Heterogeneous Intramolecular Electric Field as a Descriptor of Diels-Alder Reactivity

External electric fields have proven to be an effective tool in catalysis, on par with pressure and temperature, affecting the thermodynamics and kinetics of a reaction. However, fields in molecules are complicated heterogeneous vector objects, and there is no universal recipe for grasping the exact features of these fields that implicate reactivity. Herein, we demonstrate that topological features of the heterogeneous electric field within the reactant state and of the quantum mechanical electron density-a scalar reporter on the field experienced by the system-can be identified as rigorous descriptors of the reactivity to follow. We scrutinize specifically the Diels-Alder reaction. Its 3D nature and the lack of a singular directionality of charge movement upon barrier crossing make the effect of the electric field not obvious. We show that the electric field topology around the dienophile double bond and the associated changes in the topology of the electron density in this bond are predictors of the reaction barrier. They are also the metrics to rationalize and predict how the external field would inhibit or enhance the reaction. The findings pave the way toward designing external fields for catalysis and reading the reactivity without an explicit mechanistic interrogation, for a variety of reactions.