Systematic Evaluation of 1,2-Migratory Aptitude in Alkylidene Carbenes

Article abstract of DOI:10.1021/jacs.0c12400

Alkylidene carbenes undergo rapid inter- and intramolecular reactions and rearrangements, including 1,2-migrations of β-substituents to generate alkynes. Their propensity for substituent migration exerts profound influence over the broader utility of alkylidene carbene intermediates, yet prior efforts to categorize 1,2-migratory aptitude in these elusive species have been hampered by disparate modes of carbene generation, ultrashort carbene lifetimes, mechanistic ambiguities, and the need to individually prepare a series of 13C-labeled precursors. Herein we report on the rearrangement of 13C-alkylidene carbenes generated in situ by the homologation of carbonyl compounds with [13C]-Li-TMS-diazomethane, an approach that obviates the need for isotopically labeled substrates and has expedited a systematic investigation (13C{1H} NMR, DLPNO-CCSD(T)) of migratory aptitudes in an unprecedented range of more than 30 alkylidene carbenes. Hammett analyses of the reactions of 26 differentially substituted benzophenones reveal several counterintuitive features of 1,2-migration in alkylidene carbenes that may prove of utility in the study and synthetic application of unsaturated carbenes more generally.

Full text of DOI:10.1021/jacs.0c12400

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Systematic Evaluation of 1,2-Migratory Aptitude in Alkylidene
Carbenes
Harvey J. A. Dale, Chris Nottingham, Carl Poree, and Guy C. Lloyd-Jones*
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ABSTRACT: Alkylidene carbenes undergo rapid inter- and intra-
molecular reactions and rearrangements, including 1,2-migrations of
β-substituents to generate alkynes. Their propensity for substituent
migration exerts profound influence over the broader utility of
alkylidene carbene intermediates, yet prior efforts to categorize 1,2-
migratory aptitude in these elusive species have been hampered by
disparate modes of carbene generation, ultrashort carbene lifetimes,
mechanistic ambiguities, and the need to individually prepare a series
of 13C-labeled precursors. Herein we report on the rearrangement of
13C-alkylidene carbenes generated in situ by the homologation of
carbonyl compounds with [13C]-Li-TMS-diazomethane, an approach
that obviates the need for isotopically labeled substrates and has expedited a systematic investigation (13C{1H} NMR, DLPNO-
CCSD(T)) of migratory aptitudes in an unprecedented range of more than 30 alkylidene carbenes. Hammett analyses of the
reactions of 26 differentially substituted benzophenones reveal several counterintuitive features of 1,2-migration in alkylidene
carbenes that may prove of utility in the study and synthetic application of unsaturated carbenes more generally.
It has long been recognized that some alkylidene β-
substituents (RX, RY) have a much greater propensity for
1,2-migration (e.g., H, aryl, alkynyl) than others (e.g.,
alkyl),6−8 yet only a few studies have sought to explicitly
assess this, using isotopic 13C/14C labeling. Milestones in this
regard are studies by Stang (vinyl triflates; Ph vs Me),19
Thamattoor (cyclopropanated phenanthrenes; H vs Ph,13 Me
vs Ph14), and Tykwinski20 (Colvin rearrangement and
vinylidene dibromides; −CCSiR3 vs alkyl, Ar, alkenyl).
While these studies confirmed several postulated trends of
relative migratory aptitudes (e.g., H > alkyne > Ph > Me), the
scope contrasts the extensive studies reported for saturated
carbenes.21−23 As such, systematic analysis of structure−
reactivity relationships in alkylidene carbenes remains limited
and subject to a number of caveats.2 For example, migratory
aptitudes determined from different carbene precursors, under
different rearrangement conditions, may or may not be directly
comparable on a microscopic level. Moreover, while
diazoalkenes and cyclopropanated phenanthrenes are consid-
ered reliable precursors to bona fide alkylidene carbenes, the
INTRODUCTION
■
Alkylidene carbenes1−3 can be liberated, inter alia, by the
deprotonation of terminal alkenyl (pseudo)halides,4−6 ther-
molysis of diazoalkenes,7−12 and photolysis of cyclopropanated
phenanthrenes,13−15 Scheme 1A. Alkylidene carbenes are
extremely short-lived, readily undergoing 1,2-migration of a
β-substituent to generate an alkyne.16 This has been applied in
well-established synthetic methodologies, such as the Corey−
Fuchs reaction17 and the Seyfirth−Gilbert,8−10 Colvin,7,12 and
Fritsch−Buttenberg−Wiechell (FBW) rearrangements.2 How-
ever, this propensity for 1,2-migration can interfere with other
desired modes of reactivity, such as H−Y insertion and [1 +
2]-cycloaddition,1,18 especially when these require intermo-
lecular interception of the alkylidene carbene.
