Abstract. Organic molecules, the structural parameters of whichOrganic molecules, the structural parameters of which
(carbon ± carbon bond lengths, bond and torsion angles) differ(carbon ± carbon bond lengths, bond and torsion angles) differ
appreciably from the typical most frequently encountered values,appreciably from the typical most frequently encountered values,
are discussed. Using many examples of `record-breaking' mole-are discussed. Using many examples of `record-breaking' molecules,
the limits of structural distortions in carbon compounds andcules, the limits of structural distortions in carbon compounds and
their unusual chemical properties are demonstrated. Particulartheir unusual chemical properties are demonstrated. Particular
attention is devoted to strained compounds not yet synthesisedattention is devoted to strained compounds not yet synthesised
whose properties have been predicted using quantum-chemicalwhose properties have been predicted using quantum-chemical
calculations. Factors that ensure the stability of such compoundscalculations. Factors that ensure the stability of such compounds
are outlined. The bibliography includes 358 references.are outlined. The bibliography includes 358 references.
I. Introduction
The experimentally determined lengths of carbon ± carbon bonds
of one type in the molecules of various organic compounds are
usually very close. Thus the lengths of single and multiple
carbon ± carbon bonds usually deviate only slightly (as a rule, by
less than 0.01 ± 0.02 #A) from the values obtained by averaging over
a large number of experimentally determined bond lengths. These
values are often referred to as `typical' or `standard' geometric
parameters. Some standard lengths of carbon ± carbon bonds
determined by X-ray diffraction analysis are listed in Table 1.1 ± 4
The same is true, although to a lesser extent (due to the smaller
values of the corresponding force constants), for the bond angles
the departure of which from the standard values is normally
several degrees. The torsion angles usually vary over broader
limits than bond angles; however, in some cases, in particular, for
fragments with multiple bonds, these angles are also characteristic
parameters.
The standard molecular geometric parameters are fundamental
values used in stereochemistry.5 The invariance of these
parameters underlies various types of molecular models and
various methods for structure calculation, in particular, molecular
mechanics methods.6
Meanwhile, in the molecules of some compounds, the bond
(or torsion) angles and the bond lengths sharply deviate from the
typical values. The synthesis of such compounds is often stimulated
by a chemist's desire to overstep the limits of the existing
theoretical views and concepts. A vivid example is the synthesis of
four- and three-membered carbocyclic compounds performed
successfully by W H Perkin at the end of the XIX century,7, 8
despite the opinion of scholars of authority in those days who
considered the synthesis of small rings to be impossible.9
A different tendency has been observed in recent years: one
can name a number of compounds with appreciably distorted
molecular geometry the successful synthesis of which was pre-
CO2Et
CO2Et
CO2Et
CO2Et
CO2Et
CO2Et
1) NaOEt
2) Br(CH2)3Br
1) NaOEt
2) Br(CH2)2Br
I V Komarov Department of Chemistry, Taras Shevchenko Kiev National
University, ul. Vladimirskaya 64, 01033 Kiev, Ukraine.
Fax (7-38 044) 226 12 73. E-mail: ik214@mail:yahoo.com
Received 26 October 2000
Uspekhi Khimii 70 (12) 1123 ± 1151 (2001); translated by Z P Bobkova
DOI 10.1070/RC2001v070n12ABEH000633
Organic molecules with abnormal geometric parameters
I V Komarov
Contents
I. Introduction 991
II. Stability of strained molecules 992
III. Abnormally long and short C7C bonds 993
IV. Elongated and shortened C=C bonds 995
V. Variations of the triple carbon ± carbon bond lengths in organic compounds 995
VI. Distortions of bond angles at the tetrahedral carbon atom 996
VII. Distortions of bond and torsion angles at the double bond in alkenes 1001
VIII. Distortions of the bond and torsion angles in the molecules of aromatic compounds 1005
IX. Distortions of cumulated double bonds 1008
X. Bending of the X17C:C7X2 fragment 1010
Table 1. Typical (averaged) lengths of some carbon ± carbon bonds.
Type of bond Length /#A
Single bond
C…sp3
†7C…sp3
† 1.53
C…sp3
†7C…sp2
† 1.51
C…sp3
†7C…sp† 1.47
C…sp2
†7C…sp2
† 1.48
C…sp†7C…sp† 1.38
Double bond
C…sp2
†=C…sp2
† 1.32
C…sp2
†=C…sp† 1.31
C…sp†=C…sp† 1.28
Triple bond a
C…sp†:C…sp† 1.186
a The data of Ref. 4.
Russian Chemical Reviews 70 (12) 991 ± 1016 (2001) # 2001 Russian Academy of Sciences and Turpion Ltd
ceded by theoretical predictions of their possible existence and
calculations of their spectral properties. In any case, synthesis and
study of these compounds were favourable for the accumulation
of knowledge on the nature of the chemical bond and mechanistic
details for reactions of organic compounds.10 Research along this
line has resulted in the development of new original methods of
synthesis and experimental techniques which made an invaluable
contribution to modern synthetic organic chemistry.11, 12 The
non-trivial syntheses of highly deformed molecules, together
with many total syntheses of natural compounds,13 can be
regarded as classical achievements of modern chemical science.
What properties are inherent in substances the molecules of
which have highly distorted bond lengths and angles? What is the
degree of distortion of the molecular geometry of organic compounds
that results in a qualitative (discontinuous) change in their
properties? What is the maximum attainable degree of distortion
of bond lengths and bond (torsion) angles and do calculations
reproduce the observed structural characteristics? In this review,
we consider the recent publications concerned with these prob-
lems.{
The literature on the synthesis and structural studies of
compounds with distorted geometric parameters of molecules is
very extensive. This review does not claim to be an exhaustive
analysis of all these studies; the author's goal was to illustrate the
limits of the possible geometric distortions of organic molecules
using a number of interesting examples. Among the vast material,
studies devoted to `record-holder' molecules with the greatest
distortions of bond lengths and bond and torsion angles either
observed experimentally or calculated are discussed. However,
structural chemistry is so rapidly developing that any unusual
molecule soon loses the record-breaker title.18
The review discusses compounds the molecules of which are
stable despite substantial distortions of the molecular geometry.
The structures of these compounds are studied by physical
methods, most often by X-ray diffraction analysis. Therefore,
first, it is pertinent to discuss the specific features of the structures
of strained molecules which allow them to reach the stability
needed to study them by physical methods.
II. Stability of strained molecules
Organic molecules with abnormal geometric parameters possess
increased energy. A usual quantitative characteristic of these
molecules is strain energy, which is defined as the difference
between the experimental standard enthalpy of formation of the
molecule and the enthalpy calculated for the `strainless' (often
hypothetical) molecule containing the same number of atoms and
the same sequence of bonds between them but no distortion of
bond lengths or bond angles and no non-valence intramolecular
interactions (for example, steric repulsion).19 The concept of
molecular strain is widely used in chemistry, although it is not
exact because the calculation schemes for the enthalpies of
formation of strain-free molecules are arbitrary and often different.20
Therefore, when comparing strain energies, one has to be
sure that they have been calculated by the same methods.
Normally, calculations involve summation of the strain increments
known for the structural fragments present in the mole-
cule.19
Molecules for which this enthalpy difference is great are
referred to as strained. It should be noted that the criteria for
regarding one or another structure as strained are quite arbitrary.
Even the adamantane molecule with a strain energy of
7.6 kcal mol71 can be regarded as `strained', although its
molecular model seems misleadingly unstrained.14, 15 We shall
discuss molecules with strain energies many times exceeding that
of adamantane. Such molecules are often reactive and susceptible
to intra- and intermolecular reactions which are not typical of
strainless analogues. The combination of these properties is
associated with the qualitative notion of `instability', while the
factors due to which the chemical transformations of strained
molecules can be retarded or entirely avoided are associated with
`stability' of the molecules.
Most highly strained `record-breaker' compounds known to
date exist owing to kinetic stability. Despite the substantial strain
energy of the molecules of these compounds, their structures
correspond to minima on potential energy surfaces (PES),21
indicating the possibility of preventing decomposition and
relaxation of the geometrically distorted fragments to the
unstrained state.
The stability against structural changes that bring a fragment
with distorted bonds and angles to the `normal' state is provided
most often by the fact that this fragment is incorporated into a ring
or a rigid polycyclic cage. Alternatively, steric repulsion of bulky
groups, especially tert-butyl substituents, also helps to avoid
relaxation of a distorted fragment to an unstrained state.22 The
molecules of compounds 1 and 2 with a twisted double bond can
serve as examples of strained molecules having a distorted fragment
within a polycycle or bulky groups.
To attain stability of strained molecules, it is necessary to
prevent them from entering reactions either with one another
(oligomerisation, polymerisation) or with other potential reactants
(solvents, oxygen, moisture, etc.). These reactions can be
prevented by creating steric restrictions around the reaction
centres. For example, tetrahedrane 3 is so reactive that it has not
been prepared until now, in spite of considerable effort,{ whereas
tetra-tert-butyltetrahedrane (4), in which the strained C4 core is
shielded, has been isolated and studied, in particular, by X-ray
diffraction analysis.
The instability of strained molecules is also related to their
tendency to undergo intramolecular rearrangements. Kinetic
stability due to electronic factors is an effective method for
preventing these rearrangements. A classical example is cubane
(5) in which the possible rearrangement pathways are forbidden
by the orbital symmetry rules. The strain energy of molecule 5 is
very high (157 kcal mol71; determined using data on the heat of
2
Steric repulsion
Steric repulsion
1
Rigid tricyclic cage
H
H
H
H
But
But
But
But
3
4 5
{ This review covers studies published before the beginning of 2001.
Analysis of publications on this topic up to mid-1970s was carried out by
Greenberg and Liebman.14, 15 The publications for this review were
collected using the STN electronic databases (Scientific Technical Network,16
first of all, the REGISTRY database, which contains information
on more than 18 000 000 organic and inorganic compounds), Chemical
Abstracts and Beilstein as well as the Cambridge Structural Database
(CSDB; the version of April 2001 presents structural information on more
than 233 000 compounds).17
{ From here on, the formulae of compounds not obtained experimentally
are drawn in parentheses.
992 I V Komarov
combustion of cubane 23);} however, cubane does not decompose
even at temperatures above the melting point (130 ± 131 8C).26
The strain energy of compound 5, as well as that for other
molecules described below, is markedly higher than that required
for rupture of the C7C bond. However, the stability of cubane is
secured by even distribution of the steric strain over the whole
carbon skeleton.
The exceptionally stable C60 fullerene (6) in the molecule of
which strain is uniformly distributed over all the 90 carbon ±
carbon bonds can serve as yet another example of stable but very
strained molecules. The heats of combustion of C60 and C70
fullerenes and their standard enthalpies of formation, which can
be used to estimate the strain energy, have been determined
experimentally.27
In some cases, the concept of thermodynamic stability of
strained molecules is discussed but this term is often used
improperly. For example, it has been claimed 28 that coordination
of a metal atom to a distorted fragment can ensure `thermodynamic
stability' of strained ligands, in particular, trans-cycloalkenes.
The overlap of molecular p orbitals of a strained alkene
with the vacant orbitals of the transition metal and interaction of
the occupied d orbitals of the metal with the p* orbital of the
double bond (dative bond) finally stabilise the complex. However,
in our opinion, this is a case of kinetic stability. Thermodynamic
stability implies reversible transformations, for example, those
between a complex with a ligand containing a distorted structural
fragment and a complex with a strain-free analogue of the same
ligand. Most transformations of strained molecules are irreversible;
therefore, their thermodynamic stability is seldom encoun-
tered.
An example is provided by compound 7, stable in methanol.29
The driving force of the spontaneous formation of compound 7,
the molecule of which contains a strained twisted amide fragment,
in equilibrium with zwitter-ion 8 is the steric strain in the bicyclic
system, which decreases upon cyclisation.
It makes sense to discuss the stability of a compound when
conditions for its isolation or investigation are known. For
example, a large number of compounds unstable at room temperature
have been studied in inert matrices at 4 ± 77 K.30 Lowtemperature
isolation in solid matrices of inert gases prevents
diffusion and, hence, excludes intermolecular reactions of the
compounds under study. Moreover, intramolecular transformations,
even those having an energy barrier of only several calories
per mole are also retarded.31
One more method that provides a sufficient (in particular, for
spectroscopic studies at room temperature) lifetime of reactive
species should also be mentioned, namely, preparation of these
species inside cavities of large macromolecules Ð carcerands and
hemicarcerands. In recent years, several studies have been published
(see below) devoted to spectroscopic and chemical properties
of compounds the isolation and investigation of which at
room temperature could not even be discussed before the advent
of this method, for example, cyclobutadiene and dehydroben-
zene.32
III. Abnormally long and short C7C bonds
The characteristic lengths of C7C, C=C and C:C bonds (see
Table 1) can be regarded as fundamental parameters in chemistry.
Deviations from `normal' values are seldom encountered, and
they serve as an indicator for the occurrence of steric or electronic
effects.
The quest for the longest C(sp3)7C(sp3) bond has been called
a `real Odyssey.' 33 Considerable attention was devoted to hexaalkyl-
and hexaarylethanes such as 9 ± 11,34 ± 36 in the molecules of
which the central C7C bond is longer than 1.64 #A.
The main cause for bond elongation is steric repulsion
between bulky groups. The elongated bonds are weakened,
which accounts for the thermal instability of these hydrocarbons.34
In the case of compound 9, molecular mechanics (MM2)
calculations} for the molecular geometry were carried out and
good agreement between experimental and calculated values was
obtained.
In 1996, Toda et al.37 have reported exceptionally long C7C
bonds in two benzocyclobutane derivatives, 12 (1.720 #A) and 13
(1.710 and 1.724 #A).
