Magnetic resonance in systems with equivalent spin-1/2 nuclides. Part 2: Energy values and spin states

In an earlier paper (Part 1), featuring group-theoretical analysis, it was shown that the isotropic EPR spectra of free radical (S = 1/2) species XLn, where the n equivalent nuclei also have spin 1/2, have a more complicated form than anticipated from the usual (first-order) oversimplified analysis. The nucleus of X is taken to be spin-less. The latter predicts n + 1 lines with intensity ratios given by the coefficients of the binomial expansion; for systems with n = 3, the EPR spectrum in fact consists of 6 lines. Analogous considerations hold for NMR spectroscopy of XLn non-radicals. For n ⩾ 3 systems, the degeneracy of the energy levels cannot be completely removed by the Zeeman electronic and nuclear interactions. Explicit solutions for n = 3 (analytic, as well as computational) of the spin-hamiltonian for the energies and spin states have been obtained and are given in the present work. Discussion of the underlying theory, invoking exchange degeneracy, is included herein in some detail, focusing on line positions and relative spectral intensities.