Coupled transitions and higher-order effects in isotropic ESR spectra

Abstract

Analytical expressions are derived which quite accurately describe the eigenvalues and eigenvector coefficients for a two-nucleus radical ( I 1 = 3 2 and I 2 = 1 2 ) in the situation where strong mixing of nuclear spin states occurs because the two hyperfine coupling constants are of the same sign and almost equal in magnitude. The extent of mixing is governed by just two parameters, the energy level separation corrected to second order and the cross product of the second-order shifts. These expressions are also used to probe the important effect of the nuclear g-factor difference in altering the extent of mixing in the M S = − 1 2 manifold from that in the M s = + 1 2 manifold. This asymmetry of mixing enhances the intensity of “forbidden” (coupled) transitions. In the special case of equal hyperfine coupling constants for the two nuclei, a simple relationship is derived showing how the relative intensities of the “allowed” and “Forbidden” transitions vary with the hyperfine coupling and the difference in nuclear g factors. As well as giving numerical results in good agreement with exact matrix diagonalization calculations, these expressions have the merit of providing considerable insight into the nature and mechanism of higher-order effects. The discussion is illustrated by reference to the ESR spectra of the FClO 3 − and FSO 2 radicals while higher-order effects in the ESR spectra of the 11 BF 3 − , 33SOF 3, and H 11BO − radicals are also briefly described. The present approach is compared with previous treatments of higher-order effects by Fessenden, Morton and Preston, and Burkhard and Fischer.