σ bond
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chemistry Chemistry is the science, scientific study of the properties and behavior of matter. It is a natural science that covers the Chemical element, elements that make up matter to the chemical compound, compounds made of atoms, molecules and ions ...
, 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 Diatomic molecules () are molecules composed of only two atoms, of the same or different chemical elements. If a diatomic molecule consists of two atoms of the same element, such as hydrogen () or oxygen (), then it is said to be homonuclear. Ot ...
using the language and tools of
symmetry group In group theory, the symmetry group of a geometric object is the group of all transformations under which the object is invariant, endowed with the group operation of composition. Such a transformation is an invertible mapping of the ambient ...
s. In this formal approach, a σ-bond is symmetrical with respect to rotation about the bond axis. By this definition, common forms of sigma bonds are s+s, pz+pz, s+pz and dz2+dz2 (where z is defined as the axis of the bond or the internuclear axis). Quantum theory also indicates that molecular orbitals (MO) of identical symmetry actually mix or ''hybridize''. As a practical consequence of this mixing of diatomic molecules, the wavefunctions s+s and pz+pz molecular orbitals become blended. The extent of this mixing (or hybridization or blending) depends on the relative energies of the MOs of like symmetry. For homodiatomics ( homonuclear diatomic molecules), bonding σ orbitals have no nodal planes at which the wavefunction is zero, either between the bonded atoms or passing through the bonded atoms. The corresponding
antibonding In chemical bonding theory, an antibonding orbital is a type of molecular orbital that weakens the chemical bond between two atoms and helps to raise the energy of the molecule relative to the separated atoms. Such an orbital has one or more no ...
, or σ* orbital, is defined by the presence of one nodal plane between the two bonded atoms. Sigma bonds are the strongest type of covalent bonds due to the direct overlap of orbitals, and the electrons in these bonds are sometimes referred to as sigma electrons. The symbol σ is the Greek letter
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 ...
. When viewed down the bond axis, a σ MO has a
circular symmetry In geometry, circular symmetry is a type of continuous symmetry for a planar object that can be rotated by any arbitrary angle and map onto itself. Rotational circular symmetry is isomorphic with the circle group in the complex plane, or the ...
, hence resembling a similarly sounding "s" atomic orbital. Typically, a
single bond In chemistry, a single bond is a chemical bond between two atoms involving two valence electrons. That is, the atoms share one pair of electrons where the bond forms. Therefore, a single bond is a type of covalent bond. When shared, each of th ...
is a sigma bond while a multiple bond is composed of one sigma bond together with pi or other bonds. A double bond has one sigma plus one pi bond, and a triple bond has one sigma plus two pi bonds.


Polyatomic molecules

Sigma bonds are obtained by head-on overlapping of atomic orbitals. The concept of sigma bonding is extended to describe bonding interactions involving overlap of a single lobe of one
orbital Orbital may refer to: Sciences Chemistry and physics * Atomic orbital * Molecular orbital * Hybrid orbital Astronomy and space flight * Orbit ** Earth orbit Medicine and physiology * Orbit (anatomy), also known as the ''orbital bone'' * Orbito ...
with a single lobe of another. For example,
propane Propane () is a three-carbon alkane with the molecular formula . It is a gas at standard temperature and pressure, but compressible to a transportable liquid. A by-product of natural gas processing and petroleum refining, it is commonly used a ...
is described as consisting of ten sigma bonds, one each for the two C−C bonds and one each for the eight C−H bonds.


Multiple-bonded complexes

Transition metal complexes that feature multiple bonds, such as the dihydrogen complex, have sigma bonds between the multiple bonded atoms. These sigma bonds can be supplemented with other bonding interactions, such as π-back donation, as in the case of W(CO)3( PCy3)2(H2), and even δ-bonds, as in the case of chromium(II) acetate.


Organic molecules

Organic molecules are often cyclic compounds containing one or more rings, such as benzene, and are often made up of many sigma bonds along with pi bonds. According to the sigma bond rule, the number of sigma bonds in a molecule is equivalent to the number of atoms plus the number of rings minus one. :''N''σ = ''N''atoms + ''N''rings − 1 This rule is a special-case application of the
Euler characteristic In mathematics, and more specifically in algebraic topology and polyhedral combinatorics, the Euler characteristic (or Euler number, or Euler–Poincaré characteristic) is a topological invariant, a number that describes a topological space ...
of the graph which represents the molecule. A molecule with no rings can be represented as a tree with a number of bonds equal to the number of atoms minus one (as in
dihydrogen Hydrogen is the chemical element with the symbol H and atomic number 1. Hydrogen is the lightest element. At standard conditions hydrogen is a gas of diatomic molecules having the formula . It is colorless, odorless, tasteless, non-toxic, and ...
, H2, with only one sigma bond, or ammonia, NH3, with 3 sigma bonds). There is no more than 1 sigma bond between any two atoms. Molecules with rings have additional sigma bonds, such as benzene rings, which have 6 C−C sigma bonds within the ring for 6 carbon atoms. The anthracene molecule, C14H10, has three rings so that the rule gives the number of sigma bonds as 24 + 3 − 1 = 26. In this case there are 16 C−C sigma bonds and 10 C−H bonds. This rule fails in the case of molecules which, when drawn flat on paper, have a different number of rings than the molecule actually has - for example, Buckminsterfullerene, C60, which has 32 rings, 60 atoms, and 90 sigma bonds, one for each pair of bonded atoms; however, 60 + 32 - 1 = 91, not 90. This is because the sigma rule is a special case of the
Euler characteristic In mathematics, and more specifically in algebraic topology and polyhedral combinatorics, the Euler characteristic (or Euler number, or Euler–Poincaré characteristic) is a topological invariant, a number that describes a topological space ...
, where each ring is considered a face, each sigma bond is an edge, and each atom is a vertex. Ordinarily, one extra face is assigned to the space not inside any ring, but when Buckminsterfullerene is drawn flat without any crossings, one of the rings makes up the outer pentagon; the inside of that ring is the outside of the graph. This rule fails further when considering other shapes - toroidal fullerenes will obey the rule that the number of sigma bonds in a molecule is exactly the number of atoms plus the number of rings, as will nanotubes - which, when drawn flat as if looking through one from the end, will have a face in the middle, corresponding to the far end of the nanotube, which is not a ring, and a face corresponding to the outside.


See also

* Bond strength * Molecular geometry


References


External links


IUPAC-definition
{{DEFAULTSORT:Sigma Bond Chemical bonding