Competitive 1,2-C Atom Shifts in the Strained Carbene Spiro[3.3]hept-1-ylidene Explained by Distinct Ring-Puckered Conformers

Article abstract of DOI:10.1021/acs.joc.6b02445

Spiro[3.3]hept-1-ylidene is a markedly strained carbene reaction intermediate that was generated by high-vacuum flash pyrolysis (HVFP) of the corresponding p-tosylhydrazone sodium salt. Five hydrocarbons were produced from the Bamford-Stevens reactant in 82% overall yield. The carbene undergoes two [1,2]-sigmatropic rearrangements via competing 1,2-C atom shifts. Ring-contraction yields cyclopropylidenecyclobutane, while ring-expansion affords bicyclo[3.2.0]hept-1(5)-ene. The ring contraction is regiospecific despite the formation of some 1-methylenespiro[2.3]hexane. It does not originate from the carbene under HVFP conditions. Instead, it comes from a methylenecyclopropane-type rearrangement of chemically activated cyclopropylidenecyclobutane. Similarly, some chemically activated bicyclo[3.2.0]hept-1(5)-ene rearranges to 1,2-dimethylenecyclopentane via electrocyclic ring-opening. Accounting for the conversion of primary products to secondary ones, relative yields indicate that ring-contraction within the carbene prevails over ring-expansion by a factor of 6.7:1. Computational chemistry was used to assess the structures, conformations, energies, strain energies, transition states, and activation energies of these rearrangements with the goal of explaining product selectivities. The dual-ringed carbene is predicted to assume four distinct geometric conformations that have a bearing on transition-state selection. The reactive cyclobutylidene units of two conformers are significantly puckered, like cyclobutylidene itself, while those of the other two are flatter. The selectivity of the title carbene is compared with that of spiro[2.3]hex-4-ylidene.

Full text of DOI:10.1021/acs.joc.6b02445

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Article
Competitive 1,2-C Atom Shifts in the Strained Carbene Spiro[3.3]hept-1-
ylidene Explained by Distinct Ring-Puckered Conformers
Murray G. Rosenberg, Theodor Schrievers, and Udo H Brinker
J. Org. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.joc.6b02445 • Publication Date (Web): 02 Dec 2016
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Competitive 1,2-C Atom Shifts in the Strained Carbene
Spiro[3.3]hept-1-ylidene Explained by Distinct Ring-
Puckered Conformers
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Murray G. Rosenberg,§ Theodor Schrievers,‡ and Udo H. Brinker*,†,§
†Institute of Organic Chemistry, University of Vienna, Währinger Strasse 38, A-1090 Vienna,
Austria
§Department of Chemistry, The State University of New York at Binghamton, P. O. Box 6000,
Binghamton, NY, 13902-6000, United States
ABSTRACT: Spiro[3.3]hept-1-ylidene is a markedly strained carbene reaction intermediate that
was generated by high-vacuum flash pyrolysis (HVFP) of the corresponding p-tosylhydrazone
sodium salt. Five hydrocarbons were produced from the Bamford–Stevens reactant in 82%
overall yield. The carbene undergoes two [1,2]-sigmatropic rearrangements via competing 1,2-C
‡
Some material taken in part from Ph.D. Dissertation, Ruhr-University Bochum, Bochum, Germany, December 21, 1989.
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atom shifts. Ring-contraction yields cyclopropylidenecyclobutane while ring-expansion affords
bicyclo[3.2.0]hept-1(5)-ene. The ring-contraction is regiospecific despite the formation of some
1-methylenespiro[2.3]hexane. It does not originate from the carbene under HVFP conditions.
Instead, it comes from a methylenecyclopropane-type rearrangement of chemically activated
cyclopropylidenecyclobutane. Similarly, some chemically activated bicyclo[3.2.0]hept-1(5)-ene
rearranges to 1,2-dimethylenecyclopentane via electrocyclic ring-opening. Accounting for the
conversion of primary products to secondary ones, relative yields indicate that ring-contraction
within the carbene prevails over ring-expansion by a factor of 6.7:1. Computational chemistry
was used to assess the structures, conformations, energies, strain energies, transition states, and
activation energies of these rearrangements with the goal of explaining product selectivities. The
dual-ringed carbene is predicted to assume four distinct geometric conformations that have a
bearing on transition state selection. The reactive cyclobutylidene units of two conformers are
significantly puckered, like cyclobutylidene itself, while those of the other two are flatter. The
selectivity of the title carbene is compared with that of spiro[2.3]hex-4-ylidene.
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■ INTRODUCTION
Carbenes are neutral molecules that feature a divalent C atom.1–7 Stabilizing tetravalency is
restored when the hypovalent C atom obtains a Lewis octet. If possible, this occurs after fast
isomerization(s).8 Computational chemistry is now widely used to supplement the experimental
results of these short-lived, high-energy reaction intermediates.9 The carbene spiro[3.3]hept-1-
ylidene (1) (Figure 1a) is a 2,2-dialkyl-substituted derivative (Figure 1b) of the small-ring
carbene cyclobutylidene (2)10 (Figure 1c). Spiro[2.3]hex-4-ylidene (3)11–13 is one too (Figure
1d). Carbene 1 is a homolog of 3, which in turn could be seen as “2°-norspiro[3.3]hept-1-
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ylidene.” The remarkable thing about carbene 3 is that, in lieu of 1,1'-bi(cyclopropylidene) (4), 1-
methylenespiro[2.2]pentane (5), and spiro[2.3]hex-4-ene (7), it forms bicyclo[2.2.0]hex-1(4)-ene
(6) exclusively by ring-expansion (Scheme 1).11–13 This [1,2]-sigmatropic rearrangement is
atypical of cyclobutylidenes,10 because 1,2-C atom shifts invariably lead to ring-contraction
products. Thus, a study of carbene 1 was undertaken to determine the proclivity of its 1,2-C atom
shift(s).
