A mapping approach to surface hopping.

Area of Science:

• Computational Chemistry
• Quantum Dynamics
• Molecular Modeling

Background:

• Nonadiabatic dynamics are crucial in many chemical processes.
• Existing methods like Fewest-Switches Surface Hopping (FSSH) have limitations in accuracy and consistency.
• Quasiclassical mapping approaches offer an alternative but often lack rigorous quantum mechanical grounding.

Purpose of the Study:

• To develop a novel computational method that combines the strengths of FSSH and quasiclassical mapping dynamics.
• To ensure internal consistency between electronic and nuclear degrees of freedom during nonadiabatic transitions.
• To provide a rigorously derivable method from quantum mechanics with systematic convergence properties.

Main Methods:

• Developed the Mapping Approach to Surface Hopping (MASH) method.
• Propagated nuclear trajectories on the active adiabatic potential-energy surface.
• Implemented deterministic surface transitions based on electronic mapping variables in phase space.
• Derived MASH from the quantum-classical Liouville equation (QCLE), including momentum rescaling and frustrated hops.
• Introduced a quantum-jump procedure for systematic accuracy convergence and decoherence corrections.

Main Results:

• MASH ensures internal consistency between electronic and nuclear motion.
• The method is rigorously derived from quantum mechanics (QCLE).
• Simulations on model systems demonstrate MASH consistently outperforms FSSH in accuracy.
• MASH achieves higher accuracy at a comparable computational cost to FSSH.

Conclusions:

• MASH provides a more accurate and consistent description of nonadiabatic molecular dynamics compared to FSSH.
• The rigorous quantum mechanical foundation allows for systematic improvements and error control.
• This method offers a powerful new tool for simulating complex chemical reactions and photophysical processes.