Tunneling Time and the Breakdown of Born-Oppenheimer Approximation

Area of Science:

• Physical Chemistry
• Molecular Biophysics
• Quantum Mechanics

Background:

• Electron transfer reactions are fundamental in biological and chemical systems.
• Long-distance electron tunneling is crucial for processes like photosynthesis and respiration.
• The Born-Oppenheimer approximation is commonly used but may fail in specific quantum tunneling scenarios.

Purpose of the Study:

• To investigate the impact of tunneling time on electron transfer rates.
• To analyze the breakdown of the Born-Oppenheimer approximation in electron tunneling.
• To understand the transition in distance dependence of electron transfer rates.

Main Methods:

• Theoretical analysis of electron tunneling dynamics.
• Examination of the Born-Oppenheimer approximation's validity.
• Study of the relationship between tunneling time and electron transfer coupling.

Main Results:

• Tunneling time can be comparable to nuclear vibrational periods.
• The Born-Oppenheimer approximation breaks down at the tails of electronic wave functions.
• A transition in the distance dependence of electron transfer rates is observed, separating Born-Oppenheimer and non-Born-Oppenheimer regimes.

Conclusions:

• Tunneling time is a critical factor influencing electron transfer mechanisms.
• The crossover in distance dependence is directly linked to the electron's tunneling time.
• This work provides insights into quantum effects governing long-distance electron transfer.