Revisiting Mayr's reactivity database: expansion, sensitivity analysis, and uncertainty quantification

Abstract

Rate constants for reactions between nucleophiles and electrophiles can be efficiently estimated by the Mayr–Patz equation, log k = s_N(N + E), which relies on three reactivity parameters as input. Utilising this equation, the Mayr group established a reference set for determining reactivity parameters of uncharged π-nucleophiles with positively charged electrophiles (benzhydrylium ions). Subsequently, the initial reference set was expanded by uncharged quinone methide electrophiles and carbanionic nucleophiles, resulting in an extension of the reactivity scales toward stronger nucleophiles and weaker electrophiles. For this work, the extended reference set was systematically analysed by automated algorithms to identify key aspects for future expansions. Lower bounds for reaction-to-species and reaction-to-parameter ratios were determined, ensuring minimal overfitting during parameter optimisation. It is also shown that the removal of electrophilic or nucleophilic species with high species-specific model errors in their predicted rate constants had positive results on the overall model error, with one species having a particularly great influence. These findings and the proposed methods may help future efforts to determine reliable data sets for the construction of Mayr-type reactivity scales.