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

Luning Zhao, Zhen Tao, Fabijan Pavošević, Andrew Wildman, Sharon Hammes-Schiffer, Xiaosong Li

Research output: Contribution to journalArticlepeer-review

52 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)4052-4058
Number of pages7
JournalJournal of Physical Chemistry Letters
Issue number10
StatePublished - May 21 2020
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Materials Science
  • Physical and Theoretical Chemistry


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