Nucleophilicity and Electrophilicity Parameters for Predicting Absolute Rate Constants of Highly Asynchronous 1,3-Dipolar Cycloadditions of Aryldiazomethanes

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 = sN(N + E) (eq 1) for determining
the nucleophile-specific parameters N and sN 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 sN 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 sN, and the
ratio of experimental to calculated rate constants was suggested to
be a measure for the energy of concert ΔG‡concert = RT ln­(k2exptl/k2calcd). 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.