A comment on the pseudo-nuclear Zeeman effect

Abstract

For high-spin systems whose magnetic sublevels are arranged in doublets at zero field, the electron-paramagnetic-resonance (EPR) spectra are commonly described by an effective spin Hamiltonian. We show that also in this approach, if the mixing of the electron spin states by the hyperfine interaction is negligible, a proper description of electron-nuclear double resonance (ENDOR) spectra can be obtained using a nuclear spin Hamiltonian in which the electron spin angular momentum operator is replaced by its expectation value. Appropriate values of this expectation value can be obtained from a wave function correct to first-order in the electron Zeeman interaction. In terms of perturbation theory, such a description is more logical than the conventional practice based on the inclusion of a second-order cross term, the so-called pseudo-nuclear Zeeman effect, which involves both the electron Zeeman interaction and the hyperfine interaction. We illustrate our analysis with calculations of the expectation value of the electron spin angular momentum and of the energies of the hyperfine levels for a high-spin cobalt complex, which we studied by EPR and ENDOR recently.