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

Article abstract of DOI:10.1021/jacs.8b09995

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 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 (²-pyrazolines, cyclopropanes, and substituted ethylenes) arise from intermediate ¹-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.

Full text of DOI:10.1021/jacs.8b09995

Article
pubs.acs.org/JACS
Cite This: J. Am. Chem. Soc. XXXX, XXX, XXX−XXX
Nucleophilicity and Electrophilicity Parameters for Predicting
Absolute Rate Constants of Highly Asynchronous 1,3-Dipolar
Cycloadditions of Aryldiazomethanes
Harish Jangra,† Quan Chen,†,‡ Elina Fuks, Ivo Zenz,§ Peter Mayer, Armin R. Ofial,* Hendrik Zipse,*
and Herbert Mayr*
̈
̈
̈
Department Chemie, Ludwig-Maximilians-Universitat Munchen, Butenandtstr. 5-13, 81377 Munchen, Germany
S
* Supporting Information
ABSTRACT: 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 cyclo-
additions of these aryldiazomethanes with acceptor-substi-
tuted 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‡
= RT ln(k2exptl/k2calcd). Quantum chemical
concert
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.
predicting and analyzing cycloaddition reactivities on the
basis of linear-free-energy relationships.
INTRODUCTION
■
1,3-Dipolar cycloadditions (Huisgen reactions) represent the
most general approach to 5-membered heterocycles.1 They
have been used for the total synthesis of natural products2 and
for the preparation of organic functional materials.3 The
copper-catalyzed reaction of azides (R-N3) with alkynes has
become the most generally applicable click reaction.4 Although
a concerted mechanism with a cyclic transition state has been
well established for most Huisgen reactions,5−7 evidence for a
stepwise course via diradical or zwitterionic intermediates has
been reported in several cases.6,8 Since the late 1970s,
reactivities and regioselectivities of cycloaddition reactions
have commonly been interpreted on the basis of perturbational
molecular orbital theory.7,9 Recently, the groups of Houk and
Bickelhaupt have shown that detailed insight in the
mechanisms of these reactions can be obtained by the
“distortion/interaction energy” or “activation strain” model,
respectively.10−12 We now report a novel approach to
Equation 1, in which nucleophiles are characterized by two
solvent-dependent parameters, N and sN, and electrophiles are
characterized by one parameter, E, has been demonstrated to
predict rate constants of a large variety of electrophile-
nucleophile combinations if one or both reaction centers are
carbon.13,14
1g k20°C = sN(N + E)
(1)
While the electrophilicity parameter E of a certain electrophile
is derived from the rate constants of its reactions with a series
of C-centered nucleophiles, the N and sN parameters of a
certain nucleophile are derived from the rates of its reactions
with a series of C-centered reference electrophiles. Since
Received: September 14, 2018
© XXXX American Chemical Society
A
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reactions, in which one and only one new bond is formed in the
rate-determining step, were used for the derivation of the
reactivity parameters E, N, and sN, eq 1 cannot be expected to
be applicable to multicenter processes. However, we now
report that the relative reactivities of Michael acceptors toward
aryldiazomethanes15 correlate well with the electrophilicities E
of Michael acceptors, which have previously been derived from
the one-bond reactivities of the electron-deficient π-systems
toward carbanions and ylides.16 We will furthermore show that
eq 1 can even be used to predict absolute rate constants for the
reactions of highly electrophilic dipolarophiles with aryldiazo-
methanes, whereas less electrophilic dipolarophiles react faster
than predicted by eq 1 due to the concerted formation of two
new σ-bonds. In the latter cases, deviations of the measured
cycloaddition rate constants from those calculated by eq 1 can
be considered to be a measure for the energy of concert
ΔG‡concert, as defined in eq 2.17
Scheme 1. Reaction of Aryldiazomethane 1d with
Benzhydrylium Tetrafluoroborate 2e-BF4
ΔG‡
= RT ln(k2exptl/k2
)
calcd
(2)
concert
RESULTS AND DISCUSSION
■
Phenyldiazomethane 1a and its para-substituted derivatives
1b−d, which have UV absorption maxima between 290 and
380 nm, were employed for this study (Chart 1). For the
Scheme 2. Proposed Mechanism for the Formation of 3 and
4
Chart 1. Aryldiazomethanes (1) and Benzhydrylium
Tetrafluoroborates (2-BF4) Used in This Work
a
Formal hydride shift, which may include further intermediates.
determination of the reactivity parameters N and sN for 1a−d
the rates of their reactions with a set of colored benzhydrylium
ions of known electrophilicities E13a,h (2a−g in Chart 1) were
measured.
generated by diazotation of primary amines19 as well as in acid-
catalyzed Schmidt reactions of alkyl azides.20
Determination of Nucleophile-Specific Parameters N
and sN for Aryldiazomethanes 1b−d.18 Product Studies.
The reaction of 1d with 2e gave a mixture of (E)- and (Z)-
configured ethylenes, which was hydrogenated to furnish 3 and
4 in a 1:2 ratio and 78% yield of isolated products (Scheme 1).
The mechanism for their formation is rationalized in Scheme
2. The reaction between 1d and 2e yields a diazonium ion A,
which spontaneously loses N2 accompanied by a hydride shift,
leading to carbenium ion B, or an aryl shift, leading to
carbenium ion C. Deprotonation yields the olefins D and E,
respectively, the precursors of the isolated products 3 and 4.
