Simulation of the dynamics of electron transfer reactions in polar solvents: Semiclassical trajectories and dispersed polaron approaches

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Abstract
Simulation methods for exploring the microscopic aspects of electron transfer (ET) reactions are developed. For the high temperature limit, where anharmonicity effects are crucial, we develop a semiclassical trajectory (ST) method. This method treats the reaction by considering the time dependence of the electronic energy gap along the classical trajectories of the solvent molecules. The ST approach, which appears as an ad hoc approach, might be at present the most rigorous practical models for simulating ET reactions. That is, this method reproduces the results of the quantum mechanical harmonic test case in the high temperature statistical limit. More importantly, for anharmonic systems it provides a rate constant which depends on the proper activation free energy; this dependence cannot be evaluated by any of the current quantum mechanical methods. For the low temperature range we develop a ‘‘dispersed polaron’’ model that uses the Fourier transform of the microscopic energy gap to evaluate the harmonic Franck–Condon factors of the system. These Franck–Condon factors are then used to evaluate the quantum mechanical harmonic rate constant. The potential of our approach is outlined by considering its implementation in studies of several key problems. This includes: (i) Studies of the effect of solvent dynamics and the role of dielectric relaxation times. (ii) Studies of the actual microscopic activation free energy. (iii) Exploration of the role of vibronic channels in the inverted region. (iv) Transition between the adiabatic and diabatic limits.