Data enhanced Hammett-equation: reaction barriers in chemical space

It is intriguing how the Hammett equation enables control of chemical reactivity throughout chemical space by separating the effect of substituents from chemical process variables, such as reaction mechanism, solvent, or temperature. We generalize Hammett's original approach to predict potential energies of activation in non aromatic molecular scaffolds with multiple substituents. We use global regression to optimize Hammett parameters ρ and σ in two experimental datasets (rate constants for benzylbromides reacting with thiols and ammonium salt decomposition), as well as in a synthetic dataset consisting of computational activation energies of ∼2400 S_N2 reactions, with various nucleophiles and leaving groups (-H, -F, -Cl, -Br) and functional groups (-H, -NO₂, -CN, -NH₃, -CH₃). Individual substituents contribute additively to molecular σ with a unique regression term, which quantifies the inductive effect. The position dependence of substituents can be modeled by a distance decaying factor for S_N2. Use of the Hammett equation as a base-line model for Δ-machine learning models of the activation energy in chemical space results in substantially improved learning curves reaching low prediction errors for small training sets.