Alternatively, the nonrearranged olefin D may be formed by
concerted proton and N2 elimination from diazonium ion A.
From the 3/4 ratio one can derive that the aryl shift is faster
than the competing processes. Concerted N2 departure and
1,2-shifts have previously been observed from diazonium ions
Kinetics. The rates of the reactions of the diazomethanes 1
with the benzhydrylium ions 2 were followed photometrically
under pseudo-first-order conditions by monitoring the decay of
the UV−vis absorbance of 2 in the presence of a large excess of
1, following the procedure reported previously.18 The resulting
second-order rate constants k2 for the reactions between
aryldiazomethanes 1 and benzhydrylium ions 2, which
correspond to the slopes of the plots of the pseudo-first-
order rate constants kobs vs [1], are listed in Table 1. Linear
correlations between lg k2 and the electrophilicity parameters E
of 2 (Figure 1) indicate the applicability of eq 1. The slopes of
the correlation lines and the negative intercepts on the abscissa
correspond to the nucleophilicity parameters sN and N,
respectively, of 1 (Table 1).
The second-order rate constants for the reactions of 2e-BF4
with the aryldiazomethanes listed in Table 1 correlate linearly
B
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exptl
Table 1. Second-Order Rate Constants k2
for the
Chart 2. Michael Acceptors 5−12 and Their Electrophilicity
a
Reactions of the Aryldiazomethanes 1 with Benzhydrylium
Parameters E
Tetrafluoroborates 2-BF4 in Dichloromethane at 20 °C
(M−1 s−1
)
exptl
ArCHN2
N (sN)
electrophile
k2
a
1a (X = H)
9.35 (0.83)
2g
2e
2d
2b
2a
2f
2e
2d
2c
2b
2f
2e
2c
2b
2a
2e
2d
2c
2b
7.56 × 10−1
1.19 × 102
5.80 × 102
6.85 × 103
1.45 × 105
8.46
3.66 × 101
3.02 × 102
4.59 × 102
2.51 × 103
6.21 × 10−1
4.55
1b (X = Br)
1c (X = CN)
8.87 (0.82)
7.66 (0.80)
7.17 (0.83)
4.85 × 101
3.38 × 102
2.93 × 103
1.51
1d (X = NO2)
9.49
a
Electrophilicities E from refs 16 and 23.
2.16 × 101
1.26 × 102
a
Data from ref 18.
68% isolated yield, respectively, via tautomerization of the
initially formed Δ1-pyrazolines.
with the Hammett substituent constants σp (r2 = 0.9909).21
The resulting Hammett reaction constant of ρ = −2.34 will be
discussed in the context of the kinetics of reactions of 1a−d
with Michael acceptors (see below).
Products of the Reactions of Aryldiazomethanes 1
with Michael Acceptors. The reactions of the aryldiazo-
methanes 1a−d with the Michael acceptors 5−12 (Chart 2)
give either pyrazolines (from 5−7 and 10) or nitrogen-free
products (from 8−9 and 11−12). As shown in Table 2,
phenyldiazomethane (1a) reacts smoothly with methyl acrylate
(5a)22 and methyl vinyl ketone (5b) at room temperature,
affording the 5-phenyl-Δ2-pyrazolines 13a and 13b in 98% and
Under similar conditions, diethyl fumarate (6) undergoes
1,3-dipolar cycloadditions with aryldiazomethanes 1a and 1b
to give Δ1-pyrazolines, which tautomerize with formation of 5-
aryl-Δ2-pyrazolines 14a as a single diastereomer or 14b as a
mixture of cis/trans-isomers.24 The Δ1-pyrazoline initially
formed from maleimide 7 and aryldiazomethane 1b
tautomerizes to give the Δ2-pyrazoline 16 (63%) with the
aryl group in conjugation to the double bond. Ethenesulfonyl
fluoride (ESF, 10), employed as a second generation click
reagent by Sharpless,23d,25 also undergoes smooth 1,3-dipolar
cycloadditions with aryldiazomethanes 1a, 1c, and 1d and
yields the 5-aryl-Δ2-pyrazolines 15a−d by subsequent
Figure 1. Plots of lg k2exptl for the reactions of the aryldiazomethanes 1a−d with the reference electrophiles 2a−g (in CH2Cl2 at 20 °C) versus their
electrophilicity parameters E.
C
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Table 2. Pyrazolines 13−16 Formed by Reactions of the Aryldiazomethanes 1a−d with the Dipolarophiles 5−7 and 10
a
Yield of isolated products.
tautomerization. X-ray crystallography confirmed the structure
of 15d (Figure 2).26
The reaction of benzylidene Meldrum’s acid derivative 8a
with 2.5 equiv of phenyldiazomethane (1a) in dichloro-
methane at 0 °C furnished the cyclopropane ( )-17 in 62%
yield (Scheme 3). It is likely that the 1,3-dipolar cycloaddition
of 1a with 8a initially leads to pyrazoline F, in analogy to the
reactions in Table 2. Subsequent migration of the electron-rich
p-(dimethylamino)phenyl group and extrusion of molecular
nitrogen generates the Michael acceptor G, which undergoes
another cycloaddition with a second equivalent of diazoalkane
1a to deliver pyrazoline H. Finally, loss of N2 from H generates
the spirocycle ( )-17, which was purified by column
chromatography and isolated as a racemate of a single
diastereomer, which was identified by X-ray single crystal
structure analysis (Figure 3). We did not search for other
diastereomers in the mother liquors and have not explored the
origin of the high stereoselectivity of the reaction of G with 1a.
