Hyperfine tensors for a model system for the oxygen evolving complex of photosystem II: calculation of the anisotropy shift that occurs beyond the strong exchange limit

Abstract

Broken-symmetry density functional calculations have been used to calculate effective ⁵⁵Mn hyperfine (A) tensors for a mixed-valence tetranuclear manganese complex, a model system for the S₂ state of the oxygen-evolving complex of photosystem II. Recent investigations carried out in our laboratory showed that for calculations within the strong exchange limit, density functional calculations cannot reproduce the relative magnitude of the anisotropy of the hyperfine tensors of the Mn^III center compared to the Mn^IV centers. In this work we therefore go beyond the strong exchange limit and investigate the effect of multiplet mixing, induced by zero-field splitting, on the effective hyperfine tensors through a perturbational treatment within the numerical spin projection procedure. Results show that the inclusion of zero-field splitting leads to a shift of the anisotropy from the Mn^III ion towards the three Mn^IV ions, thus reconciling the calculated and experimentally observed anisotropy pattern. However, the final results are quite sensitive to the energy gap between the ground (doublet) and the first excited (quartet) state and therefore critically depend on the appropriate choice of the isotropic exchange coupling constants.