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(a)
(c)
(b)
(d)
Figure 1. The strained carbene (a) spiro[3.3]hept-1-ylidene (1) is a (b) 2,2-dialkyl-substituted (R
= –CH2–) derivative of (c) cyclobutylidene (2). Carbene 1 is a homolog of (d) spiro[2.3]hex-4-
ylidene (3), which avoids characteristic ring-contraction in favor of ring-expansion (Scheme 1).
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Scheme 1. [1,2]-Sigmatropic Rearrangements of Carbene 3
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Cyclobutylidenes can be trapped intermolecularly by alkenes14 and alkynes,15 but this report
delves into their intramolecular isomerizations.14–17 The spin multiplicity of cyclobutylidenes,10
due to the two nonbonding electrons, is uncharacteristic of dialkylcarbenes. The ring-enforced
small bond angle of the bicoordinate C atom raises the triplet state energy thereby permitting a
1
singlet ground electronic state. The spin-paired (n2p0) electron configuration of the divalent C
atom also fosters classical hyperconjugation and nonclassical hypervalent C1···C3 bonding,18–20
depending on the amount of ring-puckering.20 The isomerization of carbene 2 to cyclobutene (8)
(Scheme 2a) is slower than that to methylenecyclopropane (9) (Scheme 2b), which is the major
product.14–17,19,21 Energy is required to break the C1···C3 “bond”22 in 2 (i.e., dashed red line of 2
in Scheme 2). A flatter form of 2, which is better suited for stabilizing hyperconjugation,20 may
exist (vide infra). However, a bridging H atom introduces strain in the transition state (TS) of the
1,2-H atom shift as flattened TS(2/8) progresses to planar 8 (Scheme 2a). Whereas the formation
of 8 from 2 is topologically impeded, ring-puckered 2 is conformationally predisposed to form 9
because 2 already resembles TS(2/9) (Scheme 2b). Sometimes the primary products isomerize to
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yield small amounts of secondary products. For example, some 8 undergoes electrocyclic ring-
opening to 1,3-butadiene (Scheme 2a) and the well-known degenerate rearrangement of 9
proceeds via the trimethylenemethane (10) diradical (Scheme 2b).23–26
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Scheme 2. [1,2]-Sigmatropic Rearrangements of Cyclobutylidene (2)a
a Dashed red line of 2 represents its elongated nonclassical C–C single bond.
Gibbs free energy of activation (G‡) values for isomerizations of 2 have been computed
using the CCSD(T)/DZP theoretical model:19 (1) 1,2-H atom shift (G‡ = 9.7 kcal/mol), (2) 1,2-
C atom shift (G‡ = 10.5 kcal/mol), and (3) 1,3-C–H bond insertion (G‡ = 14.6 kcal/mol). The
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computed G‡ between the 1,2-C atom shift 2→9 and the 1,2-H atom shift 2→8 is thus 0.8
kcal/mol.19 From eq 1, one arrives at a 9:8 ratio of 0.26 at T = 25 °C. However, this ratio is
contrary to those established by numerous experiments. Ring-contraction is decisively favored
(Scheme 2b) with a 9:8 ratio of (8.7 ± 4):1.14–17,19,21 The experimental G‡ is thus (–1.2 ± 0.3)
kcal/mol at T = 25 °C, according to eq 2. It is worth noting that the product selectivity of 2 does
not reflect the amount of ring-strain energy (Es) present in each product. The Es value of 9 is 39.5
kcal/mol whereas that for 8 is only 28.7 kcal/mol.27–29 These values are affirmed in this report.
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‡
‡
G‡
RT
9: 8  e
 e G(29) G( 28)
(1)
(2)
RT
G‡ = [G‡( → ) – G‡ 8 ] = –RTln(9:8)
2
9
2
( → )
2-Alkylcyclobutylidenes 11 yield alkylidenecyclopropanes and alkylcyclobutenes to a lesser
extent (Scheme 3).16,30–32 The type of carbene precursor used (e.g., gem-dibromo compound16 or
p-tosylhydrazone alkali salt17) and the reaction conditions (e.g., T = –78 to 0 °C/RLi/Et2O or T
= 120 to 310 °C/p = (0.1–1.0) × 10–4 Torr) affect the scope of the isomerizations. For example,
the debromination of 2-alkyl-1,1-dibromocyclobutanes produces alkylidenecyclopropanes 12a in
high yield (Scheme 3a) whereas alkylcyclobutenes 12c–e are not formed at all (Scheme 3c–e).30
Carbene 1 should undergo a 1,2-C atom shift leading to regiospecific 1°-ring-contraction (cf.
Scheme 3a and Figure 1a, b), but it might also undergo a 2°-ring-expansion (cf. Scheme 3c and
Figure 1a, b, d), as does carbene 3 (cf. Scheme 1), because it features an embedded 2,2-dialkyl-
substituted cyclobutylidene (Figure 1b).
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Scheme 3. Reactions of 2-Alkylcyclobutylidenes 11
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■ RESULTS AND DISCUSSION
Spiroannulation of cyclobutanone was achieved herein using 1-bromo-1-ethoxycyclopropane
(13)33–36 (Scheme 4). This method gave spiro[3.3]heptan-1-one (15)37 in 78% overall yield. The
corresponding Bamford–Stevens32,38 reactant 17 was efficiently fragmented using a high-vacuum
flash pyrolysis (HVFP) apparatus (see Supporting Information Figure S22) to liberate carbene 1
(Scheme 4).