Styrene derivatives 18a,c were obtained through the
reactions of 1a,c with bis(phenylsulfonyl)ethene 12 (Figure
4a). Monitoring the reaction of 1c with 12 in CDCl3 at
1
ambient temperature by H NMR spectroscopy shows the
initial formation of 5-aryl-Δ1-pyrazoline 19 within several
seconds (Figure 4b).27 The rate of this reaction is too fast to
be followed by NMR spectroscopy, but could be determined
Figure 2. Crystal structure of ( )-15d (ellipsoids are shown on 50%
probability level at T = 100 K).
D
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with 9b or 11b in diethyl ether at −45 and −10 °C,
respectively,31 it is not certain that 21 and 22 are also formed
through initial 1,3-dipolar cycloadditions, because the Δ1-
pyrazoline from 9b with phenyldiazomethane (1a) was
calculated to be an endergonic species (see below).
Scheme 3. Reaction of Arylidene Meldrum’s Acid 8a with
Phenyldiazomethane 1a and Proposed Mechanism for the
Formation of ( )-17
Kinetics of the Reactions of Aryldiazomethanes with
Michael Acceptors. The kinetics of the reactions of
aryldiazomethanes 1a−d with various Michael acceptors
from Chart 2 were followed by UV−vis spectroscopy using
the methods described previously.16 Generally, pseudo-first-
order conditions were employed. In most cases the
dipolarophiles were used in excess (>10 equiv) over 1 and
the kinetics were measured by following the decay of the
absorbances of the phenyldiazomethanes 1 (295−380 nm,
Chart 1). In the reactions with the colored electrophiles 8, 9,
and 11, compounds 1 were used in excess, however. The rates
of the latter reactions were derived from the time-dependent
absorbances of the styrene-chromophore in 8, 9, and 11.
As illustrated for the reaction of 1b with 10 in Figure 5, the
pseudo-first order rate constants kobs were obtained by least-
squares fitting of the exponential function At = A0 exp(−kobst)
+ C to the time-dependent absorbance At of the minor
compound. The pseudo-first-order rate constants kobs were
proportional to the concentrations of the major compounds as
shown by the inset of Figure 5, and the slopes of the
correlations kobs (s−1) vs the concentrations of the excess
compounds gave the second-order rate constants k2
(M−1
exptl
s−1) listed in Table 3.
If the reactions of the phenyldiazomethanes 1 with the
acceptor substituted ethylenes 5−12 would proceed stepwise,
with rate-determining formation of zwitterionic intermediates,
as illustrated in Scheme 5, the observed rate constants should
equal those calculated by eq 1 because only one new bond is
formed in the rate-determining step, as in the reactions used
for deriving the reactivity parameters E, N, and sN.13
To examine this possibility, we have used eq 1 to calculate
the second-order rate constants k2calcd for the formation of the
zwitterionic intermediates depicted in Scheme 5 from the one-
bond nucleophilicities N and sN of the diazoalkanes 1 (Table
1) and the one-bond electrophilicities E of the Michael
acceptors 5−12 (Chart 2). Table 3 shows that all rate
constants k2exptl measured for the reactions of 1a−d with 8b,c,
9a, 11a,b, and 12 differ by less than a factor of 50 from the rate
calcd
exptl
Figure 3. Crystal structure of ( )-17 (ellipsoids are shown on 50%
probability level at T = 100 K).
constants k2
calculated by eq 1, while k2
is much larger
calcd
than k2
for reactions of 1a−c with 5a, 5b, and 6.
A graphical illustration of these relationships is presented in
Figure 6, where the blue line represents k2calcd, calculated by eq
1
by UV−vis spectrometry (see below). As shown by the H
1 for the formation of zwitterions from 1a (N = 9.35, sN
=
NMR spectra in Figure 4b, 19 undergoes a quick N2
elimination accompanied by hydrogen shift28 and is completely
converted into the 1,1-(bis-sulfonyl)-3-aryl-propene 20 within
2 h.29 On a longer time scale, hydrogen migration converts 20
into 18c, which was characterized by single crystal X-ray
crystallography (Figure 4c).
0.83) and the electrophiles 5−12 (E from Chart 2). The
shaded area of Figure 6 shows that a fair agreement between
exptl
calcd
k2
and k2
(deviation < factor 50) holds for all reactions
of phenyldiazomethane (1a) with Michael acceptors of E >
−11. The kinetic data thus indicate that the strongest
electrophiles of this series either react via zwitterionic
intermediates or via nonsynchronous concerted reactions
with transition states resembling zwitterions. Table 3 and
Benzylidenemalononitrile (9b) reacts with phenyldiazo-
methane (1a) in dichloromethane with formation of trans-
2,3-diphenylcyclopropane 2130 (Scheme 4). The trans-
configuration (that is, the C2 symmetry) of 22, which was
obtained from 1a and benzylidene-indane-1,3-dione (11b),
was derived from the identical 13C NMR chemical shifts of the
exptl
Figure 6 furthermore show that the deviations between k2
and k2
calcd
increase with decreasing electrophilicities of the
Michael acceptors. Whereas the small deviations (<factor 100)
exptl
calcd
1
between k2
and k2
in the right part of Figure 6 cannot
carbonyl groups and the AA′BB′ system in the H NMR
spectrum for the four aromatic protons of the indan-1,3-dione
moiety. Though Schuster and co-workers observed the
formation of Δ1-pyrazolines by the reactions of diazomethane
reliably be interpreted,32 the large deviations on the left
indicate the operation of a concerted mechanism, and the term
RT ln(k2exptl/k2calcd) can be considered as a measure for the
E
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1
Figure 4. (a) Reactions of aryldiazomethanes 1a and 1c with bissulfonylethene 12. (b) Mechanism for the formation of 18c monitored by H
NMR spectroscopy (200 MHz) of the reaction mixture [reaction of 1c (0.10 M) with 12 (0.10 M) in CDCl3 at 20 °C using 1,1,2,2-
tetrachloroethane (0.1 M) as an internal standard]. (c) Crystal structure of 18c (ellipsoids are shown on 50% probability level at T = 173 K).