6
N O
7Me
Me
COÀ
2
NH‡
2
8Me
Me
N OH
H
+
OH
Me
Me
1.67 #A
11
But
But
But
But
But
But
But
But
But
But
But
But
1.671 #A
10
F3C CF3
F3C
F
CF3
F
Me
Me
Me Me
1.639 #A
1.647 #A
1.640 #A
9
Ph
Ph
1.720(4) #A
12
Ph
Ph
PhPh
Ph
Ph
PhPh
Cl
Cl Cl
Cl
Me Me
1.724(5) #A1.710(5) #A
13
PhCl
PhCl
} These data are somewhat outdated; however, more precise values have
not yet been reported. The strain energy of the cubane molecule presented
here is consistent with rough values determined from the heats of
combustion of various cubane derivatives and with calculated values.24, 25
} Most of the calculation methods mentioned in the review are described in
a book by Jensen.21
Organic molecules with abnormal geometric parameters 993
These values are almost 0.18 #A greater than the standard
length of a single carbon ± carbon bond; therefore, it is not
surprising that some doubts have been cast upon the X-ray
diffraction data published. Before the study by Toda et al.,37
examples of compounds with even longer C7C bonds had been
reported; however, a thorough verification showed the results of
structural studies of these compounds to be incorrect. Thus the
lengths of the central bonds in the molecule of compound 14,
a photoisomer of [2.2]tetrabenzoparacyclophane 15, have been
reported 38 to be 1.77 #A. Later, it was found that the measurements
were carried out for a mixture of the photoisomers 14 and 15
rather than for a crystal of pure 14.39 In subsequent studies of a
pure sample of 14 at 170 K, the lengths of the central bonds were
found to be 1.648 #A.40
Repeated studies 41 of the compound 12 have confirmed,
nevertheless, the validity of the previously obtained data,37 and
quantum-chemical calculations (B3LYP/6-31G*) reproduced
them satisfactorily.42 Model calculations [B3LYP/DZ(2d,p)] for
the 1,1,2,2-tetraphenylbenzocyclobutene molecule also provided
a Ph2C7CPh2 bond length consistent with the value found
experimentally 37 in compound 12. These calculations demonstrated
the importance of taking into account the electron
correlation in order to obtain correct values for geometric
parameters of the strained molecules. It was also shown 41 that
satisfactory interpretation of the observed elongation of the C7C
bond requires that only steric effects (repulsion between bulky
groups) be taken into account without considering hyperconjugation
effects.43 This conclusion is also confirmed by recently
published data on the synthesis and X-ray diffraction analysis of
the even more sterically hindered compound 16.44, 45 The C7C
bond length in the four-membered ring of 16 equals 1.729 #A, i.e., it
is longer than those in the molecules 12 and 13.
The distance between the carbon atoms formally not bound to
each other in bicyclo[1.1.1]pentane (17) and its derivatives is close
to the lengths of the `stretched' C7C bonds given above. The
C(1)7C(3) distance in this simple hydrocarbon measured by
electron diffraction 46 is 1.874 #A (or 1.845 #A according to another
publication 47). The search through the CSDB for the shortest
C(1)7C(3) distance among the bicyclo[1.1.1]pentane derivatives
gave a value of 1.80 #A in bis(3-iodobicyclo[1.1.1]pentan-1-ylpyridinium)iodide
triiodide 18.48 In this case, the X-ray diffraction
data can best be interpreted by assuming that structures containing
[1.1.1]propellane contribute to the resonance hybrid. In the
molecules of bicyclo[1.1.1]pentane derivatives, the non-bonded
bridging carbon atoms are so close to each other that the `throughspace'
electronic interaction is clearly identified.49
The above-mentioned studies raise the question of what is the
longest distance between carbon atoms in a molecule that enable
the existence of a chemical bond between them.
Proceeding from the empirical definition of the chemical
bond { proposed by Pauling 50 without restricting the consideration
to saturated systems, one can find examples of structures
with formal C7C bonds longer than 1.729 #A, which is the value
established for molecule 16.
For example, a distance between carbon atoms equal to 2.83 #A
has been found recently in the crystal of dimer 19, formed by two
tetracyanoethylene radical anions (20). Nevertheless, the results of
structural, magnetic, and spectroscopic studies are consistent with
the existence of a chemical bond between them.51 This twoelectron
four-centre bond results from the p ± p binding interaction
between the radical anions 20 and the Coulomb repulsion
between them. It was shown that the dimers are metastable
species, i.e., their formation is an endothermic process; in the
solid phase, they can be stabilised upon interaction with metal
cations.
Apparently, it is impossible to establish the limiting bond
length of any type on the basis of merely geometric criteria such as
`longer (or shorter) than..'; it is necessary to invoke conceptual
models of chemical binding including new ones. Some new
approaches to the determination of the nature of the chemical
bond could be provided by Bader's theory.52 This theory is based
on the mathematical analysis of topological characteristics of the
total molecular electron density function either found experimentally
or calculated. In terms of this theory, it is possible to give
strict criteria for the occurrence of a bonding interaction between
a pair of atoms, irrespective of the distance between them.
A number of studies have been devoted to the search for
strained molecules with short carbon ± carbon single bonds. For
example, the length of the exocyclic bond in bicubane 21 was
found to be 1.458 #A,53 which was explained by rehybridisation of
the carbon orbitals. The exocyclic bonds in cubane have a greater
s-character and, therefore, they are shorter than the standard
C(sp3)7C(sp3) bonds. The steric strain that could result in
elongation of the central C7C bond in compound 21 is insignificant,
unlike that in the molecule of 1,1H
-biadamantane 22 (the
length of the central bond in 22 is 1.578 #A 54).
The central bond in bicubane can be compared with that in
butadiene, the length of which is 1.383 #A, according to electron
diffraction data;55 however, in the latter compound, this bond is
further shortened due to conjugation.
Schleyer and Bremer 56 not only compared the experimental
and calculated (MNDO, MP2/3-21G, 6-31G*) lengths of the
central bonds in molecules 23 ± 25, similar to the bicubane
molecule, but also carried out model calculations for ethane
(MP2/3-21G) with variation of the C7C7H bond angle. It was
shown that an increase in this angle to 150 8 entails energy
redistribution between molecular orbitals, resulting in strengthening
of the C7C bond. The calculated (MP2/6-31G*) length of the
C7C central bond in bitetrahedrane 25 is 1.438 #A. The compound
25 has not yet been synthesised; however, Ermer et al.57 believe
that the hexa-tert-butyl derivative of this compound could be
prepared.
D
hn
14 15
16
1.729 #A
But
But
Ph
Ph
Cl
Cl
H H
1 3
17
18
NIIN I
+
IÀ
3
CN
CN
NC
NC NC
NC
CN
CN
52.83 #A
27
19
C C
C C
N
NN
N
20
7
{ According to Pauling, `... there is a chemical bond between two atoms or
groups of atoms in the case that the forces acting between them are such as
to lead to an aggregate with sufficient stability to make it convenient for
the chemist to consider it as an independent molecular species.'
994 I V Komarov
The angle strain in the cyclopropane molecule is known to
result in shortening of the formally single C7C bonds (1.499 #A).58
In the bicyclobutane (26) molecule, which is the smallest one
among the molecules of bicyclic hydrocarbons, two cyclopropane
rings are fused; the central C7C bond exhibits properties of the
double bond (for example, electrophilic reagents readily add at
this bond to give cyclobutane derivatives) and is abnormally short
(1.497 #A). X-Ray diffraction study of bicyclobutane derivatives
showed that the length of the central bond depends on the angle
between the planes of the three-membered rings. In the compound
26, this angle is *122.7 8, while in its derivatives 27, this angle is
much smaller (*87 8) and the C(1)7C(3) bond is much shortened
(1.408 #A), i.e., this is one of the shortest single bonds known to
date.59
IV. Elongated and shortened C=C bonds
Analysis of the structures deposited in the CSDB shows that
abnormally long formally double C=C bonds are found in
systems containing long chains of conjugation (see, for example,
compound 28).60 In aromatic derivatives (see, for example, compound
29),61 the C C bonds can also be elongated. The shortest
formally double carbon ± carbon bonds have been found in a
number of strained molecules (for example, in molecule 30).62
Exceptionally long carbon ± carbon double bonds have also been
found in twisted alkenes. The elongation of these bonds is due to a
decrease in the degree of p-bonding.
Let us consider the compounds the molecules of which
incorporate the shortest (30) and the longest (31) 63
C(sp2)=C(sp2) bonds known to date.
The length of the double bond in ethynylcyclopropene 30 is
approximately an average between the bond lengths found in
strain-free alkene and alkyne molecules Ð 1.255 #A. Even very
high-level calculations provide overestimated lengths for the
C=C bond in this molecule.62
Ab initio (HF/3-21G, 6-31G*) calculations for benzo[1,2 : 4,5]dicyclobutene
32 predicted 64 two types of isomerism, one type
being due to different bond lengths (32a and 32b, 32c) and the
other type being due to different positions of the double bonds
(32b and 32c). X-Ray diffraction analysis 63 of the compound 31
did not confirm the results of calculations reported earlier.64 The
structural parameters found experimentally for 31 and those
determined by quantum-chemical calculations for the hydrocarbon
32 (B3LYP/6-31G*, MP2/6-31G*) correspond to the structure
32d with elongated bonds in the benzene ring. However, it
should be emphasised that in this case, we are dealing with
aromatic bonds rather than purely double bonds (as in alkenes).
V. Variations of the triple carbon ± carbon bond
lengths in organic compounds
The deviations of the lengths of triple carbon ± carbon bonds in
organic compounds from typical values are less pronounced than
similar deviations in the case of single or double bonds. For
example, according to analysis of the CSDB data,4 the difference
in the C:C bond lengths in acetylene and its alkyl derivatives is
less than 0.05 #A.
It is noteworthy that triple bond lengths determined by
electron or neutron diffraction are often greater than those
found by the conventional X-ray diffraction technique for the
same compound (the difference can reach 0.02 #A or even more).
This is due to the fact that X-rays are scattered by the electron
density of the object and the electron density maxima (centroids)
identified as `atoms' in the X-ray diffraction method do not
always coincide with the positions of the atomic nuclei. The
electron density maxima can be displaced towards each other in
the case of high concentration of the electron density in the
interatomic space, which is often the case for multiple bonds
including triple bonds. However, in modern X-ray diffraction
software packages, this effect can easily be taken into account.
Nevertheless, statistic analysis covering only those parameters in
the CSDB which have been determined by electron diffraction in
the gas phase results in an even smaller scatter of the C:C bond
lengths, namely, 0.012 #A.4
As a rule, elongation or shortening of triple bonds is mainly
due to electronic factors. For example, this bond is shorter in the
molecules of acetylene derivatives containing electron-withdrawing
substituents at the triple bond.65 (Note that this is equally true
for double carbon ± carbon bonds.) Elongated C:C bonds have
been found in conjugated systems, for example, in butadiyne 55
[1.2176(6) #A], although the lengths of these bonds in vinylacetylene
and propynal molecules exceed only slightly the average
value. The steric factors in linear alkynes in which substituents at
the C:C bond are far from each other are minimised.
It can be suggested that the loss of p-bonding caused by
bending of the X7C:C7X fragment (X is any substituent) in
cycloalkynes would result in elongation of the triple bond. Nevertheless,
in most of the known strained molecules of cycloalkynes,
the length of the triple bond is close to the typical value. For
example, in compound 33, despite the substantial bending of the
Si7C:C7Si fragment, the C:C bond length is equal to 1.22 #A,
which virtually coincides with the average value (1.201 #A) for silylsubstituted
alkynes.66
1.458 #A
21
1.578(2) #A 1.480 #A
22
23
1.468 #A
24 25
1.438 #A
26
Me Me
O
1.408 #A
27
Ph Ph
H
1.413(2) #A
28
CO2Me
OH
Cl
CO2Me
HO
Cl
1.416(2) #A
29
OO
C CH1.255 #A
30
But
But
Ph
Ph
Ph
Ph
1.540(5) #A
31
32a 32b 32c 32d
Organic molecules with abnormal geometric parameters 995
VI. Distortions of bond angles at the tetrahedral
carbon atom
The modern theory of the structure of carbon compounds is
underlain by the hypothesis advanced independently by Van't
Hoff 67 and LeBel 68 in 1874 stating that a tetracoordinated carbon
atom has a tetrahedral or a nearly tetrahedral configuration.
Later, the results of numerous studies including X-ray diffraction
analysis have confirmed Van't Hoff's and LeBel's hypothesis
based on empirical data, and the sp3-hybridisation concept has
explained simply and conveniently the stability of the tetrahedral
configuration. However, as soon as somewhat more than a decade
after the publication,67, 68 Baeyer, who considered distortions of
the tetrahedral configuration of the carbon atom, stated the
foundations of strain theory.69
The types of distortion of bond angles at the sp3-hybridised
carbon atom are illustrated in Fig. 1. First of all, this is a decrease/
increase in one bond angle (the angle between the other two bonds
usually correspondingly increases/decreases; this is the so-called
scissors distortion) as well as distortions leading to flattening of
the carbon configuration, i.e., tetrahedral compression and digonal
twist. Special mention should be made of configurations in
which all atoms attached to a given carbon atom are located on
one side of the plane passing through it, namely, inverted and
pyramidal configurations to which an umbrella-type distortion
leads. Rigorous mathematical analysis of the disortions of the
CX4 fragment has been reported.70 ± 72
It should be noted that in experimental or theoretical study of
the electron density distribution in the molecules characterised by
highly distorted bond angles at carbon atoms, the regions of
increased electron density between the atoms { do not lie on the
straight lines connecting the atomic nuclei but are displaced from
these lines. These bonds have been referred to as curved (banana)
bonds; a classic example of these bonds is found in the cyclopropane
molecule. The displacement of the maxima of DED
(covalent electron density) outwards the ring in cyclopropane
derivatives reaches 0.2 #A or more. An even greater shift of the
DED maxima away from the internuclear lines, up to 0.5 #A, was
found in tetrahedrane derivatives. Banana bonds are found not
only in the molecules with small rings but also in highly strained
cage systems.74
Subsequently, in particular in the analysis of structural data
for cyclic and strained cage molecules, the notion of bond path
was defined as the interatomic line along which the total electron
density is a maximum relative to any `lateral' displacement and
has a minimum in the so-called saddle point.52, 73 ± 75 A bond path
is not necessarily a straight line; the presence of this line implies a
chemical bond between the given atoms.76 These and some other
definitions constitute the foundation of the modern quantum
theory of interatomic interactions and chemical bonding, developed
by Bader.52
In Bader's theory, the bond path angle at an atom is
determined by the angle between the tangents to two neighbouring
bond paths. In strained molecules, the bond paths are curved, as
indicated above. In particular, in a cyclopropane molecule, the
bond path angle is *78.8 8 rather than 60 8, which has been
confirmed by a number of X-ray diffraction studies of the electron
density distribution in this type of system. Therefore, in the case of
strained molecules, it would be more appropriate to discuss the
bond path angles.
