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We present a kinetic analysis of the non-adiabatic decay mechanism of an excited state hydrated electron to the ground state. The theoretical treatment is based on a quantized, gap dependent golden rule rate constant formula which describes the non-adiabatic transition rate between two quantum states. The rate formula is expressed in terms of quantum time correlation functions of the energy gap, and of the non-adiabatic coupling. These gap dependent quantities are evaluated from three different sets of mixed quantum-classical molecular dynamics simulations of a hydrated electron equilibrated a) in its ground state, b) in its first excited state, and c) on a hypothetical mixed potential energy surface which is the average of the ground and the first excited electronic states. The quantized, gap-dependent rate results are applied in a phenomenological kinetic equation which provides the survival probability function of the excited state electron. Although the lifetime of the equilibrated excited state electron is computed to be very short (well under 100 fs), the survival probability function for the non-equilibrium process in pump-probe experiments yields an effective excited state lifetime of around 300 fs, a value consistent with the findings of several experimental groups and previous theoretical estimates

Nuclear quantum effects on the nonadiabatic decay mechanism of an excited hydrated electron