TheInfoList

A covalent bond is a
chemical bond A chemical bond is a lasting attraction between atom An atom is the smallest unit of ordinary matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday ...
that involves the sharing of
electron pair In chemistry Chemistry is the scientific discipline involved with Chemical element, elements and chemical compound, compounds composed of atoms, molecules and ions: their composition, structure, properties, behavior and the changes they underg ...
s between
atom An atom is the smallest unit of ordinary matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of atom ...

s. 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
electron The electron is a subatomic particle (denoted by the symbol or ) whose electric charge is negative one elementary charge. Electrons belong to the first generation (particle physics), generation of the lepton particle family, and are general ...

s, is known as covalent bonding. For many
molecule A scanning tunneling microscopy image of pentacene molecules, which consist of linear chains of five carbon rings. A molecule is an electrically Electricity is the set of physical phenomena associated with the presence and motion I ...

s, 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 bonds are much more common than
ionic bonds Ionic bonding is a type of chemical bond A chemical bond is a lasting attraction between atoms, ions or molecules that enables the formation of chemical compounds. The bond may result from the Coulomb's law, electrostatic force of attraction be ...
. Covalent bonding also includes many kinds of interactions, including , π-bonding, ,
agostic interactionAgostic interaction is a term in organometallic chemistry for the interaction of a coordinatively-unsaturated transition metal with a C−H bond, when the two electrons involved in the C−H bond enter the empty d-orbital of a transition metal, re ...
s,
bent bond In organic chemistry, a bent bond, also known as a banana bond, is a type of covalent bond, covalent chemical bond with a geometry somewhat reminiscent of a banana. The term itself is a general representation of electron density or configuration ...
s,
three-center two-electron bond A three-center two-electron (3c–2e) bond is an electron-deficient chemical bond A chemical bond is a lasting attraction between atoms, ions or molecules that enables the formation of chemical compounds. The bond may result from the Coulomb ...
s and
three-center four-electron bondThe 3-center 4-electron (3c–4e) bond is a model used to explain bonding in certain hypervalent molecules such as tetratomic and hexatomic interhalogenAn interhalogen compound is a molecule File:Pentacene on Ni(111) STM.jpg, A scanning tunnelin ...
s. 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 chemistry Chemistry is the scientific Science () is a systematic enterprise that builds and organizes knowledge Knowledge is a familiarity or awareness, of someone or something, such as facts A fact is an occurrence in t ...
. In the molecule , the
hydrogen Hydrogen is the chemical element with the Symbol (chemistry), symbol H and atomic number 1. Hydrogen is the lightest element. At standard temperature and pressure, standard conditions hydrogen is a gas of diatomic molecules having the che ...

atoms share the two electrons via covalent bonding. Covalency is greatest between atoms of similar
electronegativities Electronegativity, symbolized as '' χ'', is the tendency of an atom An atom is the smallest unit of ordinary matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. ...

. 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.

# History

The term ''covalence'' in regard to bonding was first used in 1919 by
Irving Langmuir Irving Langmuir (; January 31, 1881 – August 16, 1957) was an American chemist A chemist (from Greek ''chēm(ía)'' alchemy; replacing ''chymist'' from Medieval Latin Medieval Latin was the form of Latin Latin (, or , ) is a class ...

in a ''
Journal of the American Chemical Society The ''Journal of the American Chemical Society'' (also known as JACS) is a weekly peer-reviewed Peer review is the evaluation of work by one or more people with similar competencies as the producers of the work ( peers). It functions as a for ...
'' 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 bond In chemistry, a double bond is a covalent bond A covalent bond is a chemical bond A chemical bond is a lasting attraction between atom An atom is the smallest unit of ordinary matter In classical physics and general chemistry, ...

s and
triple bond A triple bond in chemistry Chemistry is the study of the properties and behavior of . It is a that covers the that make up matter to the composed of s, s and s: their composition, structure, properties, behavior and the changes they un ...