A number of publications have been devoted to the study of
electron density distribution in organic molecules. In these studies,
the term `bond angle' is used to imply the angle between the bond
paths and not between the straight lines connecting the atomic
nuclei. However, the vast majority of structural studies discuss the
angles between the internuclear straight lines. Therefore, in this
review, we also consider the latter type of angle unless otherwise
indicated.
It should be noted that the Bader's topological approach and
definition, in terms of its rigorous theory, of the bond path and
some other key concepts of the molecular structure theory are
drawing increasing attention of researchers. In particular, the
classical term `bond length' (the distance between the nuclei) is
replaced in this theory by the notion of `bond path length.' In the
case of a strained molecule, the bond path length would naturally
be longer than the internuclear distance. For example, in the
cyclopropane molecule, the distance between the carbon nuclei
(bond length) is 1.499 #A,77 and the bond path length between them
is *1.53 #A, i.e., it is nearly equal to the typical C7C bond length
(see Table 1). An even greater inconsistency between the internuclear
distances and the bond path lengths is found for cage
systems, in particular, for icosahedral carboranes.78
1. Scissors type distortion: a decrease in the C7C7C bond
angle
A considerable decrease in the C7C7C bond angle is found in
molecules of cyclic compounds with small rings. A lot of information
on the methods of synthesis and properties of these compounds
has been accumulated to date. Many fundamental
theoretical concepts, for example, the concept of steric strain and
banana bonds, have been developed upon investigations of
molecules with three- or four-membered carbocycles.14, 26, 79 ± 81
We shall consider several prominent examples of research along
this line.
In the CSDB, we found eighteen structures with a bond angle
at a saturated carbon atom smaller than 50 8. The molecules of
these compounds contain three-membered rings, and most of
them contain multiple bonds in the rings. The smallest A7C7A
angles (A is any atom) are typical of compounds with C=N and
Si
Si
Si
Si
Si
Me
Me
Me
Me
Me Me
Me
Me
Me
Me
1.22 #A
33
X
C
X
X
X
X
C
X
X
X
C XX
X
X
X
C
X
X
X
C
X
X
X
X
X C
I
XX
X
C
X
C
X X
XX
X X
IV
X
X
C
X
X
X
a b c d
II III
Figure 1. Distortions of bond angles at the tetrahedral carbon atom:
scissors (a), tetrahedral compression (b), digonal twist (c), umbrella (d ).
Carbon atom configuration: (I ) planar, (II ) inverted, (III ) pyramidal,
(IV ) intermediate between the tetrahedral and pyramidal.
{ Normally, this is so-called deformation electron density (DED), which
characterises the difference between the electron density of the molecule
and that calculated as a sum of the electron densities of isolated spherical
atoms located at the same distance from each other.73
996 I V Komarov
N=N bonds in the three-membered rings. In compounds 34 82
and 35,83 the angle at the saturated carbon atom is somewhat
smaller than that in cyclopropene derivatives (for example, in
compound 36).84 This is due to the fact that the C=N or N=N
double bonds are shorter than the C=C bond, and the C7N
single bonds are longer than the C7C bonds in cyclopropane (the
C7C bond length in cyclopropane is 1.499 #A).77 Both factors
result in a decrease in the angle between the single bonds in
unsaturated three-membered heterocycles.
Among the compounds containing saturated three-membered
carbon rings with reduced C7C7C angles, bicyclobutane derivative
37 should be mentioned.85 In the molecule of this compound,
the bond between the bridging carbon atoms is shortened and,
therefore, the opposing C7C7C angle in the three-membered
rings is reduced.
Compounds with reduced bond angles at saturated carbon
atoms exhibit unusual reactivity due to the strain in their molecules.
As an example, we shall consider derivatives of a hydrocarbon
which has not yet been synthesised, tetrahedrane 3.
Ab initio quantum-chemical calculations of different
levels (SCF/4-31G,86 G2 87) give a strain energy of 129 ±
137 kcal mol71 for the unsubstituted tetrahedrane molecule.
This value is greater than the dissociation energy of a single C7C
bond (72 ±117 kcal mol71) 88 and exceeds (in relation to one
carbon atom) the molecular strain in other hydrocarbons studied
to date. It is not surprising that numerous early attempts to
synthesise tetrahedrane and its derivatives have failed.14, 89, 90
Only in 1978, did Maier et al.91 synthesise the first tetrahedrane
derivative, tetra-tert-butyltetrahedrane 4, by photochemical
transformations of tetra-tert-butylcyclopentadienone.
The seeming simplicity of the reaction scheme conceals great
efforts of researchers aimed at selecting the optimal conditions for
the preparation of a compound the possibility of isolation of
which seemed unlikely at that time. The compound 4 is a stable
crystalline substance isomerising into tetra-tert-butylcyclobutadiene
only at 130 8C. Stability is attained owing to the presence of
bulky tert-butyl substituents, which ensure the steric shielding (socalled
`corset effect') of the central strained fragment of the
molecule by shielding it from the attack by reagents and preventing
intramolecular rearrangements. The tert-butyl groups in the
molecule 4 are remote from each other as far as possible but in the
transformations of compound 4, they approach each other, which
results inevitably in an increase in the strain energy.
Tri-tert-butylisopropyltetrahedrane (38) proved to be much
less stable than the compound 4: its thermal isomerisation to
cyclobutadiene 39 proceeds over several minutes at 80 8C.92
For a long period, researchers did not succeed in preparing
other tetrahedrane derivatives.
It was another 10 years after the synthesis of 4 before a new
derivative was prepared; this was tri-tert-butyl(trimethylsilyl)tetrahedrane
(40).93, 94 The approach to substituted cyclopropenyldiazomethane
proposed by Masamune et al. 95 permitted Maier
and co-workers to prepare other silyl- 96 and alkyl-substituted 92
tetrahedranes.
The reaction of compound 41 with the fluoride ion affords
highly reactive trisubstituted tetrahedrane 42.96
X-Ray diffraction data for the compound 4 showed that the
C7C bond length in it (1.485 #A) 97 is shorter than the typical value
(1.53 #A) and is even shorter than the C7C bond length in
cyclopropane (1.499 #A).77 This is due to rehybridisation of the
cage atoms and bond bending. Early molecular mechanics calculations
(MM2) showed that, due to the steric repulsion of the tertbutyl
groups, the chiral structure (group of symmetry T ) is
energetically more favourable (by 2 ± 6 kcal mol71) than the
achiral structure (Td).98 This conclusion was confirmed by ab
initio quantum-chemical calculations [B3LYP/6-311+G(d)//
B3LYP/6-31G(d)].99 The difference between the energies of these
forms was 0.5 ± 2.0 kcal mol71. The chemical properties of the
compound 4 have also been studied. Besides the above-mentioned
thermal rearrangement of the substituted tetrahedrane 4 into
tetra-tert-butylcyclobutadiene, protonation with gaseous HCl
and oxidation into the corresponding radical cation are known.100
2. Scissors type distortion: an increase in the C7C7C bond
angle
Increased bond angles in the molecules with tetrahedral carbon
atoms are observed, naturally, in the same cases where substantially
reduced bond angles are found. For example, in the tetratert-butyltetrahedrane
molecule discussed in the preceding Section,
the angles between the exocyclic bonds and the bonds in the
tetrahedral cage are 144.7 8, according to X-ray diffraction data.97
A search through the CSDB provided examples of structures with
even larger C7C7C angles. The vast majority of these compounds
are spiropentane (43) or bicyclobutane (26) derivatives.
According to X-ray diffraction analysis, the bond angles at the
spiro carbon atom in the spiropentane molecule amount to 137.6 8
and 136.7 8.101 The largest C7C7C bond angles were found in
bridged derivatives of 43 Ð molecules 44 ± 46 (the greater of the
two increased bond angles is given for each molecule).102
MeO2S
N
N
CF3
1.228 #A
48.68
35
But
But
But
49.181.279 #A
36
Si
Pri
Pri
SiMe3
SiMe3
N
Ph
P
SiMe3
Cy2N
Cy2N
1.254 #A
1.630 #A
47.48
34
Pri
Cy is cyclohexyl.
Me
O O
MeMe
48.88
1.442 #A
37
Me
But But
But But
O
hn
But But
But But
O
hn
But
But
But
But4
But
Pri
But
But38
But Pri
But But
39
But
R
But
But40, 41
But R
But But
R
But
But
N2
But
R = SiMe3 (40), SiMe2OPri (41).
42
But
H
But
But
Organic molecules with abnormal geometric parameters 997
Analysis of DED maps for spiropentane and its derivatives
has been carried out.101 In all cases, substantial exocyclic dispacement
of DED maxima in the planes of the three-membered rings
was found.
An increase in one bond angle at the tetracoordinated carbon
atom to 180 8 would result in a configuration intermediate
between the tetrahedral and pyramidal ones (see Fig. 1 d ). The
carbon atoms in dicubane 47 may have a similar configuration.
The possibility of synthesis of dicubane has been discussed.103 The
C7C7C bond angle in this molecule was calculated to be
*175 8.
According to calculations (MP2/6-31-G*, HF/6-31G*),104 a
carbon configuration with a C(2)7C(1)7C(6) angle of *180 8 is
also possible in the molecule of compound 48.
This highly reactive tricyclo[3.1.0.01,3]hexane derivative was
detected by IR spectroscopy in an inert matrix at 15 K.105
3. Planar configuration of a tetracoordinated carbon atom
In recent years, researchers have devoted particular attention to
types of distortion such as tetrahedral compression and digonal
twist, resulting in a flattened CX4 fragment.106 ± 110
The search for compounds with such an unusual structure was
stimulated by a publication by Hoffmann et al.,111 in which the
molecular orbitals in a hypothetical planar methane molecule
were analysed and suggestions were made about possible ways of
stabilisation of the planar configuration of carbon. According to
qualitative analysis of the electronic structure of the planar
methane molecule, the carbon atom in this molecule should be
sp2-hybridised. This atom should have two electrons in a nonhybridised
p orbital and should form two two-electron two-centre
C7H bonds and one two-electron three-centre H_C_H bond.
The strain energy of this molecule substantially exceeds the
C7H bond dissociation energy; the energy difference (MP2/6-31G*//6-31G*)
between the tetrahedral (Td) and planar (D4h)
methane configurations amounts to 159.7 kcal mol71. The possibility
of existence of the planar structure, even as the transition
state in the methane inversion, has been called in question.112
Calculations 113 [MCSCF/6-31G(d,p), 6-31+G(d,p), TZV+
+G(d,p)] showed that the planar structure with D4h symmetry
does not match any minimum on the PES, whereas the planar
structure with Cs symmetry corresponds to a saddle point on the
PES. A molecule with this symmetry could represent a transition
state formed in the methane inversion: its energy is almost
40 kcal mol71 lower than the energy of the molecule with D4h
symmetry (nevertheless, its strain energy is still greater than the
energy of C7H bond rupture by 7 kcal mol71). The same
conclusion has also been drawn by other researchers,114 who
used extended basis sets [6-311+G(3df,2p), 6-311G*] to analyse
the problem of methane inversion.
Hoffmann et al.111 were the first to consider stabilisation
factors of a planar configuration of the formally tetracoordinated
carbon atom. One of these factors is electronic stabilisation caused
by substituents exhibiting s-donor and/or p-acceptor properties;
the former provide the deficient s-electron density, while the latter
delocalise the increased p-electron density. Delocalisation of the
lone electron density of the carbon atom with a planar configuration
in the (4n+2p)-system should also facilitate stabilisation.
The idea of electronic stabilisation has been further extended
by Schleyer and coworkers,115 who found by RHF/STO-3G
calculations that the energy of 1,1-dilithiocyclopropane molecule
with a planar carbon (49a) is lower by 7 kcal mol71 than the
energy of the corresponding molecule with the tetrahedral carbon
configuration (49b).
Later, Sorger and Schleyer 110 made calculations for a number
of molecules that may have a planar configuration of a tetracaroordinated
carbon atom stabilised by s-donor and/or p-acceptor
substituents. These include, for example, 1,1- and 1,2-dilithioethylenes
(50 and 51, respectively) and 3,3-dilithio-1,2-diboracyclopropane
(52).
According to calculations (B3LYP/6-31G*), for the lastmentioned
compound, the energy of the molecule with a planar
carbon configuration is 18.7 kcal mol71 lower than that in the
case of tetrahedral configuration.
1,1-Dilithio-2,2,3,3-tetramethylcyclopropane (53) has been
synthesised;116 however, its structure has not been determined.
The structural studies for this type of compound are complicated
by the high degree of aggregation.
