Paramagnetic species dipolar interaction

Apart from their short lifetimes, another important reason for not observing the O species is dipolar interaction. As explained later (Section IV), if the distance between one O species and another paramagnetic center (O or a metal ion) decreases, the linewidth may increase to the extent that the 0 species become EPR invisible. In this category of EPR invisible O species, there are not only the short-lived O produced according to Eq. (8), but also the long-lived O formed by heat pretreatment or adsorption, as discussed in the following section. 

When paramagnetic species contain more than one unpaired electron (S > 1 /2), dipolar interaction between the latter creates 2S + 1 electronic sublevels and leads to the fine structure of EPR spectrum. This is, for example, the case for Fe ions (S — 5/2), which are discussed in Section III.B.2. For those species, the spin Hamiltonian takes the form ... 

Observed linewidths of NMR signals in paramagnetic systems vary enormously and the conditions that govern the observed widths are considerably more complex than in diamagnetic systems. Swift (30) reviewed the problem some years ago. Relaxation times of spin-j nuclei are governed by dipolar and hyperfine exchange (Fermi contact) relaxation processes. The dipolar interaction is normally dominant except in some delocalized systems in which considerable unpaired spin density exists on nuclei far removed from the metal ions (e.g. Ti-radicals). Distinction between the two processes can be made by consideration of the different mathematical expressions involved. For dipolar relaxation when o)fx 1 (t = rate constant for rotation of the species containing the coupled pair and to, = nuclear resonance frequency) ... 

Flavin semiquinones in solution, being typical n radicals, ordinarily saturate very easily with microwave power. The center of the spectrum saturates more easily than do the outer wings [139,140,145]. Exceptions have been found where other paramagnetic species are in the vicinity of the semiquinone. Addition of paramagnetic metal ions to solutions containing flavin semiquinones can greatly decrease the saturability of the radical because of dipolar interactions with the metal ions [146], Similar behavior has been encountered in enzyme systems (below). 

However, a good fit by mere observation does not necessarily prove the underlying assumptions. Moreover, powder spectra of molecular sieves are generally very complicated. This is mainly due to three reasons (1) the spectra consist of several overlapping signals, associated with paramagnetic species on different sites (2) the site symmetry in molecular sieves is low (3) many effects - dipolar interactions, quadrupole... 

Point-dipole approximation with delocalized electron spin This method is an extension of the point-dipole approximation, applicable to paramagnetic species with spin density distributed over several atoms. Hyperfine (hf) interactions in hydrogen-bonded systems and trapping site structure with surrounding ions can be elucidated. An example briefly discussed in Section 2.2.2 is the model deduced from ENDOR measurements on X-irradiated Li-formate for the trapping of CO2 ion radicals in a crystal matrix. The dipolar hfc is composed of contributions from spin densities at three atoms as indicated by the sketch to the right in Fig. 2,12. A procedure to add the contributions described in Appendix A2.1 involves the following steps. 

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