A New Quantum Chemical Approach to the Magnetic Properties of Oligonuclear Transition‐Metal Complexes: Application to a Model for the Tetranuclear Manganese Cluster of Photosystem II

Abstract

Abstract Broken‐symmetry DFT calculations on transition‐metal clusters with more than two centers allow the hyperfine coupling constants to be extracted. Application of the proposed theoretical scheme to a tetranuclear manganese complex that models the S 2 state of the oxygen‐evolving complex of photosystem II yields hyperfine parameters that can be directly compared with experimental data. The picture shows the metal–oxo core of the model and the following parameters; exchange coupling constant J ij , the expectation value of the site‐spin operator ${{\left\langle {{\rm S}_{\rm z}^{({\rm{{\rm K}}})} } \right\rangle }}$ , and the isotropic hyperfine coupling ${{{\rm A}_{{\rm{{\rm iso}}}}^{{\rm{({\rm K})}}} }}$ parameters. magnified image The reliable correlation of structural features and magnetic or spectroscopic properties of oligonuclear transition‐metal complexes is a critical requirement both for research into innovative magnetic materials and for elucidating the structure and function of many metalloenzymes. We have developed a novel method that for the first time enables the extraction of hyperfine coupling constants (HFCs) from broken‐symmetry density functional theory (BS‐DFT) calculations on clusters. Using the geometry‐optimized tetranuclear manganese complex [Mn 4 O 6 (bpy) 6 ] 4+/3+ as a model, we first examine in detail the calculation of exchange coupling constants J through the BS‐DFT approach. Complications arising from the indeterminacy of experimentally fitted J constants are identified and analyzed. It is found that only the energy levels derived from Hamiltonian diagonalization are a physically meaningful basis for comparing theory and experiment. Subsequently, the proposed theoretical scheme is applied to the calculation of 55 Mn HFCs of the Mn III,IV,IV,IV state of the complex, which is similar to the S 2 state of the oxygen‐evolving complex (OEC) in photosystem II of oxygenic photosynthesis. The new approach performs reliably and accurately, and yields calculated HFCs that can be directly compared with experimental data. Finally, we carefully examine the dependence of HFC on the J value and draw attention to the sensitivity of the calculated values to the exchange coupling parameters. The proposed strategy extends naturally to hetero‐oligonuclear clusters of arbitrary shape and nuclearity, and hence is of general validity and usefulness in the study of magnetic metal clusters. The successful application of the new approach presented here is a first step in the effort to establish correlations between the available spectroscopic information and the structural features of complex metalloenzymes like OEC.