Applicability of Transition State Theory to the (Proton-Coupled) Electron Transfer in Photosynthetic Water Oxidation with Emphasis on the Entropy of Activation

Abstract

Recent advancements in the study of the protein complex photosystem II have clarified the sequence of events leading to the formation of oxygen during the S3 → S4 → S0 transition, wherein the inorganic Mn4Ca(µ-O)6(OHx)4 cluster finishes photo-catalyzing the water splitting reaction (Greife et al., Nature 2023, 617, 623–628; Bhowmick et al., Nature 2023, 617, 629–636). During this final step, a tyrosine radical (TyrZ), stable for a couple of milliseconds, oxidizes a cluster-bound oxygen while the hydrogen bonding patterns of nearby waters shift a proton away. A treatment of this redox reaction within the context of accepted transition state theories predicts rate constants that are significantly higher than experimentally recovered values (1012 s−1 versus 103 s−1). In an effort to understand this disparity, temperature-dependent experiments have revealed large entropic contributions to the rates with only a moderate enthalpy of activation. We suggest that the entropic source may be related to the observed proton rearrangements, and further possible near isoenergetic variations in the nearby extended H-bonding network delaying the realization of an ‘ideal’ transition state. In the following, we explore this relation in the context of Eyring’s transition state theory and Marcus’ electron transfer theory and evaluate their compatibility with the experimental evidence.