Dipolar hyperfine coupling

It is well-known that the hyperfine interaction for a given nucleus A consists of three contributions (a) the isotropic Fermi contact term, (b) the spin-dipolar interaction, and (c) the spin-orbit correction. One finds for the three parts of the magnetic hyperfine coupling (HFC), the following expressions [3, 9] ... 

Aniosotropic hyperfine coupling results primarily from dipolar interactions between a magnetic nucleus and an unpaired electron in a p, d, or f orbital. Such interactions give rise to a Hamiltonian... 

The Florence NMRD program (8) (available at www.postgenomicnmr.net) has been developed to calculate the paramagnetic enhancement to the NMRD profiles due to contact and dipolar nuclear relaxation rate in the slow rotation limit (see Section V.B of Chapter 2). It includes the hyperfine coupling of any rhombicity between electron-spin and metal nuclear-spin, for any metal-nucleus spin quantum number, any electron-spin quantum number and any g tensor anisotropy. In case measurements are available at several temperatures, it includes the possibility to consider an Arrhenius relationship for the electron relaxation time, if the latter is field independent. 

HypB protein, 47 289 HypC protein, 47 289 Hyperfine coupling, 13 149-178 anisotropic, 13 150-161 Hyperfine coupling anisotropic dipolar, 13 150-154 nuclear Zeeman interaction, 13 155 quadrupole interaction, 13 154, 155 factors affecting magnitude of metal influence of charge on metal, 13 169-170 isotropic and anisotropic, 13 166-170 libration, 13 170... 

Fig. 3.8. Energy levels, transition frequencies and transition probabilities per unit time (Wo. W and W2) in a magnetically coupled I-S system ((A) dipolar coupling (B) contact coupling). A is the contact hyperfine coupling constant The order of the levels is for g, < 0.

Here /, is the 13C nuclear spin, S is the unpaired electronic spin, and A j- is the Fermi contact hyperfine coupling tensor. This coupling is identical for all 13C nuclei as long as the C60 ion is spherical, but becomes different for different nuclei after the Jahn-Teller distortion leading to an inhomogeneous frequency distribution. The homogeneous width of the 13C NMR lines is, on the other hand, mainly determined by the electron-nuclear dipolar interaction... 

The width of the distribution in the absence of digging, about 80 mT (a), is too large to be exclusively due dipolar ( 20 mT) and hyperfine-coupling ( 10 mT). The following result suggests that it is due to a distribution of the exchange-coupling parameter J z. 

Hole Digging Method to Study Dipolar Distributions and Hyperfine Couplings... 

Figure 10.39. 13C hyperfine and electron spin-rotation splitting of the N = 0 and 1 rotational levels of 13CO+, and the observed transitions [111]. The large splitting is mainly due to the 13C Fermi contact interaction. The smaller splittings are due to the spin-rotation interaction and the dipolar hyperfine coupling. 

The magnetic dipolar hyperfine coupling also has familiar matrix elements ... 

Finally, an interesting paper by Tokdemir and Nelson looks at irradiated inosine single crystals [87], The authors have used calculations on the anisotropic hyperfine couplings as an aid in identifying free radical structures. They find that the computed dipolar coupling eigenvectors correlate well with the experimental results. The input Cartesian coordinates used for the calculations were obtained from the crystallographic data. 

The contribution of the hyperfine interactions to the relaxation rates of the radical depends on whether the dominant contribution comes from the anisotropic (dipolar) or the isotropic (scalar) part of the hyperfine interaction. Usually, the anisotropic contribution predominates because this interaction can be readily modulated by the tumbling motion of the molecule. However, in radicals and radical anions such as the trifluoroaceto-phenone (115,116), the rotation of the CF3 group may modulate the isotropic part of the hyperfine interaction and the scalar relaxation W0 could dominate the dipolar transition W2. In such a case, the authors have pointed out that the sign of the resulting CIDNP will be independent of the sign of the isotropic hyperfine coupling constants. 

---