Machine Learning Determination of New Hammett’s Constants for meta- and para-Substituted Benzoic Acid Derivatives Employing Quantum Chemical Atomic Charge Methods

Abstract

Hammett's constants σ quantify the electron donor or electron acceptor power of a chemical group bonded to an aromatic ring. Their experimental values have been successfully used in many applications, but some are inconsistent or not measured. Therefore, developing an accurate and consistent set of Hammett's values is paramount. In this work,we employed different types of machine learning (ML) algorithms combined with quantum chemical calculations of atomic charges to predict theoretically new Hammett's constants σ m , σ p , σ m 0 , σ p 0 , σ p + , σ p − , σ R , and σ I for 90 chemical donor or acceptor groups. New σ values (219), including previously unknown 92, are proposed. The substituent groups were bonded to benzene and meta-and para-substituted benzoic acid derivatives. Among the charge methods (Mulliken, Loẅdin, Hirshfeld, and ChelpG), Hirshfeld showed the best agreement for most kinds of σ values. For each type of Hammett constant, linear expressions depending on carbon charges were obtained. The ML approach overall showed very close predictions to the original experimental values, with meta-and para-substituted benzoic acid derivative values showing the most accurate values. A new consistent set of Hammett's constants is presented, as well as simple equations for predicting new values for groups not included in the original set of 90.

A Hammett's analysis of the substituent effect in functionalized diketopyrrolopyrrole (DPP) systems: Optoelectronic properties and intramolecular charge transfer effects

“…In this article, we investigated correlations between our set of ML-based Hammett's constants (σ) 40 and different opto-and electrochemical properties of mono-and di-substituted DPP derivatives.…”

“…In this article, we investigated correlations between our set of ML‐based Hammett's constants () 40 and different opto‐ and electrochemical properties of mono‐ and di‐substituted DPP derivatives. Density functional theory (DFT), time‐dependent DFT (TDDFT), and the ab initio second‐order algebraic diagrammatic construction (ADC(2)) method were employed.…”

“…Thus, some efforts have been made to find ways to calculate them. In this work, we used our machine learning (ML) 40 set of Hammett's constants for substituents with unknown and recomputed others to produce more consistent new sets. Our ML procedure employed the quantum chemical Hirshfeld atomic charges 41 of different carbon atoms in 180 meta ‐ and para ‐substituted benzoic acid derivatives, generating a consistent set of constants for general use.…”

“…Table 1 lists the values of our Hammett's constants for the 20 substituent groups plus the hydrogen used in this work. 40 The available experimental values of σ in the literature [18][19][20]22,24,25,35,42,43 are collected in Table S1 of the Supporting Information (SI). The chemical structures of the investigated substituent groups are depicted in Figure S1.…”

“…T A B L E 1 ML-based Hammett's constants 40 for the set of different substituents used in this work. F I G U R E 1 DPP core with the position of the substituent group X indicated.…”