Abstract

The dimensionless Marcus coefficients, beta and gamma, 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 {beta, gamma} 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.