We develop mixed quantum-classical methods to study proton-coupled electron transfer (PCET)

Many chemical and biological processes involve coupling between the transfer of electrons and protons. This phenomenon, known as proton-coupled electron transfer (PCET), is at the heart of energy conversion reactions in photosynthesis and respiration. Both the splitting of water to produce oxygen by the oxygen evolving complex in photosystem II and the reduction of oxygen to water by cytochrome c oxidase in aerobic respiration, involve multiple PCET steps. Hence, a deep understanding of the rate and mechanism of these reactions helps us in designing more efficient artificial photosynthesis devices and solar cells.

The rate and mechanism of these reactions are significantly influenced by transitions between different electronic states, i.e. nonadiabatic transitions, and also the tunneling motion of proton through energy barrier. As a result, Newton equations of motion, i.e. classical molecular dynamics simulations, are not capable of describing such processes. Ideally, a full quantum dynamical treatment should be used to study these reactions, but it is not a feasible task in large realistic systems, both now and in the foreseeable future. The alternative approach is to develop mixed quantum-classical methods where the transferring protons and electrons are treated quantum mechanically while the rest of the system, i.e. environmental degrees of freedom, are treated classically. In this pinboard you will find two such methods that have been developed to study nonadiabatic dynamics of vital processes such as PCET.

Mixed quantum-classical Liouville (MQCL) has been applied on PCET for the first time and has been shown to capture the exact state population dynamics of model PCET reactions more accurately than does the commonly-used fewest-switches surface hopping (FSSH) method. The reason is that in MQCL, the classical trajectories are evolved either on single adiabatic surfaces or on the mean of two coherently coupled adiabatic surfaces, as opposed to only on single adiabatic surfaces in FSSH.

The other method, ring polymer surface hopping (RPSH) is a combination of ring polymer molecular dynamics (RPMD) with FSSH. In RPSH method, the nonadiabatic electronic transitions are described by the FSSH algorithm, and the nuclear quantum effects are incorporated through ring polymer quantization, thus making RPSH a well-tailored theoretical tool for describing the electronic and nuclear quantum dynamics in processes like PCET.

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