The coupled transfer of electrons and protons is a central feature of biological and molecular catalysis, yet fundamental aspects of these reactions remain poorly understood. In this study, we extend the ring polymer molecular dynamics (RPMD) method to enable direct simulation of proton-coupled electron transfer (PCET) reactions across a wide range of physically relevant regimes. In a systembath model for symmetric, co-linear PCET in the condensed phase, RPMD trajectories reveal distinct kinetic pathways associated with sequential and concerted PCET reaction mechanisms, and it is demonstrated that concerted PCET proceeds by a solvent-gating mechanism in which the reorganization energy is mitigated by charge cancellation among the transferring particles. We further employ RPMD to study the kinetics and mechanistic features of concerted PCET reactions across multiple coupling regimes, including the fully non-adiabatic (both electronically and vibrationally nonadiabatic), partially adiabatic (electronically adiabatic, but vibrationally non-adiabatic), and fully adiabatic (both electronically and vibrationally adiabatic) limits. Comparison of RPMD with the results of PCET rate theories demonstrates the applicability of the direct simulation method over a broad range of conditions; it is particularly notable that RPMD accurately predicts the crossover in the thermal reaction rates between different coupling regimes while avoiding a priori assumptions about the PCET reaction mechanism. Finally, by utilizing the connections between RPMD rate theory and semiclassical instanton theory, we show that analysis of ring-polymer configurations in the RPMD transition path ensemble enables the a posteriori determination of the coupling regime for the PCET reaction. This analysis reveals an intriguing and distinct "transient-proton-bridge" mechanism for concerted PCET that emerges in the transition between the proton-mediated electron superexchange mechanism for fully non-adiabatic PCET and the hydrogen atom transfer mechanism for partially adiabatic PCET. Taken together, these results provide a unifying picture of the mechanisms and physical driving forces that govern PCET across a wide range of physical regimes, and they raise the possibility for PCET mechanisms that have not been previously reported.

Concerted proton-electron transfer (CPET) reactions in iron carboxy-tetraphenylporphyrin complexes have been investigated using both experimental and theoretical methods. Synthetic heme models abstract H+ and e− from the hydroxylamine TEMPOH or an ascorbate derivative, and the kinetics of the TEMPOH reaction indicate concerted transfer of H+ and e−. Phenylene linker domains vary the electron donor/acceptor separation by approximately 4 Å. The rate data and extensive molecular simulations show that the electronic coupling decay constant (β) depends on conformational flexibility and solvation associated with the linker domain. Our best estimate of β is 0.23 ± 0.07 Å−1, a value that is near the low end of the range (0.2–0.5 Å−1) established for electron transfer reactions involving related linkers. This is the first analysis of β for a CPET reaction.

We investigate the cluster size convergence of the energy and observables using two forms of density matrix embedding theory (DMET): the original cluster form (CDMET) and a new formulation motivated by the dynamical cluster approximation (DCA-DMET). Both methods are applied to the half-filled one-and two-dimensional Hubbard models using a sign-problem free auxiliary-field quantum Monte Carlo impurity solver, which allows for the treatment of large impurity clusters of up to 100 sites. While CDMET is more accurate at smaller impurity cluster sizes, DCA-DMET exhibits faster asymptotic convergence towards the thermodynamic limit. We use our two formulations to produce new accurate estimates for the energy and local moment of the two-dimensional Hubbard model for U/t = 2,4,6. These results compare favorably with the best data available in the literature, and help resolve earlier uncertainties in the moment for U/t = 2.

We use quantized molecular dynamics simulations to investigate the competition between concerted and sequential proton-coupled electron-transfer (PCET) reaction mechanisms in inorganic catalysts. By analyzing reactive nonadiabatic PCET trajectories and computing both concerted and sequential rate constants, we characterize various molecular features that govern inorganic PCET reactions, including the solvent polarity, ligand-mediated electron–proton interactions, and intrinsic proton-transfer (PT) energy barrier. Using atomistic simulations with over 1200 atoms, we find that the symmetric iron biimidazoline system is extremely biased toward the concerted mechanism because of the strong ligand-mediated electron–proton interaction and the short PT distance. However, by investigating system-bath models in which electron–proton interactions are shielded, which are representative of ruthenium terpyridylbenzoates and iron (tetraphenylporphyrin)­benzoates, we predict that a crossover between the concerted and sequential PCET mechanisms may be possible either by increasing the polarity of the solvent or by increasing the intrinsic PT energy barrier. In addition, we predict the possibility of a crossover in the PCET mechanism by directly varying the strength of the ligand-mediated electron–proton interactions. The results presented here reveal new strategies for altering the competition between the competing PCET mechanisms and design principles for controlling PCET in catalytic systems.

We investigate the performance of the recently developed kinetically-constrained ring polymer molecular dynamics (KC-RPMD) method for the description of model condensed-phase electron transfer (ET) reactions in which solvent and donor-acceptor dynamics play an important role. Comparison of KC-RPMD with results from Golden-Rule rate theories and numerically exact quantum dynamics calculations demonstrates that KC-RPMD accurately captures the combination of electronic- and nuclear-dynamical effects throughout the Marcus (intermediate solvent friction) and Zusman (large solvent friction) regimes of ET. It is also demonstrated that KC-RPMD accurately describes systems in which the magnitude of the diabatic coupling depends on the position of a dynamical donor-acceptor mode. In addition to these successes, however, we present an unsurprising failure of KC-RPMD to capture the enhancement of the ET rate in the low solvent friction regime associated with nuclear coherence effects. In this analysis, we re-visit several aspects of the original KC-RPMD formulation, including the form of the kinetic constraint and the choice of the mass of the auxiliary electronic variable. In particular, we introduce a Langevin bath for the auxiliary electronic variable to correct for its unphysically low coupling with the nuclear degrees of freedom. This work demonstrates that the KC-RPMD method is well suited for the direct simulation of non-adiabatic donor-acceptor chemistries associated with many complex systems, including those for which solvent dynamics plays an important role in the reaction mechanism.