Data enhanced Hammett-equation: reaction barriers in chemical space.

O Anatole Von Lilienfeld,Guido Falk Von Rudorff,Marco Bragato

doi:10.1039/d0sc04235h

Abstract

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 SN2 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 SN2. 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.

Highlights

Chemical reactions are difficult to study and model from a theoretical point of view
We use global regression to optimize Hammett parameters r and s in two experimental datasets, as well as in a synthetic dataset consisting of computational activation energies of $2400 SN2 reactions, with various nucleophiles and leaving groups (–H, –F, –Cl, –Br) and functional groups (–H, –NO2, –CN, –NH3, –CH3)
We extended the Hammett equation to a chemical space that is outside the scope of the original model by working on a computational data set of SN2 reactions on small molecules with an ethylene scaffold

Summary

Introduction

Chemical reactions are difficult to study and model from a theoretical point of view. K is either the equilibrium or rate constant for a substituted reactant, K0 refers to the unsubstituted reactant, r is a constant that depends only on the reaction, taking into account conditions such as temperature and solvent and s depends only on the type of substituent and its position on the molecule. This model is compelling since it gives an intuitive concept of electron donating and electron withdrawing effects[3,4,5,6] in the context of free energy differences. R has shown to be hardly transferable and even exhibit an inconsistent temperature dependence.[3]

Methods

Results

Conclusion