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Scheme 4. Synthesis of Carbene 1 Precursor
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Five hydrocarbons were obtained in 82% overall yield upon HVFP (T = 250 °C; p = 9 × 10–4
Torr) of Bamford–Stevens reactant 17. The product set profile listed in Table 1 shows their
relative percentages. Standard 1-D NMR, IR, and MS experiments were performed to identify
the products from known spectra. The major product was cyclopropylidenecyclobutane (18)39–43
followed by l-methylenespiro[2.3]hexane (19).39,40,44 Lesser amounts of bicyclo[3.2.0]hept-1(5)-
ene (20) 11,12,45–47 and 1,2-dimethylenecyclopentane (21)45,48,49 were also formed. An unidentified
hydrocarbon (22) was formed in trace amounts. Plausible candidates are shown in Chart 1: (1)
spiro[bicyclo[1.1.0]butane-2,1'-cyclobutane] (22a), (2) trans-tricyclo[3.2.0.01,4]heptane (trans-
22b),50 (3) spiro[3.3]hept-1-ene (22c),51 and (4) (prop-2-en-1-ylidene)cyclobutane (22d).
Table 1. Products from HVFP of Bamford–Stevens Reactant 17a
Product
Yieldb
(rel.%)
69.3
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17.0
8.6
4.3
0.8
c
a Reaction conditions: T = 250 °C; p = 9 × 10–4 Torr. b Overall yield = 82%. c See Chart 1.
Chart 1. Possible Structures of Trace Product 22
The rates of interconversion and positions of equilibria for the thermal rearrangement of 18
to 19 (Scheme 5) have been assessed at T = 190 to 220 °C and p < 100 Torr.39,40 Higher
pressures caused 18 to dimerize to tetraspiro[2.0.24.0.37.0.311.03]tetradecane.40 In the same
fashion, 4 dimerizes to tetraspiro[2.0.24.0.27.0.210.03]dodecane.52 When the data for 18Ý19 are
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extrapolated to T = 250 °C, the 18:19 ratio becomes 1.12:1, assuming H and S vary
insignificantly from T = 190 to 250 °C. Isomers 18 and 19 should have almost equal Gibbs free
energy (G) values because Keq is close to unity. The empirical E = E(18) – E(19) = –
0.39 kcal/mol was confirmed in this report using computational chemistry (vide infra). The
cyclobutylidene(dimethylene)methane (23) diradical is a plausible reaction intermediate in the
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equilibrium 18Ý19 (Scheme 5). The activation energy (Ea) for 18→19 (Scheme 5a) is reported
to be (39.7±2) kcal/mol with a frequency factor (A) of 1.8 × 1014 s–1.39,40 When the Arrhenius
activation parameters are converted into those of the unimolecular Eyring equation,53 the data
entail a G‡ value of 36.9 kcal/mol (Scheme 5a).
Scheme 5. Methylenecyclopropane-Type Rearrangement of 18 to 19
The HVFP of Bamford–Stevens reactant 17 resulted in a 18:19 ratio of 4.08:1 (Table 1),
which is rapidly preserved as the isomers are physically trapped at T = –196 °C. This proportion
suggests that internal ring-contraction 1→18 (Scheme 6a) surpasses external ring-contraction
1→19 (Scheme 6b) by a factor of 4.08 and that G‡ for the two ring-contractions in 1 is –1.5
kcal/mol, according to eq 3. However, the ratio and corresponding G‡ value may be severely
skewed because products 18 and 19 can interconvert through diradical 23 (Scheme 5).
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Scheme 6. Potential Rearrangements of Carbene 1
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G‡ = [G‡
) – G‡ 19 ] = –RTln(18:19)
(3)
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( →
)
If some 18 is depleted during the reaction then the intrinsic 18:19 ratio would be greater than
4.08:1 and the G‡ value (eq 3) would be more negative than –1.5 kcal/mol. Indeed, the exo
methylene group of 19 casts doubt on its direct formation from 1. Recall that 2-alkyl-substituted
cyclobutylidenes 11 often form alkylidenecyclopropanes 12a regiospecifically.30 The preference
for 12a (Scheme 3a) can be traced back to its internal C–C double bond, which is more highly
substituted than the external C–C double bond of 12b (Scheme 3b). A likely resolution involves
chemical activation (see Supporting Information Figure S37),54,55 which is commonly observed
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for carbene reactions that are initiated by HVFP.56,57 Although the G‡ value of 36.9 kcal/mol
for the intramolecular rearrangement 18→19 (Scheme 5a) is substantial, it can be readily
overcome because the energy released from 1→18 (cf. A→C in Supporting Information Figure
S37) is ~–60 kcal/mol. An accelerated isomerization of 18 to 19 (cf. C→E in Supporting
Information Figure S37) is plausible because the excess energy of vibrationally excited 18*
cannot be dissipated well. Collisional deactivation by the other gas-phase molecules in the HVFP
chamber is infrequent. To support the hypothesis that 19 does not stem from 1, Ea values for
1→18 and 1→19 were computed and compared to obtain a theoretical ratio of 18:19 (vide
infra). The Boltzmann distribution treatment of 1 in eq 3 does not provide G‡ values for these
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elementary steps. As noted, the computed G‡ value for 1,2-C atom shift in cyclobutylidene was
reported to be 10.5 kcal/mol.19 However, a more rigorous value of 6.7 kcal/mol was recently
reported.58 This value accords better with the experimental 9:8 ratio and it should serve as a
benchmark concerning the ring-contraction of 2 and its derivatives, such as 1.
