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 ΔG
‡
concert = RT ln(k
2
exptl/k
2
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.