s. 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 The octet rule is a chemical A chemical substance is a form of matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultim ...
), 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 Quantum mechanics is a fundamental theory A theory is a reason, rational type of abstraction, abstract thinking about a phenomenon, or the results of such thinking. The process of contemplative and rational thinking is often associated with ...
is needed to understand the nature of these bonds and predict the structures and properties of simple molecules.
Walter Heitler Walter Heinrich Heitler (; 2 January 1904 – 15 November 1981) was a German physicist A physicist is a scientist A scientist is a person who conducts scientific research The scientific method is an Empirical evidence, empirical me ...
and
Fritz London Fritz Wolfgang London (March 7, 1900 – March 30, 1954) was a German physicist A physicist is a scientist A scientist is a person who conducts scientific research The scientific method is an Empirical evidence, empirical method ...
are credited with the first successful quantum mechanical explanation of a chemical bond (
molecular hydrogen Hydrogen is the chemical element Image:Simple Periodic Table Chart-blocks.svg, 400px, Periodic table, The periodic table of the chemical elements In chemistry, an element is a pure substance consisting only of atoms that all have the sam ...
) in 1927. English translation in 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 In atomic theory and quantum mechanics, an atomic orbital is a Function (mathematics), mathematical function describing the location and wave-like behavior of an electron in an atom. This function can be used to calculate the probability of find ...
of participating atoms.

# Types of covalent bonds

Atomic orbitals (except for s orbitals) have specific directional properties leading to different types of covalent bonds. s are the strongest covalent bonds and are due to head-on overlapping of orbitals on two different atoms. A
single bond In chemistry Chemistry is the study of the properties and behavior of . It is a that covers the that make up matter to the composed of s, s and s: their composition, structure, properties, behavior and the changes they undergo duri ...

is usually a σ bond. Pi (π) bonds are weaker and are due to lateral overlap between p (or d) orbitals. A
double bond In chemistry, a double bond is a covalent bond A covalent bond is a chemical bond A chemical bond is a lasting attraction between atom An atom is the smallest unit of ordinary matter In classical physics and general chemistry, ...

between two given atoms consists of one σ and one π bond, and a
triple bond A triple bond in chemistry Chemistry is the study of the properties and behavior of . It is a that covers the that make up matter to the composed of s, s and s: their composition, structure, properties, behavior and the changes they un ...

is one σ and two π bonds. Covalent bonds are also affected by the electronegativity of the connected atoms which determines the
chemical polarity In chemistry Chemistry is the scientific Science () is a systematic enterprise that builds and organizes knowledge Knowledge is a familiarity or awareness, of someone or something, such as facts A fact is an occurrence in ...
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 Geometry (from the grc, γεωμετρία; '' geo-'' "earth", '' -metron'' "measurement") is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space that are related with distance, shape, size, ...

asymmetry Asymmetry is the absence of, or a violation of, symmetry (the property of an object being invariant to a transformation, such as reflection). Symmetry is an important property of both physical and abstract systems and it may be displayed in prec ...

, or else
dipole In electromagnetism Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electric charge, electrically charged particles. The electromagnetic force is ...

s may cancel out resulting in a non-polar molecule.

# Covalent structures

There are several types of structures for covalent substances, including individual molecules, molecular structures,
macromolecular A macromolecule is a very large molecule A scanning tunneling microscopy image of pentacene molecules, which consist of linear chains of five carbon rings. A molecule is an electrically Electricity is the set of physical phenom ...
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 The compound Compound may refer to: Architecture and built environments * Compound (enclosure), a cluster of buildings having a shared purpose, usually inside a fence or wall ** Compound (fortification), a version of the above fortified with ...
, SO2, , and CH4. In molecular structures, there are weak forces of attraction. Such covalent substances are low-boiling-temperature liquids (such as
ethanol Ethanol (also called ethyl alcohol, grain alcohol, drinking alcohol, or simply alcohol) is an organic Organic may refer to: * Organic, of or relating to an organism, a living entity * Organic, of or relating to an anatomical organ (anatomy), ...

), and low-melting-temperature solids (such as
iodine Iodine is a chemical element In chemistry, an element is a pure Chemical substance, substance consisting only of atoms that all have the same numbers of protons in their atomic nucleus, nuclei. Unlike chemical compounds, chemical ele ...

and solid CO2). Macromolecular structures have large numbers of atoms linked by covalent bonds in chains, including synthetic polymers such as
polyethylene Polyethylene or (incorrectly) polythene (abbreviated PE; IUPAC name polyethene or poly(methylene)) is the most common plastic in use today. It is a polymer, primarily used for packaging (plastic bags, plastic films, geomembranes and container ...

and
nylon Nylon is a generic designation for a family of synthetic polymerSynthetic polymers are human-made polymers, often derived from petroleum oil. From the utility point of view they can be classified into three main categories: thermoplastics, ela ...

