Real-Space and Real-Time Propagation for Correlated Electron-Nuclear Dynamics Based on Exact Factorization

Area of Science:

• Quantum chemistry
• Theoretical chemistry
• Computational physics

Background:

• Simulating electron-nuclear dynamics is crucial for understanding molecular behavior.
• Existing methods using exact factorization suffer from numerical instability due to non-Hermitian terms.
• Accurate treatment of electron-nuclear correlation (ENC) is essential for reliable simulations.

Purpose of the Study:

• To develop a numerically stable method for real-space, real-time propagation of correlated electron-nuclear dynamics.
• To introduce a Hermitian-type ENC term to overcome numerical instabilities.
• To investigate the capture of quantum (de)coherence and nonadiabatic phenomena.

Main Methods:

• Proposed a Hermitian-type ENC term dependent on the electron density matrix and nuclear quantum momentum.
• Implemented real-space and real-time propagation for coupled electron-nuclear systems.
• Applied the method to a one-dimensional model Hamiltonian for excited state molecular dynamics.

Main Results:

• Achieved stable numerical propagation of electronic wave functions coupled to nuclear motion.
• Demonstrated the ability of the Hermitian ENC term to capture quantum (de)coherence.
• Successfully simulated nonadiabatic phenomena in excited state molecular dynamics.

Conclusions:

• The proposed Hermitian-type ENC term provides a stable and accurate approach for electron-nuclear dynamics.
• This method enables the study of quantum decoherence and nonadiabatic effects in molecular systems.
• The approach is extendable to many-body electronic states using real-time time-dependent density functional theory.