A Practical Approach to Wave Function Propagation, Hopping Probabilities, and Time Steps in Surface Hopping...

Area of Science:

• Computational Chemistry
• Quantum Dynamics
• Theoretical Chemistry

Background:

• The fewest switches surface hopping (FSSH) algorithm is crucial for simulating quantum dynamics in complex systems.
• Accurate wave function propagation and hopping probability calculations are essential for FSSH reliability.
• Existing FSSH methods struggle with systems featuring numerous electronic states and trivial crossings.

Purpose of the Study:

• To compare established wave function propagation and hopping probability calculation methods within FSSH.
• To identify robust schemes for accurately simulating quantum dynamics in challenging multi-state systems.
• To develop a computationally feasible approach for achieving high accuracy in FSSH simulations.

Main Methods:

• Evaluation of several established FSSH approaches for wave function propagation and hopping probability calculation.
• Investigation of single versus multiple time-step strategies for FSSH simulations.
• Development and application of a robust scheme combining local diabatic and adiabatic interpolation methods.

Main Results:

• Single time-step FSSH approaches fail to accurately capture dynamics unless the time step approaches zero.
• A robust multi-time-step scheme dynamically selects quantum time steps for improved accuracy and efficiency.
• Scattering calculations confirm the feasibility of using large classical time steps with the proposed scheme.

Conclusions:

• The developed robust scheme significantly enhances the accuracy and efficiency of FSSH simulations.
• This approach effectively handles complex systems with multiple electronic states and trivial crossings.
• The findings offer broad applicability for future quantum dynamics simulations.