In the 2010s, machine learning emerged as a powerful tool for guiding catalyst discovery. More specifically, machine learning models such as multivariate linear regression have been applied to study the linear free energy relationships (LFERs) in catalytic asymmetric organic reactions. These relationships describe the effects that ligand substituents have on reaction outcomes, namely enantioselectivity, and can be extrapolated to predict the performance of ligands outside the known dataset. However, machine learning approaches require well-defined molecular descriptors for the steric and electronic properties of ligands in order to make accurate predictions. Sterimol parameters emerged as a good candidate for quantifying the steric environment induced by ligands.
In Matthew Sigmans seminal work published in 2012, Sterimol parameters were implemented in asymmetric catalysis for the first time in the analysis of an asymmetric Nozaki-Hiyama-Kishi reaction (Figure 2). In initial ligand screening the team found that the steric hindrance of the ester substituent on the oxazoline-proline-based ligand scaffold was pertinent to the overall enantioselectivity of the reaction. When attempting to use the Charton modification of the Tafts parameters for probing the LFERs, they observed breaks in linearity with respect to several "isopropyl-like" substituents with large Charton values (Figure 3, left). However, this break did not exist when the Sterimol B parameter was used instead. All of the substituents studied demonstrated good linear correlation between their Sterimol B value and the reaction enantioselectivity (Figure 3, right).
Sigman attributed the superiority of Sterimol B in this prediction over Charton values to the inherent limitations of the experimentally based Charton values. He noted that the Charton model assumes that the substituent can rapidly rotate around the X-axis. However, in the context of asymmetric catalysis, only one conformation of the substituent provides the transition state with lowest energy, which leads to the formation of the major enantiomer. Therefore, Charton values tend to overestimate the steric effects of substituents that are non-symmetrical around the X-axis, because they can only describe the net conformer of a certain substituent. Sterimol parameters, in contrast, are not derived from experimental results, which are sometimes idiosyncratic as a result of distinct mechanisms. By virtue of their origin, namely quantum chemical calculations, Sterimol parameters can more accurately interpret the steric effects of a substituent in its static form. Sterimol B, in particular, can approximate the steric repulsive effect of the exact conformer with the lowest energy. Table 1 demonstrates the differences of the two parameters. For example, while they have the same Sterimol B values, the Charton value of the isopropyl-like CHPr substituent is significantly larger than that of i-Pr due to overestimation. This explains why better correlation was obtained with Sterimol B.
To date, the Sigman lab has applied Sterimol parameters in the analysis of several catalytic asymmetric reactions. Sterimol parameters are also utilized by chemists worldwide to improve the enantioselectivity for various catalytic reactions, such as conjugative addition, Tsuji-Trost reaction, C–H activation, cyclopropanation, etc.