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Chemical bond by sharing of electron pairs

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, when they share electrons, is known as covalent bonding. For many molecules, the sharing of electrons allows each atom to attain the equivalent of a full valence shell, corresponding to a stable electronic configuration. In organic chemistry, covalent bonding is much more common than ionic bonding. Covalent bonding also includes many kinds of interactions, including σ bonding, π bonding, metal to metal bonding, agostic interactions, bent bonds, three center two electron bonds and three center four electron bonds. The term covalent bond dates from 1939. The prefix co means jointly, associated in action, partnered to a lesser degree, etc. ; thus a "co valent bond", in essence, means that the atoms share "valence", such as is discussed in valence bond theory. In the molecule , the hydrogen atoms share the two electrons via covalent bonding. Covalency is greatest between atoms of similar electronegativities. Thus, covalent bonding does not necessarily require that the two atoms be of the same elements, only that they be of comparable electronegativity. Covalent bonding that entails the sharing of electrons over more than two atoms is said to be delocalized.

The term covalence in regard to bonding was first used in 1919 by Irving Langmuir in a Journal of the American Chemical Society article entitled "The Arrangement of Electrons in Atoms and Molecules". Langmuir wrote that "we shall denote by the term covalence the number of pairs of electrons that a given atom shares with its neighbors." The idea of covalent bonding can be traced several years before 1919 to Gilbert N. Lewis, who in 1916 described the sharing of electron pairs between atoms (and in 1926 he also coined the term "photon" for the smallest unit of radiant energy). He introduced the Lewis notation or electron dot notation or Lewis dot structure, in which valence electrons (those in the outer shell) are represented as dots around the atomic symbols. Pairs of electrons located between atoms represent covalent bonds. Multiple pairs represent multiple bonds, such as double bonds and triple bonds. An alternative form of representation, not shown here, has bond forming electron pairs represented as solid lines. Lewis proposed that an atom forms enough covalent bonds to form a full (or closed) outer electron shell. In the diagram of methane shown here, the carbon atom has a valence of four and is, therefore, surrounded by eight electrons (the octet rule), four from the carbon itself and four from the hydrogens bonded to it. Each hydrogen has a valence of one and is surrounded by two electrons (a duet rule) – its own one electron plus one from the carbon. The numbers of electrons correspond to full shells in the quantum theory of the atom; the outer shell of a carbon atom is the n = 2 shell, which can hold eight electrons, whereas the outer (and only) shell of a hydrogen atom is the n = 1 shell, which can hold only two. While the idea of shared electron pairs provides an effective qualitative picture of covalent bonding, quantum mechanics is needed to understand the nature of these bonds and predict the structures and properties of simple molecules. Walter Heitler and Fritz London are credited with the first successful quantum mechanical explanation of a chemical bond (molecular hydrogen) in 1927. Their work was based on the valence bond model, which assumes that a chemical bond is formed when there is good overlap between the atomic orbitals of participating atoms.

Atomic orbitals (except for s orbitals) have specific directional properties leading to different types of covalent bonds. Sigma (σ) bonds are the strongest covalent bonds and are due to head on overlapping of orbitals on two different atoms. A single bond is usually a σ bond. Pi (π) bonds are weaker and are due to lateral overlap between p (or d) orbitals. A double bond between two given atoms consists of one σ and one π bond, and a triple bond is one σ and two π bonds.

Bonds with one or three electrons can be found in radical species, which have an odd number of electrons. The simplest example of a 1 electron bond is found in the dihydrogen cation, H2+. One electron bonds often have about half the bond energy of a 2 electron bond, and are therefore called "half bonds". However, there are exceptions: in the case of dilithium, the bond is actually stronger for the 1 electron Li2+ than for the 2 electron Li2. This exception can be explained in terms of hybridization and inner shell effects. The simplest example of three electron bonding can be found in the helium dimer cation, He2+. It is considered a "half bond" because it consists of only one shared electron (rather than two); in molecular orbital terms, the third electron is in an anti bonding orbital which cancels out half of the bond formed by the other two electrons. Another example of a molecule containing a 3 electron bond, in addition to two 2 electron bonds, is nitric oxide, NO. The oxygen molecule, O2 can also be regarded as having two 3 electron bonds and one 2 electron bond, which accounts for its paramagnetism and its formal bond order of 2. Chlorine dioxide and its heavier analogues bromine dioxide and iodine dioxide also contain three electron bonds. Molecules with odd electron bonds are usually highly reactive. These types of bond are only stable between atoms with similar electronegativities.

In three center two electron bonds ("3c–2e") three atoms share two electrons in bonding. This type of bonding occurs in boron hydrides such as diborane (B2H6), which are often described as electron deficient because there are not enough valence electrons to form localized (2 centre 2 electron) bonds joining all the atoms. However the more modern description using 3c–2e bonds does provide enough bonding orbitals to connect all the atoms, so that the molecules can instead be classified as electron precise. Each such bond (2 per molecule in diborane) contains a pair of electrons which connect the boron atoms to each other in a banana shape, with a proton (the nucleus of a hydrogen atom) in the middle of the bond, sharing electrons with both boron atoms. In certain cluster compounds, so called four center two electron bonds also have been postulated.

After the development of quantum mechanics, two basic theories were proposed to provide a quantum description of chemical bonding: valence bond (VB) theory and molecular orbital (MO) theory. A more recent quantum description is given in terms of atomic contributions to the electronic density of states.

An analogous effect to covalent binding is believed to occur in some nuclear systems, with the difference that the shared fermions are quarks rather than electrons. High energy proton proton scattering cross section indicates that quark interchange of either u or d quarks is the dominant process of the nuclear force at short distance. In particular, it dominates over the Yukawa interaction where a meson is exchanged. Therefore, covalent binding by quark interchange is expected to be the dominating mechanism of nuclear binding at small distance when the bound hadrons have covalence quarks in common.