Real-Time Time-Dependent Nuclear−Electronic Orbital Approach: Dynamics beyond the Born–Oppenheimer Approximation

The
quantum mechanical treatment of both electrons and nuclei is
crucial in nonadiabatic dynamical processes such as proton-coupled
electron transfer. The nuclear−electronic orbital (NEO) method
provides an elegant framework for including nuclear quantum effects
beyond the Born–Oppenheimer approximation. To enable the study
of nonequilibrium properties, we derive and implement a real-time
NEO (RT-NEO) approach based on time-dependent Hatree-Fock or density
functional theory, in which the electronic and nuclear degrees of
freedom are propagated in a time-dependent variational framework.
Nuclear and electronic spectral features can be resolved from the
time-dependent dipole moment computed using the RT-NEO method. The
test cases show the dynamical interplay between the quantum nuclei
and the electrons through vibronic coupling. Moreover, vibrational
excitation in the RT-NEO approach is demonstrated by applying a resonant
driving field, and electronic excitation is demonstrated by simulating
excited state intramolecular proton transfer. This work shows that
the RT-NEO approach is a promising tool to study nonadiabatic quantum
dynamical processes within a time-dependent variational description
for the coupled electronic and nuclear degrees of freedom.