Hyperfine coupling nuclear spin

Spin Density Properties from the Electron Propagator Hyperfine and Nuclear Spin-Spin Couplings... 

Figure 1.10. (a) Second-order spin-rotation interaction occurring via L. (b) Second-order pseudo-contact hyperfine interaction occurring via L. (c) Electron coupled nuclear spin-spin interaction, (d) Second-order interaction of R and L. 

If one or more spin-coupling terms also occur (e.g. hyperfine or nuclear spin-spin), then each such spin-Hamiltonian parameter matrix Y occurs in the transition energy and intensity expressions within combinations of type... 

The first derivative is the hyperfine coupling constant g (as measured by ESR), the second derivative with respect to two different nuclear spins is the NMR coupling constant, J (Planck s constant appears owing to the convention of reporting coupling constants in Hertz, and the factor of 1/2 disappears since we implicitly only consider distinct pairs of nuclei). 

Here and H describe radicals A and B of the radical pair and He the interaction of their electrons. The other terms in equation (15) are H g, the spin orbit coupling term, H g and Hgj, representing the interaction of the externally applied magnetic field with the electron spin and nuclear spin, respectively Hgg is the electron spin-spin interaction and Hgi the electron-nuclear hyperfine interaction. 

The leading term in T nuc is usually the magnetic hyperfine coupling IAS which connects the electron spin S and the nuclear spin 1. It is parameterized by the hyperfine coupling tensor A. The /-dependent nuclear Zeeman interaction and the electric quadrupole interaction are included as 2nd and 3rd terms. Their detailed description for Fe is provided in Sects. 4.3 and 4.4. The total spin Hamiltonian for electronic and nuclear spin variables is then ... 

Conversion of magnetic hyperfine coupling constants A into internal fields for Fe When the nuclear spin is decoupled from the electronic spin by application of an external field, the hyperfine coupling, according to (4.76), is defined as... 

Nuclear hyperfine coupling results in a multi-line ESR spectrum, analogous to the spin-spin coupling multiplets of NMR spectra. ESR spectra are simpler to understand than NMR spectra in that second-order effects normally do not alter the intensities of components on the other hand, ESR multiplets can be much more complex when the electron interacts with several high-spin nuclei, and, as we will see in Chapter 3, there can also be considerable variation in line width within a spectrum. 

Equation (2.3) describes line positions correctly for spectra with small hyperfine coupling to two or more nuclei provided that the nuclei are not magnetically equivalent. When two or more nuclei are completely equivalent, i.e., both instantaneously equivalent and equivalent over a time average, then the nuclear spins should be described in terms of the total nuclear spin quantum numbers I and mT rather than the individual /, and mn. In this coupled representation , the degeneracies of some multiplet lines are lifted when second-order shifts are included. This can lead to extra lines and/or asymmetric line shapes. The effect was first observed in the spectrum of the methyl radical, CH3, produced by... 

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