The identities of the alkylidene β-substituents (RX, RY;
Scheme 1B) influence the propensity for 1,2-migration, and
both their relative and absolute migratory aptitudes should be
considered. These factors dictate not only which group (RX,
RY) migrates but also the intrinsic lifetime of the carbene
during which it can be diverted. Furthermore, this lifetime is
contingent on both substituents: the migrator and the
stationary (or “bystander”) β-substituent, and thus one-
dimensional trends for absolute migratory aptitude are
inherently misleading.2 Measurement of absolute rates of 1,2-
migration requires direct detection of the alkylidene carbene,
with Phillips, Hadad, and Thamattoor reporting the first
observation in solution (PhMeCC:) by femtosecond
spectroscopy just 2 years ago.15
Received: November 27, 2020
Published: January 11, 2021
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Scheme 1. Alkylidene Carbene Liberation, Reactivity,
Migratory Aptitudes, and Bystander Effects
Scheme 2. Expedient in Situ Generation and Rearrangement
of 13C-Labeled Alkylidene Carbenes (5)
Preparation of [13C]-TMSDAM. Application of the Colvin
rearrangement, Scheme 2, required in situ preparation of
lithium [13C]-trimethylsilyldiazomethane ([13C]-Li-
TMSDAM) by deprotonation (LDA) of [13C]-TMSDAM.
The commercially available unlabeled TMSDAM reagent is
conventionally prepared from TMSCH2Cl via the correspond-
ing Grignard.29 However, after a range of preliminary
experiments involving TMS13CH2X (X = Cl, Br, I) we pursued
an alternative route based on amine diazotization.30 The
requisite 13C-labeled amine (11) was prepared via a multistep
chromatography-free sequence, starting from 13CH3OH (7),
Scheme 3. With the amine 11 in hand, we utilized Lebel’s
diazotization procedure and after careful reoptimization for
13C-labeled synthesis31 prepared a large stock solution of
[13C]-TMSDAM (12, 0.6 M in 2-Me-THF; dried over
molecular sieves).
a
Primary alkenyl triflates are likely the most reliable liberator of bona
b
fide carbenes of all the alkenyl (pseudo)halides. KtOBu is a common
choice for generating “free” carbenes. Alkylidene carbenes can also
c
undergo R−X insertion following ylide formation from Lewis bases
d
(e.g., THF, THT, NEt3). C−H insertions appear only to be feasible
e
on an intramolecular basis. Diazoalkenes are not readily isolable, and
are postulated to be liberated from e.g., silylated α-diazoalkoxides, N-
nitrosocarbonamides, and N-(1-aziridinyl)aldimines.1,2
possible intermediacy of carbenoids24−28 must also be
considered when, for example, alkenyl halides are employed.
Furthermore, although not previously discussed, the highly
reactive nature of alkylidene carbenes poses additional
questions about the microscopic basis for product selection,
especially when both substituents are efficient and thus
competitive migrators. In such cases, incomplete conforma-
tional equilibration in, and/or dynamic bypassing of, an
incipient carbene cannot be excluded a priori. Thus, even when
the formation of the free alkylidene carbene appears likely, a
fundamental question remains as to whether the observed
selectivity is established at the migration stage or influenced by
prior “upstream” events.
Determination of Migratory Aptitudes. By use of a
single set of standardized conditions (Scheme 4), a broad
Scheme 3. Preparation of [13C]-TMSDAM (12)
RESULTS AND DISCUSSION
■
With all of the above issues in mind, we sought a systematic
analysis of structure−reactivity relationships for 1,2-migration
in alkylidene carbenes. As noted above, the measurement of
relative migratory aptitude requires isotopic labeling (13C,
14C), and if the label is installed in the precursor bearing the β-
substituents, this becomes impractical and expensive if a large
array of examples is to be surveyed. Herein we report on (a)
the use the Colvin rearrangement7,12,20 (Scheme 2) to expedite
generation of isotopically labeled, bona fide alkylidene carbenes
from unlabeled carbonyls and (b) an extensive analysis of the
1,2-migratory aptitudes by quantum chemical calculations (KS-
DFT; DLPNO-CCSD(T)).
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a
Scheme 4. Colvin Rearrangement of Aromatic Aldehydes and Ketones (1) Employing Lithiated [13C]-TMSDAM
a
[13C]-Li-TMSDAM generated in situ from LDA (1.0−1.2 equiv) and [13C]-TMSDAM (12, 1.0 equiv). Alkyne isotopomer ratios were determined
by H and 13C NMR spectroscopy after isolation by chromatography. Selectivities for diaryl alkynes were calculated by integration of the two
1
alkynyl 13C resonances; no significant effects from differential rates of longitudinal relaxation (T1) were observed, with selectivities corroborated by
integration of parent/13C−13C satellite signals for each ipso carbon; see Supporting Information.
range of aldehydes and ketones were converted to the
corresponding [13C]-alkynes via Colvin rearrangement with
[13C]-Li-TMSDAM. In situ low-temperature 13C{1H} NMR
spectroscopic analysis of the reaction of [13C]-4-fluorobenzo-
phenone with [13C]-Li-TMSDAM confirmed >85% consump-
tion of the ketone in under 20 min at −78 °C to generate
intermediates (tentatively assigned, see below and Supporting
Information, as [13C2]-2/3) and substantial rearrangement to
example with 4-(N,N-diethylamino)benzophenone, migration
of ArX dominated (F4‑N(Et)2 = 79%; ΔΔG‡
= −2.1 kJ
195K
mol−1), whereas the converse was found with 4-nitro-
benzophenone (F4‑NO2 = 16%; ΔΔG‡
= +2.7 kJ mol−1).
195K
Hammett analysis, Figure 1, revealed a modest sensitivity to
electronic perturbation (ρ ≈ −0.7) and, interestingly, a small
but significant deviation from linearity across the series, with
1
the alkyne ([13C2]-6-Ph,Ar4‑F; JCC = 183 Hz), as expected of
an aryl alkylidenecarbene.32 Controlled warming to −50 °C led
to complete alkyne formation within minutes.
