On the calculation of quantum mechanical electron transfer rates

Area of Science:

• Chemical Physics
• Quantum Mechanics

Background:

• Electron transfer reactions are fundamental in chemistry and biology.
• Accurately calculating electron transfer rates is crucial for understanding these processes.
• Current methods often struggle with varying electronic coupling strengths.

Purpose of the Study:

• To develop a simple, accurate interpolation formula for electron transfer rates.
• To bridge the gap between different theoretical limits (e.g., adiabatic and non-adiabatic).
• To provide a computationally efficient method for predicting reaction rates.

Main Methods:

• Developed a novel interpolation formula requiring only Fermi's golden rule and Born-Oppenheimer rates.
• Validated the formula using a one-dimensional scattering problem with exact quantum mechanical calculations.
• Combined the formula with Wolynes theory and ring polymer molecular dynamics (RPMD) approximations.
• Tested against hierarchical equations of motion (HEOM) for spin-boson models.

Main Results:

• The interpolation formula accurately predicts electron transfer rates as a function of electronic coupling.
• The formula successfully incorporates effects of nuclear tunneling, zero-point energy, and solvent friction.
• Performance was comparable to established methods (RPMD and Wolynes theory) in their respective limits.

Conclusions:

• The proposed interpolation formula offers a versatile and accurate approach to calculating electron transfer rates.
• It provides a reliable method for systems with arbitrary electronic coupling strengths.
• This work advances the computational modeling of condensed-phase electron transfer reactions.