Marcus derived a curved equation from the analysis of crossing the reactant state parabola and the product state parabola (Figure ), and a follow-up work offers a thermodynamically rigorous description. This model predicts a Brønsted slope α near 0.5 for reactions close to zero driving force. A serious assumption in the Marcus formation of the curve is that the parabolae of the reactant and the product states have identical shape. These shapes are influenced by factors such as bonding, conjugation, sterics, solvation, and non-covalent interactions. 9 This oversimplification obscures the true origins of deviations from linear BEP relationships. Koeppl and Kresge demonstrated that allowing bond strengths and reaction distances to vary realistically produces a sigmoid Brønsted slope, better reflecting real systems. For example, hydrolysis reactions with observed Brønsted slopes of 0.6 at thermoneutral conditions deviate from Marcus predictions. Similarly, Richard and Jencks found significant deviations in Brønsted slopes for general base catalysis, attributing them to differential charge development in the transition state and reactant-product asymmetry. 12 These studies introduce reaction-specific corrections. Each of these formulations and models has made distinct assumptions. These formulations have significantly advanced our understanding of kinetic-thermodynamic relationships, but often address aspects in isolation.