F
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Hammett reaction constant of ρ = −1.3033 can be derived
from the rate constants which Huisgen and Geittner reported
for the reactions of eight ring-substituted aryldiazomethanes
with ethyl acrylate in DMF at 25 °C.22a
Scheme 4. Reactions of 9b and 11b with
Phenyldiazomethane 1a
The dependence of rate constants on solvent polarity has
often been used as a criterion to differentiate concerted
cycloadditions from cycloadditions through zwitterionic
intermediates.22b,34 Whereas [2 + 2] cycloadditions of
tetracyanoethylene with enol ethers, which proceed via
zwitterionic intermediates, are 3−4 orders of magnitude faster
in acetonitrile than in cyclohexane,34,35 the solvent dependence
of various Diels−Alder reactions of tetracyanoethylene is so
small that there are no significant correlations with any of the
known solvent polarity parameters.36
Solvent dependences of the rates of 1,3-dipolar cyclo-
additions were reported to be generally rather small. While the
rate constants for the reactions of phenyldiazomethane (1a)
with ethyl acrylate increased by a factor of 2.4 from
cyclohexane to acetonitrile at 25 °C and correlated fairly
with Reichardt’s ET values,37 the rates of the corresponding
reactions with norbornene were almost independent of solvent
polarity.22b
a
Determined by 1H NMR spectroscopy (with 1,1,2,2-tetrachloro-
ethane as an internal standard).
Table 4 shows that the reactions of phenyldiazomethane
(1a) with the Michael acceptors 6 and 9−12 proceed slightly
faster in the polar solvents acetonitrile and DMSO than in
dichloromethane or THF. Though 12, the strongest electro-
phile of the investigated Michael acceptors, showed the largest,
and 6, the weakest among the investigated electrophiles,
showed the smallest solvent dependence, Table 4 does not
reveal a clear correlation between electrophilicity of the
dipolarophile and the magnitude of the solvent effect.
Quantum Chemical Calculations of the Cycloaddi-
tions. Details of the reaction pathways for the reactions of
phenyldiazomethane (1a) with selected electrophiles have
been calculated using the same quantum chemical methods as
in our recent quantitative analysis of ketone reactivity.38 This
involves geometry optimizations at the (U)B3LYP39-D340/6-
31+G(d,p)41 level of theory in combination with the
polarizable continuum model (PCM) for dichloromethane
and UA0 radii.42 Thermochemical corrections to Gibbs
energies (Corr. ΔG) and enthalpy (Corr. ΔH) at 298.15 K
have been calculated using the rigid rotor/harmonic oscillator
model without any scaling. Single point calculations have also
been performed for all stationary points at the PCM-
(CH2Cl2,UA0)/(U)B2PLYP43-D3/def2TZVPP44 level in
order to verify the validity of all mechanistic conclusions
(see the Supporting Information). Given the slightly better
agreement between experimentally measured Gibbs activation
energies with those calculated at the PCM(CH2Cl2,UA0)/
(U)B3LYP-D3/6-31+G(d,p) level used for geometry opti-
mization, only the latter results will be discussed in the
following.
Figure 5. Monoexponential decay of the absorbance A (at 290 nm) vs
time for the reaction of 10 (4.86 × 10−3 M) with 1b (8.63 × 10−5 M)
in CH2Cl2 at 20 °C. Inset: Correlation of kobs vs the concentration of
10.
energy of concert (eq 2) due to the stabilization of the
transition state by the simultaneous formation of two new
bonds (Figure 7).
In line with these interpretations, variation of the
nucleophilic reactivities of the diazomethanes 1 affects the
rates of the cycloadditions with the highly electrophilic
Michael acceptors 12 and 10 to the same degree as the one-
bond reactivities toward carbenium ion 2e (Figure 8a).
Comparable charge flows in the transition states of these
reactions are thus indicated. The smaller dependence of the
rate constants for the reactions with diethyl fumarate (6) on
the nucleophilicities of the diazomethanes 1 is in accord with a
high degree of concertedness of these reactions.
