Sigma bond
Overview
 
In chemistry
Chemistry
Chemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry is concerned with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds....

, sigma bonds (σ bonds) are the strongest type of covalent
Covalent bond
A covalent bond is a form of chemical bonding that is characterized by the sharing of pairs of electrons between atoms. The stable balance of attractive and repulsive forces between atoms when they share electrons is known as covalent bonding....

 chemical bond
Chemical bond
A chemical bond is an attraction between atoms that allows the formation of chemical substances that contain two or more atoms. The bond is caused by the electromagnetic force attraction between opposite charges, either between electrons and nuclei, or as the result of a dipole attraction...

. They are formed by head-on overlapping between atomic orbitals. Sigma bonding is most clearly defined for diatomic molecules using the language and tools of symmetry group
Symmetry group
The symmetry group of an object is the group of all isometries under which it is invariant with composition as the operation...

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).
Encyclopedia
In chemistry
Chemistry
Chemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry is concerned with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds....

, sigma bonds (σ bonds) are the strongest type of covalent
Covalent bond
A covalent bond is a form of chemical bonding that is characterized by the sharing of pairs of electrons between atoms. The stable balance of attractive and repulsive forces between atoms when they share electrons is known as covalent bonding....

 chemical bond
Chemical bond
A chemical bond is an attraction between atoms that allows the formation of chemical substances that contain two or more atoms. The bond is caused by the electromagnetic force attraction between opposite charges, either between electrons and nuclei, or as the result of a dipole attraction...

. They are formed by head-on overlapping between atomic orbitals. Sigma bonding is most clearly defined for diatomic molecules using the language and tools of symmetry group
Symmetry group
The symmetry group of an object is the group of all isometries under which it is invariant with composition as the operation...

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). Quantum theory also indicates that molecular orbitals (MO) of identical symmetry actually mix. As a practical consequence of this mixing of diatomic molecules, the wavefunction
Wavefunction
Not to be confused with the related concept of the Wave equationA wave function or wavefunction is a probability amplitude in quantum mechanics describing the quantum state of a particle and how it behaves. Typically, its values are complex numbers and, for a single particle, it is a function of...

s s+s and pz+pz molecular orbital
Molecular orbital
In chemistry, a molecular orbital is a mathematical function describing the wave-like behavior of an electron in a molecule. This function can be used to calculate chemical and physical properties such as the probability of finding an electron in any specific region. The term "orbital" was first...

s become blended. The extent of this mixing (or blending) depends on the relative energies of the like-symmetry MO's.

For homodiatomics, bonding σ orbitals have no nodal planes between the bonded atoms. The corresponding antibonding, or σ* orbital, is defined by the presence of a nodal plane between these two bonded atoms.

Sigma bonds are the strongest type of covalent bond
Covalent bond
A covalent bond is a form of chemical bonding that is characterized by the sharing of pairs of electrons between atoms. The stable balance of attractive and repulsive forces between atoms when they share electrons is known as covalent bonding....

s, and the electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...

s in these bonds are sometimes referred to as sigma electrons.

The symbol σ is the Greek letter sigma (s). When viewed down the bond axis, a σ MO resembles an s atomic orbital
Electron configuration
In atomic physics and quantum chemistry, electron configuration is the arrangement of electrons of an atom, a molecule, or other physical structure...

.

Sigma bonds in polyatomic compounds

They are obtained by head on overlapping of atomic shells. The concept of sigma bonding is extended, albeit loosely, to describe bonding interactions involving overlap of a single lobe of one orbital
Atomic orbital
An atomic orbital is a mathematical function that describes the wave-like behavior of either one electron or a pair of electrons in an atom. This function can be used to calculate the probability of finding any electron of an atom in any specific region around the atom's nucleus...

 with a single lobe of another. For example, propane
Propane
Propane is a three-carbon alkane with the molecular formula , normally a gas, but compressible to a transportable liquid. A by-product of natural gas processing and petroleum refining, it is commonly used as a fuel for engines, oxy-gas torches, barbecues, portable stoves, and residential central...

 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. The σ bonding in such a polyatomic molecule is highly delocalized, which conflicts with the two-orbital, one-bond concept. Despite this complication, the concept of σ bonding is extremely powerful and therefore pervasive.

Sigma bonds in multiple-bonded species

Compounds that feature multiple bonds, such as ethylene
Ethylene
Ethylene is a gaseous organic compound with the formula . It is the simplest alkene . Because it contains a carbon-carbon double bond, ethylene is classified as an unsaturated hydrocarbon. Ethylene is widely used in industry and is also a plant hormone...

 and chromium(II) acetate
Chromium(II) acetate
Chromium acetate hydrate, also known as chromous acetate, is the coordination compound with the formula Cr242. This formula is commonly abbreviated Cr242. This red-coloured compound features a quadruple bond...

, have sigma bonds between the multiple bonded atoms. These sigma bonds are supplemented by π-bonds, e.g. in the case of ethylene, and even δ-bonds, e.g. in the case of chromium(II) acetate
Chromium(II) acetate
Chromium acetate hydrate, also known as chromous acetate, is the coordination compound with the formula Cr242. This formula is commonly abbreviated Cr242. This red-coloured compound features a quadruple bond...

.

Sigma bonds in organic molecules

Organic molecules are often made up of one cyclic compound
Cyclic compound
In chemistry, a cyclic compound is a compound in which a series of atoms is connected to form a loop or ring.While the vast majority of cyclic compounds are organic, a few inorganic substances form cyclic compounds as well, including sulfur, silanes, phosphanes, phosphoric acid, and triboric acid. ...

 or more, such as benzene
Benzene
Benzene is an organic chemical compound. It is composed of 6 carbon atoms in a ring, with 1 hydrogen atom attached to each carbon atom, with the molecular formula C6H6....

, 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.
Nb σ = Nb atoms + Nb rings - 1


This can easily be concluded by realizing that the creation of bonds between atoms that are not connected in a ring requires the same number of atoms minus one (such as in hydrogen gas, H2, where there is only one sigma bond, or ammonia
Ammonia
Ammonia is a compound of nitrogen and hydrogen with the formula . It is a colourless gas with a characteristic pungent odour. Ammonia contributes significantly to the nutritional needs of terrestrial organisms by serving as a precursor to food and fertilizers. Ammonia, either directly or...

, NH3, where there are only 3 sigma bonds), and that rings do not obey this rule (such as benzene rings, which have 6 sigma bonds within the ring for 6 carbon atoms).

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