Functional Mode Electron-Transfer Theory.

Area of Science:

• Physical Chemistry
• Quantum Mechanics
• Spectroscopy

Background:

• Electron transfer (ET) is fundamental to chemical and biological processes.
• Understanding the interplay between electronic transitions and molecular vibrations is crucial for ET theories.
• Existing models often simplify the complex vibrational landscape influencing ET rates.

Purpose of the Study:

• To develop a quantitative method correlating electron transfer with molecular vibration.
• To derive electron transfer rates considering multiple vibrational modes under varying vibronic coupling.
• To validate a new functional mode electron-transfer theory using a betaine-30 solvated system.

Main Methods:

• Identified reaction coordinate by maximizing Pearson's correlation coefficient between atomic displacement and diabatic energy gap.
• Derived electron transfer rates in the fast molecular vibration limit for strong and weak vibronic coupling.
• Applied constrained density functional theory (DFT) to determine electronic coupling strength.

Main Results:

• Seven essential vibrational modes of betaine-30 account for over 60% of reorganization energy.
• Electron transfer is primarily driven by intramolecular quantum tunneling due to fast vibrational modes.
• The reaction operates in the inverted Marcus region with a significant Franck-Condon factor, yielding a calculated rate of 0.30 ps⁻¹ at 300 K.

Conclusions:

• The developed theory accurately predicts electron transfer rates, validating its approach.
• Quantum tunneling significantly contributes to electron transfer, even in systems with large driving forces.
• The study highlights the importance of identifying essential vibrational modes for accurate ET rate calculations.