In
organic chemistry
Organic chemistry is a subdiscipline within chemistry involving the scientific study of the structure, properties, and reactions of organic compounds and organic materials, i.e., matter in its various forms that contain carbon atoms.Clayden, J.; ...
, a bent bond, also known as a banana bond, is a type of
covalent
A covalent bond is a chemical bond that involves the sharing of electrons to form electron pairs between atoms. These electron pairs are known as shared pairs or bonding pairs. The stable balance of attractive and repulsive forces between atoms ...
chemical bond
A chemical bond is a lasting attraction between atoms or ions that enables the formation of molecules and crystals. The bond may result from the electrostatic force between oppositely charged ions as in ionic bonds, or through the sharing of ...
with a geometry somewhat reminiscent of a
banana
A banana is an elongated, edible fruit – botanically a berry – produced by several kinds of large herbaceous flowering plants in the genus ''Musa''. In some countries, bananas used for cooking may be called "plantains", distinguis ...
. The term itself is a general representation of
electron density
In quantum chemistry, electron density or electronic density is the measure of the probability of an electron being present at an infinitesimal element of space surrounding any given point. It is a scalar quantity depending upon three spatial va ...
or configuration resembling a similar "bent" structure within small ring molecules, such as
cyclopropane
Cyclopropane is the cycloalkane with the molecular formula (CH2)3, consisting of three methylene groups (CH2) linked to each other to form a ring. The small size of the ring creates substantial ring strain in the structure. Cyclopropane itself ...
(C
3H
6) or as a representation of double or triple bonds within a compound that is an alternative to the
sigma
Sigma (; uppercase Σ, lowercase σ, lowercase in word-final position ς; grc-gre, σίγμα) is the eighteenth letter of the Greek alphabet. In the system of Greek numerals, it has a value of 200. In general mathematics, uppercase Σ is used as ...
and
pi bond
In chemistry, pi bonds (π bonds) are covalent chemical bonds, in each of which two lobes of an orbital on one atom overlap with two lobes of an orbital on another atom, and in which this overlap occurs laterally. Each of these atomic orbitals ...
model.
Small cyclic molecules
Bent bonds
are a special type of
chemical bond
A chemical bond is a lasting attraction between atoms or ions that enables the formation of molecules and crystals. The bond may result from the electrostatic force between oppositely charged ions as in ionic bonds, or through the sharing of ...
ing in which the ordinary
hybridization
Hybridization (or hybridisation) may refer to:
*Hybridization (biology), the process of combining different varieties of organisms to create a hybrid
*Orbital hybridization, in chemistry, the mixing of atomic orbitals into new hybrid orbitals
*Nu ...
state of two atoms making up a chemical bond are modified with increased or decreased
s-orbital
In atomic theory and quantum mechanics, an atomic orbital is a function describing the location and wave-like behavior of an electron in an atom. This function can be used to calculate the probability of finding any electron of an atom in any sp ...
character in order to accommodate a particular
molecular geometry
Molecular geometry is the three-dimensional arrangement of the atoms that constitute a molecule. It includes the general shape of the molecule as well as bond lengths, bond angles, torsional angles and any other geometrical parameters that determ ...
. Bent bonds are found in strained
organic compound
In chemistry, organic compounds are generally any chemical compounds that contain carbon-hydrogen or carbon-carbon bonds. Due to carbon's ability to catenate (form chains with other carbon atoms), millions of organic compounds are known. The ...
s such as
cyclopropane
Cyclopropane is the cycloalkane with the molecular formula (CH2)3, consisting of three methylene groups (CH2) linked to each other to form a ring. The small size of the ring creates substantial ring strain in the structure. Cyclopropane itself ...