Like 18, product 20 is chemically activated when it is formed by HVFP (Scheme 6c). That is
because some 21 was formed from 20 (Scheme 6d). Although Es is relieved by 20→21, the Ea
barrier for the electrocyclic ring-opening of the four-membered ring must be overcome. Since the
first step 1→20 is very exothermic (cf. A→C in Supporting Information Figure S37),55–57
vibrationally excited 20* has ample excess energy for the secondary step (cf. C→E in
Supporting Information Figure S37) to occur. When the secondary byproducts are included, the
tendency for the ring-contraction(s) vs ring-expansion of 1 can be quantified by calculating the
relative percentages of (18 + 19) vs (20 + 21), as listed in Table 1. An empirical ratio of 6.7:1 is
obtained, but this value could be too high. If conjugated diene 21 oligomerized during HVFP or
workup then a lower percentage of 21 would have been integrated in the gas chromatography
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(GC) analysis. This may explain why only 82% of the theoretical yield from 17 was obtained
(Table 1). In any case, this ratio is conversely related to the unusual ratio of 0:1 observed for 3
(Scheme 1),11–13 wherein ring-expansion occurs exclusively.
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Rearrangements of carbene 1 by means other than 1,2-C atom shifts were explored. Four
candidates were proposed for the identity of 22 (Chart 1). The formation of each involves well-
known carbene chemistry.1–8 Spiro[bicyclo[1.1.0]butane-2,1'-cyclobutane] (22a) would be
formed by an intraannular 1,3-C–H bond insertion reaction of 1 (Scheme 6e). This may be
possible if the 1°-ring in 1 is significantly puckered, as is the case with cyclobutylidene (2). Even
so, 2 itself does not undergo a 1,3-C–H bond insertion to bicyclo[1.1.0]butane. The substantial
amount of ring-strain energy in 22a makes it an unlikely contender for the identity of 22. trans-
Tricyclo[3.2.0.01,4heptane (trans-22b)50 would be formed by an interannular 1,3-C–H bond
insertion reaction of 1 (Scheme 6f). Buckeled ‘house’ane derivative trans-22b features a central
cyclopropane and two antiperiplanar four-membered rings. The formation of a ‘house’ane from a
2,2-dialkyl-substituted cyclobutylidene, by a related 1,3-C–H bond insertion reaction, is already
known.59 Alkylcarbenes often undergo rapid 1,2-H shifts to form alkenes. However, this
rearrangement is much less pronounced in 2-alkylcyclobutylidenes (e.g., Scheme 3c, d).30–32
Spiro[3.3]hept-1-ene (22c)51 would arise from a 1,2-H shift in 1 (Scheme 6g). Although there is
acute bending of the nominally sp2-hybridized C1 and C2 atoms in 22c, angle strain within such
a C–C double bond is only a minor barrier toward its formation.12,28,60 If 1 yields vibrationally
excited 22c* then chemically activation would facilitate electrocyclic ring-opening to conjugated
diene 22d (Scheme 6h; cf. C→E in Supporting Information Figure S37). Thus, candidates 22c
(Scheme 7) and 22d (Scheme 8) were independently synthesized, but still no conclusion could be
made about the identity of trace hydrocarbon 22.
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Scheme 7. Independent Synthesis of Spiro[3.3]hept-1-ene (22c)
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Scheme 8. Independent Synthesis of (Prop-2-en-1-ylidene)cyclobutane (22d)
Computational chemistry was used to model cyclobutylidenes 1–3. The four-membered ring
of cyclobutane is not flat for various reasons (e.g., the eight C–H bonds would all be eclipsed).
Torsional strain is relieved by ring-puckering. Cyclobutane’s ring-puckering dihedral angle () is
35° and the ring-puckering inversion barrier TS, through flat cyclobutane, is 1.5 kcal/mol.61,62
Torsional strain in spiro[3.3]heptane63 is reduced by ring-puckering in both four-membered
rings.62,64 Carbene 1 is a similar molecule. Of course, its four-membered rings are different from
each other (Figure 1a). Nevertheless, both four-membered rings of 1 pucker to reduce strain. Its
dual four-membered rings are stabilized by ring-puckering of the 1°- and 2°-rings (Figure 1a).
2°-Ring-puckering inversion in 1 (Figure 1a) yields two geometric isomers (+ac)-1 (Figure 2a)
and (–ac)-1 (Figure 2b). 1°-Ring-puckering inversion in 1 (Figure 1a) interconverts optical
isomers 1 (i.e., {(±ac)-}1 in Figure 2c) and ent-1 (i.e., ent-{(±ac)-}1 in Figure 2d). Besides
inversion, two discrete amounts of 1°-ring-puckering in 1 leads to geometric conformers 1a and
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1b (vide infra). Four geometric conformers are therefore possible because 2°-ring-puckering also
occurs: (1) (+ac)-1a, (2) (–ac)-1a, (3) (+ac)-1b, and (4) (–ac)-1b. If the optical isomers of 1
(i.e., ent-1) are included then there are a total of 2 × 22 = 8 conformers. Equilibrium geometries
of 1 were obtained using the (U)B3LYP/6-31G(d) theoretical model. The 3-D Cartesian
coordinates and corresponding 2-D renderings (Figure S34) are in the Supporting Information.
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(a)
(b)
(c)
(d)
Figure 2. 2°-Ring-puckering inversion in carbene 1 gives (a) positive anticlinal and (b) negative
anticlinal geometric conformers (+ac)-1 and (–ac)-1, respectively. 1°-Ring-puckering inversion
in 1 results in the (c) {(±ac)-}1 and (d) ent-{(±ac)-}1 optical conformers.
