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Entangled quantum electronic wavefunctions of the Mn4CaO5 cluster in photosystem II

Abstract

It is a long-standing goal to understand the reaction mechanisms of catalytic metalloenzymes at an entangled many-electron level, but this is hampered by the exponential complexity of quantum mechanics. Here, by exploiting the special structure of physical quantum states and using the density matrix renormalization group, we compute near-exact many-electron wavefunctions of the Mn4CaO5 cluster of photosystem II, with more than 1 × 1018 quantum degrees of freedom. This is the first treatment of photosystem II beyond the single-electron picture of density functional theory. Our calculations support recent modifications to the structure determined by X-ray crystallography. We further identify multiple low-lying energy surfaces associated with the structural distortion seen using X-ray crystallography, highlighting multistate reactivity in the chemistry of the cluster. Direct determination of Mn spin-projections from our wavefunctions suggests that current candidates that have been recently distinguished using parameterized spin models should be reassessed. Through entanglement maps, we reveal rich information contained in the wavefunctions on bonding changes in the cycle.

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Figure 1: Orbital energy levels and electron occupancies of the four Mn sites for the XRD model.
Figure 2: Error of the DMRG total energy relative to the m = ∞ limit (ΔE) versus the number of renormalized basis states m kept per block.
Figure 3: Orbital energy levels and electron occupancies of four Mn sites for the refined structure.
Figure 4: Potential energy curves for the two low-lying electronic surfaces Sππ* and Sσσ* connected to the ground state at the refined structure and the XRD structure, respectively.
Figure 5: Quantum orbital entanglement maps between the localized active-space orbitals of the Mn ions (Mn1–4) and O atoms (O1–5) for the S0–S3 states in the Kok cycle.

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Acknowledgements

Y.K. and T.Y. were supported in part by a Grant-in-Aid for Scientific Research (C) (grant no. 25410030) and a Grant-in-Aid for Scientific Research (B) (grant no. 25288013), respectively, from MEXT, Japan. Y.K. and T.Y. acknowledge support from the Institute for Molecular Science and a grant of CPU time from the Research Center for Computational Science. G.K-L. Chan was supported by the US Department of Energy, Office of Science (DE-FG02-07ER46432).

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Y.K. conceived and designed the study, and performed the calculations. Y.K. and T.Y. developed the computer implementations. All authors analysed and interpreted the data, discussed the results, and co-wrote the paper.

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Correspondence to Yuki Kurashige.

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Kurashige, Y., Chan, GL. & Yanai, T. Entangled quantum electronic wavefunctions of the Mn4CaO5 cluster in photosystem II. Nature Chem 5, 660–666 (2013). https://doi.org/10.1038/nchem.1677

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