Quantum decoherence and the isotope effect in condensed phase nonadiabatic molecular dynamics simulations

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Abstract
In this paper, we explore in detail the way in which quantum decoherence is treated in different mixed quantum‐classical molecular dynamics algorithms. The quantum decoherence time proves to be a key ingredient in the production of accurate nonadiabatic dynamics from computer simulations. Based on a short time expansion to a semiclassical golden rule expression due to Neria and Nitzan [J. Chem. Phys. 99, 1109 (1993)], we develop a new computationally efficient method for estimating the decay of quantum coherence in condensed phase molecular simulations. Using the hydrated electron as an example, application of this method finds that quantum decoherence times are on the order of a few femtoseconds for condensed phase chemical systems and that they play a direct role in determining nonadiabatic transition rates. The decay of quantum coherence for the solvated electron is found to take ≊50% longer in D2O than in H2O, providing a rationalization for a long standing puzzle concerning the lack of experimentally observed isotope effect on the nonadiabatic transition rate: Although the nonadiabatic coupling is smaller in D2O due to smaller nuclear velocities, the smaller coupling in D2O adds coherently for a longer time than in H2O, leading to nearly identical nonadiabatic transition rates. The implications of this isotope dependence of the nonadiabatic transition rate on changes in the quantum decoherence time for electron transfer and other important chemical reactions are discussed.