Covalent bond

"Covalent" redirects here. For other uses, seeCovalent (disambiguation).

A covalent bond forming H₂(right) where twohydrogen atomsshare the twoelectrons

Acovalent bondis achemical bondthat involves the sharing ofelectronsto formelectron pairsbetweenatoms.These electron pairs are known asshared pairsorbonding pairs.The stable balance of attractive and repulsive forces between atoms, when they shareelectrons,is known as covalent bonding.For manymolecules,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 thanionic bonding.

Covalent bonding also includes many kinds of interactions, includingσ-bonding,π-bonding,metal-to-metal bonding,agostic interactions,bent bonds,three-center two-electron bondsandthree-center four-electron bonds.The termcovalent bonddates from 1939.The prefixco-meansjointly, 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 invalence bond theory.

In the moleculeH
₂,thehydrogenatoms share the two electrons via covalent bonding.Covalency is greatest between atoms of similarelectronegativities.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 bedelocalized.

History

Early concepts in covalent bonding arose from this kind of image of the molecule ofmethane.Covalent bonding is implied in theLewis structureby indicating electrons shared between atoms.

The termcovalencein regard to bonding was first used in 1919 byIrving Langmuirin aJournal of the American Chemical Societyarticle entitled "The Arrangement of Electrons in Atoms and Molecules". Langmuir wrote that "we shall denote by the termcovalencethe 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 toGilbert 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 theLewis notationorelectron dot notationorLewis 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 asdouble bondsandtriple 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 (theoctet 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 then= 2 shell, which can hold eight electrons, whereas the outer (and only) shell of a hydrogen atom is then= 1 shell, which can hold only two.

While the idea of shared electron pairs provides an effective qualitative picture of covalent bonding,quantum mechanicsis needed to understand the nature of these bonds and predict the structures and properties of simple molecules.Walter HeitlerandFritz Londonare 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 theatomic orbitalsof participating atoms.

Types of covalent bonds

Atomic orbitals(except for s orbitals) have specific directional properties leading to different types of covalent bonds.Sigma (σ) bondsare the strongest covalent bonds and are due to head-on overlapping of orbitals on two different atoms. Asingle bondis usually a σ bond.Pi (π) bondsare weaker and are due to lateral overlap between p (or d) orbitals. Adouble bondbetween two given atoms consists of one σ and one π bond, and atriple bondis one σ and two π bonds.

Covalent bonds are also affected by theelectronegativityof the connected atoms which determines thechemical polarityof 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 requiresgeometricasymmetry,or elsedipolesmay cancel out, resulting in a non-polar molecule.

Covalent structures

There are several types of structures for covalent substances, including individual molecules,molecular structures,macromolecularstructures and giant covalent structures. Individual molecules have strong bonds that hold the atoms together, but generally, there are negligible forces of attraction between molecules. Such covalent substances are usually gases, for example,HCl,SO₂,CO₂,andCH₄.In molecular structures, there are weak forces of attraction. Such covalent substances are low-boiling-temperature liquids (such asethanol), and low-melting-temperature solids (such asiodineand solid CO₂). Macromolecular structures have large numbers of atoms linked by covalent bonds in chains, including synthetic polymers such aspolyethyleneandnylon,and biopolymers such asproteinsandstarch.Network covalent structures(or giant covalent structures) contain large numbers of atoms linked in sheets (such asgraphite), or 3-dimensional structures (such asdiamondandquartz). These substances have high melting and boiling points, are frequently brittle, and tend to have high electricalresistivity.Elements that have highelectronegativity,and the ability to form three or four electron pair bonds, often form such large macromolecular structures.

One- and three-electron bonds

LewisandMO diagramsof an individual 2e^-bond and 3e^-bond

Bonds with one or three electrons can be found inradicalspecies, which have an odd number of electrons. The simplest example of a 1-electron bond is found in thedihydrogen 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 ofdilithium,the bond is actually stronger for the 1-electronLi⁺
₂than for the 2-electron Li₂.This exception can be explained in terms ofhybridizationand inner-shell effects.

