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

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.