,
oxirane
Ethylene oxide is an organic compound with the formula . It is a cyclic ether and the simplest epoxide: a three-membered ring consisting of one oxygen atom and two carbon atoms. Ethylene oxide is a colorless and flammable gas with a faintly swee ...
and
aziridine
Aziridine is an organic compound consisting of the three-membered heterocycle . It is a colorless, toxic, volatile liquid that is of significant practical interest. Aziridine was discovered in 1888 by the chemist Siegmund Gabriel. Its derivati ...
.
In these compounds, it is not possible for the carbon atoms to assume the 109.5°
bond angle
Bond or bonds may refer to:
Common meanings
* Bond (finance), a type of debt security
* Bail bond, a commercial third-party guarantor of surety bonds in the United States
* Chemical bond, the attraction of atoms, ions or molecules to form chemical ...
s with standard sp
3 hybridization. Increasing the p-character to sp
5 (i.e. s-density and p-density) makes it possible to reduce the bond angles to 60°. At the same time, the carbon-to-hydrogen bonds gain more s-character, which shortens them. In cyclopropane, the maximum electron density between two carbon atoms does not correspond to the internuclear axis, hence the name ''bent bond''. In cyclopropane, the ''interorbital angle'' is 104°. This bending can be observed experimentally by
X-ray diffraction
X-ray crystallography is the experimental science determining the atomic and molecular structure of a crystal, in which the crystalline structure causes a beam of incident X-rays to diffract into many specific directions. By measuring the angles ...
of certain cyclopropane derivatives: the
deformation density
Deformation can refer to:
* Deformation (engineering), changes in an object's shape or form due to the application of a force or forces.
** Deformation (physics), such changes considered and analyzed as displacements of continuum bodies.
* De ...
is outside the line of centers between the two carbon atoms. The carbon–carbon
bond length
In molecular geometry, bond length or bond distance is defined as the average distance between nuclei of two bonded atoms in a molecule. It is a transferable property of a bond between atoms of fixed types, relatively independent of the rest of ...
s are shorter than in a regular alkane bond: 151
pm versus 153 pm.
Cyclobutane
Cyclobutane is a cycloalkane and organic compound with the formula (CH2)4. Cyclobutane is a colourless gas and commercially available as a liquefied gas. Derivatives of cyclobutane are called cyclobutanes. Cyclobutane itself is of no commercial ...
is a larger ring, but still has bent bonds. In this molecule, the carbon bond angles are 90° for the planar conformation and 88° for the puckered one. Unlike in cyclopropane, the C–C bond lengths actually increase rather than decrease; this is mainly due to 1,3-nonbonded
steric repulsion
Steric effects arise from the spatial arrangement of atoms. When atoms come close together there is a rise in the energy of the molecule. Steric effects are nonbonding interactions that influence the shape ( conformation) and reactivity of ions ...
. In terms of reactivity, cyclobutane is relatively inert and behaves like ordinary
alkane
In organic chemistry, an alkane, or paraffin (a historical trivial name that also has other meanings), is an acyclic saturated hydrocarbon. In other words, an alkane consists of hydrogen and carbon atoms arranged in a tree structure in which ...
s.
Walsh orbital model
An alternative model utilizes semi-localized
Walsh orbitals in which cyclopropane is described as a carbon sp
2 sigma bonding and in-plane pi bonding system. Critics of the Walsh orbital theory argue that this model does not represent the
ground state
The ground state of a quantum-mechanical system is its stationary state of lowest energy; the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with energy greater than the ground state. ...
of cyclopropane as it cannot be transformed into the localized or fully delocalized descriptions via a unitary transformation.
Double and triple bonds
Two different explanations for the nature of double and triple
covalent bond
A covalent bond is a chemical bond that involves the sharing of electrons to form electron pairs between atoms. These electron pairs are known as shared pairs or bonding pairs. The stable balance of attractive and repulsive forces between atoms ...
s in
organic
Organic may refer to:
* Organic, of or relating to an organism, a living entity
* Organic, of or relating to an anatomical organ
Chemistry
* Organic matter, matter that has come from a once-living organism, is capable of decay or is the product ...
molecules were proposed in the 1930s.
