Analysis of Isotropic EPR Spectra

While most paramagnetic species encountered in heterogeneous catalysis will be associated with polycrystaUine oxides, it is instructive to first examine the analysis of simple EPR spectra for systems with isotropic symmetry (found in fluid solution). When more than one equivalent nucleus is present in the system, then the energy state described by Equation 1.20 will be split by each equivalent nucleus. 

For a radical consisting of m sets of equivalent nuclei, each counting n number of equivalent nuclei, then the total number of lines is given by 

As described earlier, the number of lines in the EPR spectrum is given by the simple equation 2nl + 1 and this holds true for n equivalent nuclei. For example, for five equivalent protons (I = 1/2), then (2 x 5 x 1/2) -i- 1 = 6 lines, producing a sextet hyperfine pattern with an intensity ratio of 1 5 10 10 5 1 (Table 1.2). 

As the number of nuclei increases, the complexity of the spectrum rapidly increases since the spectral density depends on the number of inequivalent nuclei according to  

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