Electron tunneling dynamics in anharmonic bath

Area of Science:

• Quantum Mechanics
• Chemical Physics
• Theoretical Chemistry

Background:

• Understanding particle tunneling in complex environments is crucial for various chemical and physical processes.
• Anharmonic baths introduce significant complexity to standard quantum mechanical models.
• Previous models often struggle to accurately capture temperature dependencies in transition probabilities.

Purpose of the Study:

• To determine the tunneling transition probability for a particle interacting with an anharmonic bath.
• To develop a general expression for transition probability using Keldysh functions.
• To investigate the temperature dependence of key energetic parameters like reorganization energy and reaction heat.

Main Methods:

• Application of the time-dependent Hartree approximation.
• Calculation of transition probability using the noninteracting-blip approximation.
• Expression of reorganization energy and renormalized reaction heat using correlation matrices for solvent and internal modes.

Main Results:

• A general expression for tunneling transition probability is derived in terms of medium Keldysh functions.
• The noninteracting-blip approximation reveals that the rate constant is independent of activation energy at high temperatures.
• Both reorganization energy (E(r)) and renormalized reaction heat (ε) are found to be temperature-dependent in quantum and classical regimes.

Conclusions:

• The time-dependent Hartree and noninteracting-blip approximations provide a robust framework for studying tunneling in anharmonic systems.
• The temperature dependence of reorganization energy and reaction heat highlights the importance of environmental factors.
• This work offers insights into the dynamics of quantum transitions in complex, dissipative environments.