Analysis of Frozen Solution Spectra

The next section deals with the analysis of frozen solution spectra. 

Frozen solution spectra must be taken in solvents that form good glasses. A random but homogeneous distribution of the species to be studied is required to obtain a well-resolved spectrum. Notably, some solvents, such as toluene, can crack when frozen, thus giving rise to more features than predicted as spectra 

Early treatments of powder patterns attempted to deal with the spatial distribution of resonant fields by analytical mathematics.9 This approach led to some valuable insights but the algebra is much too complex when non-axial hyperfine matrices are involved. Consider the simplest case a single resonance line without hyperfine structure. The resonant field is given by eqn (4.3). Features in the first derivative spectrum correspond to discontinuities or turning points in the absorption spectrum that arise when dB/dB or dB/dcp are zero  

These equations have three solutions (i) 9 = 0 (ii) 9 = 90°, q = 0 and (iii) 9 = (p = 90°. Since 9 and cp are in the g-matrix axis system, observable features are expected for those fields corresponding to orientations along the principal axes of the g-matrix. This being the case, the principal values of the g-matrix are obtained from a straightforward application of eqn (4.10). 

The g-value of a free electron is a scalar, ge = 2.00232. In a radical species, g becomes a matrix because of the admixture of orbital angular momentum into S through spin-orbit coupling. The components of the g-matrix thus differ from ge to the extent that p-, d-, or f-orbital character has been incorporated, and they differ from one another, depending on which p-, d-, or f-orbitals are involved. 

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