, and biopolymers such as
protein Proteins are large biomolecule , showing alpha helices, represented by ribbons. This poten was the first to have its suckture solved by X-ray crystallography by Max Perutz and Sir John Cowdery Kendrew in 1958, for which they received a No ...

s and
starch Starch or amylum is a polymeric A polymer (; Greek '' poly-'', "many" + '' -mer'', "part") is a substance Substance may refer to: * Substance (Jainism), a term in Jain ontology to denote the base or owner of attributes * Chemical substance ...
. Network covalent structures (or giant covalent structures) contain large numbers of atoms linked in sheets (such as
graphite Graphite (), archaically referred to as plumbago, is a Crystallinity, crystalline form of the element carbon with its atoms arranged in a Hexagonal crystal system, hexagonal structure. It occurs naturally in this form and is the most stable for ...

), or 3-dimensional structures (such as
diamond Diamond is a Allotropes of carbon, solid form of the element carbon with its atoms arranged in a crystal structure called diamond cubic. At Standard conditions for temperature and pressure, room temperature and pressure, another solid form of ...

and
quartz Quartz is a hard, crystalline mineral composed of silica (silicon dioxide). The atoms are linked in a continuous framework of SiO4 silicon-oxygen Tetrahedral molecular geometry, tetrahedra, with each oxygen being shared between two tetrahedra, ...

). These substances have high melting and boiling points, are frequently brittle, and tend to have high electrical
resistivity Electrical resistivity (also called specific electrical resistance or volume resistivity) is a fundamental property of a material that measures how strongly it resists electric current An electric current is a stream of charged particle In p ...
. Elements that have high
electronegativity Electronegativity, symbolized as '' χ'', is the tendency for an atom An atom is the smallest unit of ordinary matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume ...

, and the ability to form three or four electron pair bonds, often form such large macromolecular structures.

# One- and three-electron bonds

Bonds with one or three electrons can be found in
species, which have an odd number of electrons. The simplest example of a 1-electron bond is found in the
dihydrogen cation The dihydrogen cation or hydrogen molecular ion is a cation An ion () is a particle, atom or molecule with a net electric charge, electrical charge. The charge of the electron is considered negative by convention. The negative charge of an ...
, . 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 Dilithium, Li2, is a strongly electrophilic In 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 che ...
, the bond is actually stronger for the 1-electron 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 The helium dimer is a van der Waals molecule with formula He2 consisting of two helium Helium (from el, ἥλιος, helios Helios; Homeric Greek: ), Latinized as Helius; Hyperion and Phaethon are also the names of his father and son re ...
cation, . 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 Nitric oxide (nitrogen oxide or nitrogen monoxide) is a colorless gas with the formula . It is one of the principal oxides of nitrogen. Nitric oxide is a free radical: it has an unpaired electron, which is sometimes denoted by a dot in its che ...

, 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 Paramagnetism is a form of magnetism Magnetism is a class of physical attributes that are mediated by magnetic field A magnetic field is a vector field In vector calculus and physics, a vector field is an assignment of a vector to e ...
and its formal bond order of 2.
Chlorine dioxide Chlorine dioxide is a chemical compound with the formula ClO2 that exists as yellowish-green gas above 11 °C, a reddish-brown liquid between 11 °C and −59 °C, and as bright orange crystals below −59 °C. It is an oxidizi ...

and its heavier analogues
bromine dioxide Bromine dioxide is the chemical compound A chemical compound is a chemical substance composed of many identical molecules (or molecular entity, molecular entities) composed of atoms from more than one chemical element, element held together by ...
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.

# Resonance

There are situations whereby a single
Lewis structure#REDIRECT Lewis structure Lewis structures, also known as Lewis dot formulas, Lewis dot structures, electron dot structures, or Lewis electron dot structures (LEDS), are diagrams that show the bonding between atom An atom is the smallest unit o ...
is insufficient to explain the electron configuration in a molecule, hence a superposition of structures is 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 orderBond order, as introduced by Linus Pauling, is defined as the difference between the number of Bonding molecular orbital, bonds and Antibonding molecular orbital, anti-bonds. The bond number itself is the number of electron pairs (bonds) between a p ...
. The
nitrate Nitrate is a polyatomic ion A polyatomic ion, also known as a molecular ion, is a covalently bonded A covalent bond is a chemical bond A chemical bond is a lasting attraction between atoms, ions or molecules that enables the format ...

ion is one such example with three equivalent structures. The bond between the
nitrogen Nitrogen is the chemical element upright=1.0, 500px, The chemical elements ordered by link=Periodic table In chemistry Chemistry is the science, scientific study of the properties and behavior of matter. It is a natural science ...