The same conclusion can also be drawn from the Hammett
correlations shown in Figure 8b. The Hammett reaction
constants for 12 (ρ = −2.42) and 10 (ρ = −2.61) are of similar
magnitude as ρ for the reactions of 1 with the one-bond
electrophile 2e (ρ = −2.34). The reactions of aryldiazo-
methanes with diethyl fumarate (6) in dichloromethane at 20
°C, on the other hand, show a significantly less negative
reaction constant (ρ = −1.58) indicating a smaller degree of
negative charge transfer in the transition states. A similar
Figure 9 compares the Gibbs energy profiles for the
reactions of phenyldiazomethane (1a) with five representative
electrophiles. The initially formed encounter complexes, which
are minima in potential energy, are omitted in these energy
profiles, as they are endergonic species (ΔrG0 > 0) and do not
affect the kinetics. In all five cases, concerted (3 + 2)-
cycloadditions are calculated to be the minimum energy
pathways with Gibbs energies of activation, which agree within
5 kJ mol−1 with the experimental ΔG‡ obtained by applying
the experimental rate constants k2 from Table 3 in the Eyring
equation. The direct formation of the thermodynamically
G
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Table 3. Second-Order Rate Constants of Reactions between Aryldiazomethanes (1a−d) and Michael Acceptors (5−12) in
Dichloromethane at 20 °C
a
ArCHN2
electrophile
k2
(M−1 s−1
)
k2
(M−1 s−1
)
k2exptl/k2
ΔG‡
(kJ mol−1
)
exptl
calcd
calcd
concert
1a
5a
5b
6
4.87 × 10−2
2.22 × 10−1
4.05 × 10−1
3.33 × 10−1
7.58
4.80 × 101
1.51 × 10−2
6.81
1.33 × 10−8
7.07 × 10−7
9.88 × 10−8
1.48 × 10−3
1.69 × 10−1
1.47
6.26 × 10−2
5.32 × 10−3
2.32 × 10−2
2.34 × 10−1
3.43 × 101
4.85 × 10−8
5.45 × 10−5
2.29 × 10−3
1.33 × 101
7.87 × 10−9
2.86 × 10−4
1.34
3.7 × 106
3.1 × 105
4.1 × 106
2.3 × 102
4.5 × 101
3.3 × 101
2.4 × 10−1
1.3 × 103
1.0 × 101
6.2
4.3 × 101
4.8 × 106
1.6 × 104
1.0 × 103
5.0 × 101
4.9 × 106
6.4 × 102
3.4 × 101
9.3 × 103
7.1 × 102
4.1 × 101
37
31
37
b
8a
8b
8c
9a
10
11a
11b
12
6
−
−
−
−
b
b
b
17
b
2.38 × 10−1
1.45
−
−
−
b
b
1.48 × 103
2.34 × 10−1
8.46 × 10−1
2.33
1b
37
24
17
c
7
10
12
6
10
12
7
b
6.59 × 102
3.87 × 10−2
1.83 × 10−1
4.56 × 101
1.74 × 10−2
5.82 × 10−2
2.16 × 101
−
1c
38
16
b
−
1d
1.87 × 10−6
8.25 × 10−5
22
10
12
16
b
5.32 × 10−1
−
a
b
c
1
Calculated by eq 1 with N and sN from Table 1 and E from Chart 2. Too small to be significant (see text). Determined by H NMR
spectroscopy.
Scheme 5. Stepwise 1,3-Dipolar Cycloadditions of
Aryldiazomethanes with Acceptor-Substituted Ethylenes
Figure 7. Comparison of measured activation Gibbs energies ΔG‡
exptl
with ΔG‡
calculated for the formation of zwitterions from E, N,
calcd
and sN by eq 1.
The calculated high Gibbs energy of the Δ1-pyrazoline from
1a and 9a indicates, however, that in this case conversion of
the cycloadduct into the isolated cyclopropane and not the 1,3-
dipolar cycloaddition may be rate-determining. This inter-
pretation is supported by the observation that 9a is the only
Michael acceptor which is below the calculated line in Figure 6.
The excellent agreement between the measured rate constants
for the reaction of 1a with 9a and that calculated for the 1,3-
dipolar cycloaddition in Figure 9 indicates, on the other hand,
that the barrier for nitrogen expulsion from the corresponding
Δ1-pyrazoline cannot be much higher than that for
retroaddition.
exptl
Figure 6. Correlation of lg k2
for the reactions between the
Michael acceptors 5−12 and phenyldiazomethane (1a) versus the
electrophilicity parameters E of the Michael acceptors.
favored cyclopropanes (+ N2) from the reactants generally
requires higher activation energies. This suggests that also in
those reactions listed in Table 3, where pyrazoline formation
was not observed as in the reactions with 5a, 10, and 12, Δ1-
pyrazolines are the initially formed products, which may
undergo subsequent reactions.
As shown by the geometrical parameters in Figure 10, the
development of the new C−N bond lags far behind that of the
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diazomethane to electrophilic dipolarophile in the transition
states (Figure 10). The latter parameter increases from −0.2 e
in the transition state of 5a to −0.43 e in the most
asynchronous transition state for 8c.
Though the data in Figure 10 are in line with highly
unsymmetrical transition states in the reactions of phenyl-
diazomethane (1a) with highly electrophilic dipolarophiles, the
question arises, how the concerted 1,3-dipolar cycloaddition
mechanisms, derived from the quantum chemical calculations,
concur with the zwitterion-like transition states derived from
the kinetic data in Figure 6. Figure 9 shows that, on their way
to cyclopropanes, the reactions of 1a with 8c (E = −9.15) or
12 (E = −7.50) initially yield zwitterions over barriers which
are only 7 and 17 kJ mol−1 higher than the barriers for the
concerted reactions, indicating that in the case of strong
electrophiles (E > −11) concerted and stepwise cycloadditions
proceed over comparable barriers. Obviously the interaction
between the reaction centers at the “long” new bonds is so
weak that the energy of the transition state is hardly affected.