Prior studies on alkylidene carbenes liberated by photolysis
of [13C1]-cyclopropanated phenanthrenes have shown 1,2-
migration is highly selective (exclusive) for H over Ph 13 and
for Ph over Me 14,19 (i.e., H ≫ Ph ≫ Me). Exclusive H-
migration was also observed herein, with no attenuation by
electronic20 (1-H,Ar4‑OMe) and isotopic perturbation (1-
D,Ar4‑OMe), the latter indicative that the selectivity is not
predicated on quantum tunneling. Analogously, exclusive aryl
migration was observed for aryl/alkyl alkylidene carbenes
i
t
generated from 1-Alk,Ph, where Alk = Me, Pr, Bu. However,
benzophenones (1-ArX,ArY) gave both alkyne 13C-isotopomers
in quantifiable ratios, with spectroscopic differentiation
1
achieved by a combination of H, 13C, 19F NMR spectroscopy
1
1
and, where necessary, H−1H COSY and H−13C/19F−13C
HMBC analysis. The fractional migration of ArX (FX) in each
case was quantified by 13C NMR (see Supporting Informa-
tion), with values corroborated by integration of multiple
distinct pairs of 13C signals. The relative migratory aptitude of
ArX, kX/kH, was then determined via eq 1.
Figure 1. Hammett analysis of the Colvin rearrangement of
monosubstituted benzophenones. [13C]-Li-TMSDAM generated in
situ from LDA (1.2 equiv) and [13C]-TMSDAM (1.0 equiv) prior to
the addition of ketone. Product isotopomer ratios were determined by
13C{1H} NMR, with selectivity corroborated by integration of
multiple distinct pairs of 13C signals. Substituent constant (σ) for
N(iPr)2 estimated from N(Pr)2. Use of KHMDS in place of LDA gave
identical isotopomer ratios within experimental error for cases where
the alkyne could be isolated in reasonable yield (X = 4-N(Me)2, 4-
OMe, 4-F).
kX
kH
FX
1 − FX
=
(1)
Migratory aptitudes were initially determined for 17 mono-
m/p-substituted benzophenones 1-Ph,ArX, with substituents
spanning from very electron-deficient (X = 4-NO2; σ = 0.78)
to highly electron-rich (X = 4-N(Me)2; σ = −0.83). Relative
migratory aptitudes were found to be approximately propor-
tional to the electron-richness of the migrating group. For
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selectivity tending toward a plateau for the most electron-
donating substituents. No improvements in linearity were
observed with other substituent parameters, e.g., σp .
function stability tests, all species were treated as closed-shell
singlets in their ground states (see Supporting Information for
details).
+
Ultradonating, anionic substituents (e.g., X = 4-S−)
unfortunately proved impractical, affording no alkyne products.
However, exploration of other substituents led to ferrocenyl
(Fc) as an interesting exception: although C-sp2 hybridized, π-
conjugated, and strongly electron-donating, phenyl migration
dominated, giving >99:1 Ph:Fc, Scheme 4. To probe the
influence of the “stationary” substituent on migratory
aptitudes, we next generated truncated Hammett correlations
using an additional 13 benzophenones, in this case 4,4′-
disubstituted 1-ArX,ArY; Y = p-N(Me)2, p-CF3; Figure 2.
To ensure the accuracy of optimized geometries for carbenic
species, a range of KS-DFT functionals were carefully
benchmarked against highly correlated DLPNO-CCSD(T)/
CCSD(T)-F12 reference calculations, using several model
alkylidene carbenes (PhMeCC:, Ph2CC:; see Supporting
Information). PBE0+GD3BJ, ωB97XD, and B3LYP+GD3BJ
were considered sufficiently robust in this regard, affording
disparate energies but, crucially, equilibrium geometries in
close agreement with the coupled-cluster surfaces.
Initial DLPNO-CCSD(T) computations established a
thermally feasible pathway from acetophenone (1-Me,Ph) to
1-phenylpropyne (6-Me,Ph), Figure 3. Consistent with Colvin
and Hamill’s original proposal7 and later work by Gilbert,9 the
diazoalkene MePhCCN2 (4-Me,Ph) was identified as a key
intermediate, formed via a nucleophilic addition,41,42 [1,3]-silyl
migration, and elimination sequence. Although the ionic nature
of the intermediates mean that quantitative comparisons made
in the absence of explicit solvation should be interpreted with
caution, lithiated silyl ether 3-Me,Ph appears to be marginally
favored over lithium alkoxide 2-Me,Ph (ΔG195K = −5 kJ
mol−1), in a delicately balanced [1,3]-Brook equili-
brium,43−46,32 in which pre-equilibrium between lithium α-
diazoalkoxide 2-Me,Ph and cyclic siliconate 7-Me,Ph is
kinetically insignificant.
Elimination of LiOTMS from silyl ether 3-Me,Ph generates
diazoalkene 4-Me,Ph, which contrary to most depictions, has a
bent structure on the ground state surface, thus resembling a
diazonium ylide rather than a heterocumulene.47,48 Dediazo-
niation of Z-4-Me,Ph affords singlet carbene 5-Me,Ph.
Analogously, E-4-Me,Ph (not shown) generates 5-Ph,Me.
