Generalized spin mapping for quantum-classical dynamics

Area of Science:

• Quantum dynamics
• Chemical physics
• Computational chemistry

Background:

• Nonadiabatic dynamics are crucial in molecular processes.
• Previous spin-mapping methods were limited to two-level systems.
• Accurate simulation of complex quantum systems remains a challenge.

Purpose of the Study:

• Generalize the spin-mapping approach to N-level systems.
• Develop a method that preserves SU(N)-symmetry and avoids subspace leakage.
• Provide a computationally efficient and accurate tool for nonadiabatic dynamics.

Main Methods:

• Generalization of a spin-mapping technique to N-level systems.
• Mapping to a classical phase space preserving SU(N)-symmetry.
• Derivation of an N-dependent zero-point energy parameter determined by the Casimir invariant.

Main Results:

• Reproduces the Meyer-Miller-Stock-Thoss Hamiltonian without extended phase space.
• Enables approximation of correlation functions using classical trajectories.
• Benchmark calculations on the Fenna-Matthews-Olson complex show superior accuracy over Ehrenfest dynamics.

Conclusions:

• The generalized spin mapping offers a robust and accurate method for N-level nonadiabatic dynamics.
• This approach provides a significant improvement in accuracy compared to conventional methods.
• The method is computationally competitive with other advanced mapping techniques.