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 = .

## Aromaticity

In
organic chemistry Organic chemistry is a branch of chemistry Chemistry is the study of the properties and behavior of . It is a that covers the that make up matter to the composed of s, s and s: their composition, structure, properties, behavior and th ...
, when a molecule with a planar ring obeys
Hückel's rule 100px, Benzene, the most widely recognized aromatic compound with six (4''n'' + 2, for ''n'' = 1) delocalized electrons. In organic chemistry, Hückel's rule predicts whether a Plane (geometry), planar ring molecule will have ...
, where the number of π electrons fit the formula 4''n'' + 2 (where ''n'' is an integer), it attains extra stability and symmetry. In
benzene Benzene is an organic Organic may refer to: * Organic, of or relating to an organism, a living entity * Organic, of or relating to an anatomical organ (anatomy), organ Chemistry * Organic matter, matter that has come from a once-living organ ...

, the prototypical aromatic compound, there are 6 π bonding electrons (''n'' = 1, 4''n'' + 2 = 6). These occupy three delocalized π molecular orbitals (
molecular orbital theory In 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 composed of atoms ...
) or form conjugate π bonds in two resonance structures that linearly combine (
valence bond theory In chemistry Chemistry is the scientific Science () is a systematic enterprise that builds and organizes knowledge Knowledge is a familiarity or awareness, of someone or something, such as facts A fact is an occurrence in t ...
), creating a regular
hexagon In geometry Geometry (from the grc, γεωμετρία; ' "earth", ' "measurement") is, with , one of the oldest branches of . It is concerned with properties of space that are related with distance, shape, size, and relative position of ...

exhibiting a greater stabilization than the hypothetical 1,3,5-cyclohexatriene. In the case of
heterocyclic A heterocyclic compound or ring structure is a cyclic compound A cyclic compound (''ring compound'') is a term for a compound in the field of chemistry Chemistry is the scientific discipline involved with Chemical element, elements and c ...
aromatics and substituted
benzene Benzene is an organic Organic may refer to: * Organic, of or relating to an organism, a living entity * Organic, of or relating to an anatomical organ (anatomy), organ Chemistry * Organic matter, matter that has come from a once-living organ ...

s, the electronegativity differences between different parts of the ring may dominate the chemical behavior of aromatic ring bonds, which otherwise are equivalent.

## Hypervalence

Certain molecules such as
xenon difluoride Xenon difluoride is a powerful fluorinating agent with the chemical formula , and one of the most stable xenon compounds. Like most Covalent bond, covalent inorganic fluorides it is moisture-sensitive. It Chemical decomposition, decomposes on con ...
and
sulfur hexafluoride Sulfur hexafluoride (SF6) or sulphur hexafluoride (British spelling Despite the various English dialects spoken from country to country and within different regions of the same country, there are only slight regional variations in Engli ...
have higher co-ordination numbers than would be possible due to strictly covalent bonding according to the
octet rule The octet rule is a chemical A chemical substance is a form of matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultim ...
. This is explained by the
three-center four-electron bondThe 3-center 4-electron (3c–4e) bond is a model used to explain bonding in certain hypervalent molecules such as tetratomic and hexatomic interhalogenAn interhalogen compound is a molecule File:Pentacene on Ni(111) STM.jpg, A scanning tunnelin ...
("3c–4e") model which interprets the molecular wavefunction in terms of non-bonding
highest occupied molecular orbital Image:CO2 LUMO.gif, upright=1.2, 3D model of the lowest unoccupied molecular orbital in CO2 In chemistry, HOMO and LUMO are types of molecular orbital In chemistry Chemistry is the scientific discipline involved with Chemical element, ...
s in
molecular orbital theory In 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 composed of atoms ...
and
resonance Resonance describes the phenomenon of increased amplitude The amplitude of a ic is a measure of its change in a single (such as or ). There are various definitions of amplitude (see below), which are all s of the magnitude of the differ ...
of sigma bonds in
valence bond theory In chemistry Chemistry is the scientific Science () is a systematic enterprise that builds and organizes knowledge Knowledge is a familiarity or awareness, of someone or something, such as facts A fact is an occurrence in t ...
.