In this report, a cyclobutylidenen value represents the acute deviation of the three-point
C2–C1–C4 -plane from the three-point C2–C3–C4 -plane reference (Figure 3). Mathematical
details are presented in the Supporting Information (cf. Figure S35). Values of n were
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calculated by measuring those of dihedral angle n(C1–C2–C4–C3), using a graphical user
interface,65 and then by applying the → relation plotted in Figure S36 (see Supporting
Information). Geometric conformers 1a and 1b are easily distinguished by their markedly
different 1°-ring-puckering dihedral angle (1°) values (Figure 4). The curves in Figure 4 were
obtained by varying 1° while leaving the 2°-ring unconstrained. The 1° values of (±ac)-1a are
~45° more than those of (±ac)-1b, which are slightly affected by 2°-ring puckering. The 2°-ring-
puckering dihedral angle (2°) values of 1a and 1b (Figure 5), with unconstrained 1°-rings, were
found using dihedral angle 2°(C4–C7–C5–C6) and Figure S36 (see Supporting Information).
The algebraic sign of 2° thus matches the corresponding (+ac) or (–ac) stereodescriptor of 1.
Similarly, the  values of 2 (Figure 1c) were found using (C1–C2–C4–C3) and Figure S36 (see
Supporting Information) while the 1° values of 3 (Figure 1d) were found using 1°(C4–C5–C3–
C6) and Figure S36 (see Supporting Information).
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Figure 3. Ring-puckering dihedral angle (n) values of cyclobutylidenes were based on the
asymmetric model shown above. See Figure S35) in the Supporting Information for more details.
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Figure 4. The energies of cyclobutylidenes 1 and 2 are minimized by pronounced ring-puckering
( = 65°), which shields the divalent C atom. The presence of the conjoined 2°-ring in 1 (Figure
1a) leads to four geometric conformers (i.e., four minima): (a) (+ac)-1a, (b) (+ac)-1b, (c) (–ac)-
1a, and (d) (–ac)-1b. Cyclobutylidene 3 (Figure 1d) is completely different because its geometry
is optimal when the 1°-ring is flat. The energy profiles were computed using the B3LYP/6-
31G(d)//B3LYP/6-31G(d) theoretical model and normalized according to eq 4.
The energy profiles of Figure 5 were computed by varying the 2° values of 1a and 1b, while
leaving each 1°-ring unconstrained. Three trends are conspicuous: (1) the energy of geometric
conformer 1a is always lower than that of 1b, (2) the energy difference (E) between them
varies little as a function of 2°, and (3) 2°-ring-puckering inversion through 2° = 0° does not
affect the energies of 1a and 1b much. Yet, the conformation of the 2°-ring can influence which
conformation the reactive 1°-ring of 1 must adopt for each TS.
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Figure 5. 2°-Ring-puckering in 1a leads to geometric isomers (+ac)-1a and (–ac)-1a whereas
the less-ring-puckered form 1b gives (+ac)-1b and (–ac)-1b. The energy profiles were computed
using the B3LYP/6-31G(d)//B3LYP/6-31G(d) theoretical model.
The energy profiles of carbenes 1–3 shown in Figure 4 were computed by varying (1°) of the
four-membered rings. Each curve is normalized according to eq 4 in order to compare it with the
others. The original plots with vertical axes of E(hartree) are in the Supporting Information (cf.
Figure S28–Figure S33). The curves for (+ac)-1 and (–ac)-1 show that (+ac)-1a (1° = 65°) and
(–ac)-1a (1° = 65°) are lower in energy than the less-ring-puckered conformers (+ac)-1b (1° =
19°) and (–ac)-1b (1° = 25°), respectively. Furthermore, the steep gradients found for carbenes
1a suggest that they are more persistent than carbenes 1b. The energy profiles for the ent-1
isomers (Figure 2d) are mirror-images of those for the 1 isomers, with respect to the 1°-ring-
puckering inversion energy barriers at 1° = 0°, so they are omitted in Figure 4.
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E  Emin
Normalized Energy 
Emax  Emin
(4)
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Monocyclic 2 was computed to have a markedly ring-puckered conformation (“2a”;  = 65°)
based on the ring-puckering dihedral angle (C1–C2–C4–C3) (see the Supporting Information).
This result affirms a previous report.20 A flatter conformer of 2 (“2b”;  = 28°) is unsteadily
positioned on a shoulder-like region of the potential energy profile (Figure 4). Its authenticity
depends on the theoretical model used.20 The curve for carbene 3 is strikingly different from
those of 1 and 2 (Figure 4). Its 1°-ring-puckering inversion point at 1° = 0°, for which the four-
membered ring is flat, does not represent a transition state energy barrier between conformers. It
signifies the equilibrium geometry of 3 (Figure 1d, Figure 6).
Figure 6. The atypical regiospecificity of 3 (Scheme 1) is due to its planar four-membered ring,
which maximizes interaction between the highest filled Walsh orbital of the three-membered ring
and the unfilled p orbital of the divalent C atom. The necessary orbital alignment is impaired
with increased 1°-ring-puckering and the energy of 3 rises concomitantly (Figure 4).