Spectroscopic detection of the [CAl4]27 dianion has been
reported.117 It was suggested that the planar (according to
B3LYP/6-311+G* calculations) [CAl4]27 dianion can be stabilised
in the solid phase by an appropriate counter-ion, for
example, Na+.
Organometallic compounds of transition metals the molecules
of which contain a tetracoordinated carbon atom with a planar
configuration are also known. Complex 54 was the first crystallographically
characterised compound of this type.
It is of interest that only two years after the publication of the
paper by Cotton and Millar 118 reporting the structural data for
complex 54, Keese et al.119 noticed the unusual planar environment
of the carbon atom (marked by an asterisk) in this compound.
Quite a few other complexes of this type are also known;107
however, the mechanisms of stabilisation of the planar configuration
of the carbon atom in them are different.108 In most of the
molecules, the carbon atom under interest is a part of an
unsaturated (often, aromatic) system, which is an additional
stabilising factor. Molecules in which a tetracoordinated carbon
158.28
44
162.58
45
O
O
S137.68
43
164.08
46
47
1758
C O1
6
2 48
H
H
H
H
Li
Li
1
Li
Li
1
49a 49b
C C
H
HLi
Li
50
Li
Li
H
H
51
HB
HB
Li
Li
52
Li
Li
Me
Me
Me
Me
53
998 I V Komarov
atom with a sum of bond angles equal to *360 8 is stabilised only
by s-donor and p-acceptor substituents (as has initially been
suggested for planar methane analogues) are found rather rarely;
among them, compounds 55, 56 were the first to be characterised
and studied 108 (the carbon atom having a planar configuration is
marked by an asterisk).
Stabilisation of a planar methane molecule can be attained by
oxidation to give a mono- or di-cation. As shown by calculations
[ST4CCD/6-311+G(2df,2p)],120 the carbon atom in CH2‡
4 has a
planar environment (the symmetry group is C2u rather than D4h).
This cation has been detected experimentally in mass spectra.121
The attempts to synthesise compounds in which the carbon
atom with a planar configuration would be embedded into a rigid
carbon cage have not yet been crowned with success. Hoffmann et
al.111 suggested that this type of carbon atom could exist in
[n.n.n.n]fenestranes
Numerous studies have been devoted to the synthesis of
fenestranes; elegant strategies for their synthesis have been developed.106
However, fenestranes with trans-fused five- and fourmembered
rings (the case in which the greatest distortions of the
bond angles at the central carbon atom are expected) have not yet
been obtained. Of the fenestranes studied by X-ray diffraction
analysis, the greatest distortion has been found in the molecule of
[4.4.4.5]fenestrane derivative 57,122 in which the opposing bond
angles at the central carbon atom are 128 8 and 129 8.
A highly distorted tetrahedral, although still not perfectly
planar, configuration of the central carbon atom is also expected
in the hypothetical structure 58, which was called bowlane;
initially, a pyramidal configuration of the central carbon atom
was suggested for this compound.123
Ab initio calculations (HF/6-31G*) have shown 124 that the
bowlane molecule should have C2u symmetry and a distorted
tetrahedral configuration of the central carbon atom with maximum
sizes of the opposing angles at this atom of 170.9 8 and
148.1 8. The predicted strain energy of the molecule 58
(RMP2/6-31G*, 166 kcal mol71) is approximately the same as
that found experimentally for cubane (157 ± 181 kcal mol71);23
therefore, the synthesis of bowlane appears quite possible.125
However, it is beyond doubt that the reactivity of the distorted
CC4 fragment accessible to attack by reagents from outside would
hamper the synthesis. Even in the case of [4.4.4.5]fenestranes (in
which the distortion of this fragment is less pronounced), the
reactivity is still rather high. Many thermal and photochemical
reactions of [4.4.4.5]fenestranes proceed with cleavage of the
bonds at the central carbon atom.126
The first and not yet synthesised neutral saturated hydrocarbon
with a predicted perfectly planar configuration of the
carbon atom the structure of which corresponds to a minimum on
the PES is dimethanospiro[2.2]octaplane (59).
The MP2/6-31G(d ) calculations predict for the compound 59
a structure with D2h symmetry and a perfect planar configuration
of the central carbon atom.127, 128 The highest occupied molecular
orbital in 59 is represented by the p orbital of the central atom with
a lone electron pair. Unusual physical properties of the octaplane
59 were predicted, in particular, a low ionisation potential
(*5 eV) comparable with those of alkali metals. In this compound,
the planar carbon atom is shielded by the hydrocarbon
cage, which may decrease the reactivity.
4. The inverted and pyramidal configurations of the
tetracoordinated carbon atom
Now we shall consider examples of molecules containing a carbon
atom with bonds located on one side of the plane that passes
through this atom (see Fig. 1 b,c). Inverted and pyramidal configurations
should be distinguished.123, 129 The inversion means
that one bond of the carbon atom points to a direction opposite to
its direction in the tetrahedral configuration, resulting in a fragment
with C3u symmetry (see Fig. 1 b). In the pyramidal CX4
fragment, the carbon atom occupies a vertex of a tetragonal
pyramid with C4u symmetry (see Fig. 1 c ).
The existence of inverted configurations was first discussed in
relation to propellanes, i.e., structures in which two bonded
carbon atoms are additionally connected by three bridges.
The first representative of small-ring propellanes, [3.2.1]propellane
(60), was synthesised in 1969.130 At about the same time,
discussion concerning the inverted configuration of the carbon
atom was initiated. It was suggested that in small-ring propellanes
such as 60 ± 63, unusual configuration of the central atoms is
possible. The results of X-ray diffraction analysis of 8,8-dichlorotricyclo[3.2.1.01,5]octane
(64) provided the first evidence supporting
this hypothesis.131
[3.2.1]Propellane 60 proved to be thermally stable but still
extremely reactive (it reacts with oxygen and enters into diverse
radical addition reactions).130 An even more strained propellane
(61) was stabilised only in an argon matrix at 29 K.132 It appeared
that the simplest [1.1.1]propellane 63 could hardly be expected to
Me
Me
Me
Me
BC
CoB
Co
C
Me3Si
Me3Si
Men
n = 4 (55), 3 (56)
OMeMeO
V V
2
OMeMeO
2
54
C*
*
C
(CH2)n
(CH2)n
(H2C)n
(H2C)n
Br
HN
O
H
Me
H
O
H
57
C
58
C
59
(CH2)n
(CH2)n
(CH2)n
[n, n, n]propellanes
60 61 62 63
Cl Cl
64 65 66 67
Organic molecules with abnormal geometric parameters 999
be more stable. However, in 1982, Wiberg and Walker 133 predicted
theoretically the possibility of synthesis and the highest
stability, among the compounds 61 ± 63, for [1.1.1]propellane and
later they synthesised it. For the compound 63, not only the
possibility of synthesis and stability were predicted, but also the
enthalpy of formation and photoelectron and IR spectra were
calculated. The [1.1.1]propellane molecule is the first polyatomic
molecule for which correct theoretical predictions preceded the
synthesis.134
The relative stability of 63 is interpreted in the following
way.134 The molecules 61 ± 63 have approximately equal strain,
while the strain of the corresponding bicyclic hydrocarbons
65 ± 67 with no bond between the central carbon atoms sharply
increases on passing from [2.2.1]bicycloheptane (65) to [1.1.1]bicyclopentane
(67).135 Since the reactions of propellanes include
rupture of the bond between the bridging carbon atoms to give
species having the skeleton of the corresponding bicyclic hydrocarbons,
the energy barrier to the reactions of [1.1.1]propellane is
higher than the corresponding values typical of its homologues.
[1.1.1]Propellane was first synthesised from 1,3-dibromobicyclo[1.1.1]pentane,
which is difficult to obtain.
Later, a procedure for the synthesis of the propellane 63 from
more easily accessible precursors was developed;136 this allows the
preparation of tens of grams of this compound.
A similar approach has been used to prepare substituted
[1.1.1]propellane derivatives.137 The latest achievements in the
synthesis, study of the chemical properties and application of
[1.1.1]propellanes are covered in a review.138
The structure of [1.1.1]propellane was determined using vibrational
spectroscopy,139 gas-phase electron diffraction 140 and
X-ray diffraction analysis.141 The results of investigations by
these methods confirmed the presence of the inverted configuration
of the carbon atoms at the bridgehead in the structure of this
compound.
The nature of the bond between the central carbon atoms in
the compound 63 was the subject of numerous theoretical
studies.134 The energy of this bond was estimated (based on
MP2/6-31G* calculations) to be approximately 70% of the energy
of a single C7C bond (59 kcal mol71).142
Experimental information on the nature of the central bond in
propellanes are provided by studies on the electron density
distribution from X-ray diffraction data. Studies of this type
have been attempted;141, 143 however, the accuracy of experimental
data proved to be inadequate to draw ultimate conclusions.
The most accurate results of X-ray structure determination (at
81 K) and electron density distribution have been reported 143 for
two [1.1.1]propellane derivatives, compounds 68 and 69.
As expected, the DED maxima for non-bridging bonds
proved to be concentrated outside the three-membered rings,
which is typical of bent (banana) bonds. However, the DED
values between the central carbon atoms are negative for both
molecules. Nevertheless, this fact alone does not prove the absence
of bonds between these atoms and does not contradict the results
of the electron density calculation carried out by Wiberg.144
The negative DED values on the lines connecting atoms are
encountered quite often; this is due to over-subtraction of the
electron density of the `pro-molecule' (combination of spherical
non-interacting atoms) from the total density. This is due to the
nature of the DED maps Ð they are differential. Therefore, in
investigations of these bonds, a more promising approach
includes analysis of the electron distribution topology and construction
of non-differential maps, in particular, the Laplacian
(the second derivative) of the experimental and theoretical electron
density.75
The inverted configuration of the bridgehead carbon atoms
was also observed in bicyclobutane derivatives (the structure was
determined by microwave spectroscopy 145).
In this molecule, the C(1)7H and C(3)7H bonds form an angle
of 11.5 8 with the plane passing through the C(1), C(2) and C(4)
atoms.
X-Ray diffraction data for other bicyclobutane derivatives
with inverted configurations of bridgehead carbon atoms have
also been published.146 ± 148
The Cambridge Database contains also structural data on
bicyclobutane heteroanalogues which also incorporate carbon
atoms with inverted configurations. Examples are provided by
compounds 70 ± 72 (the carbon atoms with inverted configurations
are marked by asterisks).149 ± 151
The presence of carbon with inverted configuration in 1,4dehydrocubane
has been doubted based upon the results of
theoretical (ab initio 6-31G*) and experimental data.152 ± 154 It is
more likely that this highly unstable molecule exists as singlet
biradical 73a and contains no diagonal bond, as shown in 73b.
Theoretical calculations have been performed for the molecules
of polycyclic hydrocarbons 74 ± 76 [MP2/6-31G(d,p),
6-311++G(d,p), B3LYP/6-31G(d,p)] 155 and [2.2.2]propellatriene
77 (CASSCF/6-31G*),156 in order to find other structure
types where existence of `inverted' carbon atoms is possible.
CO2H
HO2C
HgO
Br2
Br
Br
MeLi
CBr2
Cl Cl
Br
Br BuLi
Br
CH2Cl
BuLi
Cl Cl
68 69
H H
1
4
3
2
1 3
2(4)
H H
11.58
Projection along the straight line
passing through C(2) and C(4)
N
Ph
Ph
Ph
*
70
Si Si
Me
Me
Me3Si SiMe3
Me
Me
71
* *
P P
Me3Si
But
But
But
But
But
But
*
72
73a 73b
1000 I V Komarov
The pyramidal configuration of the carbon atom (see Fig. 1 d)
is more exotic than the inverted one, and calculation methods still
remain the most efficient tool for the investigation of compounds
with this type of atom. Noteworthy are studies by Minkin et
al.,157, 158 who were the first to demonstrate that among the
possible non-tetrahedral configurations of the carbon atom in
methane, the pyramidal rather than planar configuration is
energetically most favourable. The researchers cited discuss the
factors that stabilise the pyramidal configuration; they are similar
to those for the planar configuration, namely, the presence of
s-donor or p-acceptor substituents as well as incorporation of a
pyramidal carbon atom in a rigid polycyclic cage, especially in
small rings.
Known and structurally characterised systems with a pyramidal
configuration of carbon (as well as compounds with the planar
configuration of carbon) are represented exclusively by organometallic
compounds of transition metals. Some of these structures
are deposited in the CSDB; most of them are carbido clusters of
iron, ruthenium, or osmium in which the carbon atom occupies an
open cavity formed by metal atoms. The most frequently encountered
types of structures are those present in compounds 78, 79
(with the so-called butterfly geometry 159, 160) and compounds 80,
81, in which the carbon atom lies below the base of the tetragonal
pyramid formed by the metal atoms.161, 162
In recent years, interest in these clusters has substantially
increased because they were shown to be the key intermediates in
the catalytic reduction of CO with hydrogen to give hydrocarbons,
i.e., the Fischer ± Tropsch synthesis.163 The first complex of
this type was prepared as a side product of the reaction of
Fe3(CO)12 with alkynes;161 at present, preparative procedures for
the synthesis of these compounds in high yields have been
developed.164 The carbon atoms in carbido clusters form s- and
p-bonds involving transition metal d orbitals; this stabilises the
clusters. Similar complexes containing no carbido (interstitial)
ligands are less stable.
Numerous theoretical studies of hypothetical organic molecules
having the carbon atoms with pyramidal configuration have
been carried out. About 10 years ago, the lack of computer
resources and the absence of advanced software did not allow
sufficiently accurate and reliable determination of the structural
parameters of strained molecules. Many structures calculated at
that time have later (according to the results of more advanced
methods of calculation) proved unreal, i.e., either not matched by
minima on the PES or inaccurate. For example, [1.1.1.1]- and
[2.2.2.2]paddlanes (82, 83), which were initially supposed to have
pyramidal configurations of carbon atoms, did not correspond to
minima on the PES calculated by modern ab initio methods.124
The molecular mechanics calculations for bowlane 58 had also
showed the presence of a carbon atom with pyramidal configuration,
but ab initio calculations carried out later refuted this
conclusion.