Linus Pauling
Linus Carl Pauling (; February 28, 1901August 19, 1994) was an American chemist, biochemist, chemical engineer, peace activist, author, and educator. He published more than 1,200 papers and books, of which about 850 dealt with scientific top ...
proposed that the double bond results from two equivalent tetrahedral orbitals from each atom,
[.] which later came to be called ''banana bonds'' or ''tau bonds''.
Erich Hückel
Erich Armand Arthur Joseph Hückel (August 9, 1896, Berlin – February 16, 1980, Marburg) was a German physicist and physical chemist. He is known for two major contributions:
*The Debye–Hückel theory of electrolytic solutions
*The Hückel m ...
proposed a representation of the double bond as a combination of a
sigma bond
In chemistry, sigma bonds (σ bonds) are the strongest type of covalent chemical bond. They are formed by head-on overlapping between atomic orbitals. Sigma bonding is most simply defined for diatomic molecules using the language and tools of s ...
plus a
pi bond
In chemistry, pi bonds (π bonds) are covalent chemical bonds, in each of which two lobes of an orbital on one atom overlap with two lobes of an orbital on another atom, and in which this overlap occurs laterally. Each of these atomic orbitals ...
. The Hückel representation is the better-known one, and it is the one found in most textbooks since the late-20th century.
Both models represent the same total electron density, with the orbitals related by a
unitary transformation
In mathematics, a unitary transformation is a transformation that preserves the inner product: the inner product of two vectors before the transformation is equal to their inner product after the transformation.
Formal definition
More precisely, ...
. We can construct the two equivalent bent bond orbitals ''h'' and ''h''
' by taking linear combinations ''h'' = ''c''
1σ + ''c''
2π and ''h''
' = ''c''
1σ – ''c''
2π for an appropriate choice of coefficients ''c''
1 and ''c''
2. In a 1996 review,
Kenneth B. Wiberg
Kenneth Berle Wiberg (born September 22, 1927) is an American Professor Emeritus of organic chemistry at Yale University. He contributed to many aspects of organic chemistry including physical and synthetic aspects.
Scholarship
In the area of sy ...
concluded that "although a conclusive statement cannot be made on the basis of the currently available information, it seems likely that we can continue to consider the σ/π and bent-bond descriptions of ethylene to be equivalent."
Ian Fleming
Ian Lancaster Fleming (28 May 1908 – 12 August 1964) was a British writer who is best known for his postwar ''James Bond'' series of spy novels. Fleming came from a wealthy family connected to the merchant bank Robert Fleming & Co., a ...
goes further in a 2010 textbook, noting that "the overall distribution of electrons
..is exactly the same" in the two models.
[.]
Other applications
The bent bond theory can also explain other phenomena in organic molecules. In
fluoromethane
Fluoromethane, also known as methyl fluoride, Freon 41, Halocarbon-41 and HFC-41, is a non-toxic, liquefiable, and flammable gas at standard temperature and pressure. It is made of carbon, hydrogen, and fluorine. The name stems from the fact that ...
(CH
3F), for instance, the experimental F–C–H bond angle is 109°, which is greater than the calculated value. This is because according to
Bent's rule
In chemistry, Bent's rule describes and explains the relationship between the orbital hybridization of central atoms in molecules and the electronegativities of substituents. The rule was stated by Henry A. Bent as follows:
The chemical structu ...
, the C–F bond gains p-orbital character leading to high s-character in the C–H bonds, and H–C–H bond angles approaching those of sp
2 orbitals – e.g. 120° – leaving less for the F–C–H bond angle. The difference is again explained in terms of bent bonds.
Bent bonds also come into play in the
gauche effect, explaining the preference for gauche conformations in certain substituted alkanes and the
alkene ''cis'' effect associated with some unusually stable alkene
''cis'' isomers.
References
External links
NMR experiment
{{chemical bonds
Chemical bonding