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There is a cyclopropylcarbene-like unit in 3 comprising the C1–C4 atoms (Figure 6). It
exemplifies the bisected form of cyclopropylcarbene,66 wherein the plane of the n orbital bisects
the three-membered ring. The four-membered ring, of course, prevents rotation of the C3–C4
bond but it also ensures that the bisected form remains in the exo form,67 with regard to the
parent cyclopropylcarbene. The fragmentation of 3 to ethene and cyclobutyne68 is thereby
precluded. The crucial aspect is the interaction of the highest filled Walsh orbital of the three-
membered ring and the empty p orbital on the divalent C atom (Figure 6). The Walsh-to-p orbital
interaction is maximized when the pertinent orbitals are aligned. For this, planarity of the four-
membered ring is key. The contiguous orbital interaction is responsible for the regiospecific ring-
expansion of 3 to 6 (Scheme 1c). Ring-expansion of the carbene spiro[2.4]hept-4-ylidene (28)45
supports the validity of this hypothesis (Figure 7). Only compound 20 was formed from 28 when
it was generated by HVFP.11,12 Carbene 28 must have a significant Walsh-to-p orbital interaction
(cf. Figure 6). The five-membered 1°-ring of 28 is expected to be almost flat. The four-
membered 1°-rings of (±ac)-1b are somewhat puckered (Figure 4), but the 2°-ring of 1b has no
Walsh orbitals because it is a four-membered ring. Hence, the 1→20 ring-expansion reaction is
not enhanced (Scheme 6c), as is the case for the 3→6 and 28→20 ring-expansion reactions.
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Figure 7. The carbene spiro[2.4]hept-4-ylidene (28) undergoes exclusive ring-expansion to 20.
This atypical regiospecificity is akin to 3→6 (Scheme 1c).
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Relative energies and select measurements of the optimized geometric conformers of singlet
5
6
spiro[3.3]hept-1-ylidene (11) and triplet spiro[3.3]hept-1-ylidene (31) are listed in Table 2. There
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1
1
1
are four distinct geometric conformers of 1 (i.e., (+ac)-1a, (–ac)-1a, (+ac)-1b, and (–ac)-
1b), but there are only two geometric conformers of 31 (i.e., 3(+ac)-1 and 3(–ac)-1). Although the
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3
3
2°-ring of 1 experiences ring-puckering, the 1°-ring of 1 has only one conformation. It is flat
(i.e., 1° = 0°). Thus, the 1°-ring-puckering inversion point at 1° = 0° (Figure 4) marks the
3
1
equilibrium geometry of 1 and of 3. Evidently, there is no energetic benefit (and possibly a
detriment) from any cyclobutylidene ring-puckering if the nominally empty p orbital of the
divalent C atom gains electron density from exocyclic bonding electrons or from nonbonding
1
electrons. This appears to be the case with 3, due to the Walsh MO of its aptly positioned
cyclopropane, and with 31 and 32, which have a 3(n1p1) electron configurations. Furthermore, the
3
bond angle (C4–C1–C2) of 1 is 99°, which is very far from the ideal H–C–H bond angle of
133.9° in 3CH2.9,69,70 Thus, it is understandable why cyclobutylidene 1 has a singlet ground state.
According to the UQCISD(T)(fc)/6-311G(d,p)//(U)B3LYP/6-31G(d) theoretical model used
herein, the singlet–triplet energy gap (ES–T) of 3 is –9.0 kcal/mol and that of (+ac)-1 is –5.2
kcal/mol. For reference, values for 2 have been reported to be –5.9 kcal/mol20 and –9.3
kcal/mol.58
Table 2. Computed Measurements of Carbene 1a
b
b
Carbene
r(C1–C3)
1° 2° (C4–C1–C2)
relE
(Å)
(kcal/mol) (deg) (deg)
[0]c
(deg)
1(+ac)-1a
65
22
102
1.75d
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b
b
Carbene
r(C1–C3)
(Å)
relE
1° 2° (C4–C1–C2)
(kcal/mol) (deg) (deg)
(deg)
102
87
1(–ac)-1a
1(+ac)-1b
1(–ac)-1b
3(+ac)-1
0.6
1.1
2.4
5.2
5.1
65 –17
19 23
25 –18
1.75d
2.22
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2.20
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2.06
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–24
99
2.06
a
Computed using the UQCISD(T)(fc)/6-311G(d,p)//(U)B3LYP/6-31G(d) theoretical model.
See the Computational Methods section and Supporting Information for details. b See Supporting
Information Figure S35 and related text for details. c Defined as reference state. d See ref. 22.
Figure S38 (see Supporting Information is provided as a general energy profile for the
elementary steps presented in Table 4, which lists pertinent energy and structural data regarding
the conformations of 1 and its transformations to products 18–22. For example, the 1°-ring-
puckering inversion Ea barrier for (+ac)-1b is 1.3 kcal/mol and that for (–ac)-1b is 2.3 kcal/mol
(Table 4). Further inspection reveals that the dimensions of 1a are more compatible with those of
certain transition states whereas 1b more closely resembles others. However, structural similarity
is no guarantee that the TS will be energetically accessible. Indeed, the isomerization reactions
(Scheme 6) that confer a stabilizing Lewis octet around the divalent C atom of 1 may be
selectively driven by the optimum relief of strain in either or both four-membered rings of 1,
which are conjoined by the spirocyclic C4 atom (Figure 1a). The UQCISD(T)(fc)/6-
311G(d,p)//B3LYP/6-31G(d) theoretical model was used to compute relative energies and strain
energies of 1 and its products to explore this idea (see Supporting Information Figure S23–
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Figure S25 and Table 4). Details about how energy (E) values were corrected and converted to
enthalpy (H) values are described in the Computational Methods section and Supporting
Information. The energies of C7H10 molecules are reported relative to (+ac)-1a (see Supporting
Information Figure S23–Figure S25), because it is the lowest-energy conformer of 1. Similarly,
the energies of C4H6 molecules are reported relative to “2a” (see Supporting Information Figure
S26) and those of C6H8 molecules are reported relative to 3 (see Supporting Information Figure
S27). The group equivalent method71 was used to construct homodesmotic bond-separation
reactions,72–75 which were used to compute Es values of 1 and related molecules (see Supporting
Information Figure S23–Figure S25), 2 and related molecules (see Supporting Information
Figure S26), and 3 and related molecules (see Supporting Information Figure S27). The balanced
chemical equations and heat of reaction (H°) values (T = 298.15 K; p = 1 atm) are tabulated in
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Table S2 (see the Supporting Information). Note that Es = –H° and that geometric features
(e.g., cis vs trans C–C double bond) of the cyclic molecules were matched in the acyclic ones.