The C4u structure of pyramidane (84) with the pyramidal
configuration of a carbon atom corresponds to a local minimum
on the PES (MINDO/3,165 HF/STO-3G 166 and HF/6-31G* 124).
Rasmussen and Radom 167 have reported results of ab initio
calculations (B3LYP/6-31G(d)//MP2/6-31G(d)) for hemialkaplane
(bowlane 58 is a representative of this class of polycyclic
hydrocarbons) and hemispiroalkaplane molecules; according to
their data, the central carbon atom has a pyramidal configuration.
The general formulae of hemialkaplanes (on the left) and hemispiroalkaplanes
(on the right) are shown below:
On the basis of calculations of the molecular strain and the socalled
apical strain (which characterises the strain of the separate
molecular fragment containing the carbon atom with the pyramidal
configuration), the researchers concluded that hemispirobioctaplane
85, hemispirooctaplane 86 and hemispirobinonaplane 87
are the most promising synthetic targets. Analogues of the systems
85 ± 87 containing methyl groups (for example, compound 88)
might prove to be easier to prepare because the presence of methyl
groups contributes to the kinetic stability of the molecule. The
compounds 85 ± 88 were predicted to be highly basic.167
The existence of rigid polycyclic organic molecules, for which
the presence of a carbon atom with a pyramidal configuration had
been predicted, was later proved experimentally. For example,
Wiberg et al.168, 169 have detected one of them, namely, highly
reactive tricyclo[2.1.0.01,3]pentane 89.
VII. Distortions of bond and torsion angles at the
double bond in alkenes
The research into the distortions of the bond and torsion angles in
the molecules of alkenes has a long-standing history. Back in 1890,
Baeyer 170 arrived at the conclusion that substantial strain should
be expected in the trans-cyclohexene molecule and, therefore,
isomerisation of cis-cyclohexene into the trans-isomer is unlikely.
Later, when analysing the strain in unsaturated bicyclic molecules,
Bredt,171, 172 formulated a rule according to which the cage of
camphane, pinane or other related compounds cannot have a
double bond to a bridgehead position. At present, vast theoretical
and experimental material on this point has been accumulated and
reflected in numerous reviews (see, for example, studies
28, 173 ± 176).
The types of distortion of a planar alkene fragment are
illustrated by Fig. 2.
Mathematical analysis of the distortions of the bond and
torsion angles in the ethylene molecule has been described in detail
in the literature (see, for example, reviews 28, 177).
Distortions of only one type are seldom encountered in alkene
molecules. However, in most cases, the prevailing type of distortion
can be distinguished, which determines the total strain of
74 75 76 77
COOC
M
OC
M
M
M
OC CO
CO
CO
CO
CO
CO
CO
OC
OC
OC C CO
80, 81
C
Fe(CO)3
(OC)3Fe
A
(OC)3Fe
Fe(CO)3
A = H+ (78), CO (79)
78, 79
M = Fe (80), Ru (81)
M
82 83 84
C
C
85 86
87
Me Me
MeMe
88
89
Organic molecules with abnormal geometric parameters 1001
the alkene.28 Below we consider compounds in which the strain of
the molecule is mainly due to the contribution of one type of
distortion.
1. In-plane distortions of an sp2-hybridised carbon atom
The bond angles at the sp2-hybridised carbon atom can differ
appreciably from the ideal value, equal to 120 8. Indeed, the
internal C7C=C angle in cyclopropene derivatives can be twice
as small. The results of a search through the CSDB demonstrated
that this angle is about 60 8 in the molecules of cyclopropene
derivatives that also contain an exocyclic double bond (there are
10 structures of this type), for example, 90, 91.178, 179
In these molecules, a major contribution to the resonance
hybrid is made by canonical forms with the cyclopropenylium
cation. In other cyclopropene derivatives, the internal C7C=C
angle is close to 60 8; for example, in molecule 92 this angle is
61.9 8.180
The external R7C=C angles in cyclopropene derivatives can
be greater than 150 8 in the case of bulky R substituents, for
example, the angle is 155.6 8 in molecule 93.181 Bond angles
exceeding 150 8 have also been found at exocyclic double bonds
in compounds with saturated three-membered rings. The deviations
of these angles from 150 8 are caused by steric repulsion of
bulky groups (as in compound 94) 182 or by the fact that double
bonds are incorporated in rings (as, for example, in compound
95).183
A decrease in the R7C=C angle results in pyramidalisation
of the carbon atoms of the double bond. This fact was predicted
theoretically:184 model calculations (RHF/STO-3G) showed that
if the H7C=C angles in the planar ethane molecule are less than
100 8, pyramidalisation becomes energetically favourable. X-Ray
diffraction analysis of compound 96 confirmed this fact
experimentally.185 In molecule 96, the C7C=C angles in the
cyclopropene fragment amount to 64.8 8 and 65.3 8, and the c
angle characterising pyramidalisation equals 17.6 8.
For the norbornene molecule (97), pyramidalisation of the
carbon atoms of the double bond was predicted theoretically (for
example, according to the STO-3G ab initio calculations,186 the
hydrogen atoms at the double bond are displaced in the endodirection
and the c amounts to 4.9 8). X-Ray diffraction data for
norbornene have not been obtained.
In a norbornene derivative, anhydride of exo,exo-2,3-norborn-5-enedicarboxylic
acid (98), the structure of which has been
determined by neutron diffraction, the c angle proved to be
7.4 8.187 In compound 99, as shown by X-ray diffraction analysis,
the fusion of two norbornyl cages (and, probably, steric repulsion
between the cyclopentane rings) accounts for quite a noticeable
pyramidalisation: c = 22.7 8.188, 189
An exceptionally high pyramidalisation of the carbon atoms
at the double bond can be expected, according to calculations
(HF, TCSCF, MP2, B3LYP, B3PW91/6-31G*),190 in compounds
100 ± 103, the synthesis of which has been reported.191 ± 195
It follows from calculations that each of the tricyclic structures
100 ± 103 is matched by two minima on the PES, which correspond
to the endo- and exo-isomers. In the case of the compounds
100 and 101, a lower energy is found for endo-isomers (their energy
is 2.2 ± 7.5 kcal mol71 lower than that of the corresponding exoisomers),
whereas for the compound 103, the exo-isomer is lower
in energy (by 2.2 ± 3.3 kcal mol71). The carbon atoms of the
double bonds in the compounds 100 ± 103 should be strongly
pyramidalised (c > 40 8). Experimental verification of these theoretical
conclusions would be a complicated task because the
strained molecules 100 ± 103 are highly reactive (for example, the
existence of the compound 103 can only be proved by analysing
the products of reactions involving this molecule).193
NMe2
Me2N NMe2
+
90
Cl
OMe
Me Me
61.9(1)8
9291
SMe Me Me Me
Me
Me
Me
Me
158.18
9493
CO2H
Ph But155.68
OMe
O
Cl
C
C
155.68
95
H
H97
c = 4.98
c = 22.78
99
N
N
N
O
O Me
Ph
Ph
Me
Me
Me
Me
96
c = 17.68
98
c = 7.48
H
H
O
O
O
100 101 102 103
Bu4N+F7
Cl Br
Cl
Cl
Br
SiMe3
Cl
Br
MeLi
O
Ph
Ph
O
Ph
Ph
b c da
Figure 2. Types of distortion of the planar alkene fragment: (a) in-plane
distortions; (b ± d) out-of-plane distortions: (b) twist, (c) syn- and (d) anti-
pyramidalisation.
1002 I V Komarov
2. Twisting of the double bond
The loss of p-bonding upon distortion of the torsion angles at the
double bond (twist) is partially counterbalanced by rehybridisation
of carbon atoms, resulting in their pyramidalisation.196 ± 198
Therefore, when comparing the degree of twisting of double bonds
in the molecules of different alkenes, it is not always legitimate to
use the dihedral angle between the aC(1)b and cC(2)d planes
(Fig. 3). Therefore, the so-called twist angle t was introduced,
which is found as the arithmetic mean of the aC(1)C(2)d and
bC(1)C(2)c dihedral angles.
t =
aC…1†C…2†d ‡ bC…1†C…2†c
2
.
This angle is equal to the angle between the aC(1)b and cC(2)d
planes in the case where no pyramidalisation takes place. The
degree of pyramidalisation of the C(1) and C(2) atoms is evaluated
from the departure of the aC(1)C(2)c and bC(1)C(2)d dihedral
angles from 180 8 and from the pyramidalisation angles wC(1) and
wC(2):
wC(1) = bC(1)C(2)c7bC(1)C(2)d + p,
wC(2) = aC(1)C(2)d7bC(1)C(2)d + p.
The results of theoretical investigations demonstrate that
twisting of the molecule of an alkene with all electron-donating
or all electron-withdrawing substituents by 90 8 (t = 90 8 or
790 8) should give rise to a singlet biradical,199 ± 201 and the
maximum twisting in the molecules of non-symmetrical alkenes
(so called push ± pull alkenes) yields bipolar species.202 Twisted
systems correspond to the transition state of the cis ± transisomerisation
of alkenes. For simple alkenes, the activation free
energy of the cis ± trans-isomerisation found experimentally lies in
the range from 51 to 67 kcal mol71 (see Refs 203 ± 205). For
push ± pull alkenes, this barrier is substantially lower.202 This is
why the `record-holder' molecules in which the t angle for the
C=C bond is close to 90 8 (or 790 8) are represented in the CSDB
by push ± pull alkenes. For example, according to X-ray diffraction
data, in the molecules 104 and 105, the t angles are 85.1 8 and
84.3 8, respectively.206, 207
When the double bond is conjugated with other p-bonds or
aromatic systems, the barrier to the cis ± trans-isomerisation also
decreases. Among the structures of compounds with conjugated
double bonds, numerous examples can be found in which the jtj
values are close to 90 8. Thus in the octaisopropylcyclooctatetraene
molecule (106), the t angles for all multiple bonds exceed
64 8.208
If push ± pull alkenes and compounds with conjugated double
bonds are excluded from consideration, the number of
structures with t angles lying in the range of 20 8 < jtj < 90 8
included in the CSDB sharply decreases. Considerable twist-type
distortions of the C=C bond were found both in acyclic and in
cyclic or polycyclic compounds.
a. Acyclic twisted alkenes
In acyclic alkenes, twist distortions take place if bulky substituents
are present at the double bond. The largest twist of the double
bond not incorporated in a ring or a polycyclic system and bearing
only hydrocarbon substituents is expected in the tetra-tert-butylethylene
molecule (107). Numerous attempts at synthesising this
compound were undertaken; however, they have not yet met with
success. Ab initio (BLYP/DZd) calculations for the molecule
107 209 predict a singlet ground state (D2 symmetry) with t =
45 8, slight pyramidalisation and a strain energy of 93 kcal mol71.
The energy of the triplet state of 107 with t & 87 8 would be
12 kcal mol71 higher than the energy of its singlet state.
The alkenes 2, 108, and 109 have been prepared by methods used
in the attempts to synthesise the compound 107. In the molecules
of these compounds, as in the molecule of 107, the quaternary
carbon atoms are linked directly to the double bonds. However,
the steric repulsion in the molecules 2, 108 and 119 is weaker than
that in tetra-tert-butylethylene due to the presence of additional
bonds between substituents.210 ± 213
Krebs et al. 214, 215 approached very closely the synthesis of the
compound 107; they succeeded in synthesising tetrakis(2-formylpropan-2-yl)ethylene
(110) (t = 28.6 8, according to X-ray diffraction
data). However, the formyl groups proved to be so nonreactive
that the researchers were unable to reduce them to the
methyl groups.
The relatively low reactivity of the double bond in the
compounds 2 and 108 ± 110 should also be mentioned. In all
probability, this is due to the shielding of the p-system by bulky
substituents. The cis ± trans-isomerisation of strained alkenes
proceeds much more readily than isomerisation of unstrained
compounds (the energy barrier can be almost twice as low in the
former case). This was used in a study 205 to estimate the energy
barrier to the isomerisation of alkenes. Since isomerisation of
strained alkenes takes place at relatively low temperatures, side
reactions do not complicate the kinetic measurements. The standard
enthalpies of formation (with an applied correction for steric
effects found by MM2 calculations) of these alkenes were
employed to calculate the activatiom barrier to the cis ± transisomerisation
(69.5 Æ 0.9 kcal mol71), which does not depend on
the nature of substituents at the double bond.
HNO2N
HNO2N
NO2
NO2
104
NPriPriN
O
Me O
105
Me
H
N
H
N
Pri Pri
Pri
Pri
PriPri
Pri
Pri
106
But
But
But
But
107
OHC
OHC CHO
CHO
110108 109
Stereo-
formulae
Newman
projections
along the
C=C bond
cb
da
c
b
d
a
b a
c
b a
t
I II
cd
da
III
b
d
a
c
IV
c d
c d
b
a
t
d
b
a
c
t
d
Figure 3. Twist distortion of the C=C bond and definition of the twist
angle t: (I ) unstrained double bond; (II ) twisting of double bond without
pyramidalisation of the carbon atoms; (III, IV ) twisting + pyramidalisation;
a ± d are substituents.
