Uncertainty Quantification of Reactivity Scales

Abstract

​According to Mayr, polar organic synthesis can be rationalized by a simple empirical relationship linking bimolecular rate constants to as few as three reactivity parameters. Here, we propose an extension to Mayr’s reactivity method that is rooted in uncertainty quantification and transforms the reactivity parameters into probability distributions. Through uncertainty propagation, these distributions can be transformed into uncertainty estimates for bimolecular rate constants. Chemists can exploit these virtual error bars to enhance synthesis planning and to decrease the ambiguity of conclusions drawn from experimental data. We demonstrate the above at the example of the reference data set released by Mayr and co-workers [J. Am. Chem. Soc. 2001, 123, 9500; J. Am. Chem. Soc. 2012, 134, 13902]. As by-product of the new approach, we obtain revised reactivity parameters for 36 π-nucleophiles and 32 benzhydrylium ions.

Uncertainty Quantification of Reactivity Scales

“…For a critical analysis of log k, we recommend to explicitly calculate the empirical distribution of log k MPE by an interactive tool that can be accessed through the project-related GitLab repository. [6] We further encourage the community to assess future theoretical predictions of reactivity parameters in the context of parameter uncertainty (as discussed in this study, cf. Tables 3 and 4).…”

“…Reactionspecific weights can be accessed through the project-related GitLab repository. [6] For the weighting procedure to be sound from a statistical perspective, it is important that, after reaching self-consistency, the residuals of species S, d r f ðlog kÞg S , are zero-centered (m S ' 0, cf. Eq.…”

“…Parameter uncertainty estimates and histograms of empirical distributions can be accessed through the project-related GitLab repository. [6] A representative example is provided in Figure 6.…”

“…In this work, we introduce uncertainty quantification (UQ) into Mayr's reactivity approach. This combined approach, which we made openly available, [6] enables users to perform virtual measurements of log k, which are reported as expectation � deviation -just like physical measurements. Usually, virtual measurement uncertainty (or prediction uncertainty) is significantly larger than physical measurement uncertainty, which can be attributed to a more comprehensive list of uncertainty components including parameter uncertainty, model discrepancy/inadequacy, and numerical noise.…”

Quantitative Structure–Reactivity Relationships for Synthesis Planning: The Benzhydrylium Case

“…The subsequent descriptor calculations were performed with self-written Python code, which can be accessed through the project-related GitLab repository. 71 After preprocessing the data with Scikit-learn 0.24.2, 72 either ordinary least-squares MLR was performed with the same package or GPR with GPy (version 1.10.0). 73…”