Insights on the Marcus Equation, Derived Coefficients and Spaces

The dimensionless Marcus coefficients, β and γ, derived from the Marcus equation for activation free energy, are fundamentally connected to both reaction free energy and intrinsic activation free energy. Their introduction establishes a novel metric for classifying chemical reactions by defining reaction spaces that rationalize reactions based on the underlying energetic characteristics. This study extends beyond mere classification, introducing a comprehensive framework for representing chemical reactions within a parametric {β, γ} space, uniquely accommodating any reaction within a normalized range [0,1]. Through analysis of a data set comprising 5,269 dipolar [3 + 2] cycloaddition reactions, we demonstrate the framework's applicability, uncovering novel patterns and behaviors. These findings enhance the understanding of linear and quadratic free energy relationships, providing chemists with a powerful tool for reaction categorization and design, thereby advancing computational chemistry and reaction design methodologies.