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| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Electron paramagnetic resonance | 3/7 | https://en.wikipedia.org/wiki/Electron_paramagnetic_resonance | reference | science, encyclopedia | 2026-05-05T10:04:27.171248+00:00 | kb-cron |
In general, the g factor is not a number but a 3×3 matrix. The principal axes of this tensor are determined by the local fields, for example, by the local atomic arrangement around the unpaired spin in a solid or in a molecule. Choosing an appropriate coordinate system (say, x,y,z) allows one to "diagonalize" this tensor, thereby reducing the maximal number of its components from 9 to 3: gxx, gyy and gzz. For a single spin experiencing only Zeeman interaction with an external magnetic field, the position of the EPR resonance is given by the expression gxxBx + gyyBy + gzzBz. Here Bx, By and Bz are the components of the magnetic field vector in the coordinate system (x,y,z); their magnitudes change as the field is rotated, so does the frequency of the resonance. For a large ensemble of randomly oriented spins (as in a fluid solution), the EPR spectrum consists of three peaks of characteristic shape at frequencies gxxB0, gyyB0 and gzzB0. In first-derivative spectrum, the low-frequency peak is positive, the high-frequency peak is negative, and the central peak is bipolar. Such situations are commonly observed in powders, and the spectra are therefore called "powder-pattern spectra". In crystals, the number of EPR lines is determined by the number of crystallographically equivalent orientations of the EPR spin (called "EPR center"). At higher temperatures, the three peaks coalesce to a singlet, corresponding to giso, for isotropic. The relationship between giso and the components is:
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{\displaystyle (g_{\mathrm {iso} })^{2}=(g_{xx})^{2}+(g_{yy})^{2}+(g_{zz})^{2}}
One elementary step in analyzing an EPR spectrum is to compare giso with the g-factor for the free electron, ge. Metal-based radicals giso is typically well above ge whereas organic radicals, giso ~ ge. The determination of the absolute value of the g factor is challenging due to the lack of a precise estimate of the local magnetic field at the sample location. Therefore, typically so-called g factor standards are measured together with the sample of interest. In the common spectrum, the spectral line of the g factor standard is then used as a reference point to determine the g factor of the sample. For the initial calibration of g factor standards, Herb et al. introduced a precise procedure by using double resonance techniques based on the Overhauser shift.
=== Hyperfine coupling === Since the source of an EPR spectrum is a change in an electron's spin state, the EPR spectrum for a radical (S = 1/2 system) would consist of one line. Greater complexity arises because the spin couples with nearby nuclear spins. The magnitude of the coupling is proportional to the magnetic moment of the coupled nuclei and depends on the mechanism of the coupling. Coupling is mediated by two processes, dipolar (through space) and isotropic (through bond). This coupling introduces additional energy states and, in turn, multi-lined spectra. In such cases, the spacing between the EPR spectral lines indicates the degree of interaction between the unpaired electron and the perturbing nuclei. The hyperfine coupling constant of a nucleus is directly related to the spectral line spacing and, in the simplest cases, is essentially the spacing itself. Two common mechanisms by which electrons and nuclei interact are the Fermi contact interaction and by dipolar interaction. The former applies largely to the case of isotropic interactions (independent of sample orientation in a magnetic field) and the latter to the case of anisotropic interactions (spectra dependent on sample orientation in a magnetic field). Spin polarization is a third mechanism for interactions between an unpaired electron and a nuclear spin, being especially important for
π
{\displaystyle \pi }
-electron organic radicals, such as the benzene radical anion. The symbols "a" or "A" are used for isotropic hyperfine coupling constants, while "B" is usually employed for anisotropic hyperfine coupling constants. In many cases, the isotropic hyperfine splitting pattern for a radical freely tumbling in a solution (isotropic system) can be predicted.
==== Multiplicity ====