous in atomic and molecular physics, the parity selection rule, unlike the ortho/para selection rule, should not be violated in these experiments. In other words, the nuclear spin interaction considered by Wigner and enumerated by Curl et al. may mix different spin species but cannot mix parity. This is clearly demonstrated in figure 2 of Sun et al. (2). Figure 2A (2) shows that there is an interconversion between the B2u and B3u species, and figure 2B shows that there is no interconversion between the B2u and Ag species. The symbols g and u represent symmetric and antisymmetric states with respect to the molecule-fixed inversion operation, i.e., interchange of two pairs of H nuclei and inversion of space. However, all rotational functions are g with respect to this operation, and thus it turns out for a planar molecule like ethylene that g and u nuclear spin functions are associated with rotational-nuclear-spin wave functions of + and - parity. Thus, B2u ↔ B3u conversion in ethylene is parity allowed but B2u ↔ Ag is parity forbidden, as indeed shown in figure 2 of Sun et al. (2).

This leaves an interesting problem to be solved. The authors should be able to determine the magnitude of the interaction term from the observed interconversion rate. In order to do this, the authors need to locate a pair or pairs of levels with the B2u and B3u symmetry that are accidentally or systematically (9) close through which the conversion proceeds. They also need to estimate collision cross sections that are temperature dependent. Experimentally, it will be interesting to measure the temperature dependence of the conversion rate. Also measuring the conversion rate caused by other gases will be interesting, especially paramagnetic gases such as oxygen. It is well known that para-H2 converts to ortho-H2 much faster in the presence of O2. The mechanism of such conversion must be different from that considered by Curl et al.

Which other molecules will be interesting to study? Benzene, C6H6, has spin modifications with six different symmetries: A1g, A2g, E2g, B1u, B2u, and E1u. Here also, the molecule is planar, so one might expect that the parity selection rule will be equivalent to g ↔ g and u ↔ u. Because rotational levels in this symmetric-top molecule with K = 6n (where n ≠ 0) systematically consist of very nearly degenerate B1u-B2u nuclear spin pairs, rotational levels with quantum number K = 6n + 3 consist of very nearly degenerate A1gA2g nuclear spin pairs, and the E nuclear spin functions do not cluster, one can further speculate (9) that conversion rates within the nuclear spin A species or within the B species will be much faster than rates between A and E or between B and E species. Ethane, C2H6, has spin modifications with seven different symmetries A1, A4, E1, E2, E3, E4, and G. Because the molecular symmetry group of ethane does not have any element corresponding exactly to inversion in space, the connection between symmetry species and parity is more complicated than for the planar molecules mentioned above. One can thus wonder if permutation-inversion symmetry species together with systematic level clustering will in the end provide a more unified way of discussing allowed nuclear spin conversions than parity together with accidental degeneracies does. In any case, a study of nuclear spin conversion rates in other highly symmetric molecules will almost certainly reveal further subtleties of the mechanism. However, the experiments will become more challenging as one goes to heavier molecules because of the larger rotational partition function.

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