Organic molecules with abnormal geometric parameters 1003
According to the results of a search through the CSDB, the
greatest twist distortion of the double bond among acyclic
compounds is found in compound 111.216
In the tetra(trialkylsilyl)ethylene 111, the t angle equals 49.6 8
(note that this value is greater than that predicted for tetra-tertbutylethylene
107), no pyramidalisation of the carbon atoms of
the C=C bond takes place, and the double bond length (1.370 #A)
exceeds the typical value (1.32 #A).
b. trans-Cycloalkenes
Among monocyclic compounds, a substantial distortion of the
double bond (mainly twist-type distortion) can be attained in
trans-cycloalkenes in which the number of carbon atoms in the
ring does not exceed nine. trans-Cyclooctene (112) is the unsubstituted
compound with the smallest ring that can be isolated in a
pure state at room temperature.217, 218 The structure of transcyclooctene
was determined by electron diffraction.219 According
to these studies, the C7C=C7C dihedral angle in the molecule
112 amounts to 136 8. For a derivative of trans-cyclooctene,
compound 113, X-ray diffraction data have been published.220
The C(8)7C(9)7C(10)7C(11) dihedral angle in the molecule
113 is 139.3 8.
Further contraction of the ring containing a trans-double
bond results in a substantial increase in the reactivity and the
tendency for isomerisation to the cis-form. trans-Cycloheptene
(114) can be synthesised at low temperatures.221 Complexes of 114
with transition metals stable at room temperature have also been
obtained.222 Unsubstituted trans-cyclohexene (like trans-cyclopentene)
has not been experimentally detected yet.
Monocyclic compound 115 with the smallest-possible ring
containing a trans-double bond and stable at room temperature
contains a silicon atom in the seven-membered ring and methyl
groups in the a-positions relative to the double bond.223 This
compound proved to be sufficiently stable to be studied by X-ray
diffraction analysis. The kinetic stability is ensured by the methyl
group, while the presence of two C7Si bonds, which are longer
than C7C bonds, makes the strain in the molecule 115 lower than
that found in trans-cycloheptene.
A substantial distortion of the double bond in 115 is reflected
in the size of the C7C=C7C dihedral angle, which is 130.97 8. It
is of interest that the H7C=C7H dihedral angle is 173 8, and
pyramidalisation of the carbon atoms in the molecule 115 is
insignificant. The C=C bond length (1.330 #A) deviates only
slightly from the typical value, despite the substantial distortion
of the dihedral angles. It should be noted that trans-cycloalkenes
are chiral; the racemic 115 was partially resolved by column
chromatography using a chiral adsorbent.
c. Polycyclic compounds with twisted double bonds: anti-Bredt
alkenes
Among numerous anti-Bredt alkenes deposited in the CSBD, one
can find structures in whose molecules a trans-double bond is
incorporated into an eight-membered ring. As examples, one can
mention compounds 116 and 117 (the molecule of 116 contains
also a twisted amide bond 224).
The following parameters have been found for the molecule
116:225 the angle t = 10.8 8, the average degree of pyramidalisation
of the carbon atoms at the double bond w = 28.45 8.
The size of the t angle attests to an even greater twist distortion
of the double bond (t = 29.3 8) in the molecule 117, although the
degree of pyramidalisation in this molecule is lower, w = 17.1 8.226
The alkene 117 is very sensitive to moisture and atmospheric
oxygen; the compound 116 is less reactive.
Anti-Bredt alkenes with a trans-double bond incorporated in
rings containing not more than seven carbon atoms are known.
The substantial strain in the molecules of these compounds
accounts for their enhanced reactivity. The exceptionally reactive
alkene 1 contains a trans-cyclohexene ring.227, 228 This compound
was stabilised in a solid argon matrix, and the IR absorption
frequency for its double bond was determined. The unusually low
frequency (1481 cm71) indicates that the p-bonding has been
considerably reduced as a result of angle distortion in the molecule
of 1.
An even more strained molecule of 9-phenyl-1(9)homocubene
(118) contains a trans-`double' bond in the five-membered ring.
No spectroscopic or structural characteristics have been obtained
so far for this compound because of its high reactivity.229 The
compound 118 rearranges into carbene 119 even at low temper-
atures.
This reaction is uncommon for alkenes (the reverse transformation
takes place much more often); the fact that this reaction
does proceed implies that the properties of the double bond
change substantially upon geometric distortion.
Although the compounds 1 and 118 can be regarded as
`record-breaking twisted alkenes', the p orbitals of their `double'
bonds are not orthogonal: the calculated t values are much smaller
than 90 8 (for example, t = 64 8 in the molecule of 1).227, 228 Due to
the pyramidalisation of non-bridging carbon atoms of the C=C
bonds, the orbital overlap is partly restored and the t value
decreases. Perhaps, an ideally orthogonal arrangement of the p
orbitals could be realised in `fixed betweenenes' (or orthogonenes)
120, 121 (MM2 and semiempirical calculations; no ab initio
calculations for these structures have been carried out).230 Tentative
results on the synthesis of orthogonenes have been pub-
lished.231
3. Out-of-plane distortions of angles at the C=C bond:
pyramidalisation
It is well-known that alkenes in which the double bond occurs in a
non-symmetric environment are often characterised by a pyramidal
configuration of the double-bond carbon atoms. This pyramidalisation
is slight; the reasons for it are discussed in the
SiMe3
SiMe3
111
ButMe2Si
ButMe2Si
112
O O
Me
Me
Bu
O
Me
8
9
10
11
113
Si
Me
Me
Me
Me
114 115
N
MeO2C O
116
Br
EtO
Cl117
Ph
118
Ph
119
n n
nn
120, 121
n = 0 (120), 1 (121).
1004 I V Komarov
literature (see, for example, the reviews 232, 233). Pyramidalisation
accompanies also in-plane and twist distortion of a double bond
(see above). Calculations 234 have shown that anti-pyramidalisation
of the carbon atoms of the double bond is energetically more
favourable than syn-pyramidalisation. However, this conclusion
requires verification by means of more advanced methods of
calculations than those used in the study cited.234
In this Section, we consider compounds the structural features
of which impose pronounced syn-pyramidalisation. As a rule,
these compounds contain a rigid polycyclic cage having two
mutually perpendicular planes of symmetry one of which accommodates
the double bond.175 Examples of non-symmetric molecules
have also been reported.235 When discussing
pyramidalisation in these molecules, in addition to w, it is
convenient to use the angle f
The first synthesised compound with a considerable pyramidalisation
of the carbon atoms at the double bond (122) was
reported more than 30 years ago;236 at present, dozens of
compounds of this type are known, for example, 123,237, 238
124,239 ± 241 125 242 and 126.
In the cubene molecule (126), the angle f, according to the
SCF/3-21G calculations, is equal to 84.1 8.243 The possibility of
synthesis of the compound 126 was predicted theoretically and
then realised in practice.244 Rough thermodynamic data for
cubene 245 and the first results of the study of chemical properties
of this highly reactive compound 246 have been published. The
calculations showed that, despite the pronounced pyramidalisation
of the double-bond carbon atoms, the overlap of the p
orbitals in the molecule 126 is sufficient for regarding this
compound as an alkene rather than a biradical (TCSCF/6-31G*
for the singlet state, ROHF/6-31G* for the biradical).153 This is
also indicated by an observed reaction typical of alkenes with
highly pyramidalised carbon atoms of the double bond,247
namely, cubene dimerisation to give the corresponding propellane
127 with subsequent transformation into tetraenes 128 and 129.
The attempts to synthesise derivatives with even more pyramidalised
carbon atoms of the C=C bond, prismene, have so far
been unsuccessful.248 Both prismene isomers, 130 and 131, have
been studied theoretically [HF/6-31G(d), MP2/6-31G(d)].249
According to calculations, the energy of the molecule 131 is
lower than the energy of 130.
VIII. Distortions of the bond and torsion angles in
the molecules of aromatic compounds
Cyclic unstrained aromatic systems are normally planar. The
benzene structure,250 which serves as a sort of standard in
discussion of the nature of aromaticity,251 has been studied in
the gas phase (spectroscopic methods and electron diffraction)
with high accuracy: the molecule has D6h symmetry, the carbon
atoms form a regular hexagon, and the C7C bond length is
1.399 Æ 0.001 #A.
The types of distortion investigated for benzene derivatives
include changes in the bond angles in the aromatic ring plane and
out-of-plane distortions; compounds with `conformations' similar
to those of cyclohexane, i.e., a chair, a boat, and a twist
`conformation,' have been obtained (Fig. 4). Below we consider
only benzene derivatives (strained molecules of aromatic heterocyclic
compounds have received much less attention in the
literature).
1. Changes in the bond angles in the plane of the benzene ring
The C7C7X bond angles at the carbon atoms of the benzene
ring can markedly depart from the ideal value, equal to 120 8.
These distortions may be caused, in particular, by annelation of
small rings to benzene. Mills and Nixon 252 postulated that
annelation of cyclopentane to benzene shifts the equilibrium
between the two Kekule structures.
Later, the hypothesis of the existence of an equilibrium
between the Kekule structures in benzene derivatives was admitted
to be faulty;50 however, localisation of the double bonds
induced by annelation of strained rings was actually discovered.253
The first experimental proof of this phenomenon was
provided by the synthesis of cyclohexatrienes 132 and 133.254
cosf = 7
R
R
f
a
b R
R
cosb
cos(0.5a)
122
123 124 125 126
F7
Br
SiMe3
126 127
+
128 129
130 131
} These designations of angles are used only in this Section.
X
a
a ag
Symmetrical Asymmetrical
a b c d
X
b
e f
Figure 4. Bond angle distortions in benzene derivatives. (a) in the ring
plane; (b ± f ) out-of-plane distortions: (b) chair, (c) symmetrical boat,
(d ) asymmetrical boat, (e) twist, (f ) deviations of the C7X bond from the
ring plane. The angles characterising the degree of distortion are marked.}
Organic molecules with abnormal geometric parameters 1005
The compound 133 contains, according to X-ray diffraction
analysis, noticeably alternating bonds in the central ring. The
unusually easy hydrogenation of the central ring in 132 also points
indirectly to a substantial localisation of the double bonds.255
Thermochemical data for this reaction have been published.256
However, in this type of compound, localisation of the double
bonds can be interpreted by assuming a smaller contribution of
the structure 134, with antiaromatic cyclobutadiene rings, to the
resonance hybrid. Calculations (B3LYP/6-31G*) demonstrated
that it is the bond localisation caused by annelation rather than
other p-effects (aromaticity ± antiaromaticty) that is responsible
for the structure of these compounds.257
The clear-cut bond alternation has been found by X-ray
diffraction analysis 258 in the molecules of naphthalene derivative
135. The bond angles at the carbon atom at the peri-positions of
the naphthalene ring differ appreciably from 120 8.
Alternation of single and double bonds was to be expected in
dehydrocyclobuta- and cyclopropabenzenes. It proved to be very
difficult to perform the synthesis and X-ray diffraction analysis of
strained compounds such as 136 ± 143. However, unexpectedly, no
noticeable bond alternation was found in the molecules of these
compounds.259
On the one hand, these results are at variance with the
calculations (MP2/3-21G, HF/6-31G*) for model systems (benzene
molecules with distorted C7C7H bond angles), according
to which the decrease in the C7C7H angle to 90 8 is accompanied
by pronounced localisation of the double bonds.260 However,
on the other hand, clear-cut alternation of bonds was found in the
benzene ring annelated to bicyclic fragments. In the most strained
molecule of this type of compound, tris(tetrahydrobicyclo[2.1.1]hexa)benzene
(144), noticeable bond alternation was found, first,
by ab initio calculations [6-31G(D)(LDF)],261 [MP2/6-31G(D)],262
and then by X-ray diffraction analysis.263 The C7C7C angle in
the structure 144 is equal to 102.3 8 (which is much smaller than
120 8). The reason for the observed bond alternation in the
structure 144 is currently under discussion.
The alternation might be caused by the strain in the bicyclic
fragments of 144, which results in elongation of those bonds in the
benzene ring at which the bicyclic fragments are annelated.
A similar effect was observed for the compound 145.101
2. Out-of-plane distortions of the benzene ring
a. Compounds with benzene rings in the boat `conformation'
Among the molecules in which the benzene rings are distorted to
form a boat `conformation' typical of the cyclohexane ring,
cyclophanes should be mentioned first of all.264 In recent years,
strained molecules of meta-, para- ([n]- and [n.n]-) cyclophanes
have been vigorously studied. The synthesis and properties of
these compounds have been considered in detail in reviews.265 ± 268
The interest in these compounds, like that in the benzene
derivatives 133 ± 143 described above (cyclobuta- and cyclopropabenzenes
can be treated as [n]orthocyclophanes), is related
to some extent to the discussion of the nature of aromaticity.
In the case of [n]paracyclophanes, the benzene ring is not
strained when n = 9; however, with a decrease in the bridge length,
the ring becomes non-planar; in addition, the exocyclic C7C
bonds are also distorted, in particular, they decline from the plane
of the two adjacent bonds of the benzene ring (see Fig. 4 for the
definition of the a and b angles characterising these distortions).
Analogous distortions of the benzene rings in [n]metacyclophanes
take place when n 4 7. In [n.n]para- and -metacyclophanes, the
benzene rings deviate substantially from the planar configuration
at n 4 3.
[2.2]Metacyclophane was synthesised in 1899,269 and
[2.2]paracyclophane was prepared in 1949 270 by closure of the
bridge. In the case of homologues with smaller n values, [n]paracyclophanes
with n 4 7, or [n]metacyclophanes with n 4 6, this
classical approach is inapplicable. The syntheses of cyclophanes
with small n values include isomerisation of appropriately substituted
valence isomers of benzene as the key stage. Six isomers of
this type can be conceived (if only the CH fragments are
combined, while charged species are excluded).267 Different
research groups have used four isomers,271 most often, 3,3H
bicyclopropenyl
derivatives.265
A decrease in the length of the bridge in cyclophane molecules
results in a dramatic increase in their reactivity. The unsubstituted
cyclophanes with the smallest n (with a saturated bridge) known to
date, [4]paracyclophane (146) 272, 273 and [1.1]paracyclophane
(147),274 can be stabilised only in inert matrices at low temperatures,
while [4]metacyclophane (148) 275 and an extremely
unstable [1.1]metacyclophane derivative (compound 149) 276 were
detected as short-lived intermediates.