The two conformational isomers (5-Ph,Me and 5-Me,Ph, see
Figure 3 inset) undergo rapid equilibration relative to ensuing
1,2-migration. Both carbenes have distorted structures, and in
isomer 5-Ph,Me14 (Cipso−Cβ−Cα bond angle, 91°) the position
of the aryl ring allows stabilizing π−p* and σ−p* donor−
acceptor interactions (see inset to Figure 3). Exergonic 1,2-
phenyl migration in 5-Ph,Me (Δ‡G195K = 7 kJ mol−1) generates
alkyne 6-Me,Ph. The analogous 1,2-methyl migration from 5-
Me,Ph is noncompetitive (Δ‡G195K = 42 kJ mol−1).
On the basis of the free energy profile in Figure 3, the
dediazoniation and migration steps (4 → 5 → 6) proceed
rapidly, sequentially, and irreversibly after rate-limiting [1,3]-
silyl migration/LiOSiMe elimination (2/3 → 4). In situ 13C
NMR spectroscopic monitoring of the reaction of [13C]-1-Ph,
Ar4‑F with [13C]-Li-TMSDAM at −78 °C (see Supporting
Information) revealed two intermediates with 13C NMR shifts
and couplings (1JCC = 39 Hz) consistent with a mixture of
[13C2]-2-Ph,Ar4‑F and [13C2]-3-Ph,Ar4‑F, albeit likely present as
higher-order lithium aggregates rather than monomers.
Analysis of Relative Migratory Aptitudes. Having
identified key intermediates en route to alkyne 6, we set out
to understand which processes are responsible for the
phenomenological migratory aptitudes (Scheme 4, Figures 1
and 2). The extremely low barrier predicted for aryl migration
(Figure 3 inset) poses several subtleties for the reactions of
benzophenones, which nominally lead to highly reactive β,β-
diaryl alkylidene carbenes (ArXArYCC:, 5). In such carbenes
both substituents appear liable to undergo rapid migration,
meaning that (i) the rate of conformational equilibration in the
incipient carbene 5 cannot necessarily be assumed to be rapid
Figure 2. Truncated Hammett correlations for Colvin rearrangement
of 4,4′-disubstituted benzophenones. Left hand plot: Hammett
correlations for the rearrangement of p,p′-disubstituted benzophe-
nones 1-ArX,ArY Right hand chart: overlaid correlations normalized
according to the relative migratory aptitude of ArY in the
monosubstituted benzophenone 1-Ph,ArY. [13C]-Li-TMSDAM was
generated in situ from LDA (1.2 equiv) and [13C]-TMSDAM (1.0
equiv) prior to the addition of ketone. Isotopomer ratios in 6 were
determined by 13C{1H} NMR spectroscopy.
Strikingly, all three correlations were effectively indistin-
guishable in their gradient and curvature, as evident from
overlay following y-axis normalization. Such behavior appa-
rently precludes the involvement of any bystander effect on
intramolecular selectivity, indicating that relative migratory
aptitudes (but not absolute rates, vide infra) remain unaffected
by the polar influence of the stationary substituent. These
results also suggest that the nature of the migratory transition
states remains fundamentally comparable across all of the
substrates, irrespective of their polarity, i.e., discounting
mechanistic discontinuities in limiting cases.
Generation of Alkylidene Carbenes. Seeking to ration-
alize the observed selectivities (Scheme 4), in particular the
curvature of the Hammett correlations (Figures 1 and 2), and
to develop a general model for the 1,2-migration rates and
aptitudes, we conducted extensive quantum chemical calcu-
lations using a combination of Kohn−Sham density functional
theory (KS-DFT; Gaussian 09) and local coupled cluster
theory (DLPNO-CCSD(T); ORCA 4.0). In accordance with
previous theoretical studies,13,14,33−40 independently computed
T1 diagnostic values (DLPNO-CCSD(T), T1 < 0.02),
exploratory unrestricted KS-DFT calculations, and wave
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Figure 3. Computed reaction pathway for the Colvin rearrangement of acetophenone (1-Me,Ph). Geometries and solvation free energies were
obtained via restricted KS-DFT at the PBE0+GD3BJ/6-311+G(d,p)/IEFPCM(THF,UFF)/Ultrafine level of theory. Thermochemical corrections
were computed at T = 195 K using the rigid-rotor harmonic-oscillator approximation (GoodVibes) and linearly scaled harmonic frequencies (vscale
= 0.95), with vibrational entropies corrected in accordance with Grimme’s quasi-harmonic approach (fcutoff = 100 cm−1) and translational entropies
adjusted to reflect a standard state of 1.0 M. Single-point, gas-phase potential energies were computed at the DLPNO-CCSD(T)/ma-def2-TZVPP/
TightPNO level. A transition state for concerted elimination of LiOTMS from 2-Me,Ph leading directly to 4-Me,Ph could not be found. The
transition states for loss of LiOTMS from 3-Me,Ph leading to E-4-Me,Ph and for loss of N2 from E-4-Me,Ph leading to 5-Me,Ph are higher in
energy and are not shown. See Supporting Information for full details.
with respect to migration and (ii) nonstatistical dynamic effects
on selectivity cannot be discounted a priori. DLPNO-
CCSD(T)/ma-def2-QZVPP calculations indicate, for example,
that after extrusion of N2 from Ph2CCN2 (ΔG195K = −28 kJ
mol−1), subsequent 1,2-phenyl migration in the nascent
carbene 5 (Δ‡G195K = 10 kJ mol−1) is only marginally higher
in barrier to its degenerate conformational interconversion
(Δ‡G195K = 7 kJ mol−1).
