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

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.

Magnetic Properties of [FeFe]‐Hydrogenases: A Theoretical Investigation Based on Extended QM and QM/MM Models of the H‐Cluster and Its Surroundings

“…[24] It was shown that the BS approach reproduces the electron density of the system of coupled spins correctly, while the obtained spin densities and thus the EPR parameters could be incorrect. The fact that Fe 6 S 6 models result in almost the same hyperfine coupling constants as Fe 2 S 2 models shows that BS DFT predicts "intrinsic" hyperfine coupling constants rather than the "effective" ones.…”

The Density Functional Theory

“…The double-hybrid B2PLYP functional also affords accurate predictions, particularly for HFCs of metal nuclei, but the existence of outliers suggests that this method may lack stability. The reliable performance of the TPSSh functional has since received additional confirmation in our recent study (Pantazis et al 2009) aimed at the analysis of hyperfine coupling parameters in tetramanganese models of the OEC. A topical application of DFT for the determination of EPR parameters, highlighting the capabilities of the broken-symmetry approach, was the study of the trapped-…”

“…In a recent contribution (Pantazis et al 2009), we investigate the magnetic properties of a tetramanganese complex bearing resemblance to the OEC of PSII (Fig. 3).…”

“…The authors point out that many different sets of J values can reproduce the experimental data and proceed to exact diagonalization of the Hamiltonian and construction of a theoretical magnetic susceptibility curve to make comparisons to experiment. This approach clearly emerges as the only credible way of studying magnetic interactions with BS-DFT in oligonuclear clusters similar to the oxygen evolving complex in PSII (Pantazis et al 2009). …”

Structural Analysis of High-Spin States of S0-S4 at OEC Complex: A Theoretical Approach of Small Models

“…This spin scheme was considered in this work once HS OEC structures are well described in literature as the main spin scheme found in natural OEC. 5,6,26 We considered initially S0 with zero charge and the following states given in Table 1, according to Kok Cycle scheme, where we can check the different spin/charge arrangements considered in our calculations. For these structures all calculations were performed using the software package Gaussian 09.…”