R R
R
R
R
R133 (R = SiMe3)
1.502 #A
1.333 #A
132
134
PhPh
888 1.363 #A
1.429 #A
1.381 #A
1.418 #A
1.371 #A
135
136 137 138 139
140 141 142 143
102.38
1.438 #A
1.349 #A
144
1
2
145
1.414 #A
1.390 #A
1.398 #A
1.390 #A
1.401 #A
1.387 #A
109.78
(CH2)n
[n]metacyclophanes
(CH2)n
[n]paracyclophanes
(CH2)n(H2C)n
[n,n]paracyclophanes
(CH2)n
(H2C)n
[n,n]metacyclophanes
1006 I V Komarov
A highly unstable and, apparently, the most strained among
the known [n]paracyclophanes, bicyclo[4.2.2]decapentaene, has
been synthesised.277 The results of experimental and theoretical
studies (MP2, taking account of electron correlation) 278 suggest
that the compound has the structure 150a, which has a lower
energy than the other isomer (150b).
To study the chemical and spectral properties and the structure
of these compounds, it is necessary for them to be stable under
experimental conditions. Sufficient stability was attained for
strained cyclophanes having electron-withdrawing substituents
or bulky groups shielding the most reactive centres, i.e., bridging
carbon atoms. Among the known stabilised cyclophane derivatives,
the molecules of compounds 151 ± 154 contain the most
distorted benzene rings.279 ± 282
X-Ray diffraction data are available for the compounds 151
and 152. Appreciable distortion of the benzene ring is indicated by
the a and b angles: in the molecule 151, a = 25.6 8 and 24.3 8,
b = 26.8 8 and 22.9 8, while in the molecule 152, these parameters
are even greater: a = 27.4 8, g = 12.3 8, bmax = 48.7 8. The distance
between the opposing bridging carbon atoms in the cyclophane
derivative 151 is equal to 2.376(5) #A. Despite this heavy distortion
of the aromatic rings, no bond alternation was detected in the
compounds 151 and 152, and the bond lengths fall in the ranges
typical of unstrained benzene derivatives.
The presence of p-electron delocalisation is also indicated by
NMR studies of strained cyclophanes including compounds 153
and 154. The 1H and 13C NMR signals are exhibited in the
chemical shift regions characteristic of aromatic compounds.
Thus, despite the substantial distortions, the strained molecules
of cyclophanes can still be regarded as aromatic. The system of
p-bonds in these molecules is an `observer' rather than a `manager'
and adapts itself to changes in the s-core. This was confirmed by
ab initio calculations for strained [n]metacyclophanes.283 The
benzene ring distortion of up to a=30 8 is not accompanied by
noticeable bond alternation. It may seem that these conclusions
contradict the data on the chemical properties of strained cyclophanes,
most of all, the data on the ability of these compounds to
enter readily into Diels ± Alder and nucleophilic substitution
reactions.266 However, one should take into account the fact that
the molecules of compounds with non-planar benzene rings
possess substantial strain. The reactions of the compounds result
in strain relief, which is the driving force of their unusual chemical
transformations.265
Distorted benzene rings serve as structural blocks of fullerenes;
therefore, studies of strained cyclophanes are related to
fullerene chemistry. Particular interest was aroused by the synthesis
of compounds with fused non-planar aromatic rings, fullerene
fragments,284 for example, of 1,7-dioxa[7](2,7)pyrenophane
(155).285 In accordance with X-ray diffraction data, the pyrene
residue in this compound is distorted to a greater extent than the
similar fragment in C70 fullerene; the planes of non-annelated
benzene rings make an angle of 109.2 8.
In conclusion, it should be noted that distortions of the
benzene rings to a boat `conformation' can be found not only in
cyclophanes. In the molecules of 1,2,3-trisubstituted benzene
derivatives, this conformation results in a decrease in the steric
strain if the substituents are sufficiently bulky. According to
analysis of CSDB structures, among benzene derivatives with
bulky substituents in the 1,2,3-positions, the molecule 156 has the
most distorted benzene ring.286 The angle values a = 30.1 8,
g = 11.6 8 , and bmax = 16.4 8 are comparable with the sizes of
these angles in the cyclophane derivative 152. Nevertheless, in
compound 156, no double bond localisation is found either. The
strain in 156 accounts for the unusual reactivity of this compound,
first of all, the tendency for isomerisation into prismane 157 [with
the intermediate formation of the corresponding derivative of the
Dewar benzene (158)], in which the steric repulsion between the
tert-butyl groups is weaker than that in 156.
b. Twist and chair `conformations' of benzene rings
Due to steric repulsion of bulky substitiuents, the benzene ring can
assume twist and chair `conformations'. According to calculations,
the chair `conformation' can be found in the benzene ring of
hexa-tert-butylbenzene (159).287 This compound has not been
synthesised so far but its less strained silyl- 288 and germylcontaining
287 analogues 160 and 161 are known.
146 147
Cl
Cl148 149
150a 150b
Cl Cl
NTos
152
R = CH2SiMe3 , X = CONMe2 , Tos is p-toluenesulfonyl.
X R
R
X
R
R 151
CN
CN
NC
NC
154Cl Cl153
OO
155
MeO2C But
ButO2C But
But
CO2Me
156
CO2Me
But
But But
MeO2C CO2But
But
CO2Me
ButBut
MeO2C
CO2But
157
158
hn
hn
But
But
But
But
But
But
159
SiMe3
SiMe3
SiMe3
SiMe3
Me3Si
Me3Si
1
2
3
4
5
6
160
Organic molecules with abnormal geometric parameters 1007
X-Ray diffraction analysis of the compound 160 showed that
four carbon atoms of the benzene ring [C(1), C(3), C(4), C(6)] are
located approximately in one plane, whereas the C(2) atom lies
above this plane by *0.1 #A and the C(5) atom is *0.1 #A below
this plane. The mean value of the C7C7C7C dihedral angle
amounts to 9.8 8 and the C7Si bond deflects from the plane of the
benzene-ring bonds adjacent to it by 22.2 8. Despite the considerable
distortions of the bond angles comparable to the distortions
in the molecules 151 ± 154, the bond lengths in the benzene ring are
normal for aromatic compounds. Analysis of the spectroscopic
properties of the compound 160 shows that the compound can be
considered to be aromatic but having an unusually high reactivity.
The molecule 160, similarly to the molecule 156, is readily
rearranged on exposure to radiation giving rise to a Dewar
benzene derivative, hexakis(trimethylsilyl)bicyclo[2.2.0]hexa-2,5diene
(further [2+2]-cycloaddition to a substituted prismane was
not observed). The rearrangement of the compound 160 occurring
on heating resulted in benzene ring cleavage; in this case,
1,1,3,4,6,6-hexakis(trimethylsilyl)-1,2,4,5-hexatetraene was isolated.
Interestingly, the benzene derivative 162 containing four
tert-butyl groups in the adjacent positions is thermodynamically
less stable than the isomer 163, which is a Dewar benzene
derivative.289
The twist `conformation' of the benzene ring has been
observed in molecules of fused aromatic compounds. Typically,
these molecules contain an aromatic polycyclic system twisted to
form a helix the axis of which is either perpendicular or parallel to
the benzene-ring planes.
In the molecule 164, the angle between the terminal bonds of
the linear polybenzene system is 105 8. Despite the steric strain, the
compound 164 is exceptionally stable: it does not decompose on
heating to 400 8C.290
IX. Distortions of cumulated double bonds
Cumulenes are hydrocarbons containing two (or more) double
bonds with shared carbon atoms. Strain-free cumulene molecules,
for example, allene (1,2-propadiene) (165), 1,2,3-butatriene (166)
and 1,2,3,4-pentatetraene (167) have a linear carbon skeleton of
cumulated double bonds. The four substituents are located either
in mutually perpendicular planes (for an even number of cumulated
double bonds) or in one plane (for an odd number of these
bonds).
Distortions of cumulenes can include bending and twisting of
the linear system of bonds. For allene, these distortions can be
represented as follows:
Below we consider only allene and 1,2,3-butatriene derivatives
in which cumulated double bonds are incorporated in a ring. In
the molecules of these compounds, the cumulene fragment is not
only bent; twist type distortion is also always observed. The
properties of strained cyclic allenes have been analysed in several
reviews (see, for example, reviews 291, 292). Only few publications
have been devoted to the study of molecules with predominating
twist distortion such as [n.n]betweenallenes. In the known betweenallenes,
the z angle between the planes formed by substituents at
the terminal C(sp2) atoms deviates insignificantly from 90 8.293, 294
Even strain-free molecules of cumulenes are highly reactive
(reactions involving them readily give stabilised intermediates).295
Molecular distortions result in a further increase in reactivity and
even in a qualitative change in the chemical properties of cumu-
lenes.
1. Strained cyclic allenes
If the allene fragment is incorporated in a carbocycle that consists
of not more than ten atoms, it inevitably becomes bent and, in
addition, substituents tend to be arranged in one plane, which
implies twist distortion. Model calculations showed that bending
is always accompanied by twist Ð optimisation of an artificially
bent system of two cumulated double bonds results in a twisted
structure.296 The strain energy of the molecules of cyclic allenes
gradually increases up to j = 20 8 (by *4 kcal mol71, according
to the SCF/4-31+G calulations);297 however, subsequently it rises
very steeply.
Even slight angle distortions in allene molecules entail a
pronounced increase in the compound reactivity, which is anyway
rather high, first of all in the tendency for polymerisation. 1,2Cyclooctadiene
the strain energy of which is calculated to be only
GeMe3
GeMe3
GeMe3
GeMe3
Me3Ge
Me3Ge
161
hn
D
But
But
But
But
CO2Me
CO2Me
162
hn
D
CO2Me
CO2Me
But
But
ButBut
CO2Me
But
But
But
CO2MeBut
163
164
H
H
C C C C
H
H166
H
H
C C C
H
H165
167
C C
H
H
CCC
H
H
C C
CH
H
H
Hj = 1808
bending
C C C
H
H
H
H
z = 908
twist
C
C
C
Xn Xn
[n,n]betweenallenes
1008 I V Komarov
14 kcal mol71, has not yet been isolated in a pure state.291 Bulky
substituents at double bonds ensure the kinetic stability of allenes;
the tert-butyl derivative of 1,2-cyclooctadiene 168 represents the
smallest-ring carbocyclic allene that has been isolated at room
temperature.298 A cyclic allene with a smaller ring, 1,2-cycloheptadiene,
has been stabilised in metal complexes. For compound
169, X-ray diffraction data have been published,299
pointing to a substantial distortion (bending and twist) of the
allene fragment. Among metal complexes of this type deposited in
the CSDB, the most pronounced bending of the allene fragment is
found in the molecule of compound 170, in which the j angle is
135 8.300
1,2-Cyclohexadiene (171) has been known since 1968 when
this compound was detected as a short-lived intermediate.301
Later, it was detected by IR spectroscopy in an argon matrix at
11 ± 170 K.302 The compound 171 has now been thoroughly
studied; according to calculations, the j angle in this molecule is
138 8 (MINDO) or 134.8 8 (HF/6-31G**).291 The attempts at
synthesising 1,2-cyclopentadiene (172) have not yet met with
success.303
Cyclohexa-1,2,4-triene (`isobenzene') (173) has also been
studied.304 There is evidence that deprotonation of the compound
173 gives rise to the phenyl anion (174).305
Stable six-membered heterocyclic compounds with a 1,2-diene
fragment containing two or three heteroatoms, silicon and phosphorus,
have been synthesised. The allene fragment in the cyclic
allene 175 is less distorted than that in the six-membered carbocycle
171; however, the former is stable, which allowed X-ray
diffraction analysis of this compound.306 According to X-ray
diffraction data, the allene fragment is bent (j = 166.4 8) and the
z angle between the Si7C(1)7C(2) and Si7C(3)7C(2) planes is
64.6 8. Among stabilised cyclic compounds, the most distorted 1,2diene
group is found in diphosphaisobenzene 176. A derivative of
176, compound 177, has been investigated by X-ray diffraction
analysis.307
The values for the j (155.8 8) and z (40.7 8) angles in the
molecule 177 significantly depart from the ideal values (180 8 and
90 8, respectively); steric shielding of the central fragment caused
by the tert-butyl groups is responsible for the rather low reactivity
of compound 177.
The accumulated knowledge makes it possible to form a
picture of molecular and electronic structures of highly strained
allenes. Several variants of the spatial and electronic structures of
these compounds can be suggested. For example, for 1,2-cyclohexadiene,
apart from the chiral allene 171, structures with the
planar HC(1)C(2)H fragment and a non-bonding sp2-hybridised
orbital located in the plane of this fragment are also possible, i.e.,
zwitter-ions 178, 179, and singlet (180) and triplet (181) biradical.
The MCSCF/3-21G 308 and HF/6-31G* 309 calculations and
experimental data 302, 309, 310 favour a non-planar chiral structure,
at least, in 1,2-cycloheptadiene and 1,2-cyclohexadiene. The
calculated t angle at each double bond amounts to *20 8; this is
sufficient for effective overlap of p-orbitals.309 In the case of the
1,2-cyclopentadiene 172, ab initio (STO, MP2/3-21G) calculations
predict a relatively low energy barrier to racemisation (which
might involve the intermediate formation of singlet biradical
182) Ð 2 ± 5 kcal mol71 (see Ref. 311). This low value is within
the error of the calculation techniques; therefore, experimental
data are required to verify the results of theoretical methods.
