The origin of The Hyperfine Interaction
المؤلف:
Peter Atkins، Julio de Paula
المصدر:
ATKINS PHYSICAL CHEMISTRY
الجزء والصفحة:
ص553-554
2025-12-15
51
The origin of the hyperfine interaction
The hyperfine interaction is an interaction between the magnetic moments of the unpaired electron and the nuclei. There are two contributions to the interaction. An electron in a p orbital does not approach the nucleus very closely, so it experiences a field that appears to arise from a point magnetic dipole. The resulting inter action is called the dipole–dipole interaction. The contribution of a magnetic nucleus to the local field experienced by the unpaired electron is given by an expression like that in eqn 15.28. A characteristic of this type of interaction is that it is anisotropic. Furthermore, just as in the case of NMR, the dipole–dipole interaction averages to zero when the radical is free to tumble. Therefore, hyperfine structure due to the dipole–dipole interaction is observed only for radicals trapped in solids. An s electron is spherically distributed around a nucleus and so has zero average dipole–dipole interaction with the nucleus even in a solid sample. However, because an s electron has a nonzero probability of being at the nucleus, it is incorrect to treat the interaction as one between two-point dipoles. An s electron has a Fermi contact interaction with the nucleus, which as we saw in Section 15.6d is a magnetic inter action that occurs when the point dipole approximation fails. The contact interaction is isotropic (that is, independent of the radical’s orientation), and consequently is shown even by rapidly tumbling molecules in fluids (provided the spin density has some character). The dipole–dipole interactions of p electrons and the Fermi contact interaction of s electrons can be quite large. For example, a 2p electron in a nitrogen atom experiences an average field of about 3.4 mT from the 14N nucleus. A 1s electron in a hydrogen atom experiences a field of about 50 mT as a result of its Fermi contact interaction with the central proton. More values are listed in Table 15.3. The magnitudes of the contact interactions in radicals can be interpreted in terms of the s orbital character of the molecular orbital occupied by the unpaired electron, and the dipole–dipole inter action can be interpreted in terms of the p character. The analysis of hyperfine structure therefore gives information about the composition of the orbital, and especially the hybridization of the atomic orbitals (see Problem 15.11). We still have the source of the hyperfine structure of the C6H6 − anion and other aromatic radical anions to explain. The sample is fluid, and as the radicals are tumbling the hyperfine structure cannot be due to the dipole–dipole interaction. Moreover, the protons lie in the nodal plane of the π orbital occupied by the unpaired electron, so the structure cannot be due to a Fermi contact interaction. The explanation lies in a polarization mechanism similar to the one responsible for spin–spin coupling in NMR. There is a magnetic interaction between a proton and the α electrons (ms =+
) which results in one of the electrons tending to be found with a greater probability nearby (Fig. 15.61). The electron with opposite spin is therefore more likely to be close to the C atom at the other end of the bond. The unpaired electron on the C atom has a lower energy if it is parallel to that electron (Hund’s rule favours parallel electrons on atoms), so the unpaired electron can detect the spin of the proton indirectly. Calculation using this model leads to a hyperfine interaction in agreement with the observed value of 2.25 mT.
We saw in Sections 15.14 and 15.15 that anisotropy of the g-value and of the nuclear hyperfine interactions can be observed when a radical is immobilized in a solid. Figure 15.62 shows the variation of the line shape of the EPR spectrum of the di-tert butyl nitroxide radical (10) with temperature. At 292 K, the radical tumbles freely and isotropic hyperfine coupling to the 14N nucleus gives rise to three sharp peaks. At 77 K, motion of the radical is restricted. Both isotropic and anisotropic hyperfine couplings determine the appearance of the spectrum, which now consists of three broad peaks. Aspin probe (or spin label) is a radical that interacts with a biopolymer and with an EPR spectrum that reports on the dynamical properties of the biopolymer. The ideal spin probe is one with a spectrum that broadens significantly as its motion is restricted to a relatively small extent. Nitroxide spin probes have been used to show that the hydrophobic interiors of biological membranes, once thought to be rigid, are in fact very fluid and individual lipid molecules move laterally through the sheet-like structure of the membrane. Just as chemical exchange can broaden proton NMR spectra (Section 15.7), electron exchange between two radicals can broaden EPR spectra. Therefore, the distance between two spin probe molecules may be measured from the linewidths of their EPR spectra. The effect can be used in a number of biochemical studies. For example, the kinetics of association of two polypeptides labelled with the synthetic amino acid 2,2,6,6,-tetramethylpiperidine-1-oxyl-4-amino-4-carboxylic acid (11) may be studied by measuring the change in linewidth of the label with time. Alternatively, the thermodynamics of association may be studied by examining the temperature dependence of the linewidth.
Fig. 15.61 The polarization mechanism for the hyperfine interaction in π-electron radicals. The arrangement in (a) is lower in energy than that in (b), so there is an effective coupling between the unpaired electron and the proton.
Fig. 15.62 ESR spectra of the di-tert-butyl nitroxide radical at 292 K (top) and 77 K (bottom). Adapted from J.R. Bolton, in Biological applications of electron spin resonance, H.M. Swartz, J.R. Bolton, and D.C. Borg (ed.), Wiley, New York (1972).
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