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.

The computational road to reactivity scales

“…Box 2 describes how the reactivity parameters E, N, and s N are determined on the basis of experimental (or, alternatively but yet hypothetically, computational) log k data. 6,42,43 This section, on the other hand, discusses approaches to determine these parameters by means of regression analysis. The motivation to do so stems from the fact that determining reactivity parameters from log k is expensive for two reasons.…”

“…To avoid redundant experimental work, optimal-design approaches coupled with uncertainty quantification can guide the planning of new experiments. 6 In time-resolved (non-equilibrium) contexts, such as molecular dynamics simulations, different challenges arise since log k is an intrinsically time-averaged quantity. In pioneering work on this topic, Hoffmann et al examined the impact of structural fluctuations on the electrophilicity parameter of Michael acceptors.…”

“…To avoid redundant experimental work, optimal-design approaches coupled with uncertainty quantification can guide the planning of new experiments. 6…”

“…The Eyring equation [eqn (5)] is the common link between the molar activation free energy in solution -obtained Table 1 An example of reversed selectivity ordering for species with reactivity parameters documented in previous work. 6 While the weaker electrophile E15 is more selective toward the stronger but less sensitive nucleophile N7, the stronger electrophile E20 is more selective toward the weaker but more sensitive nucleophile N40 by quantum chemical calculations -, DG z sol , and the rate constant, k.…”

Prediction uncertainty validation for computational chemists

“…[2][3][4][5][6][7][8] This is also the case for quantum chemistry, when a level of confidence on predictions is sought out. 1,[9][10][11][12][13][14][15][16][17][18][19] In these contexts, the validation of UQ outputs is essential to enable their re-use in applications such as active learning or actionable predictions for the industry.…”