With this in mind, we considered two limiting intra-
molecular regimes for product selection (Scheme 5). In regime
1, classical Curtin−Hammett conditions prevail: conforma-
tional equilibration of 5-ArXArY is rapid and the observed
product ratio depends only on the two competing 1,2-
migration transition states. In regime 2, conformational
equilibration is slow with respect to migration and/or dynamic
matching leads to significant bypassing of 5-ArXArY as an
intermediate. As a consequence, the observed product ratio
depends on selectivity established in preceding steps of the
mechanism.
regimes 1 and 2, where stereochemical/conformational
interconversions in 4/5 are competitive with migration, the
net selectivity arises from a number of factors.
To discern which, if either, of these regimes prevails for the
benzophenone system, we first systematically probed, via
computation, the potential energy surfaces of 28 distinct β,β-
diaryl alkylidene carbenes (ArXArYCC:), constructed from
seven electronically diverse para-substituted aryl groups (X, Y
= 4-NMe2, 4-OMe, 4-Me, 4-H, 4-Cl, 4-CF3, 4-NO2). Key
stationary points were located by restricted KS-DFT, following
functional benchmarking against DLPNO-CCSD(T)/ma-def2-
QZVPP calculations. For each of the seven symmetric (X = Y)
carbenes we located a single minimum energy structure, one
migration transition state, and a C2v-symmetric transition state
leading to degenerate conformational interconversion.
For the 21 asymmetric carbenes (X ≠ Y), we identified two
ground state conformers and two migratory transition states
(Δ‡EX,mig, Δ‡EY,mig), in addition to a pseudo C2v-symmetric
transition state for conformational interconversion (Δ‡EX,conf
,
Further analysis (DLPNO-CCSD(T)/ma-def2-QZVPP)
Δ‡EY,conf). Extensive π−p* and σ−p* interactions between the
terminal α-carbon and β-aryl substituents leads to significant
geometrical distortions in both conformers of the β,β-diaryl
alkylidene carbene system, with one aryl ring adopting a
perpendicular orientation13,14 with respect to the terminal C
C bond and the other remaining planar. In all 21 of the
asymmetric carbenes, the ground state was found to be that in
which the most electron rich substituent adopts the
indicates that E/Z-isomerization of the irreversibly generated
diazoalkene 4 intermediate is expected to be slow (Δ‡G195K
=
51 kJ mol−1 for 5-Ph,Ph) compared to 1,2-aryl migration.
Thus, under regime 2, the ratio reported by the 13C-label
would correspond to stereoselectivity at the stage of LiOTMS
elimination from the lithiated silyl ether 3-ArX,ArY, not the
migratory aptitude of the β-substituents. Between the limits of
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Scheme 5. Limiting Regimes for Product Selection in the
a
Colvin Rearrangement of Benzophenones
Figure 4. Schematic potential energy surface of a β,β-diaryl alkylidene
carbene.
a
Italicization indicates that a substituent is either primed to migrate in
a specific conformer/isomer, e.g., 5-ArX, ArY, or has undergone
migration, e.g., 6-ArX, ArY.
perpendicular orientation, with increasing electron-richness
also leading to a progressive decrease in the ground state Cipso
−
Cβ−Cα bond angle (e.g., Ph2CC:, 87°; PhAr4‑NMe2CC:,
79°). The preference for the most electron rich aryl group
being perpendicular to the terminal CC bond is consistent
with it being the better donor for nonclassical π → p*
conjugation and/or σ → p* hyperconjugation (see inset to
Figure 3).
Having established the general PES topography of the β,β-
diaryl alkylidene carbenes, Figure 4, we computed theoretical
migratory aptitudes for seven carbenes derived from mono-p-
substituted benzophenones 1-Ph,ArX. Selectivities were then
computed for regime 1, where the product ratio depends solely
on [Δ‡EH,mig + ΔEX‑H − Δ‡EX,mig]. These calculations were
then repeated using a range of computational methods,
spanning different electronic structure theories (KS-DFT,
DLPNO-CCSD(T)), select DFT functionals, basis sets, and
statistical mechanics approximations, in order to assess the
method sensitivity of our analysis (see Supporting Information
for full survey).
All of the methods led to the same conclusion: the more
electron-rich aryl group in the β,β-diaryl alkylidene carbene
migrates preferentially. Quantitative comparisons with exper-
imental values proved more challenging since the transition
states differ by at most a few kJ mol−1 (log10 kX/kH = |0.8|;
ΔΔ‡G195K = |3.0| kJ mol−1). Nonetheless, the nominally
highest-level results, obtained with DLPNO-CCSD(T), as
summarized in Figure 5 (see Supporting Information for full
Figure 5. Computed Hammett correlations for mono-p-substituted
benzophenones (1-ArX,Ph; X = 4-NMe2, 4-OMe, 4-Me, 4-H, 4-Cl, 4-
CF3, 4-NO2), obtained via three different computational methods.
Relative rates were calculated at T = 195 K via kX/kH = exp[(Δ‡EH −
Δ‡EX)/(RT)], where Δ‡Ei denotes the activation barrier for migration
of Ari (i = X, H), relative to the ground state, in PhArXCC:. In each
case, single-point gas-phase energies were computed with DLPNO-
CCSD(T)/ma-def2-TZVPP/TightPNO, using geometries and sol-
vation energies obtained with one of three different KS-DFT methods
XCF/6-311+G(d,p)/IEFPCM(THF,UFF) (XCF = B3LYP+GD3BJ,
PBE0+GD3BJ, ωB97XD). Experimental correlations for all 17
benzophenones are overlaid for comparison.
