Multi-state trajectory approach to non-adiabatic dynamics: General formalism and the active state trajectory...

Area of Science:

• Quantum Chemistry
• Theoretical Chemistry
• Chemical Physics

Background:

• Simulating coupled nuclear-electronic dynamics is crucial for understanding chemical reactions.
• Existing methods like Ehrenfest and trajectory surface hopping (TSH) have limitations.
• The multi-state Meyer-Miller (MM) model provides a foundation for new simulation techniques.

Purpose of the Study:

• To derive a general theoretical framework for the multi-state trajectory (MST) approach.
• To develop a new approximation, the active state trajectory (AST), for efficient simulations.
• To provide a robust alternative to current dynamics simulation methods.

Main Methods:

• Derivation of equations of motion for coupled nuclear-electronic dynamics from the time-dependent Schrödinger equation.
• Development of the multi-state Meyer-Miller (MM) model.
• Implementation of the general MST formalism and the active state trajectory (AST) approximation.
• Comparison with exact quantum calculations and other established methods.

Main Results:

• The MST formalism provides a unified framework, incorporating diabatic and adiabatic representations.
• The AST approximation offers a computationally efficient approach using a single nuclear trajectory.
• The MST and AST methods demonstrate good numerical stability and accuracy, comparable to exact quantum calculations.
• Successful application to benchmark systems with non-adiabatic transitions and conical intersections.

Conclusions:

• The derived MST framework offers a consistent and stable description of coupled nuclear-electronic dynamics.
• The AST approximation presents a viable and accurate alternative to Ehrenfest and TSH methods.
• The MST approach, particularly AST, shows significant potential for advancing the simulation of complex chemical processes.