Postdoctoral research associate, University of Rochester
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.
Abstract: A proton transfer reaction in a linear hydrogen-bonded complex dissolved in a polar solvent is studied using mixed quantum-classical Liouville dynamics. In this system, the proton is treated quantum mechanically and the remainder of the degrees of freedom is treated classically. The rates and mechanisms of the reaction are investigated using both adiabatic and nonadiabatic molecular dynamics. We use a nonadiabatic dynamics algorithm which allows the system to evolve on single adiabatic surfaces and on coherently coupled pairs of adiabatic surfaces. Reactive-flux correlation function expressions are used to compute the rate coefficients and the role of the dynamics on the coherently coupled surfaces is elucidated.
Pub.: 23 Jul '05, Pinned: 30 Jun '17
Abstract: The nonadiabatic dynamics of model proton-coupled electron transfer (PCET) reactions is investigated for the first time using a surface-hopping algorithm based on the solution of the mixed quantum-classical Liouville equation (QCLE). This method provides a rigorous treatment of quantum coherence/decoherence effects in the dynamics of mixed quantum-classical systems, which is lacking in the molecular dynamics with quantum transitions surface-hopping approach commonly used for simulating PCET reactions. Within this approach, the protonic and electronic coordinates are treated quantum mechanically and the solvent coordinate evolves classically on both single adiabatic surfaces and on coherently coupled pairs of adiabatic surfaces. Both concerted and sequential PCET reactions are studied in detail under various subsystem-bath coupling conditions and insights into the dynamical principles underlying PCET reactions are gained. Notably, an examination of the trajectories reveals that the system spends the majority of its time on the average of two coherently coupled adiabatic surfaces, during which a phase enters into the calculation of an observable. In general, the results of this paper demonstrate the applicability of QCLE-based surface-hopping dynamics to the study of PCET and emphasize the importance of mean surface evolution and decoherence effects in the calculation of PCET rate constants.
Pub.: 03 Aug '14, Pinned: 30 Jun '17
Abstract: In a previous study [F. A. Shakib and G. Hanna, J. Chem. Phys. 141, 044122 (2014)], we investigated a model proton-coupled electron transfer (PCET) reaction via the mixed quantum-classical Liouville (MQCL) approach and found that the trajectories spend the majority of their time on the mean of two coherently coupled adiabatic potential energy surfaces. This suggested a need for mean surface evolution to accurately simulate observables related to ultrafast PCET processes. In this study, we simulate the time-dependent populations of the three lowest adiabatic states in the ET-PT (i.e., electron transfer preceding proton transfer) version of the same PCET model via the MQCL approach and compare them to the exact quantum results and those obtained via the fewest switches surface hopping (FSSH) approach. We find that the MQCL population profiles are in good agreement with the exact quantum results and show a significant improvement over the FSSH results. All of the mean surfaces are shown to play a direct role in the dynamics of the state populations. Interestingly, our results indicate that the population transfer to the second-excited state can be mediated by dynamics on the mean of the ground and second-excited state surfaces, as part of a sequence of nonadiabatic transitions that bypasses the first-excited state surface altogether. This is made possible through nonadiabatic transitions between different mean surfaces, which is the manifestation of coherence transfer in MQCL dynamics. We also investigate the effect of the strength of the coupling between the proton/electron and the 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 potential energy surfaces and the nonadiabatic couplings. Finally, we investigate the state population dynamics in the PT-ET (i.e., proton transfer preceding electron transfer) and concerted versions of the model. The PT-ET results confirm the participation of all of the mean surfaces, albeit in different proportions compared to the ET-PT case, while the concerted results indicate that the mean of the ground- and first-excited state surfaces only plays a role, due to the large energy gaps between the ground- and second-excited state surfaces.
Pub.: 17 Jan '16, Pinned: 30 Jun '17
Abstract: In this work, we derive a general mixed quantum-classical formula for calculating thermal proton-coupled electron transfer (PCET) rate constants, starting from the time integral of the quantum flux-flux correlation function. This formula allows for the direct simulation of PCET reaction dynamics via the Mixed Quantum-Classical Liouville (MQCL) approach. Owing to the general nature of the derivation, this formula does not rely on any prior mechanistic assumptions and can be applied across a wide range of electronic and protonic coupling regimes. To test the validity of this formula, we applied it to a reduced model of a condensed phase PCET reaction. Good agreement with the numerically exact rate constant is obtained, demonstrating the accuracy of our formalism. We believe that this approach constitutes a solid foundation for future investigations of the rates and mechanisms of a wide range of PCET reactions.
Pub.: 28 May '16, Pinned: 30 Jun '17
Abstract: We propose a ring polymer molecular dynamics method for the calculation of chemical rate constants that incorporates nonadiabatic effects by the surface-hopping approach. Two approximate ring polymer electronic Hamiltonians are formulated and the time-dependent Schrodinger equation for the electronic amplitudes is solved self-consistently with the ring polymer equations of motion. The beads of the ring polymer move on a single adiabatic potential energy surface at all times except for instantaneous surface hops. The probability for a hop is determined by the fewest-switches surface-hopping criterion. During a surface hop all beads switch simultaneously to the new potential energy surface with positions kept unchanged and momenta adjusted properly to conserve total energy. The approach allows the evaluation of total rate coefficients as well as electronic state-selected contributions. The method is tested against exact quantum mechanical calculations for a one-dimensional, two-state model system that mimics a prototypical nonadiabatic bimolecular chemical reaction. For this model system, the method reproduces quite accurately the tunneling contribution to the rate and the distribution of reactants between the electronic states.
Pub.: 20 Dec '12, Pinned: 30 Jun '17
Abstract: We apply a recently proposed ring polymer surface-hopping (RPSH) approach to investigate the real-time non-adiabatic dynamics with explicit nuclear quantum effects. The non-adibatic electronic transitions are described through Tully's fewest switches surface-hopping algorithm and the motion of the nuclei are quantized through the ring polymer Hamiltonian in the extended phase-space. Applying RPSH method to simulate Tully's avoided crossing models, we demonstrate the critical role of nuclear tunneling effect and zero point energy for accurately describing the transmission and reflection probabilities with low initial momenta. In addition, in Tully's extended coupling model, we show that the ring polymer quantization effectively captures decoherence, yielding more accurate reflection probabilities. These promising results demonstrate the potential of using RPSH as an accurate and efficient method to incorporate nuclear quantum effects into non-adiabatic dynamics simulations.
Pub.: 21 Jun '17, Pinned: 28 Jun '17