Hyperfine linewidth in the E.S.R. spectra of manganese(II) complexes in solution

Abstract

The theory of Baram et al. [J. chem. Phys., 58, 4558 (1973)] of magnetic resonance lineshape due to modulation of the zero-field splitting (ZFS) interaction for semi-integer spins, is extended to include the isotropic hyperfine interaction. General equations are derived for the whole range of tumbling rates. In addition specific equations are given for the relaxation matrix in the fast tumbling limit. When the tumbling rate is slower than the Larmor frequency but still faster than the hyperfine interaction and the second-order ZFS shift then only the -½ →½ hyperfine transitions are observed and explicit equations for their linewidths are derived. The theory predicts a marked dependence of the linewidth on the nuclear Zeemann azimuthal quantum number M, in both the fast and slow tumbling regions. In the second part of the paper experimental E.S.R. spectra of three Mn2+ complexes in solution are presented and analysed using our theory. The systems include Mn(ClO4)2 in methanol and ethanol and the Mn2+-adenosine-triphosphate complex in water. The solutions were studied over a wide temperature range (-50°C to + 80°C) and the spectra were found to exhibit marked M-dependent linewidths. These results were used to derive rotational correlation times and ZFS parameters for the various complexes. It is found that the ZFS interaction is temperature dependent and for the methanol and ethanol complexes it varies by more than a factor two in the temperature range studied. It is also shown that an additional relaxation mechanism, apparently due to higher-order spin-orbit coupling terms, contributes to the linewidth for the Mn2+ complexes.