As regards the chemical properties of cyclic allenes, one
should mention their enhanced tendency to enter into cycloaddition
reactions, which were used in experiments on trapping
short-lived molecules such as 1,2-cyclohexadiene. Strained allenes
undergo the Diels ± Alder reactions even with dienes having very
low reactivity. These reactions are regioselective and endo-stereoselective;
however, in the case of chiral allenes, no diastereoselectivity
was observed. This fact was interpreted using the results of
ab initio calculations (B3LYP/6-31G*),312 which showed that in
this case, the mechanism involving biradicals is preferred over the
synchronous mechanism.
2. Cyclic butatrienes
The unstrained 1,2,3-butatriene fragment can be incorporated
into a carbocycle if the number of carbon atoms in it is more than
ten. Ring contraction causes bending of the linear C=C=C=C
fragment, resulting in rehybridisation of carbon atoms and a
substantial increase in the reactivity. Tentative experimental
results showed 313 that, among unsubstituted cyclic 1,2,3-butatrienes,
the minimum size of the ring which allows isolation of this
compound at room temperature, is found in 1,2,3-cyclooctatriene
(183). Homologues with smaller rings, 1,2,3-cycloheptatriene 314
(184) and a benzene isomer, 1,2,3-cyclohexatriene 315 (185), are
highly reactive short-lived intermediates; only the products of
cycloaddition of these species to dienes have been isolated.
1,2,3-Cyclopentatriene (186) has not been prepared to date;
however, its heterocyclic analogues, 3,4-didehydrothiophene
(187) 316 and 1-tert-butoxycarbonyl-3,4-didehydro-1H-pyrrole
(188),317 have been synthesised, and their chemical properties
have been studied using trapping reactions.
But
168 169
Fe Cp
PPh3
COPFÀ
6
+
138.18
170
Pt
Ph3P
Ph3P
1358
H
H
171 172
H
H 173
KOBut
7
K+
174
SiMe2
Si
SiMe3Me3Si
Ph Ph
166.48
175
P
PBut But
But
But
176
Me2Si
P
PBut
But
But
O
N
But
Me
Me
Me177
155.88
H H
178
+
7
H H
179
7
+
H H
S- 180, T- 181
(S)-172 182 (R)-172
H H H H H H
183 184 185
Organic molecules with abnormal geometric parameters 1009
The compound 187 was prepared and identified without
substantial difficulties, although it is highly reactive. Meanwhile,
the high reactivity of the heterocyclic triene 188 became a serious
obstacle in the attempts to prove its existence. Among the strained
butatrienes known currently, the geometry of the C=C=C=C
system of bonds deviates most appreciably from linearity in the
molecule 188.317
Cyclic 1,2,3-butatrienes, like highly strained allenes, readily
react with dienes. The high reactivity of the compounds 187 and
188 can be illustrated by their reaction with benzene, which
affords cycloadducts 189 and 190.
It was suggested that rehybridisation of the carbon atoms of
the bent C=C=C=C system of bonds (like pyramidalisation of
double bonds, see above) changes the electronic properties of the
compounds 187 and 188 so dramatically that they can be regarded
as biradicals. To support this, the researchers cited 316 reported the
reaction of the heterocyclic triene 187 with tetrahydrofuran.
However, an ionic mechanism of this reaction is also possible.
It has been shown above in relation to cubene that, even in the case
of a very strong pyramidalisation of the carbon atoms of the
double bond, alkenes do not exhibit properties of biradicals.
Therefore, the conclusion that the compounds 187 and 188 are
biradicals appears unlikely and requires further analysis.
Among isolated and structurally characterised cyclic butatrienes,
we shall consider metallacyclocumulenes (191) with a fivemembered
ring consisting of a 1,2,3-butatriene fragment and a
metal (titanium or zirconium).318
The stability of compounds of the type 191 is attributable to
the additional stabilisation upon the coordination of the central
double bond to the metal. This coordination changes the electronic
structure of cumulenes; nevertheless, for some of the
complexes 191, dimerisaition to give radialene (192) has been
observed.319
This reaction is also characteristic of purely organic strained
cumulenes.320 Metallacyclocumulenes have been investigated by
X-ray diffraction analysis. The data obtained indicate that the
central double bond is elongated and that the cumulene fragment
deviates substantially from the linear geometry: the j angle varies
from 147 8 to 150 8.
X. Bending of the X17C:C7X2 fragment
The unstrained X17C:C7X2 fragment is linear. The deviations
of the bond angles at the carbon atoms from 180 8 are similar to
the analogous deviations found in allene and butatriene molecules.
The geometric distortions of the X17C:C7X2 fragment
can be characterised by variation of the a1 , a2 and y angles.
Below, we shall discuss the cis- (y = 0 8) and trans- (y = 180 8)
bendings. Note that it is the cis-bending that is found in each
organic molecule with a strained triple bond. The calculations
showed, however, that trans-bending requires less energy than cisbending
(in a similar way as anti-pyramidalisation of the double
bond is energetically more favourable than syn-pyramidalisation).234
Probably, the lower energy of the transition state which
contains a trans-bent fragment with a triple bond can account for
the preferential trans-attack of alkyne molecules by nucleophilic
reagents. This hypothesis has not been verified experimentally
because no organic molecules with a trans-bent X17C:C7X2
fragment have been synthesised to date.
1. cis-Bending
The only known way of realisation of cis-bending is incorporation
of the X17C:C7X2 fragment into a ring or a polycyclic
cage.292, 321 This fragment is bent in carbocyclic alkynes with the
number of carbon atoms not exceeding ten. The first strained
cyclic alkyne, cyclooctyne (193), was synthesised in 1938;322 later,
it was isolated in a pure state.323
Cyclooctyne is smallest-ring carbocyclic alkyne stable at room
temperature. Cycloheptyne (194) polymerises in less than 1 min
even at 725 8C in dilute solutions (at 776 8C, it is stable over
several hours).324 Homologues with smaller ring sizes, cyclohexyne
(195) 325, 326 and cyclopentyne (196),327 ± 333 are highly reactive.
They have been detected as intermediates and studied in inert
matrices.
The highly strained molecules 194 ± 196 can be prepared using
elimination and cycloelimination reactions and by carbene rearrangements.321
Elimination from appropriate precursors, hypervalent
iodine compounds, has proved effective for this purpose.334
Using this reaction, it was possible to prepare, perhaps, the most
strained known (according to MP2/6-31G* calculations) carbocyclic
molecule with a bent C7C:C7C fragment, namely,
bicyclo[2.2.1]hept-2-en-5-yne (197) molecule.335
Cyclobutyne (198) and cyclopropyne (199) have not yet been
synthesised. The results of calculations (MCSCF(4,4)/6-31G*,
MP4/6-31G*//MP2/6-31G*) indicate that the compound 198 is
186
S
187
N
O O
But
188
X = S (189), NCO2But (190).
X
X
189, 190
S
O
S
O(CH2)4OH
M =Ti, R = But, Ph; M = Zr, R = But.
Cp2M
R
R 191
Cp2Ti
Ph
Ph
TiCp2Cp2Ti
Ph
Ph
Ph
Ph192
C
C
X2
X1
y
a2
a1
193 194 195 196
SiMe3
IPh
+
7
OSO2CF3
Bu4N+F7
197
1010 I V Komarov
highly susceptible to a rearrangement to cyclopropylidenemethylene;336
apparently, this makes this molecule `elusive'. The existence
of perfluorocyclobutyne (200) as an intermediate, possibly,
more stable than 198, has now been proven experimentally.337
Metal complexes with cyclobutyne acting as a two-electron ligand
have been prepared; however, cyclobutyne itself was not formed
as an intermediate during the synthesis of these complexes.338, 339
The structure of cyclopropyne (unlike cyclobutyne) does not
correspond to a minimum on the PES, even when the PES is
calculated using advanced quantum-chemical techniques [such as
SCF, TCSCF, CISD, TC-CISD/DZP; CCSD(T)/TZ(2df,2dp)];340
Cyclopropyne is the only C3H2 isomer that has not yet been
prepared. The other three isomers Ð cyclopropenylidene (201),
propargylene (202) and propadienylidene (203), have been synthesised
and studied in inert matrices.341 It should be noted that
investigation of the potential energy surface of C3H2 arouse
considerable interest, among other reasons, due to the fact that
the molecules 201 342, 343 and 203 344 were found in the interstellar
space.
Maier et al.345, 346 synthesised a heteroanalogue of cyclopropyne,
silacyclopropyne (204).
The identification of the compound 204 was at variance with
the results of SCF/DZ calculations published previously, which
indicated that the silacyclopropyne structure has properties of a
saddle point rather than a minimum on the PES.347 Maier et al.,
who used higher-level calculations (MP2/6-31G**) demonstrated
that the structure of 204 still corresponds to a local minimum on
the PES; however, the IR frequencies they obtained differed
somewhat from those observed experimentally. Only recent
calculations 340 have given vibration frequencies on the basis of
which the compound 204 was identified. The necessity of using
advanced quantum-chemical methods for the prediction of properties
of strained molecules such as 204 was demonstrated once
again. The difference between the stabilities of cyclopropyne and
silacyclopropyne can be explained by the difference between the
energies of the carbenes and silapropadienylidenes
..
C=C=XH2
(X = C, Si), which are formed presumably upon decomposition of
the compound 199 and 204. The energy of this species with X=Si
is higher than the energy of the initial molecule 204, whereas in the
case where X=C, calculations predict the opposite situation.346
Cycloalkynes with a bent X17C:C7X2 fragment are susceptible
to addition reactions with electrophiles, nucleophiles, and
radicals.321 Cycloaddition and oligomerisation also proceed with
these molecules much more easily than with strain-free alkynes.
Indeed, whereas cyclotrimerisation of strain-free alkynes requires
catalysts (transition metal compounds), a similar reaction in the
case of cyclic strained alkynes proceeds easily without catalysts.
Moreover, the detection of benzene derivatives in the products of
elimination reactions of cyclic alkenes can serve as evidence for the
formation of highly strained alkynes as intermediates.348 Trimerisation
gave the above-discussed benzene derivative with annelated
bicyclic fragments (144).
Cyclic alkynes stable due to either bulky substituents at the
a-position relative to the C:C bond (for example, as in molecule
205 292) or annelation of benzene rings (for example, as in
molecule 206 349) have been studied by X-ray diffraction analysis.
The search through the CSDB showed that in the molecules
characterised by the most bent X17C:C7X2 fragment, the a1
and a2 angles approach *30 8.
The structure of compound 207 has been studied by electron
diffraction in the gas phase.350 ± 352
The a1 and a2 angles in the molecule 207 are 34.2 8 and 30.7 8,
which is somewhat greater than those in 205 or 206. Despite the
pronounced bond angle distortions, the C:C bond lengths in the
compounds 205 and 207 remain within the limits typical of acyclic
linear alkynes. Only in some cases (for example, in the molecule
206), was the triple bond elongated (1.20 ± 1.23 #A).
Finally, we should mention a new, original method of stabilisation
of strained molecules and reactive intermediates, which
allows one to gain spectroscopic data for these species in solutions
at room temperature. The idea of this approach is to generate
unstable molecules inside `molecular vessels' Ð carcerands and
hemicarcerands. Cyclobutadiene 353 and 1,2-dehydrobenzene
(208) 354, 355 have been fixed in this way. Warmuth 354 has tackled
the question whether the molecule 208 should be assigned to
strained alkynes or to bent cumulenes. 1,2-Dehydrobenzene was
prepared by exposure to UV light of benzocyclobutenedione
inside hemicarcerand (209). For the compound 208 stabilised in
198 199
F
F
F
F
200
C C
C
HH 201
H
C
C
C
H
202
C C C
H
H 203
C C
Si
H H
hn (254 nm)
hn (>395 nm)
C C
Si
HH
204
Cl
ButOK, ButLi
Ni(Cp)2
144
Pri
2Si
Pri
2Si
146.88
150.58
205
Si
Pri
2
Si
Pri
2
S
207
Me
Me
Me
Me
146.78 146.18
206
208a 208b
OOO
O
O
O
OO
O
O
O
O
Ph
H
Ph
H
Ph
H
Ph
H
(CH2)4 (CH2)4(H2C)4 (CH2)4
O
O
H
Ph
H
Ph
H
Ph
H
Ph
O
O
O
O
O OO
O
O O
209
Organic molecules with abnormal geometric parameters 1011
this way, it was possible to record the 1H and 13C NMR spectra
before the compound has reacted with the host molecule.
Analysis of the NMR spectra led to quite an unexpected
conclusion: the spectroscopic data are best described by a hybrid
of two contributing structures, 208a and 208b, with a predominant
contribution of 208b. This interpretation, however, is inconsistent
with the results of other studies (see, for example, Ref. 356).
2. trans-Bending
Synthesis of a molecule with a trans-bent X17C:C7X2 fragment
is a difficult task: the shortage of substituents at a triple bond
precludes creation of such a bending. However, trans-bending of
an alkyne ligand can be attained in metal complexes. The first
complex of this type 210 was prepared in 1995.357
A whole series of titanium and zirconium complexes of this type
are currently known.358 In the compound 210, the agostic
Si_H_Ti interaction ensures the trans-arrangement of substituents
at the C:C bond coordinated to titanium. The angles
a1 = 30.5 8 (for Si7C:C) and a2 = 44.8 8 (for C7C:C) indicate
a substantial distortion of bond angles at a triple bond. However,
it should be noted that metal coordination also changes substantially
the properties of a triple bond, for example, in the complex
210, the bond length is increased to 1.275(9) #A.
The author is grateful to professors M Yu Kornilov and
R R Kostikov, colleagues S P Verevkin, V V Burlakov and
V I Tararov for critical remarks, corrections and assistance in
preparing the manuscript, and to a colleague, mathematician
O B Pikhurko, for consultation and help in the solution of
mathematical problems. The author is especially grateful to
Corresponding Member of the Russian Academy of Sciences
M Yu Antipin for constructive criticism and discussion of the
manuscript. This review was written with financial support of the
Alexander von Humboldt Foundation (Germany).
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