Insights on the Marcus Equation, Derived Coefficients and Spaces

Area of Science:

• Physical Organic Chemistry
• Computational Chemistry
• Chemical Kinetics

Background:

• The Marcus equation relates activation free energy to reaction free energy.
• Classifying chemical reactions based on energetic properties is crucial for understanding reaction mechanisms.
• Existing methods may not fully capture the complex interplay between intrinsic and overall reaction energetics.

Purpose of the Study:

• To introduce dimensionless Marcus coefficients (β and γ) as a novel metric for reaction classification.
• To develop a comprehensive parametric framework ({β, γ} space) for representing chemical reactions.
• To demonstrate the framework's utility in analyzing reaction patterns and enhancing reaction design.

Main Methods:

• Derivation of dimensionless Marcus coefficients (β and γ) from the Marcus equation.
• Development of a normalized parametric space [{β, γ} space] for reaction representation.
• Analysis of a large dataset of 5,269 dipolar [3 + 2] cycloaddition reactions.

Main Results:

• Established a fundamental connection between Marcus coefficients, reaction free energy, and intrinsic activation free energy.
• Demonstrated the framework's ability to uniquely accommodate any reaction within a normalized [0,1] range.
• Uncovered novel patterns and behaviors in dipolar [3 + 2] cycloadditions using the {β, γ} space.

Conclusions:

• The {β, γ} space provides a powerful tool for categorizing chemical reactions based on energetic characteristics.
• The framework enhances the understanding of linear and quadratic free energy relationships.
• This approach advances computational chemistry and reaction design methodologies by offering a new perspective on reaction energetics.