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discussion), reproduce both the gradient and subtle curvature
of the parent Hammett correlation (Figure 1) with reasonable
fidelity. This correspondence indicates that (i) the alkylidene
carbene 5 serves as a discrete, product-determining inter-
mediate en route to alkyne 6, (ii) the 13C-isotopomer ratios
measured experimentally report the relative migratory
aptitudes of the two competing aryl substituents in the free
carbene 5, (iii) regime 1, i.e., classical Curtin−Hammett
conditions, prevail, and (iv) the curvature of the Hammett
correlation is an intrinsic feature of the 1,2-migration in the
alkylidene carbene, presumably reflecting the progressive
stabilization of the ground-state by a nonclassical π → p*
interaction with more strongly electron-donating substituents.
Independent DLPNO-CCSD(T) calculations of the barriers
to conformational interconversion in β-phenyl-β-aryl alkyli-
dene carbenes (Table 1) appear to confirm that other than for
very electron-donating substituents (e.g., X = 4-NMe2)
rearrangement proceeds under regime 1 (kconf > 5kmig).49
alkyne. Of direct relevance, however, are the absolute
migratory aptitudes of both of the β-substituents, for these
ultimately control the intrinsic lifetime of the alkylidene
carbene and thus the propensity for carbene interception
(Scheme 1). Indeed, ambiguities in the literature concerning
the apparent influence of the stationary (“bystander”)
substituent in Fritsch−Buttenberg−Wiechell rearrangements
and related processes may arise from misinterpretation or
conflation of relative versus absolute migration rates.2
We explored this question theoretically, using a set of 28
β,β-diaryl alkylidene carbenes and computing the absolute
activation barriers to 1,2-aryl migration, relative to the global
minimum on each PES, for the full matrix of carbenes. As
before, we reproduced these calculations using a range of
methods (see Supporting Information). Examples of these
results, obtained from DLPNO-CCSD(T) calculations, are
summarized Table 2 in the form of intrinsic lifetimes (τXY, ns,
Table 2. Computed Lifetimes (ns) of 28 β,β-Diaryl
a
Alkylidene Carbenes ArXArYCC: at −78°C
Table 1. Computed Relative Rates of Conformational
Interconversion versus Migration in β-Phenyl-β-aryl
X or Y
NMe2
OMe
Me
H
Cl
CF3
NO2
a
Alkylidene Carbenes
NMe2
OMe
Me
H
Cl
1
10
36
2
8
4
10
15
38
0.1
0.2
0.3
0.6
89
0.1
0.3
0.4
1.0
203
482
1554
0.2
0.3
0.3
CF3
NO2
0.1
0.2
2.2
0.1
a
−1
Lifetimes τXY = (kX,mig + kY,mig
)
were calculated at T = 195 K in
accordance with kmig = (kBT/h) exp[(−Δ‡E,mig)/(RT)]. Activation
barriers were computed by a combined KS-DFT/DLPNO-CCSD(T)
methodology, using geometries and solvation energies obtained at the
PBE0+GD3BJ/6-311+G(d,p)/IEFPCM(THF,UFF)/Ultrafine level
of theory and gas-phase, single-point energies from DLPNO-
CCSD(T)/ma-def2-TZVPP/TightPNO. Values are computed and
illustrative only.
X
k
conf/kmig
X
k
conf/kmig
NMe2
OMe
Me
1
5
6
17
41
36
97
NMe2
OMe
Me
7
19
15
17
24
20
24
H
H
Cl
CF3
NO2
Cl
CF3
NO2
a
Combined KS-DFT/DLPNO-CCSD(T) methodology, using geo-
at −78 °C). The data are also presented as a 2D contour plot
(Figure 6) in the form of the absolute barrier to aryl migration
as a function of both substituents. While the barriers and
lifetimes are necessarily highly sensitive to the exact method of
calculation, the underlying trends appear robust between
different methods. Indeed, DLPNO-CCSD(T) calculations
predict the lifetime of MePhCC: to be 3 ps under ambient
conditions, in reasonable agreement with the recent exper-
imental measurements (τ = 13.3 ps) of Phillips, Hadad, and
Thamattoor.15
The data in Table 2 and Figure 6 reveal two initially
counterintuitive trends: (i) the intrinsic lifetimes are
minimized by using electronically matched substituents, i.e.,
the barriers to migration are lowest along the diagonal in
Figure 6, and (ii) the intrinsic lifetimes are maximized by
strongly donating groups. Crucially, these lifetimes reflect the
theoretical feasibility of intramolecular or intermolecular
interception of the nascent alkylidene carbenes following its
release from a precursor (Scheme 1), and the effect of
electronic matching on the lifetime is substantial, particularly
for strongly perturbing substituents. Thus, while the intrinsic
lifetimes of the symmetric carbenes, Ar2CC:, are in the
range 0.1−1 ns, some of the asymmetric carbenes are predicted
to have lifetimes up to 3−4 orders of magnitude larger (0.1−1
μs, at −78 °C).
metries and solvation energies obtained at the PBE0+GD3BJ/6-
311+G(d,p)/IEFPCM(THF,UFF) level of theory and single-point
gas-phase energies obtained from DLPNO-CCSD(T)/ma-def2-
TZVPP/TightPNO. Calculated at T = 195 K in accordance with
k
conf/kmig = exp[(Δ‡Emig − Δ‡Econf)/(RT)], Figure 4.
