Acovalent bond is achemical bond that involves the sharing ofelectrons to formelectron pairs betweenatoms. These electron pairs are known asshared pairs orbonding pairs. The stable balance of attractive and repulsive forces between atoms, when they shareelectrons, is known as covalent bonding.[1] 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.
In the moleculeH 2, thehydrogen atoms share the two electrons via covalent bonding.[5] 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.
Early concepts in covalent bonding arose from this kind of image of the molecule ofmethane. Covalent bonding is implied in theLewis structure by indicating electrons shared between atoms.
The termcovalence in regard to bonding was first used in 1919 byIrving Langmuir in aJournal of the American Chemical Society article entitled "The Arrangement of Electrons in Atoms and Molecules". Langmuir wrote that "we shall denote by the termcovalence the number of pairs of electrons that a given atom shares with its neighbors."[6]
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[7] (and in 1926 he also coined the term "photon" for the smallest unit of radiant energy). He introduced theLewis notation orelectron dot notation orLewis 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 bonds andtriple bonds. An alternative form of representation, not shown here, has bond-forming electron pairs represented as solid lines.[8]
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.[9]
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 andFritz London are credited with the first successful quantum mechanical explanation of a chemical bond (molecular hydrogen) in 1927.[10] Their work was based on the valence bond model, which assumes that a chemical bond is formed when there is good overlap between theatomic 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. Asingle bond is usually a σ bond.Pi (π) bonds are weaker and are due to lateral overlap between p (or d) orbitals. Adouble bond between two given atoms consists of one σ and one π bond, and atriple bond is one σ and two π bonds.[8]
Covalent bonds are also affected by theelectronegativity of the connected atoms which determines thechemical 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 requiresgeometricasymmetry, or elsedipoles may cancel out, resulting in a non-polar molecule.[8]
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 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 asiodine and solid CO2). Macromolecular structures have large numbers of atoms linked by covalent bonds in chains, including synthetic polymers such aspolyethylene andnylon, and biopolymers such asproteins andstarch.Network covalent structures (or giant covalent structures) contain large numbers of atoms linked in sheets (such asgraphite), or 3-dimensional structures (such asdiamond andquartz). 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.[11]
Bonds with one or three electrons can be found inradical species, 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+ 2 than for the 2-electron Li2. This exception can be explained in terms ofhybridization and inner-shell effects.[12]
The simplest example of three-electron bonding can be found in thehelium dimer cation,He+ 2. It is considered a "half bond" because it consists of only one shared electron (rather than two);[13] 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, O2 can also be regarded as having two 3-electron bonds and one 2-electron bond, which accounts for itsparamagnetism and its formal bond order of 2.[14]Chlorine dioxide and its heavier analoguesbromine dioxide andiodine 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.[14]
Dioxygen is sometimes represented as obeying the octet rule with a double bond (O=O) containing two pairs of shared electrons.[15] However the ground state of this molecule isparamagnetic, indicating the presence of unpaired electrons. Pauling proposed that this molecule actually contains two three-electron bonds and one normal covalent (two-electron) bond.[16] The octet on each atom then consists of two electrons from each three-electron bond, plus the two electrons of the covalent bond, plus one lone pair of non-bonding electrons. The bond order is 1+0.5+0.5=2.
There are situations whereby a singleLewis structure is 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. Thenitrate ion is one such example with three equivalent structures. The bond between thenitrogen 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 is2 + 1 + 1/3 =4/3.[8]
Inorganic chemistry, when a molecule with a planar ring obeysHückel's rule, where the number ofπ electrons fit the formula 4n + 2 (wheren is 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 regularhexagon exhibiting a greater stabilization than the hypothetical 1,3,5-cyclohexatriene.[9]
In the case ofheterocyclic aromatics and substitutedbenzenes, the electronegativity differences between different parts of the ring may dominate the chemical behavior of aromatic ring bonds, which otherwise are equivalent.[9]
Inthree-center two-electron bonds ("3c–2e") three atoms share two electrons in bonding. This type of bonding occurs inboron hydrides such 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 theboron 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 certaincluster compounds, so-calledfour-center two-electron bonds also have been postulated.[18]
After the development of quantum mechanics, two basic theories were proposed to provide a quantum description of chemical bonding:valence bond (VB) theory andmolecular orbital (MO) theory. A more recent quantum description[19] is given in terms of atomic contributions to the electronic density of states.
