Nucleophilicity and Electrophilicity Parameters for Predicting Absolute Rate Constants of Highly Asynchronous...

Kinetics of the reactions of aryldiazomethanes (ArCHN₂) with benzhydrylium ions (Ar₂CH⁺) have been measured photometrically in dichloromethane. The resulting second-order rate constants correlate linearly with the electrophilicities E of the benzhydrylium ions which allowed us to use the correlation lg k = s_N( N + E) (eq 1) for determining the nucleophile-specific parameters N and s_N of the diazo compounds. UV-vis spectroscopy was analogously employed to measure the rates of the 1,3-dipolar cycloadditions of these aryldiazomethanes with acceptor-substituted ethylenes of known electrophilicities E. The measured rate constants for the reactions of the diazoalkanes with highly electrophilic Michael acceptors ( E > -11, for example 2-benzylidene Meldrum's acid or 1,1-bis(phenylsulfonyl)ethylene) agreed with those calculated by eq 1 from the one-bond nucleophilicities N and s_N of the diazo compounds and the one-bond electrophilicities of the dipolarophiles, indicating that the incremental approach of eq 1 may also be applied to predict the rates of highly asynchronous cycloadditions. Weaker electrophiles, e.g., methyl acrylate, react faster than calculated from E, N, and s_N, and the ratio of experimental to calculated rate constants was suggested to be a measure for the energy of concert Δ G^‡_concert = RT ln( k₂^exptl/ k₂^calcd). Quantum chemical calculations indicated that all products isolated from the reactions of the aryldiazomethanes with acceptor substituted ethylenes (Δ²-pyrazolines, cyclopropanes, and substituted ethylenes) arise from intermediate Δ¹-pyrazolines, which are formed through concerted 1,3-dipolar cycloadditions with transition states, in which the C-N bond formation lags behind the C-C bond formation. The Gibbs activation energies for these cycloadditions calculated at the PCM(UA0,CH₂Cl₂)/(U)B3LYP-D3/6-31+G(d,p) level of theory agree within 5 kJ mol^-1 with the experimental numbers showing the suitability of the applied polarizable continuum model (PCM) for considering solvation.