Multistate ring polymer instantons and nonadiabatic reaction rates

Area of Science:

• Quantum chemistry
• Chemical dynamics
• Statistical mechanics

Background:

• Accurate calculation of quantum canonical partition functions is crucial for understanding chemical dynamics.
• Multistate systems present challenges due to complex electronic and nuclear interactions.

Purpose of the Study:

• To introduce and validate two novel multistate ring polymer instanton (RPI) formulations: Mean-Field (MF)-RPI and Mapping Variable (MV)-RPI.
• To assess their performance in calculating rate constants for systems exhibiting adiabatic and nonadiabatic dynamics.

Main Methods:

• Derivation of two RPI formulations from an exact path integral representation.
• Application to model two-state systems coupled to a single nuclear mode.
• Numerical computation and analysis of instanton paths and electronic state populations.

Main Results:

• MF-RPI shows good agreement with literature for symmetric systems and robust performance with driving forces.
• MV-RPI provides unique insights into electronic state population changes along the instanton path.
• Both methods confirm the existence of a zero-mode and identify true instanton solutions.
• MF-RPI accurately calculates rate constants across a wide range of coupling strengths.

Conclusions:

• The developed MF-RPI and MV-RPI methods offer accurate and robust approaches for studying quantum dynamics in multistate systems.
• These methods are particularly effective for both adiabatic and nonadiabatic regimes.
• The MF-RPI provides a reliable tool for calculating reaction rate constants.