Analysis of Absolute Migratory Rates. Alkylidene
carbene intermediates are very short-lived, undergoing rapid
partitioning between 1,2-migration to generate an alkyne
versus carbene interception by insertion, cycloaddition, etc.
Scheme 1. The 1,2-migration itself proceeds via two micro-
scopically distinct competing pathways, and both experiment
and computation (Figures 1, 2, and 5) show that more
electron-donating β-substituents migrate preferentially, in
agreement with prior observations.2,13,14,19,20 It is tempting
to generalize that alkylidene carbenes with electron-donating
β-substituents rearrange faster than those with electron-
withdrawing ones. However, this would be incorrectly based
on extrapolation from relative migratory aptitudes determined
under a regime of intramolecular competition.
In fact the relative rates (migratory aptitudes) provide no
direct insight into the practical aspects of employing alkylidene
carbene intermediates because both 1,2-migrations converge,
in the absence of isotopic desymmetrization, on the same
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Figure 6. Contour map of activation barriers for 1,2-aryl migration in
28 β,β-diaryl alkylidene carbenes computed using a combined KS-
DFT/DLPNO-CCSD(T) methodology, with geometries and sol-
vation energies obtained at the PBE0+GD3BJ/6-311+G(d,p)/
IEFPCM(THF,UFF) level of theory and single-point gas-phase
energies from DLPNO-CCSD(T)/ma-def2-TZVPP/TightPNO. Ac-
tivation barriers are relative to the ground state and reported in kJ
mol−1.
Origins of the Electronic Matching Effect. The
underlying basis for the effect is summarized in Figure 7,
which is generated by analysis of various components taken
from two cross sections of the data in Figure 6. The left-hand
series displays the effect of varying the substituent (X) on the
migrating group when the bystander is phenyl; in the right-
hand series the bystander substituent is varied (Y) when the
migrating group is phenyl. Unsurprisingly both series show that
electron-rich substituents provide thermodynamic stability to
the ground state energy (ΔE) via enhanced π → p* and σ →
p* donor−acceptor interactions (see inset to Figure 3)
compared to Ph.
The second row displays the barrier to 1,2-migration
(Δ‡Emig) from the specified conformer. For variation in
migrator (X) the loss of π → p* stabilization during 1,2-
migration results in larger barriers arising with electron-rich
substituents. Conversely, for variation in bystander (Y)
electron-rich substituents reduce the barrier via inductive
transition state stabilization.
In the final row, the net effect of both sets of interactions
shows how the overall barrier to alkyne formation, relative to
the ground state, varies. In both cases the barrier is minimized
by electronically matching the migrating substituent to the
bystander. The minimum barrier is found at σ = 0 in this case,
because Ph has been selected as the reference group. As the σ
value for the reference group is changed, the point of minimum
barrier moves with it, as illustrated by the diagonal line in
Figure 6.
Figure 7. Energetic rationale for substituent matching in β,β-diaryl
alkylidene carbenes. First row: Difference in energy between the
specified conformer and the ground state (ΔEi; i = X, H). Second row:
activation barrier to migration, relative to the specified conformer
(Δ‡Emig,i). Third row: activation barrier to migration, relative to the
ground state (Δ‡Emig,i + ΔEi). Fourth row: (Δ‡Emig,X − Δ‡Emig,H) +
(ΔEX − ΔEH). All energies were obtained by a combined KS-DFT/
DLPNO-CCSD(T) methodology, using geometries and solvation
energies obtained at the PBE0+GD3BJ/6-311+G(d,p)/IEFPCM-
(THF,UFF) level of theory and single-point gas-phase energies
from DLPNO-CCSD(T)/ma-def2-TZVPP/TightPNO. All energies
are reported in kJ mol−1.
previously reported for alkylidene carbenes liberated by
photolysis.13,14
Changes to the electronics, sterics, and isotopic identity (H/
D) of the β-substituents did not detectably perturb this trend.
Thus, H-migration is not exclusively contingent on quantum-
tunneling, and the hybridization of the migrating center exerts
substantial influence over the migratory aptitude of the β-
substituent.
High-level electronic structure calculations were conducted
to explore both the mechanism and selectivity of the overall
process. Calculations, together with in situ low temperature 13
C
CONCLUSIONS
NMR spectroscopic studies, support the conclusion that the
Colvin rearrangement proceeds via the sequence shown in
Scheme 2, involving irreversible LiOSiMe3 elimination,
stereospecific dediazoniation, then 1,2-migration in the free
alkylidene carbene. Alternative routes (see Supporting
Information) to the alkyne by 1,2-migration concerted with
N2 extrusion at the diazoalkene, or reaction via an oxonium
ylide formed by THF coordination, could not be located on
the ground state PES (KS-DFT).
