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Theoretical Studies of Proton-Coupled Electron Transfer Reactions via the Mixed Quantum-Classical Liouville Approach Open Access


Other title
Theoretical chemistry
mixed quantum-classical dynamics
proton-coupled electron transfer
Type of item
Degree grantor
University of Alberta
Author or creator
Alipour Shakib, Farnaz
Supervisor and department
Hanna, Gabriel (Chemistry)
Examining committee member and department
Miller III, Thomas F. (Chemistry)
Gibbs-Davis, Juli (Chemistry)
Klobukowski, Mariusz (Chemistry)
Xu, Yunjie (Chemistry)
West, Frederick (Chemistry)
Department of Chemistry

Date accepted
Graduation date
Doctor of Philosophy
Degree level
The nonadiabatic dynamics of model proton-coupled electron transfer (PCET) reactions were investigated for the first time using a surface-hopping algorithm based on the solution of the mixed quantum-classical Liouville (MQCL) equation. This method provides a rigorous treatment of quantum decoherence effects in the dynamics of mixed quantum-classical systems, which is lacking in Tully's fewest switches surface hopping (FSSH) approach commonly used for simulating PCET reactions. Within the MQCL approach, the transferring proton and electron are treated quantum mechanically while the remainder of the system, including the donor, acceptor, and solvent, is treated classically. The classical degrees of freedom (DOF) are evolved on both single adiabatic potential energy surfaces (PESs) and on coherently coupled pairs of adiabatic PESs, while in FSSH they are evolved only on single adiabatic PESs. To demonstrate the applicability of MQCL approach to the study of PCET, we focused on a reduced model that had been previously studied using FSSH. This model is comprised of three DOF, including a proton, an electron, and a collective solvent coordinate. The proton and electron are allowed to transfer in one dimension between two point charges, representing the donor and the acceptor, which are positioned at a fixed distance from each other. Both concerted and sequential [either proton transfer before electron transfer (i.e., PT-ET) or electron transfer before proton transfer (i.e., ET-PT)] PCET reactions were studied within the context of this model. We studied these mechanisms in detail under various subsystem-bath coupling conditions and gained insights into the dynamical principles underlying these reactions. Notably, an examination of the trajectories which successfully undergo PCET (i.e., both the proton and electron, initially near the donor, transfer to the acceptor) reveals that the system spends the majority of its time on the mean of two coherently coupled adiabatic PESs. While on this mean surface, the classical DOF evolve differently than on the other surfaces and an observable of interests acquires a phase factor. Fluctuations of the classical coordinates can cause this phase factor to oscillate in time differently for each trajectory and, as a result, averaging over an ensemble of trajectories can lead to destructive interference when calculating an expectation value of an observable. In this way, the MQCL approach is able to incorporate decoherence, which is not captured in the FSSH approach. Due to this fundamental difference between the two methods, the percentages of successful PCET reactions obtained via MQCL drastically differ from those obtained via FSSH. To gain insight into the differences between the MQCL and FSSH approaches for calculating PCET observables, we calculated the time-dependent populations of the ground, first-excited, and second-excited adiabatic states for the ET-PT mechanism in the same PCET model and compared them to both the exact quantum and FSSH results. We found that the MQCL population profiles show a significant improvement over the FSSH ones, and are in good agreement with the exact quantum results. All of the mean PESs were shown to play a direct role in the dynamics of the state populations. Interestingly, our results showed that the population transfer to the second-excited state can be mediated by the dynamics on the mean of the ground and second-excited state PESs, via a sequence of nonadiabatic transitions that bypasses the first-excited state PES altogether. This is made possible by nonadiabatic transitions between different mean surfaces, which is the manifestation of coherence transfer in MQCL dynamics. We also investigated the effect of the strength of the coupling between the proton/electron and the collective solvent coordinate on the state population dynamics. Drastic changes in the population dynamics are observed, which can be understood in terms of the changes in the PESs and the nonadiabatic couplings. In addition, we investigated the state population dynamics in the PT-ET and concerted versions of the model. The PT-ET results revealed the participation of all of the mean surfaces, albeit in different proportions compared to the ET-PT reaction, while the concerted results revealed that the mean of the ground and first-excited state PESs only plays a role. We finally present a derivation of a novel mixed quantum-classical formula for calculating PCET rate constants that starts from the quantum mechanical expression for the time integral of the flux-flux correlation function. The resulting time-dependent rate coefficient has a dynamical part involving MQCL time evolution of the product species operator and an equilibrium part. This formula is general, not requiring any prior assumptions about the parameters of the system. Furthermore, since MQCL dynamics is used to evolve the product species operator, this approach treats decoherence on a more solid footing than the FSSH-based methods. The applicability of this formula is demonstrated on an extended version of the previously studied PCET model, where now the collective solvent coordinate is coupled to a harmonic oscillator bath. Our result for the rate constant is found to be in good agreement with the numerically exact result obtained via the quasi-adiabatic path integral method.
This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for the purpose of private, scholarly or scientific research. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.
Citation for previous publication
Shakib, F. A. and Hanna, G. An analysis of model proton-coupled electron transfer reactions via the mixed quantum-classical Liouville approach, J. Chem. Phys., 2014, 141, 044122-1−044122-12.Shakib, F. A. and Hanna, G. New insights into the nonadiabatic state population dynamics of model proton-coupled electron transfer reactions from the mixed quantum-classical Liouville approach, J. Chem. Phys., 2016, 144, 024110-1−024110-11.

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