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 quantify the electron or electron acceptor power of a chemical group bonded to an aromatic ring. Their experimental values have been successfully used in a large variety of applications, but some of them may have inconsistent values or were not measured. For this reason, developing an accurate and consistent set of Hammett's values is paramount. In this work, we employed the machine learning (ML) regression algorithms Decision Tree Regressor, the neural network Multilayer Perceptron Regressor, and Lasso Lars IC in a cross-validation (CV) approach combined with quantum chemical calculations of atomic charges to estimate theoretically the new Hammett's constants for 90 chemical donor or acceptor groups by employing different types of quantum chemical atomic charges of the groups as input properties. New 219 sigma values, including previously unknown ones, are proposed for 90 chemical donor or acceptor groups by employing different types of quantum chemical atomic charges of the groups as input properties. The different substituent groups were bonded to benzene and meta- and para-substituted benzoic acid derivatives. Among the investigated atomic charge methods (Mulliken, Lwdin, Hirshfeld, and ChelpG), Hirshfeld's method showed the best regressions for most of the different kinds of sigma values. For each type of Hammett constant, linear expressions depending only on the atomic charges of the group were obtained. Correlation coefficients as high as 0.945, mean squared errors (MSE) as low as 0.004, and root mean square errors (RMSE) as low 0.062, were found. The ML approach, in most cases, showed very close predictions to the original experimental values, with the values from meta- and para-substituted benzoic acid derivatives showing the most accurate values. A new consistent set of Hammetts 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 paper, we investigated correlations between Machine Learning (ML)-based Hammett's constants (𝜎) 36 and different opto-and electrochemical properties of monoand di-substituted diketopyrrolopyrrole (DPP) derivatives. Density Functional Theory (DFT), Time-Dependent DFT (TDDFT), and the ab initio second-order algebraic diagrammatic construction (ADC(2)) method were employed.…”

“…Table 1 below lists the values of Hammett's constants for the 20 substituent groups plus the hydrogen used in this work. 36 The available values of 𝜎 in the literature [18][19][20]22,23,25,30,38,39 are collected in Table S1 of the Supporting Information (SI). Also, in the SI, one can find the structures of the investigated substituent groups in Figure S1.…”

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

“…All tables containing the atomic charges, atomic charge differences, predicted and available Hammett's constants, ORCA, Gaussian and ML inputs, and optimized geometries (.xyz files) are available in a ZENODO data repository. 85…”

“…The data underlying this study are available in the published article, the Supporting Information, and in Zenodo (ref 85). A version of this study was deposited as a preprint (ref 96).…”

Bottom-Up Atomistic Descriptions of Top-Down Macroscopic Measurements: Computational Benchmarks for Hammett Electronic Parameters

“…29 In this work, we explore the ability of various charge models from Classes II−IV (what we term a bottom-up description) to describe empirically determined (i.e., topdown) Hammett parameters. 30 Benchmark studies have been published comparing smaller subsets of charge values in their predictive ability against Hammett constants, with findings usually naming Hirshfeld charges as the best predictor. 31 Hirshfeld charges have also been shown to be good predictors of electrophilic and nucleophilic trends in contexts outside Hammett constants.…”