Toward the design of chemical reactions: Machine learning barriers of competing mechanisms in reactant space

The interplay of kinetics and thermodynamics governs reactive processes, and their control is key in synthesis efforts. While sophisticated numerical methods for studying equilibrium states have well advanced, quantitative predictions of kinetic behavior remain challenging. We introduce a reactant-to-barrier (R2B) machine learning model that rapidly and accurately infers activation energies and transition state geometries throughout the chemical compound space. R2B exhibits improving accuracy as training set sizes grow and requires as input solely the molecular graph of the reactant and the information of the reaction type. We provide numerical evidence for the applicability of R2B for two competing text-book reactions relevant to organic synthesis, E2 and S N 2, trained and tested on chemically diverse quantum data from the literature. After training on 1-1.8k examples, R2B predicts activation energies on average within less than 2.5 kcal/mol with respect to the coupled-cluster singles doubles reference within milliseconds. Principal component analysis of kernel matrices reveals the hierarchy of the multiple scales underpinning reactivity in chemical space: Nucleophiles and leaving groups, substituents, and pairwise substituent combinations correspond to systematic lowering of eigenvalues. Analysis of R2B based predictions of ∼11.5k E2 and S N 2 barriers in the gas-phase for previously undocumented reactants indicates that on average, E2 is favored in 75% of all cases and that S N 2 becomes likely for chlorine as nucleophile/leaving group and for substituents consisting of hydrogen or electron-withdrawing groups. Experimental reaction design from first principles is enabled due to R2B, which is demonstrated by the construction of decision trees. Numerical R2B based results for interatomic distances and angles of reactant and transition state geometries suggest that Hammond's postulate is applicable to S N 2, but not to E2.