Mixed semiclassical-classical propagators for the Wigner phase space representation.

Area of Science:

• Physical Chemistry
• Quantum Dynamics
• Computational Chemistry

Background:

• Phase-space semiclassical (SC) propagators are essential for simulating quantum systems.
• Previous work established phase-space SC propagators, requiring further approximations for mixed systems.

Purpose of the Study:

• To formulate mixed semiclassical-classical (SC-Cl) propagators by approximating phase-space SC propagators.
• To investigate the accuracy and efficiency of the derived SC-Cl propagators compared to full methods.

Main Methods:

• Developed SC-Cl van Vleck and Herman-Kluk (HK) propagators by applying stationary phase approximation to classical degrees of freedom.
• Divided system degrees of freedom into semiclassical and classical components.
• Numerically compared the full HK propagator with the SC-Cl HK propagator.

Main Results:

• Stationary phase approximation on phase-space van Vleck propagator yields classical propagation.
• SC-Cl propagators decompose into SC and classical parts for non-interacting systems.
• SC-Cl HK propagator shows comparable accuracy to the full HK propagator but with faster convergence.
• SC-Cl HK can be more accurate than the full HK for a finite number of classical trajectories due to a balance of accuracy and efficiency.

Conclusions:

• Mixed semiclassical-classical propagators offer a computationally efficient approach for quantum dynamics.
• The SC-Cl HK propagator presents a promising alternative, balancing accuracy and computational cost.
• These methods are valuable for simulating complex chemical systems where quantum and classical behaviors coexist.