The simplest example of three-electron bonding can be found in thehelium dimercation,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, isnitric oxide,NO. The oxygen molecule, O₂can also be regarded as having two 3-electron bonds and one 2-electron bond, which accounts for itsparamagnetismand its formal bond order of 2.Chlorine dioxideand its heavier analoguesbromine dioxideandiodine dioxidealso 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.

Modified Lewis structures with 3e bonds

Nitric oxide

Dioxygen

Resonance

Main article:Resonance (chemistry)

There are situations whereby a singleLewis structureis insufficient to explain the electron configuration in a molecule and its resulting experimentally-determined properties, hence a superposition of structures is needed. The same two atoms in such molecules can be bonded differently in different Lewis structures (a single bond in one, a double bond in another, or even none at all), resulting in a non-integerbond order.Thenitrateion is one such example with three equivalent structures. The bond between thenitrogenand 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 is⁠2 + 1 + 1/3⁠=⁠4/3⁠.

Aromaticity

Main article:Aromaticity

Inorganic chemistry,when a molecule with a planar ring obeysHückel's rule,where the number ofπ electronsfit the formula 4n+ 2 (wherenis an integer), it attains extra stability and symmetry. Inbenzene,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 regularhexagonexhibiting a greater stabilization than the hypothetical 1,3,5-cyclohexatriene.

In the case ofheterocyclicaromatics and substitutedbenzenes,the electronegativity differences between different parts of the ring may dominate the chemical behavior of aromatic ring bonds, which otherwise are equivalent.

Hypervalence

Main article:Hypervalent molecule

Certain molecules such asxenon difluorideandsulfur hexafluoridehave higher co-ordination numbers than would be possible due to strictly covalent bonding according to theoctet rule.This is explained by thethree-center four-electron bond( "3c–4e" ) model which interprets the molecular wavefunction in terms of non-bondinghighest occupied molecular orbitalsinmolecular orbital theoryandresonanceof sigma bonds invalence bond theory.

Electron deficiency

Main article:Electron deficiency

Inthree-center two-electron bonds( "3c–2e" ) three atoms share two electrons in bonding. This type of bonding occurs inboron hydridessuch asdiborane(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 theboronatoms 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 certaincluster compounds,so-calledfour-center two-electron bondsalso 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) theoryandmolecular orbital (MO) theory.A more recent quantum descriptionis 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 theelectron configurationof the molecule.For valence bond theory, the atomichybrid orbitalsare filled with electrons first to produce a fully bonded valence configuration, followed by performing a linear combination of contributing structures (resonance) if there are several of them. In contrast, for molecular orbital theory alinear combination of atomic orbitalsis performed first, followed by filling of the resultingmolecular orbitalswith 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 ofbond energiesand the understanding ofreaction mechanisms.As molecular orbital theory builds the molecular wavefunction out of delocalized orbitals, it is more suited for the calculation ofionization energiesand the understanding ofspectral 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 predictsHückel's ruleof 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 byconfiguration interaction.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 neglectselectron correlationwhile the simple valence bond approach overestimates it.

Modern calculations inquantum chemistryusually 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.

Covalency from atomic contribution to the electronic density of states

Evaluation of bond covalency is dependent on thebasis setfor approximate quantum-chemical methods such as COOP (crystal orbital overlap population),COHP (Crystal orbital Hamilton population),and BCOOP (Balanced crystal orbital overlap population).To overcome this issue, an alternative formulation of the bond covalency can be provided in this way.