Table 3. Computed Measurements of Carbene 1 Transition States and Productsa
c
c
relEb
1°
2° (C4–C1–C2)d
Molecule
r(C1–C3)
(Å)
(kcal/mol) (deg) (deg)
(deg)
110
TS((+ac)-1a/18)
TS((–ac)-1a/18)
18
4.0
3.9
81
80
23
1.64
–18
110
1.65
–51.1
11.3
±180 ±14
212
1.47
TS((+ac)-1a/(+ac)-19)
(+ac)-19
70
15
19
115
1.78
–50.7
±180
211
1.48
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c
c
relEb
1°
2° (C4–C1–C2)d
Molecule
r(C1–C3)
(Å)
(kcal/mol) (deg) (deg)
(deg)
113
211
86
TS((–ac)-1a/(–ac)-19)
(–ac)-19
9.1
–50.7
3.8
84
–18
1.61
1.48
2.23
2.11
1.74
1.74
1.51
2.23
2.21
2.23
2.10
2.23
2.10
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±180 –20
TS((+ac)-1b/20)
20
–10
0
23
±15
18
–71.0
15.1
15.3
–43.8
6.9
95
TS((+ac)-1a/22a)
TS((–ac)-1a/22)
22a
73
73
78
–19
–8
–3
0
89
–16
±19
8
89
99
TS((+ac)-1b/trans-22b)
trans-22b
86
–52.2
8.1
8
88
TS((+ac)-1b/(+ac)-22c)
(+ac)-22c
28
87
–60.1
9.4
26
94
TS((–ac)-1b/(–ac)-22c)
(–ac)-22c
–4
0
–24
–26
87
–60.3
95
a Computed using the UQCISD(T)(fc)/6-311G(d,p)//B3LYP/6-31G(d) theoretical model. See the
Computational Methods section and Supporting Information for details. b Relative to (+ac)-1a. c
See Supporting Information Figure S35 and related text for details. d Atom numbering preserved
from 1 (Figure 1a).
Table 4. Reaction Energies Relative to Carbene (+ac)-1aa–c
A → B
A
TS(A/B)
Ea
B
E
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A → B
A
TS(A/B)
1.5
Ea
1.5
B
E
1.1
(+ac)-1a → (+ac)-1b
(–ac)-1a → (–ac)-1b
(+ac)-1b → ent-(+ac)-1b
(–ac)-1b → ent-(–ac)-1b
(+ac)-1a → (–ac)-1a
(+ac)-1b → (–ac)-1b
(+ac)-1a → 18
[0]
1.1
0.6
2.1
1.5
2.4
1.1
1.9
0
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
1.1
2.4
2.4
1.3
4.7
2.3
2.4
0
[0]
1.1
[0]
0.6
[0]
1.0
1.0
0.6
0.6
2.8
1.7
2.4
1.4
4.0
4.0
–51.1
–51.1
–50.7
–50.7
–71.0
–90.3
–43.8
–43.8
–52.2
–60.1
–60.3
–67.9
–70.3
–51.1
–51.7
–50.7
–51.3
–72.0
–19.4
–43.8
–44.3
–53.3
–61.1
–62.7
–7.9
–2.4
(–ac)-1a → 18
3.9
3.3
(+ac)-1a → (+ac)-19
(–ac)-1a → (–ac)-19
(+ac)-1b → 20
11.3
9.1
11.3
8.6
0.6
1.1
3.8
2.7
20 → 21
–71.0
[0]
–38.4
15.1
15.3
6.9
32.6
15.1
14.6
5.8
(+ac)-1a → 22a
(–ac)-1a → 22a
0.6
ent-(+ac)-1b→ trans-22b
(+ac)-1b → (+ac)-22c
(–ac)-1b → (–ac)-22c
(+ac)-22c → s-cis-22d
s-cis-22d → s-trans-22d
1.1
1.1
8.1
7.0
2.4
9.4
5.7
–60.1
–67.9
–25.3
–65.5
34.8
2.4
a Computed using the UQCISD(T)(fc)/6-311G(d,p)//B3LYP/6-31G(d) theoretical model. See the
b
Computational Methods section and Supporting Information for details. Energy units are
kcal/mol. c See Supporting Information Figure S38 for heading definitions.