## Electron deficiency

In
three-center two-electron bond A three-center two-electron (3c–2e) bond is an electron-deficient chemical bond A chemical bond is a lasting attraction between atoms, ions or molecules that enables the formation of chemical compounds. The bond may result from the Coulomb ...
s ("3c–2e") three atoms share two electrons in bonding. This type of bonding occurs in
boron hydrides Boranes is the name given to the class of synthetic hydrides of boron with generic formula BxHy. In the past, borane molecules were often labeled "electron-deficient" because of their multicenter bonding (in which a pair of bonding electrons links ...
such as
diborane Diborane(6), generally known as diborane, is the chemical compound A chemical compound is a chemical substance A chemical substance is a form of matter In classical physics and general chemistry, matter is any substance that has mass ...
(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 Boron is a chemical element In chemistry Chemistry is the study of the properties and behavior of . It is a that covers the that make up matter to the composed of s, s and s: their composition, structure, properties, behav ...

atoms to each other in a
banana A banana is an elongated, edible fruit In botany Botany, also called , plant biology or phytology, is the science of plant life and a branch of biology. A botanist, plant scientist or phytologist is a scientist who specia ...

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 bondA 4-center 2-electron (4c–2e) bond is a type of chemical bond A chemical bond is a lasting attraction between atoms, ions or molecules that enables the formation of chemical compounds. The bond may result from the Coulomb's law, electrostatic f ...
s also have been postulated.

# Quantum mechanical description

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.

## Comparison of VB and MO theories

The two theories represent two ways to build up the
electron configuration In atomic physics and quantum chemistry Quantum chemistry, also called molecular quantum mechanics, is a branch of chemistry focused on the application of quantum mechanics to chemical systems. Understanding electronic structure and molecul ...
of the molecule. For valence bond theory, the atomic
hybrid orbitals In chemistry Chemistry is the scientific Science () is a systematic enterprise that builds and organizes knowledge Knowledge is a familiarity or awareness, of someone or something, such as facts A fact is an occurrence in t ...
are filled with electrons first to produce a fully bonded valence configuration, followed by performing a linear combination of contributing structures (
resonance Resonance describes the phenomenon of increased amplitude The amplitude of a ic is a measure of its change in a single (such as or ). There are various definitions of amplitude (see below), which are all s of the magnitude of the differ ...
) if there are several of them. In contrast, for molecular orbital theory a
linear combination of atomic orbitals A linear combination of atomic orbitals or LCAO is a quantum superposition of atomic orbitals and a technique for calculating molecular orbitals in quantum chemistry. In quantum mechanics, electron configurations of atoms are described as wavefunct ...
is performed first, followed by filling of the resulting
molecular orbital In chemistry, a molecular orbital is a Function (mathematics), mathematical function describing the location and Matter wave, wave-like behavior of an electron in a molecule. This function can be used to calculate chemical and physical propertie ...
s with electrons. The two approaches are regarded as complementary, and each provides its own insights into the problem of chemical bonding. As valence bond theory builds the molecular wavefunction out of localized bonds, it is more suited for the calculation of
bond energies In chemistry, bond energy (''BE''), also called the mean bond enthalpy or average bond enthalpy is the measure of bond strength in a chemical bond. IUPAC defines bond energy as the average value of the gas-phase bond-dissociation energy (usually a ...
and the understanding of
reaction mechanism In chemistry Chemistry is the scientific Science () is a systematic enterprise that builds and organizes knowledge Knowledge is a familiarity or awareness, of someone or something, such as facts A fact is an occurrence in t ...

