On the design of optimal computer experiments to model solvent effects on reaction kinetics

Developing an accurate predictive model of solvent effects on reaction kinetics is a challenging task, yet it can play an important role in process development. While first-principles or machine learning models are often compute- or data-intensive, simple surrogate models, such as multivariate linear or quadratic regression models, are useful when computational resources and data are scarce. The judicious choice of a small set of training data, i.e., a set of solvents in which quantum mechanical (QM) calculations of liquid-phase rate constants are to be performed is critical to obtaining a reliable model. This is, however, made especially challenging by the highly irregular shape of the discrete space of possible experiments (solvent choices). In this work, we demonstrate that when choosing a set of computer experiments to generate training data, the D-optimality criterion value of the chosen set correlates well with the likelihood of achieving good model performance. With the Menschutkin reaction of pyridine and phenacyl bromide as a case study, this finding is further verified via the evaluation of the surrogate models regressed using D-optimal solvent sets generated from four distinct selection spaces. We also find that incorporating quadratic terms in the surrogate model and choosing the D-optimal solvent set from a selection space similar to the test set can significantly improve the accuracy of reaction rate constant predictions while using a small training dataset. Our approach holds promise for the use of statistical optimality criteria for other types of computer experiments, supporting the construction of surrogate models with reduced resource and data requirements.