Thermal equilibrium in coupled trajectory mixed quantum-classical dynamics.

Area of Science:

• Quantum dynamics
• Chemical physics
• Computational chemistry

Background:

• Detailed balance is crucial for accurate thermalization in quantum-classical non-adiabatic dynamics.
• The physical mechanism behind detailed balance in these methods remains poorly understood.
• Existing methods often struggle to achieve detailed balance from first principles.

Purpose of the Study:

• To investigate the ability of coupled trajectory mixed quantum-classical (CTMQC) dynamics to achieve detailed balance.
• To develop and evaluate a new variant of CTMQC for improved thermalization.
• To elucidate the physical mechanisms contributing to detailed balance in CTMQC.

Main Methods:

• Derivation of CTMQC from the exact factorization theorem of quantum mechanics.
• Comparison of a novel CTMQC variant (energy conserved per trajectory) with conventional CTMQC (energy conserved across ensemble) and Ehrenfest dynamics.
• Simulations on Tully models and the double arch model to assess electronic populations, coherence, and energy convergence.

Main Results:

• Conventional CTMQC (CTMQC-E) fails to reproduce detailed balance, similar to Ehrenfest dynamics.
• The new CTMQC variant shows significant improvement in detailed balance compared to Ehrenfest dynamics.
• This variant demonstrates convergence of mean electronic potential energy with increasing energy levels and retains good accuracy for electronic populations and coherence against exact quantum dynamics.

Conclusions:

• A novel CTMQC variant, conserving energy independently on each trajectory, substantially improves detailed balance in quantum dynamics.
• Geometric contributions from quantum momentum to the nuclear force are identified as the mechanism driving this improvement.
• These findings suggest CTMQC is a promising method for condensed phase simulations requiring accurate thermalization.