The real-time nuclear-electronic orbital (RT-NEO) approach provides an elegant framework for treating electrons and selected nuclei, typically protons, quantum mechanically in nonequilibrium dynamical processes. The dynamical interactions between the other nuclei and the electron-proton subsystem are described with the mixed quantum-classical NEO-Ehrenfest dynamics method. The NEO-Ehrenfest approach propagates the electrons and quantum protons in a time-dependent variational framework, while the remaining nuclei move classically on the corresponding average electron-proton vibronic surface. Our study shows that the NEO-Ehrenfest approach with a semiclassical traveling proton basis method yields accurate predictions of molecular vibrational frequencies. We also conduct NEO-Ehrenfest dynamics simulations to study an excited state intramolecular proton transfer process. These simulations reveal that nuclear quantum effects influence the predictions of proton transfer reaction rates and kinetic isotope effects due to the intrinsic delocalized nature of the quantum nuclear wave function. This work illustrates the importance of nuclear quantum effects in coupled nuclear-electronic dynamical processes and shows that the NEO-Ehrenfest approach can be a powerful tool to provide insights and predictions for these processes.

Ab initio nuclear-electronic orbital quantum dynamics

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