As a consequence, the one-bond nucleophilicities of the
diazomethanes (N, sN) and the one-bond-electrophilicities of
the dipolarophiles (E) are suitable to calculate the rates of such
cycloadditions by eq 1.
Following the distortion interaction analysis of 1,3-dipolar
cycloadditions by Houk et al. and by Bickelhaupt et al.,10 we
dissected the reaction barriers of the five reactions in Figure 9
into the distortion energies for deforming the two reactants
into their transition state geometries and the interaction
energies of the two distorted reactants when brought together
into the transition state structure. As this procedure is based on
single point energy calculations in the absence of thermal
corrections, the resulting reaction barriers given in Figure 11
are much lower than the Gibbs energies reported in Figure 9.
In agreement with earlier results by Houk and Ess for the
reaction of methyl acrylate (5a) with diazomethane,10b we
found that, in the highly concerted cycloaddition of 1a with 5a
(E = −18.84), the electrophile distortion energy is much
smaller (27 kJ mol−1) than that for the diazoalkane (69 kJ
mol−1). As the transition states become more unsymmetrical,
the distortion energies of the electrophilic alkene grow and the
distortion energies of the nucleophilic 1,3-dipole shrink with
the consequence that, for the four highly unsymmetrical
cycloadditions in Figure 11, the 1,3-dipole distortion energies
are only slightly larger (in the case of 8c even smaller) than the
dipolarophile distortion energies. According to this treatment,
the higher reactivities of the more electrophilic dipolarophiles
are predominantly due to the higher interaction energies.
Quantum Chemical Analysis of the Subsequent
Reactions of the Δ1-Pyrazolines. As described in the
subsection “Products of the Reactions of Aryldiazomethanes 1
with Michael Acceptors”, the initially generated Δ1-pyrazolines
Figure 8. Correlation of lg k2exptl for the reactions of the electrophiles
2e, 6, 10, and 12 with the aryl diazomethanes 1a−d (from Tables 1
and 3) versus (a) the nucleophilicity parameters N of aryl
diazomethanes (from Table 1) and (b) Hammett substituent
constants σp (from ref 21) for 1a−d.
new C−C bond in all transition states, whereas both bonds
have almost equal lengths in the resulting Δ1-pyrazolines.
Figure 10 furthermore shows that the atomic distances in the
two developing new bonds differ much more in the transition
states of the highly electrophilic dipolarophiles (Δ = 0.5−0.7 Å
for E > −11) than in the transition state for the reaction with
methyl acrylate (5a, Δ = 0.3 Å) for which a high degree of
concertedness was derived from the kinetic data in Figure 6.
This conclusion is confirmed by the relative bond orders (%
EV) and the amount of charge transfer from nucleophilic
exptl
Table 4. Second-Order Rate Constants k2
9−12) in Different Solvents at 20 °C
of the Reactions between Phenyldiazomethane (1a) and Michael Acceptors (6,
(M−1 s−1
)
exptl
k2
a
a
solvent
εr
ET(30)
6 (E = −17.79)
10 (E = −12.09)
9a (E = −10.80)
11b (E = −10.11)
12 (E = −7.50)
8.00 × 103
DMSO
CH3CN
CH2Cl2
THF
46.45
35.94
8.93
45.1
45.6
40.7
37.4
2.16
32.0
13.5
6.81
3.03
1.16 × 10−1
5.27 × 10−2
1.51 × 10−2
7.63
3.18
1.45
1.00
4.05 × 10−1
4.08 × 10−1
1.48 × 103
6.21 × 102
7.58
a
Relative permittivity (εr) and ET(30) were taken from ref 37.
I
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Figure 9. Energy profiles (ΔGsol, in kJ mol−1) for the reactions of 5a, 10, 9a, 8c, and 12 with 1a calculated at the PCM(UA0,CH2Cl2)/(U)B3LYP-
D3/6-31+G(d,p) level of theory.
were never isolated from the reactions of the aryldiazo-
methanes 1 with the Michael acceptors 5−12. The isolated
products were either Δ2-pyrazolines or nitrogen-free products.
Calculation of the relative stabilities of the pyrazoline
tautomers obtained from 1a and methyl acrylate (5a) and ESF
(10) showed that the Δ1-pyrazolines are, indeed, the least
stable tautomers (Scheme 6). However, according to Table 2,
generally not the most stable tautomers with phenyl in
conjugation with the endocyclic double bond were isolated but
the tautomers with the acceptor group in conjugation with the
double bond (exception: the bicyclic cycloadduct from
maleimide 7). Obviously, it is the higher acidity of the proton
in α-position to the acceptor group that controls the mode of
tautomerization.
The formation of the cyclopropanes 21 and 22 (described in
Scheme 4) may, therefore, proceed via retroaddition of the
initially formed Δ1-pyrazolines to give the starting materials,
which subsequently proceed to the cyclopropanes over the
higher barriers on the left side of Figure 9. This pathway
appears feasible, in particular for the reaction of 1a with 9a,
since in this case the corresponding Δ1-pyrazoline is an
endergonic adduct according to Figure 9.
