A covalent bond, also called a molecular bond, is a chemical bond that
involves the sharing of electron pairs between atoms. These electron
pairs are known as shared pairs or bonding pairs, and the stable
balance of attractive and repulsive forces between atoms, when they
share electrons, is known as covalent
bonding.[better source needed] For many molecules, the
sharing of electrons allows each atom to attain the equivalent of a
full outer shell, corresponding to a stable electronic configuration.
Covalent bonding includes many kinds of interactions, including
σ-bonding, π-bonding, metal-to-metal bonding, agostic interactions,
bent bonds, and three-center two-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 H
2, 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 sharing of electrons
over more than two atoms is said to be delocalized.
2 Types of covalent bonds
3 Covalent structures
4 One- and three-electron bonds
6 Quantum mechanical description
6.1 Covalency from atomic contribution to the electronic density of
7 See also
10 External links
Early concepts in covalent bonding arose from this kind of image of
the molecule of methane. Covalent bonding is implied in the Lewis
structure by indicating electrons shared between atoms.
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. 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
Types of covalent bonds
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.
Covalent bonds are also affected by the electronegativity of the
connected atoms which determines the chemical polarity of the bond.
Two atoms with equal electronegativity will make nonpolar covalent
bonds such as H–H. An unequal relationship creates a polar covalent
bond such as with H−Cl. However polarity also requires geometric
asymmetry, or else dipoles may cancel out resulting in a non-polar
There are several types of structures for covalent substances,
including individual molecules, molecular structures, macromolecular
structures and giant covalent structures. Individual molecules have
strong bonds that hold the atoms together, but there are negligible
forces of attraction between molecules. Such covalent substances are
usually gases, for example, HCl, SO2, CO2, and CH4. In molecular
structures, there are weak forces of attraction. Such covalent
substances are low-boiling-temperature liquids (such as ethanol), and
low-melting-temperature solids (such as iodine and solid CO2).
Macromolecular structures have large numbers of atoms linked by
covalent bonds in chains, including synthetic polymers such as
polyethylene and nylon, and biopolymers such as proteins and starch.
Network covalent structures (or giant covalent structures) contain
large numbers of atoms linked in sheets (such as graphite), or
3-dimensional structures (such as diamond and quartz). These
substances have high melting and boiling points, are frequently
brittle, and tend to have high electrical resistivity. Elements that
have high electronegativity, and the ability to form three or four
electron pair bonds, often form such large macromolecular
One- and three-electron 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, H+
2. 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 Li+
2 than for the 2-electron Li2. This exception can be explained in
terms of hybridization and inner-shell effects.
Comparison of the electronic structure of the three-electron bond to
the conventional covalent bond.
The simplest example of three-electron bonding can be found in the
helium dimer cation, He+
2. 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
Main article: Resonance (chemistry)
There are situations whereby a single
Lewis structure is insufficient
to explain the electron configuration in a molecule, hence a
superposition of structures are needed. The same two atoms in such
molecules can be bonded differently in different structures (a single
bond in one, a double bond in another, or even none at all), resulting
in a non-integer bond order. The nitrate ion is one such example with
three equivalent structures. The bond between the nitrogen and each
oxygen is a double bond in one structure and a single bond in the
other two, so that the average bond order for each N–O interaction
is 2 + 1 + 1/3 = 4/3.
Main article: Aromaticity
In organic chemistry, when a molecule with a planar ring obeys
Hückel's rule, where the number of π electrons fit the formula
4n + 2 (where n is an integer), it attains extra stability
and symmetry. In benzene, the prototypical aromatic compound, there
are 6 π bonding electrons (n = 1,
4n + 2 = 6). These occupy three delocalized π
molecular orbitals (molecular orbital theory) or form conjugate π
bonds in two resonance structures that linearly combine (valence bond
theory), creating a regular hexagon exhibiting a greater stabilization
than the hypothetical 1,3,5-cyclohexatriene.
In the case of heterocyclic aromatics and substituted benzenes, the
electronegativity differences between different parts of the ring may
dominate the chemical behaviour of aromatic ring bonds, which
otherwise are equivalent.
Main article: Hypervalent molecule
Certain molecules such as xenon difluoride and sulfur hexafluoride
have higher co-ordination numbers than would be possible due to
strictly covalent bonding according to the octet rule. This is
explained by the three-center four-electron bond ("3c–4e") model
which interprets the molecular wavefunction in terms of non-bonding
highest occupied molecular orbitals in molecular orbital theory and
ionic-covalent resonance in valence bond theory.
In three-center two-electron bonds ("3c–2e") three atoms share two
electrons in bonding. This type of bonding occurs in electron
deficient compounds like diborane. 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 (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.
Quantum mechanical description
Main article: Chemical bonding model
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.
Covalency from atomic contribution to the electronic density of states
In COOP, COHP and BCOOP, evaluation of bond covalency is
dependent on the basis set. To overcome this issue, an alternative
formulation of the bond covalency can be provided in this way.
The center mass cm(n,l,ml,ms) of an atomic orbital n,l,ml,ms⟩, with
quantum numbers n, l, ml, ms, for atom A is defined as
displaystyle cm^ mathrm A (n,l,m_ l ,m_ s )= frac int limits
_ E_ 0 limits ^ E_ 1 Eg_ n,l,m_ l ,m_ s rangle ^ mathrm A
left(Eright)dE int limits _ E_ 0 limits ^ E_ 1 g_ n,l,m_ l ,m_ s
rangle ^ mathrm A left(Eright)dE
n,l,ml,ms⟩(E) is the contribution of the atomic orbital
n,l,ml,ms⟩ of the atom A to the total electronic density of states
g(E) of the solid
displaystyle gleft(Eright)=sum _ mathrm A sum _ n,l sum _ m_ l
,m_ s g_ n,l,m_ l ,m_ s rangle ^ mathrm A left(Eright)
where the outer sum runs over all atoms A of the unit cell. The energy
window [E0,E1] is chosen in such a way that it encompasses all
relevant bands participating in the bond. If the range to select is
unclear, it can be identified in practice by examining the molecular
orbitals that describe the electron density along the considered bond.
The relative position CnAlA,nBlB of the center mass of nA,lA⟩
levels of atom A with respect to the center mass of nB,lB⟩ levels
of atom B is given as
displaystyle C_ n_ mathrm A l_ mathrm A ,n_ mathrm B l_
mathrm B =-leftcm^ mathrm A (n_ mathrm A ,l_ mathrm A
)-cm^ mathrm B (n_ mathrm B ,l_ mathrm B )right
where the contributions of the magnetic and spin quantum numbers are
summed. According to this definition, the relative position of the A
levels with respect to the B levels is
displaystyle C_ mathrm A,B =-leftcm^ mathrm A -cm^ mathrm
where, for simplicity, we may omit the dependence from the principal
quantum number n in the notation referring to CnAlA,nBlB.
In this formalism, the greater the value of CA,B, the higher the
overlap of the selected atomic bands, and thus the electron density
described by those orbitals gives a more covalent A–B bond. The
quantity CA,B is denoted as the covalency of the A–B bond, which is
specified in the same units of the energy E.
Bonding in solids
Coordinate covalent bond, also known as a dipolar bond or a dative
Covalent bond classification (or LXZ notation)
Linear combination of atomic orbitals
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Covalent Bonds and Molecular Structure
Structure and Bonding in Chemistry—Covalent Bonds
van der Waals
Concepts in organic chemistry
List of organic compounds