Mixed quantum-classical approach to model non-adiabatic electron-nuclear dynamics: Detailed balance and improved...

Area of Science:

• Quantum Chemistry
• Theoretical Chemistry
• Chemical Physics

Background:

• Accurately describing coupled electron-nuclear dynamics is essential for understanding chemical reactions.
• Existing methods often struggle with decoherence effects and non-Markovian behavior.

Purpose of the Study:

• To develop a novel density matrix formalism for coupled electron-nuclear dynamics.
• To investigate the influence of decoherence on electronic transitions and nuclear motion.
• To establish a theoretical framework applicable to both Markovian and non-Markovian regimes.

Main Methods:

• Introduction of an effective Hamiltonian incorporating electronic transitions and nuclear fluctuations.
• Derivation of equations of motion for electronic occupation numbers and nuclear coordinates/momenta.
• Development of a surface hopping algorithm and incorporation of virtual nuclear wave packets to model decoherence.

Main Results:

• Demonstration of Markovian dynamics for electronic occupation numbers in the strong decoherence limit.
• Observation of asymmetric transition rates, satisfying detailed balance in thermal equilibrium.
• Accurate numerical simulations achieved through phase shifts from virtual wave packets, also ensuring detailed balance.

Conclusions:

• The developed formalism provides a robust framework for studying electron-nuclear dynamics, particularly under decoherence.
• The method accurately captures key physical phenomena like detailed balance.
• The approach offers improved accuracy and applicability to complex chemical systems.