Alternatively, the cyclopropanes may be formed through the
direct conversion of the Δ1-pyrazolines. Figure 12 shows a
possible transition state for such a transformation and also
rationalizes the transformation of the Δ1-pyrazoline 19 into the
bissulfonylalkene 20. Elongation of both C−N bonds leads to
an activated complex (ΔG‡ = 75.3 kJ mol−1) on a flat surface,
which may transform into N2 complexes of a 1,3-zwitterion, an
oxathiolane, or a cyclopropane, which are minima on the
As discussed above, according to Figure 9, Δ1-pyrazolines
should be the initial reaction products in all investigated cases.
J
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Figure 10. Charge on electrophilic dipolarophile [Ch(El)] and percentage of evolution of the bond order (%Ev) in the transition states for the
reactions of phenyldiazomethane (1a) with the electrophiles 5a, 10, 9a, 8c, and 12. Charges (NBO6 and Mulliken) and %EV (Wiberg indices) are
calculated at the PCM(UA0,CH2Cl2)/(U)B3LYP-D3/6-31+G(d,p) level of theory. Distances are shown in Å.
Figure 11. Distortion-interaction analysis (DIA, ΔEsol, kJ mol−1) for the reactions of phenyldiazomethane (1a) with the electrophiles 5a, 10, 9a, 8c,
and 12. DIA is performed at the PCM(UA0,CH2Cl2)/(U)B3LYP-D3/6-31+G(d,p) level of theory.
Scheme 6. Relative Stabilities (ΔGsol, in kJ mol−1) of the
Tautomers Obtained from Reactions of
Phenyldiazomethane (1a) with Methyl Acrylate (5a) or ESF
(10) Calculated at the PCM(UA0,CH2Cl2)/(U)B3LYP-D3/
6-31+G(d,p) Level of Theory
potential energy surface but not on the Gibbs energy surface
and, therefore, immediately lose N2. According to Figure 12,
the barriers for the conversion of the oxathiolane (+78.6 kJ
mol−1) as well as of the cyclopropane intermediate (+163 kJ
mol−1) into 20 are higher than the barrier to form these
Figure 12. Energy profiles (ΔGsol, kJ mol−1) for the conversion of 19
intermediates from 19. Since we did not observe any
intermediates during conversion of 19 into 20 (Figure 4),
we have to conclude that the alkene 20 is exclusively formed
via the 1,3-zwitterion route shown in red in Figure 12. The
into 20 (N2 elimination accompanied by H shift) calculated at the
PCM(UA0,CH2Cl2)/(U)B3LYP-D3/6-31+G(d,p) level of theory.
Distances are shown in Å.
K
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untypically high barrier for 1,2-hydride migration in the
intermediate 1,3-zwitterion to give 20 can be assigned to the
nonbonding interactions of the formal carbocation center with
one of the sulfonyl oxygen atoms.
An analogous concerted extrusion of N2 may account for the
formation of the cyclopropanes 21 and 22 from 9b and 11b,
respectively (Scheme 4).
examples in Figure 9 confirm the similar magnitude of the
Gibbs activation energies for the concerted cycloadditions and
the formation of zwitterions from the strong electrophiles 8c
and 12. On the other hand, Figure 6 illustrates that less
electrophilic dipolarophiles (such as, for example, methyl
acrylate 5a) react much faster with phenyldiazomethane (1a)
than calculated by eq 1, and the ratio k2exptl/k2calcd is suggested
as a measure for concertedness (eq 2, Figure 7).
CONCLUSION
Correlations between measured rate constants and LUMO
energies exist only for narrow subgroups of Michael acceptors
sharing structural similarity at the site of nucleophilic attack.
This is seen for the terminally unsubstituted electrophiles (5a,
5b, 10, and 12) or for the arylidene Meldrum’s acid derivatives
(8a−8c) in Figure 13a. For a larger set of electrophiles,
■
The differentiation between concerted and stepwise processes
has intrigued chemists for many years. In 1962, Doering and
Roth used the term “No-mechanism” for so-called “thermo-
reorganization” reactions like the Diels−Alder and Cope and
Claisen rearrangements, in which no involvement of
intermediates was detectable.45 A common rationale for such
pericyclic reactions was provided in 1969 by Woodward and
Hoffman’s orbital symmetry rules.46 In his seminal 1984 article
entitled “Multibond Reactions Cannot Normally Be Synchro-
nous”, Dewar argued that even concerted cycloadditions
proceed via transition states resembling intermediate biradicals
or zwitterions.47 Alabugin and co-workers demonstrated that
the diradical/zwitterion dichotomy also applies to cyclo-
aromatization reactions.48 In this Article, we have introduced
a linear free energy approach to measure the energy of concert,
i.e., the difference between the activation energies of concerted
1,3-dipolar cycloadditions and of the corresponding stepwise
processes via zwitterions.
We have shown that aryldiazomethanes undergo concerted,
nonsynchronous 1,3-dipolar cycloadditions with electron-
deficient CC-double bonds to give Δ1-pyrazolines, which are
subsequently transformed into Δ2-pyrazolines, cyclopropanes,
or substituted ethylenes. The direct formation of cyclo-
propanes from the reactants involves higher barriers and
does not usually take place. Though the transformation of the
Δ1-pyrazolines into cyclopropanes may proceed via nitrogen
extrusion from the Δ1-pyrazolines and formation of inter-
mediate 1,3-zwitterions, as illustrated in Figure 12, retro-
addition with regeneration of the reactants and subsequent
reaction over the higher barriers as shown on the left side of
Figure 9 cannot generally be excluded.