The two theories represent two ways to build up theelectron configuration of the molecule.[20] For valence bond theory, the atomichybrid orbitals are 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 orbitals is performed first, followed by filling of the resultingmolecular orbitals with electrons.[8]
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 energies and the understanding ofreaction mechanisms. As molecular orbital theory builds the molecular wavefunction out of delocalized orbitals, it is more suited for the calculation ofionization energies and the understanding ofspectral absorption bands.[21]
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 rule of aromaticity, while simple valence bond theory incorrectly predicts that cyclobutadiene has larger resonance energy than benzene.[22]
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.[20] 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 correlation while the simple valence bond approach overestimates it.[20]
Modern calculations inquantum chemistry 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.
Covalency from atomic contribution to the electronic density of states
Evaluation of bond covalency is dependent on thebasis set for approximate quantum-chemical methods such as COOP (crystal orbital overlap population),[23] COHP (Crystal orbital Hamilton population),[24] and BCOOP (Balanced crystal orbital overlap population).[25] To overcome this issue, an alternative formulation of the bond covalency can be provided in this way.
where is the contribution of the atomic orbital of the atom A to the total electronic density of states of the solid
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 mass center of levels of atom A with respect to the mass center of levels of atom B is given as
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
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 covalentA−B bond. The quantity is denoted as thecovalency of theA−B bond, which is specified in the same units of the energy.
An analogous effect to covalent binding is believed to occur in some nuclear systems, with the difference that the shared fermions arequarks rather than electrons.[26]High energyproton-protonscatteringcross-section indicates that quark interchange of either u or d quarks is the dominant process of thenuclear force at short distance. In particular, it dominates over theYukawa interaction where ameson is exchanged.[27] Therefore, covalent binding by quark interchange is expected to be the dominating mechanism of nuclear binding at small distance when the boundhadrons have covalence quarks in common.[28]
^Whitten, Kenneth W.; Gailey, Kenneth D.; Davis, Raymond E. (1992). "7-3 Formation of covalent bonds".General Chemistry (4th ed.). Saunders College Publishing. p. 264.ISBN0-03-072373-6.
^Stranks, D. R.; Heffernan, M. L.; Lee Dow, K. C.; McTigue, P. T.; Withers, G. R. A. (1970).Chemistry: A structural view.Carlton, Vic.: Melbourne University Press. p. 184.ISBN0-522-83988-6.
^Weinhold, F.; Landis, C. (2005).Valency and Bonding. Cambridge. pp. 96–100.ISBN0-521-83128-8.
^Harcourt, Richard D., ed. (2015). "Chapter 2: Pauling "3-Electron Bonds", 4-Electron 3-Centre Bonding, and the Need for an "Increased-Valence" Theory".Bonding in Electron-Rich Molecules: Qualitative Valence-Bond Approach via Increased-Valence Structures. Springer.ISBN9783319166766.
^For example,General chemistry by R.H.Petrucci, W.S.Harwood and F.G.Herring (8th ed., Prentice-Hall 2002,ISBN0-13-014329-4, p.395) writes the Lewis structure with a double bond, but adds a question mark with the explanation that there is some doubt about the validity of this structure because it fails to account for the observed paramagnetism.
^L. PaulingThe Nature of the Chemical Bond (3rd ed., Oxford University Press 1960) chapter 10.
^Weinhold, F.; Landis, C. (2005).Valency and Bonding. Cambridge University Press. pp. 275–306.ISBN0521831288.
^Hofmann, K.; Prosenc, M. H.; Albert, B. R. (2007). "A new 4c–2e bond inB 6H− 7".Chemical Communications.2007 (29):3097–3099.doi:10.1039/b704944g.PMID17639154.
^Cammarata, Antonio; Rondinelli, James M. (21 September 2014). "Covalent dependence of octahedral rotations in orthorhombic perovskite oxides".Journal of Chemical Physics.141 (11): 114704.Bibcode:2014JChPh.141k4704C.doi:10.1063/1.4895967.PMID25240365.
^abcAtkins, P. W. (1974).Quanta: A Handbook of Concepts. Oxford University Press. pp. 147–148.ISBN978-0-19-855493-6.
^James D. Ingle Jr. and Stanley R. Crouch,Spectrochemical Analysis, Prentice Hall, 1988,ISBN0-13-826876-2
^Anslyn, Eric V. (2006).Modern Physical Organic Chemistry. University Science Books.ISBN978-1-891389-31-3.
^Hughbanks, Timothy; Hoffmann, Roald (2002-05-01). "Chains of trans-edge-sharing molybdenum octahedra: metal-metal bonding in extended systems".Journal of the American Chemical Society.105 (11):3528–3537.doi:10.1021/ja00349a027.
^Dronskowski, Richard; Bloechl, Peter E. (2002-05-01). "Crystal orbital Hamilton populations (COHP): energy-resolved visualization of chemical bonding in solids based on density-functional calculations".The Journal of Physical Chemistry.97 (33):8617–8624.doi:10.1021/j100135a014.
