Brazilian researchers have improved the 80-year-old Hammett equation using machine learning, unlocking unknown values for practical experiments. The Hammett equation, a chemical theory that explains the electron-donating or withdrawing nature of aromatic substituents, has been computationally analyzed to make it more precise. The equation calculates Hammett constants, which help determine the impact on reactivity from different substituents.
The team of Brazilian researchers, including Itamar Borges Jr, Julio Cesar Duarte, and Gabriel Monteiro-de-Castro from the Institute of Military Engineering in Brazil, used machine learning algorithms and available experimental values to produce a consistent set of different types of Hammett’s constants. The equation was originally developed in 1937 by Louis Hammett, a pioneer in the field of physical organic chemistry. Hammett recognized the relationship between the rate of hydrolysis of ethyl esters and the ionization of corresponding acids in water.
The Brazilian researchers utilized density functional theory (DFT) methods and machine learning algorithms to calculate new Hammett constants. By using a variety of substituents on benzene and benzoic acid derivatives, the team obtained atomic charges for the carbon atoms bonded to the analyzed groups. Machine learning techniques were then applied to produce 219 σ values, including 92 previously unknown values.
The researchers also developed simplified equations to obtain σ constants for new substituents that hadn’t been calculated before. These simplified equations, combined with knowledge of atomic charges obtained from other DFT calculations, were used to determine new σ constants.
The machine learning approach enabled the calculation of earlier values that had previously only been found experimentally. DFT calculations were used to determine the atomic charges, which were then used as inputs for the machine learning algorithm. The resulting Hammett constants corresponded to literature values from experimental results for the three substituents (-CCl, -NHCHO, and -NHCONH).
Experts in computational organic chemistry, such as Kristaps Ermanis from the University of Nottingham, believe that this work can provide previously unknown values in cases where data hasn’t been found before. However, the study’s accuracy is limited by the amount of available DFT data. Ermanis suggests that acquiring more DFT data could improve the accuracy of the machine learning method.
Matthew Grayson and his group at the University of Bath confirm the value of this work in allowing experimentalists to access previously unknown Hammett constants through simple and readily available atomic charge features.
Overall, the improvement of the Hammett equation through the application of machine learning and the calculation of new Hammett constants has the potential to enhance the understanding of chemical reactivity and facilitate practical experiments. With further advancements in DFT data and machine learning techniques, the accuracy and applicability of the equation can be improved.
