Multidimensional treatment of stochastic solvent dynamics in photoinduced proton-coupled electron transfer processes: Sequential, concerted, and complex branching mechanisms

Abstract

A theoretical approach for the multidimensional treatment of photoinduced proton-coupled electron transfer (PCET) processes in solution is presented. This methodology is based on the multistate continuum theory with an arbitrary number of diabatic electronic states representing the relevant charge distributions in a general PCET system. The active electrons and transferring proton(s) are treated quantum mechanically, and the electron-proton vibronic free energy surfaces are represented as functions of multiple scalar solvent coordinates corresponding to the single electron and proton transfer reactions involved in the PCET process. A dynamical formulation of the dielectric continuum theory is used to derive a set of coupled generalized Langevin equations of motion describing the time evolution of these collective solvent coordinates. The parameters in the Langevin equations depend on the solvent properties, such as the dielectric constants, relaxation time, and molecular moment of inertia, as well as the solute properties. The dynamics of selected intramolecular nuclear coordinates, such as the proton donor-acceptor distance or a torsional angle within the PCET complex, may also be included in this formulation. A surface hopping method in conjunction with the Langevin equations of motion is used to simulate the nonadiabatic dynamics on the multidimensional electron-proton vibronic free energy surfaces following photoexcitation. This theoretical treatment enables the description of both sequential and concerted mechanisms, as well as more complex processes involving a combination of these mechanisms. The application of this methodology to a series of model systems corresponding to collinear and orthogonal PCET illustrates fundamental aspects of these different mechanisms and elucidates the significance of proton vibrational relaxation and nonequilibrium solvent dynamics.

Theory of multiple proton–electron transfer reactions and its implications for electrocatalysis

“…Hammes-Schiffer et al have carried out simulations of orthogonal and collinear proton-electron transfer in solution (not at an electrode), such as depicted in Fig.3a and 3b, and calculated λ for both cases from a dielectric continuum model. 40,41 For the situation shown in Fig.3b, λ was indeed found to be quite large and negative, but it did not entirely cancel the λ ET + λ PT term in Eq.8. In their model, this must be due to the fact that the proton and the electron were not centered on the same sites on the donor and acceptor species, so that effectively a dipole was transferred.…”

Exploring Autoionization and Photoinduced Proton-Coupled Electron Transfer Pathways of Phenol in Aqueous Solution

“…This complicates the geminate recombination pathways, and allows for Phenol in aqueous solution surely constitutes one of the simpler test beds for ab initio calculations designed to explore near-threshold autoionization or possible excited state PCET mechanisms. 65,66 Understanding the nuclear motions associated with the solute, and any coupling to specific bath modes, are now crucial in order to reveal any role for PCET at low excitation energies and to advance a detailed understanding of our favored mechanism -autoionization -in phenol, and in larger biomolecules in which phenol (and related sub-units) acts as a chromophore.…”

Direct simulation of proton-coupled electron transfer across multiple regimes

“…53 Established methods include Ehrenfest dynamics, 41,42 mixed quantum-classical trajectory surface hopping dynamics, [43][44][45][46][47][48] the ab initio multiple spawning approach, 49 and semiclassical methods based on the Meyer-Miller-Stock-Thoss mapping. [50][51][52] However, despite their successes, these methods do not yield a dynamics that rigorously preserves detailed balance, 54,55 a feature that is valuable for the robust calculation of thermal reaction rates 56,57 and for the utilization of rare-event sampling methods.…”

“…Alternative theoretical methods have previously advanced our ability to simulate and understand coupled electronic and nuclear dynamics, [41][42][43][44][45][46][47][48][49][50][51][52] and promising new methods continue to be introduced. 53 Established methods include Ehrenfest dynamics, 41,42 mixed quantum-classical trajectory surface hopping dynamics, [43][44][45][46][47][48] the ab initio multiple spawning approach, 49 and semiclassical methods based on the Meyer-Miller-Stock-Thoss mapping.…”