Themass center⁠$cm(n,l,m_{l},m_{s})$⁠of an atomic orbital$|n,l,m_{l},m_{s}\rangle,$withquantum numbers⁠$n,$⁠⁠$l,$⁠⁠$m_{l},$⁠⁠$m_{s},$⁠for atom A is defined as

$cm^{\mathrm {A} }(n,l,m_{l},m_{s})={\frac {\int \limits _{E_{0}}\limits ^{E_{1}}Eg_{|n,l,m_{l},m_{s}\rangle }^{\mathrm {A} }(E)dE}{\int \limits _{E_{0}}\limits ^{E_{1}}g_{|n,l,m_{l},m_{s}\rangle }^{\mathrm {A} }(E)dE}}$

where$g_{|n,l,m_{l},m_{s}\rangle }^{\mathrm {A} }(E)$is the contribution of the atomic orbital$|n,l,m_{l},m_{s}\rangle$of the atom A to the total electronic density of states⁠$g(E)$⁠of the solid

$g(E)=\sum _{\mathrm {A} }\sum _{n,l}\sum _{m_{l},m_{s}}{g_{|n,l,m_{l},m_{s}\rangle }^{\mathrm {A} }(E)}$

where the outer sum runs over all atoms A of the unit cell. The energy window⁠$[E_{0},E_{1}]$⁠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$C_{n_{\mathrm {A} }l_{\mathrm {A} },n_{\mathrm {B} }l_{\mathrm {B} }}$⁠of the mass center of$|n_{\mathrm {A} },l_{\mathrm {A} }\rangle$levels of atom A with respect to the mass center of$|n_{\mathrm {B} },l_{\mathrm {B} }\rangle$levels of atom B is given as

$C_{n_{\mathrm {A} }l_{\mathrm {A} },n_{\mathrm {B} }l_{\mathrm {B} }}=-\left|cm^{\mathrm {A} }(n_{\mathrm {A} },l_{\mathrm {A} })-cm^{\mathrm {B} }(n_{\mathrm {B} },l_{\mathrm {B} })\right|$

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

$C_{\mathrm {A,B} }=-\left|cm^{\mathrm {A} }-cm^{\mathrm {B} }\right|$

where, for simplicity, we may omit the dependence from the principal quantum number⁠$n$⁠in the notation referring to⁠$C_{n_{\mathrm {A} }l_{\mathrm {A} },n_{\mathrm {B} }l_{\mathrm {B} }}.$⁠

In this formalism, the greater the value of⁠$C_{\mathrm {A,B} },$⁠the higher the overlap of the selected atomic bands, and thus the electron density described by those orbitals gives a more covalentA−Bbond. The quantity⁠$C_{\mathrm {A,B} }$⁠is denoted as thecovalencyof theA−Bbond, which is specified in the same units of the energy⁠$E$⁠.

Analogous effect in nuclear systems

An analogous effect to covalent binding is believed to occur in some nuclear systems, with the difference that the shared fermions arequarksrather than electrons.High energyproton-protonscatteringcross-sectionindicates that quark interchange of either u or d quarks is the dominant process of thenuclear forceat short distance. In particular, it dominates over theYukawa interactionwhere amesonis exchanged.Therefore, covalent binding by quark interchange is expected to be the dominating mechanism of nuclear binding at small distance when the boundhadronshave covalence quarks in common.

See also

• Bonding in solids
• Bond order
• Coordinate covalent bond,also known as a dipolar bond or a dative covalent bond
• Covalent bond classification(or LXZ notation)
• Covalent radius
• Disulfide bond
• Hybridization
• Hydrogen bond
• Ionic bond
• Linear combination of atomic orbitals
• Metallic bonding
• Noncovalent bonding
• Resonance (chemistry)

Sources

• "Covalent bonding – Single bonds".chemguide. 2000.Retrieved2012-02-05.
• "Electron Sharing and Covalent Bonds".Department of Chemistry University of Oxford.Retrieved2012-02-05.
• "Chemical Bonds".Department of Physics and Astronomy, Georgia State University.Retrieved2012-02-05.

External links

• Covalent Bonds and Molecular StructureArchived2009-02-10 at theWayback Machine
• Structure and Bonding in Chemistry—Covalent Bonds