s. As molecular orbital theory builds the molecular wavefunction out of delocalized orbitals, it is more suited for the calculation of ionization energies and the understanding of spectral absorption bands. At the qualitative level, both theories contain incorrect predictions. Simple (Heitler–London) valence bond theory correctly predicts the dissociation of homonuclear diatomic molecules into separate atoms, while simple (Hartree–Fock) molecular orbital theory incorrectly predicts dissociation into a mixture of atoms and ions. On the other hand, simple molecular orbital theory correctly predicts
Hückel's rule 100px, Benzene, the most widely recognized aromatic compound with six (4''n'' + 2, for ''n'' = 1) delocalized electrons. In organic chemistry, Hückel's rule predicts whether a Plane (geometry), planar ring molecule will have ...
of aromaticity, while simple valence bond theory incorrectly predicts that cyclobutadiene has larger resonance energy than benzene. Although the wavefunctions generated by both theories at the qualitative level do not agree and do not match the stabilization energy by experiment, they can be corrected by
configuration interaction Configuration interaction (CI) is a post-Hartree–Fock linear variational method for solving the nonrelativistic Schrödinger equation within the Born–Oppenheimer approximation for a Quantum chemistry, quantum chemical multi-electron s ...
. This is done by combining the valence bond covalent function with the functions describing all possible ionic structures or by combining the molecular orbital ground state function with the functions describing all possible excited states using unoccupied orbitals. It can then be seen that the simple molecular orbital approach overestimates the weight of the ionic structures while the simple valence bond approach neglects them. This can also be described as saying that the simple molecular orbital approach neglects
electron correlation Electronic correlation is the interaction between electrons in the electronic structure of a quantum system. The correlation energy is a measure of how much the movement of one electron is influenced by the presence of all other electrons. Ato ...

while the simple valence bond approach overestimates it. Modern calculations in
quantum chemistry Quantum chemistry, also called molecular quantum mechanics, is a branch of chemistry focused on the application of quantum mechanics to chemical systems. Understanding electronic structure and molecular dynamics using the Schrödinger equations a ...
usually start from (but ultimately go far beyond) a molecular orbital rather than a valence bond approach, not because of any intrinsic superiority in the former but rather because the MO approach is more readily adapted to numerical computations. Molecular orbitals are orthogonal, which significantly increases the feasibility and speed of computer calculations compared to nonorthogonal valence bond orbitals. However, now there is a technology for direct visualization of valence bonds by electron cloud densitometry.

## 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 of an atomic orbital , with quantum numbers , for atom A is defined as :$cm^\mathrm\left(n,l,m_l,m_s\right)=\frac$ where is the contribution of the atomic orbital of the atom A to the total electronic density of states of the solid :$g\left\left(E\right\right)=\sum_\mathrm\sum_\sum_$ where the outer sum runs over all atoms A of the unit cell. The energy window is chosen in such a way that it encompasses all of the 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 with the considered bond. The relative position of the center mass of levels of atom A with respect to the center mass of levels of atom B is given as :$C_=-\left, cm^\mathrm\left(n_\mathrm,l_\mathrm\right)-cm^\mathrm\left(n_\mathrm,l_\mathrm\right)\$ where the contributions of the magnetic and spin quantum numbers are summed. According to this definition, the relative position of the A levels with respect to the B levels is :$C_\mathrm=-\left, cm^\mathrm-cm^\mathrm\$ where, for simplicity, we may omit the dependence from the principal quantum number in the notation referring to . In this formalism, the greater the value of , 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 is denoted as the ''covalency'' of the A–B bond, which is specified in the same units of the energy .

*
Bonding in solids Solids can be classified according to the nature of the Chemical bond, bonding between their atomic or molecular components. The traditional classification distinguishes four kinds of bonding: * Covalent bonding, which forms #Network covalent solid ...
*
Bond orderBond order, as introduced by Linus Pauling, is defined as the difference between the number of Bonding molecular orbital, bonds and Antibonding molecular orbital, anti-bonds. The bond number itself is the number of electron pairs (bonds) between a p ...
*
Coordinate covalent bond A coordinate covalent bond, also known as a dative bond, dipolar bond, or coordinate bond is a kind of two-center, two-electron covalent bond A covalent bond is a chemical bond that involves the sharing of electron pairs between atoms. These e ...
, also known as a dipolar bond or a dative covalent bond * Covalent bond classification (or LXZ notation) *
Covalent radius The covalent radius, ''r''cov, is a measure of the size of an atom An atom is the smallest unit of ordinary matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All ...
* Disulfide bond * Orbital hybridisation, Hybridization * Hydrogen bond * Ionic bond * Linear combination of atomic orbitals molecular orbital method, Linear combination of atomic orbitals * Metallic bonding * Noncovalent bonding * Resonance (chemistry)

* * *