■
We have used the Colvin rearrangement of carbonyl
compounds to systematically explore the rearrangement of
alkylidene carbenes.20 In situ labeling by use of [13C]-TMS-
diazomethane, in conjunction with 13C{1H} NMR spectro-
scopic analysis of the alkyne products, expedited the
quantification of the intramolecular selectivity (migratory
aptitude) in the 1,2-migration step. Preliminary experiments
reproduced the migratory aptitudes H ≫ Ph ≫ alkyl
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spectra of 13C-labeled alkynes, computational methods,
and benchmarking calculations (PDF)
Extensive experimental studies of differentially substituted
benzophenones provided nuanced insights to the 1,2-migration
step. Hammett analysis of the intramolecular competitive
rearrangement of alkylidene carbenes generated from mono-
substituted benzophenones afforded a smooth but nonlinear
correlation, indicative that relative migratory aptitudes increase
toward a plateau for the most electron-rich substituents in the
series (Figure 1). The curvature and gradient of this
correlation remained completely invariant to changes in the
reference substituent, apparently discounting any mechanistic
discontinuity in the limiting substrates (Figure 2).
Electronic structure calculations (Figure 5) reproduced both
the gradient and curvature of the parent correlation. This is
again indicative that product selection occurs under a Curtin−
Hammett regime, with the prima facie implication that
alkylidene carbenes generated from diazoalkenes are not
subject to significant dynamic effects.50 The nonlinearity of
the Hammett correlation reflects increasing ground-state
stabilization by the β-substituents, via nonclassical π → p*
conjugation and/or σ → p* hyperconjugation (see inset to
Figure 3).
AUTHOR INFORMATION
Corresponding Author
■
Guy C. Lloyd-Jones − School of Chemistry, University of
Edinburgh, Edinburgh EH9 3FJ, U.K.; orcid.org/0000-
0003-2128-6864; Email: guy.lloyd-jones@ed.ac.uk
Authors
Harvey J. A. Dale − School of Chemistry, University of
Edinburgh, Edinburgh EH9 3FJ, U.K.
Chris Nottingham − School of Chemistry, University of
Edinburgh, Edinburgh EH9 3FJ, U.K.
Carl Poree − School of Chemistry, University of Edinburgh,
Edinburgh EH9 3FJ, U.K.
Complete contact information is available at:
https://pubs.acs.org/10.1021/jacs.0c12400
Author Contributions
A key aspect not fully deconvoluted in prior studies is that
the relative migratory aptitudes do not necessarily reflect the
overall propensity for 1,2-migration versus other competing
processes (Scheme 1). Theoretical exploration of the absolute
migratory aptitudes of a systematic matrix of 28 β,β-diaryl
alkylidene carbenes uncovered several effects not easily
quantified by experimental interrogation. Calculations suggest,
for example, that the intrinsic lifetimes are not primarily
dependent upon the electron-donating/withdrawing abilities of
the substituents per se but upon the electronic disparity
between the two substituents (Figure 6). Electron-donating
groups, while more effective competitors under conditions of
intramolecular competition, do not necessarily lead to faster
migration. Indeed, highly polarized β,β-diaryl alkylidene
carbenes appear to have lifetimes several orders of magnitude
greater than symmetric analogues (Table 2). These systems
may therefore provide new opportunities for direct spectro-
scopic detection in solution in the nano- to microsecond
regime.
The above findings on electronic matching add to a previous
rather fragmentary body of evidence suggesting that the
absolute migratory aptitude of a given substituent is not an
intrinsic property but mutually dependent on the stationary
substituent, or bystander.51 The synthetic ramifications of the
matching effect, nevertheless, are not yet completely clear. For
example, it is tempting to assume that longer intrinsic lifetimes
established by mismatching will increase the probability of
interception of the carbene (Scheme 1). However, this is
contingent on the extent to which the mismatching also
stabilizes the carbene ground-state to the competing processes.
Highly efficient bimolecular trapping processes that are
kinetically competitive but limited by diffusion may benefit
the most in this respect.
All authors have given approval to the final version of the
manuscript.
Funding
The research leading to these results has received funding from
the European Research Council under the European Union’s
Seventh Framework Programme (FP7/2007−2013)/ERC
Grant Agreement 340163.
Notes
The authors declare no competing financial interest.
ACKNOWLEDGMENTS
■
We thank Dr. Andrew Leach (University of Manchester) and
Tom Young (University of Oxford) for detailed advice on
́
electronic structure calculations on carbenes, and Dr. Andres
García Domínguez (University of Edinburgh) for a careful
reading of this manuscript.
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* Supporting Information
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J. Am. Chem. Soc. 2021, 143, 2097−2107

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(49) We initially considered this trend as possible contributing factor
to the curvature in the Hammett plot (Figure 1) but have been unable
to establish a firm conclusion in this respect.
(50) Although this conclusion is also supported by theoretical
barriers to conformational equilibration, it should be noted that
alternative regimes, in which selectivity is governed further upstream
in the mechanism (e.g., by stereoselective elimination) and the
carbenes themselves are bypassed, cannot be ruled out definitively if
for example such upstream processes exhibit analogous selectivities.
(51) For a recent example, see the following: Chen, F. J.; Lin, Y.; Xu,
M.; Xia, Y.; Wink, D. J.; Lee, D. C−H Insertion by Alkylidene
Carbenes To Form 1,2,3-Triazines and Anionic [3 + 2] Dipolar
Cycloadditions To Form Tetrazoles: Crucial Roles of Stereoelectronic
and Steric Effects. Org. Lett. 2020, 22, 718−723.
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https://dx.doi.org/10.1021/jacs.0c12400
J. Am. Chem. Soc. 2021, 143, 2097−2107