The excellent agreement between experimental activation
energies and quantum-chemically calculated values at the
PCM(UA0,CH2Cl2)/(U)B3LYP-D3/6-31+G(d,p) level of
theory for the cycloadditions shown in Figure 9 confirms the
high reliability of the employed polarizable continuum model
(PCM) to consider solvation. Charge densities and geo-
metrical parameters of the transition states depicted in Figure
10 indicate that the nonsynchronicity of the cycloadditions
increases with increasing electrophilicity of the acceptor-
substituted ethylenes. Figure 6 shows that the measured rate
constants for the cycloadditions of phenyldiazomethane (1a)
with highly reactive Michael acceptors (E > −11 in Chart 2)
are almost identical to those calculated by eq 1 from the one-
bond nucleophilicities N and sN of 1a (Table 1) and the one-
bond electrophilicities E of 5−12 (compiled with many other
E parameters in a freely accessible online database14). This
agreement indicates that the Gibbs activation energies for the
concerted nonsynchronous cycloadditions of the highly
electrophilic dipolarophiles closely resemble those for hypo-
thetical stepwise cycloadditions via zwitterionic intermediates
and that in these cases the formation of the new C−N bond
cannot contribute significantly to the stabilization of the
transition state of the concerted processes. The last two
Figure 13. Second-order rate constants lg k2exptl for the reactions of 1a
with diverse electrophiles (from Table 3) correlated with (a)
quantum-chemically calculated LUMO energies (εLUMO in Hartree,
from ref 16) and (b) methyl anion affinities ΔGsol‑sp (in kJ mol−1,
from ref 16, correlation line refers to electrophiles of E > −11 in Chart
2. Data for 9a excluded because formation of the Δ1-pyrazoline is not
rate-determining, see main text.
however, neither the LUMO energies (Figure 13a) nor the
global (ω) or the local (ωβ) Parr electrophilicity index serve as
reliable descriptors of their reactivities (see the Supporting
Information).
Figure 13b shows, however, that the cycloaddition rate
constants of the highly electrophilic Michael acceptors (that is,
those with E > −11 in Chart 2) correlate with their quantum-
chemically calculated methyl anion affinities (ΔGsol‑sp). This is
a consequence of the correlation between cycloaddition rate
constants and electrophilicities E of these Michael acceptors
shown in Figure 6 and the previously reported linear
L
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affinities.16 As the correlation between the rate constants for
the 1,3-dipolar cycloadditions and electrophilicities E breaks
down for weaker electrophiles (that is, 8a, 5b, 5a, and 6 with E
< − 11, Figure 6) the cycloaddition rate constants for these
electrophiles also do not correlate with the corresponding
methyl anion affinities (Figure 13b). While the methyl anion
affinities of 8a, 5b, 5a, and 6 cover a range of 70 kJ mol−1, the
rate constants for the (3 + 2)-cycloadditions with 1a vary only
within 1 order of magnitude, in line with the smaller amount of
charge transfer in the transition states of these reactions.
Though the empirical electrophilicity parameters E (accord-
ing to eq 1) thus do not allow to rank cycloaddition rates of
less electrophilic dipolarophiles, the possibility to predict
absolute rate constants for highly asynchronous 1,3-dipolar
cycloadditions from the reactivity parameters E, N, and sN
represents a new tool, and we are currently investigating the
applicability of this approach to other types of 1,3-dipolar
cycloadditions.
ASSOCIATED CONTENT
■
S
* Supporting Information
The Supporting Information is available free of charge on the
ACS Publications website at DOI: 10.1021/jacs.8b09995.
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Details of the product studies, X-ray structures of 15d,
17, and 18c, kinetic experiments, computational analysis,
and NMR spectra of all characterized compounds
(PDF)
Coordinates of optimized structures (ZIP)
Crystallographic data for 15d (tv444), 17 (vv089), and
18c (uo090) (CIF)
AUTHOR INFORMATION
Corresponding Authors
*ofial@lmu.de
*zipse@cup.uni-muenchen.de
*herbert.mayr@cup.uni-muenchen.de
ORCID
Armin R. Ofial: 0000-0002-9600-2793
Hendrik Zipse: 0000-0002-0534-3585
Herbert Mayr: 0000-0003-0768-5199
■
Present Addresses
‡Q.C.: Novaled GmbH, 01307 Dresden, Germany.
§I.Z.: Merck KGaA, 64293 Darmstadt, Germany.
Author Contributions
†H.J. and Q.C. contributed equally to this work.
Notes
The authors declare no competing financial interest.
ACKNOWLEDGMENTS
■
Dedicated to Professor Kendall N. Houk on the occasion of his
75th birthday. We thank the Deutsche Forschungsgemein-
schaft (SFB 749, Projects B1 and C6) for financial support and
the Leibniz Supercomputing Centre (www.lrz.de) for generous
allocation of computational resources.
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Garcia, L. A. Stereospecificity of 1,3-Dipolar Cycloadditions of p-
Nitrobenzonitrile Oxide to cis- and trans-Dideuterioethylene. J. Am.
Chem. Soc. 1985, 107, 7227−7228.
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