Investigations of Model Proton-Coupled Electron Transfer Reactions from a Mixed Quantum-Classical Liouville Perspective

Abstract

Many biological processes involve the transfer of electrons from a donor to an acceptor accompanied by the transfer of protons. This phenomenon, known as proton-coupled electron transfer (PCET), is at the heart of energy conversion reactions in photosynthesis and respiration. Theoretical methods, which treat the coupled dynamics of the transferring protons, electrons, and their environment in a quantum mechanical fashion, are required for accurately describing PCET reactions. However, the size and complexity of real systems render the application of a full quantum treatment computationally impossible. Hybrid methods which treat the transferring protons and electrons quantum mechanically, but treat the donor, acceptor, and solvent molecules classically, offer feasible yet accurate alternatives to full quantum treatments. In this study, for the first time, we adopt a surface-hopping approach based on the solution of the quantum-classical Liouville equation (QCLE) for the study of PCET reactions. The advantage of this approach over other nonadiabatic dynamics methods is that it inherently accounts for quantum coherence effects in the dynamics through phases accumulated during trajectory segments on the means of two adiabatic surfaces. As a starting point, we consider a simple model, which is comprised of three coupled degrees of freedom: an electronic coordinate, a protonic coordinate, and a solvent coordinate. Varying the parameters in the model allows us to study both concerted and sequential PCET mechanisms. For each mechanism considered, we investigate the role played by mean surface evolution in an ensemble of surface-hopping trajectories and discuss the implications of decoherence of the proton-electron subsystem on the rates of these reactions.