Electron-Nucleus Interaction Hyperfine Structure

For radicals with magnetic nuclei, the hyperfine structure of ESR spectra is produced by the interaction of the electron magnetic moment with the nuclear spin of those nuclei covered by the molecular orbital of the unpaired electron. This interaction splits further the two spin levels in a magnetic field. The hyperfine coupling is often given by the Hamiltonian HgN  

Here the first scalar term is the isotropic splitting, and the second traceless tensor term is the anisotropic dipolar splitting. Therefore the complete spin Hamiltonian for a doublet state radical expressed in terms of spin variables only (thus it is for the fictitious spin of a system in which spin-orbit coupling is nonexistent) is 

The second term here is the nuclear Zeeman interaction where gN is the nuclear g-factor, N the nuclear Bohr magneton, and ][ the nuclear spin. 

The constant of the isotropic hyperfine splitting a is given by the Fermi (25) approximation 

FIGURE 1. Schematic representation of spin polarization in the sp -bonds of a methyl radical. 

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Hyperfine structure arises through the interaction of the electron spin with a nuclear spin. Consider first the interaction of the electron spin with a single magnetic nucleus of spin , In an applied magnetic field the nuclear spin angular momentum vector, of magnitude (/ / -f l)]l/2, precesses around the direction of the field in an exactly analogous way to that of the electron spin. The orientations that the nuclear spin can take up are those for which the spin in the z-direction, M, has components of ... 

The electron magnetic moment may also interact with the local magnetic fields of the nuclear dipole moments of nuclei around it. A single electron centered on a nucleus of spin I will experience 2/ -f 1 different local magnetic fields due to the 27 - - 1 different orientations of the nuclear spin I in the external magnetic field. This interaction, which is of the order of 10 cm. i, causes a hyperfine structure in the EPR spectrum. This structure is further discussed and illustrated in Section III,B. 

The hyperfine structure (splitting) of energy levels is mainly caused by electric and magnetic multipole interactions between the atomic nucleus and electronic shells. From the known data on hyperfine structure we can determine the electric and magnetic multipole momenta of the nuclei, their spins and other parameters. 

R91 I. Bertini, J, Faraone-Mennella, C. Luchinat and A. Rosato, The Use of the Electron-Nucleus Hyperfine Interaction for Solution Structure Determination , p. 1 vol. 560,2000... 

Like solvated electrons, the pairs and the atoms are paramagnetic. Their ESR spectra reveal hyperfine structure arising from the interaction of the electron s spin with the spin of alkali nucleus. The coupling constant increases enormously with rising temperature, an increase unmatched by those observed in any other systems. This observation is consistent with the proposed dynamic equilibrium between the pairs and the atoms, higher temperatures favor the unionized atom. Apparently, the rate of conversion is high... 

In a dilute solution of a paramagnetic solute, the nuclear relaxation is often entirely dominated by the pairwise interaction between an unpaired electron, S, and nucleus, I. This is because the rapid diffusion of the solute in the solvent ensures that all nuclei are equally affected. The strong local fields produced by the electron can be coupled to the nuclei by a dipole—dipole interaction and sometimes by a scalar interaction as well. The scalar interaction is transmitted to the nucleus by similar mechanism to that producing spin-spin multiplets in n.m.r. spectra and the hyperfine structure in e.s.r. spectra. 

When there is unpaired electron density produced at the nucleus being studied, a so-called scalar interaction between the electron and the nucleus can occur. This unpaired electron density is transmitted from the free radical to the nucleus by a similar mechanism to that giving rise to the nuclear hyperfine structure in normal e.s.r. spectra. Since the unpaired electron and the nucleus are usually in different molecules, the rapid molecular motion means that the scalar interaction, which of necessity can only occur when the unpaired electron and the nucleus are close to one another, will be varying rapidly. This rapid switching on and off of the scalar interaction means that although any intermolecular nuclear hyperfine structure in the e.s.r. signal is averaged to zero, the scalar interactions may now provide an efficient... 

When there is an interaction between an unpaired electron and a magnetic nucleus, hyperfine structure may be detected. Different spectra are obtained when an isolated pair of ions, each with S = and 7=1 is allowed to interact under different conditions. A single ion would give... 

Hyperfine splitting, i.e., the coupling of the electron spin to the nuclear spin, if the latter is present, is observed in dilute systems in which the exchange interactions and dipole-dipole interactions are small. From a study of the hyperfine structure, one can sometimes determine the relative probability of finding the odd electron at a given nucleus in a molecule. 

Resolved hyperfine structure (hfs) due to the interaction of optical electrons with the magnetic moment of the Pr nucleus (1=5/2) was observed in the spectra (Fig. 3).The measured hyperfine splittings and widths of hyperfine sublevels found from the experimental line shapes are presented in Table I. 

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