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A rationale for the prevalance of 1→18 over 1→19 is illustrated by resonance forms of 1
(Scheme 9). Resonance form 1 is central because it does not exhibit destabilizing separation of
unlike electric charges, as do 1–1. Homoallylic forms 1 and 1 are 1,3-zwitterions that do
9
10
11
12
13
14
15
16
17
18
19
20
21
22
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31
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not contribute much to the overall Lewis structure of 1. Forms 1 and 1 are derivatives of the
nonclassical bicyclobutonium ion.76,77 Although they are 1,2-zwitterions, ylidic forms 1 and 1
are reasonable because the build-up of opposing charges can be immediately reconciled by C–C
double bond formation to 19 and 18, respectively. Thus, 1→18 should prevail over 1→19. The
internal ring-contraction TS(1/18) resembles form 1 (Scheme 9d), which has positive charge on
a “3°-C atom” of a “cyclopropylmethyl cation,” but the external ring-contraction TS(1/19)
resembles form 1 (Scheme 9b), which has positive charge on a “1°-C atom” of a
“cyclopropylmethyl cation.” Given these factors, one must conclude that the energy of TS(1/18)
is lower than that of TS(1/19). Indeed, TS((+ac)-1a/18) lies 7.3 kcal/mol lower than TS((+ac)-
1a/(+ac)-19) and TS((–ac)-1a/18) lies 5.2 kcal/mol lower than TS((–ac)-1a/(–ac)-19) (Table
4). Analysis of the Boltzmann factors derived from these TS E values shows that 18 is formed
in 100 rel.% yield and (±ac)-19 is formed in 0 rel.% yield. Of the two ring-contractions possible
within 1, cleavage of the more substituted C3–C4 bond dwarfs that of the C3–C2 bond (Figure
1a). The removal of spiroannulation within 1 might be the driving force behind the 1,2-C atom
shift in 1→18. This is not accomplished by 1→19. Carbene 1 also rearranges by a rare kind of
1,2-C atom shift to form ring-expansion product 20 (Scheme 6c). This isomerization is akin to
3→6 (Scheme 1), however ring-expansion of 1 to 20 is dominated by ring-contraction of 1 to 18
(Table 1 and Scheme 9). Resonance structures of 1 are less instructive in this case (Scheme 9).
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Scheme 9. Competitive 1,2-C Atom Shifts within Carbene 1
5
6
7
8
9
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12
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17
18
19
20
21
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It is clear that 20 has less E and Es than 18 (see Supporting Information Figure S24), but
more 18 was formed than was 20 (Table 1). A comparison of their transition state energies from
1 must be made. Nevertheless, a 17 rel.% excess of 20 + 21 should be formed over 18 + 19
because the energy of TS((+ac)-1b/20) is 0.2 kcal/mol lower than that of TS((+ac)-1a/18)
(Table 4). This is contrary to what was observed (Table 1). One possible solution is that the yield
of 21 is underrepresented in Table 1 due to its oligomerization. There is another possible
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explanation. Although the Ea values for TS(1/18) and TS(1/20) are similar, the populations of
1a and 1b are not. The relative yields of 18 and 20 reflect the mechanistic rate constants for
7
8
9
1a→18 and 1b→20 as well as the equilibrium constant for 1aÝ1b.
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11
12
13
14
15
16
17
18
19
20
21
22
23
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Table 5 and Table 6 list pertinent data for the [1,2]-sigmatropic rearrangements of carbene 3.
The formation of 6 (Scheme 1) is the most rapid isomerization because its Ea value is the
smallest (Table 6). The ring-expansion of 3 to 6 occurs exclusively even though 6 has both the
highest relative energy and highest ring-strain energy among the 4–7 product set (see Supporting
Information Figure S27).
Table 5. Computed Measurements of Carbene 3 Transition States and Productsa
c
relEb
1° (C4–C3–C2–C1)d (C3–C4–C5)d
Molecule
r(C4–C6)
(Å)
(kcal/mol) (deg)
(deg)
–160
(deg)
110
58
TS(3/4)
17.5
–39.1
20.5
83
±180
68
1.64
0
–120
–132
–42
1.47
4
TS(3/5)
113
210
86
1.82
–43.1
5.6
±180
–3
1.49
5
TS(3/6)
2.24
–28.5
11.0
0
0
95
2.11
6
TS(3/7)
7
–4
–117
–118
86
2.23
–56.1
0
94
2.11
a Computed using the UQCISD(T)(fc)/6-311G(d,p)//B3LYP/6-31G(d) theoretical model. See the
b
c
Computational Methods section and Supporting Information for details. Relative to 3. See
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d
Supporting Information Figure S35 and related text for details. Atom numbering preserved
5
6
from 3 (Figure 1d).
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8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
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30
31
32
33
34
35
36
37
38
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Table 6. Reaction Energies Relative to Carbene 3a–c
A→B
3→4
3→5
3→6
3→7
A
TS(A/B)
17.5
Ea
17.5
20.5
5.6
B
E
[0]
[0]
[0]
[0]
–39.1
–43.1
–28.5
–56.1
–39.1
–43.1
–28.5
–56.1
20.5
5.6
11.0
11.0
a Computed using the UQCISD(T)(fc)/6-311G(d,p)//B3LYP/6-31G(d) theoretical model. See the
b
Computational Methods section and Supporting Information for details. Energy units are
kcal/mol. c See Supporting Information Figure S38 for heading definitions.
■ CONCLUSIONS
Five hydrocarbons were formed in 82% overall yield from the high-vacuum flash pyrolysis
(HVFP) of Bamford–Stevens reactant 17. Four of them were characterized as C7H10 isomers: (1)
cyclopropylidenecyclobutane (18) (69.3 rel.%), (2) 1-methylenespiro[2.3]hexane (19) (17.0
rel.%), (3) bicyclo[3.2.0]hept-1(5)-ene (20) (8.6 rel.%), and (4) 1,2-dimethylenecyclopentane
(21) (4.3 rel.%). The fifth product was an unidentified hydrocarbon (22) made in trace amounts.
The highly strained carbene spiro[3.3]hept-1-ylidene (1) was posited as a reaction intermediate
mainly for two reasons: (1) the HVFP of a Bamford–Stevens reactant generally liberates the
corresponding carbene and (2) products 18–20 can result from the isomerization of 1. Product 21
stems from 20. Computational chemistry was used to assess the structures, conformations,
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