A modified two-sphere model for solvent reorganization energy in electron transfer

Area of Science:

• Physical Chemistry
• Theoretical Chemistry
• Computational Chemistry

Background:

• Solvent reorganization energy is crucial for understanding electron transfer processes.
• Existing models, like Marcus' theory, provide a framework but may require refinement for specific solvent polarities.
• Accurate calculation of reorganization energy is essential for predicting reaction rates in solution.

Purpose of the Study:

• To formulate solvent reorganization energy within classical thermodynamics.
• To derive a new expression for solvent reorganization energy that accounts for solvent polarity.
• To validate the modified formula by applying it to experimental electron transfer processes.

Main Methods:

• Formulation of solvent reorganization energy using classical thermodynamics and a constrained equilibrium state.
• Derivation of the reorganization energy using the first law of thermodynamics.
• Application of the two-sphere model approximation for the final formula.
• Testing the derived formula against experimental data for electron transfer reactions.

Main Results:

• Solvent reorganization energy is identified as the polarization cost for the inertial part of polarization.
• A modified formula for solvent reorganization energy is derived: λ(0) = Δq(2)/2[1/r(D) + 1/r(A) - 2/d][(ε(-1)(op) - ε(-1)(s))/(1 - ε(-1)(s))].
• The modified formula includes a factor dependent on solvent polarity, amending Marcus' model.
• The derived formula successfully reproduces experimental observations for two electron transfer processes.

Conclusions:

• The classical thermodynamic framework provides a robust method for deriving solvent reorganization energy.
• The new formula offers a more accurate prediction of solvent reorganization energy by incorporating solvent polarity.
• The findings have implications for theoretical and computational chemistry, particularly in modeling electron transfer reactions.