Chemical bond

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A chemical bond is the physical process responsible for the attractive interactions between atoms and molecules, and that which confers stability to diatomic and polyatomic chemical compounds. The explanation of the attractive forces is a complex area that is described by the laws of quantum electrodynamics. In practice, however, chemists usually rely on quantum theory or qualitative descriptions that are less rigorous but more easily explained to describe chemical bonding. In general, strong chemical bonding is associated with the sharing or transfer of electrons between the participating atoms. Molecules, crystals, and diatomic gases—indeed most of the physical environment around us—are held together by chemical bonds, which dictate the structure of matter.

Bonds vary widely in their strength. Generally covalent and ionic bonds are often described as "strong", whereas hydrogen bonds and van der Waals' bonds are generally considered to be "weak". Care should be taken because the strongest of the "weak" bonds can be stronger than the weakest of the "strong" bonds.

File:Electron dot.svg
Examples of Lewis dot-style chemical bonds between carbon C, hydrogen H, and oxygen O. Lewis dot depictures represent an early attempt to describe chemical bonding and are still widely used today.


Template:Chemical bonds Remembering that opposite charges attract, and that the electrons orbiting the nucleus are negatively charged and protons in the nucleus are positively charged, then imagine two atoms near each other which form a covalent bond.

In the simplest view of a so-called non polar/ polar covalent bond, one or more electrons—often a pair as in this example—is drawn into the space between the two atomic nuclei. Here the negatively charged electrons are attracted to the positive charges of both nuclei, instead of just their own. This overcomes the repulsion between the two positively charged nuclei of the two atoms and so this overwhelming attraction holds the two nuclei in a relatively fixed configuration of equilibrium, even though they will still vibrate at equilibrium position. In summary, covalent bonding involves sharing of electrons in which the positively charged nuclei of two or more atoms simultaneously attract the negatively charged electrons that are being shared.

In a simplified view of an ionic bond, the positive charge of one of the nuclei overwhelms the positive charge of the other nucleus, thus effectively transferring an electron from one atom to another, causing one atom to assume a net positive charge, and the other to assume a net negative charge. The bond then results from electrostatic attraction between atoms, and the atoms become positive or negatively charged ions.

All bonds can be explained by quantum theory, but in practice, simplification rules allow chemists to predict the strength, directionality, and polarity of bonds. The octet rule and VSEPR theory are two examples. More sophisticated theories are valence bond theory which includes orbital hybridization and resonance, and the linear combination of atomic orbitals molecular orbital method which includes ligand field theory. Electrostatics are used to describe bond polarities and the effects they have on chemical substances.


Early speculations into the nature of the chemical bond, from as early as the 12th century, supposed that certain types of chemical species were joined by a type of chemical affinity. In 1704, Issac Newton famously outlined his atomic bonding theory, in "Query 31" of his Opticks, whereby atoms attach to each other by some "force". Specifically, after acknowledging the various popular theories, in vogue at the time, of how atoms were reasoned to attach to each other, i.e. “hooked atoms”, “glued together by rest”, or “stuck together by conspiring motions”, Newton states that he would rather infer from their cohesion, that:

Particles attract one another by some force, which in immediate contact is exceedingly strong, at small distances performs the chemical operations, and reaches not far from the particles with any sensible effect.

In 1819, on the heels of the invention of the voltaic pile, Jöns Jakob Berzelius developed a theory of chemical combination stressing the electronegative and electropositive character of the combining atoms. By the mid 19th century, Edward Frankland, F.A. Kekule, A.S. Couper, A.M. Butlerov, and Hermann Kolbe, building on the theory of radicals, developed the theory of valency, originally called “combining power”, in which compounds were joined owing to an attraction of positive and negative poles. In 1916, chemist Gilbert N. Lewis developed the concept of the electron-pair bond, in which two atoms may share one to six electrons, thus forming the single electron bond, a single bond, a double bond, or a triple bond:


In Lewis' own words:

An electron may form a part of the shell of two different atoms and cannot be said to belong to either one exclusively.

That same year, Walther Kossel put forward a theory similar to Lewis' only his model assumed complete transfers of electrons between atoms, and was thus a model of polar bonds. Both Lewis and Kossel structured their bonding models on that of Abegg's rule (1904).

In 1927, the first mathematically complete quantum description of a simple chemical bond, i.e. that produced by one electron in the hydrogen molecular ion, H2+, was derived by the Danish physicist Oyvind Burrau.[1] This work showed that the quantum approach to chemical bonds could be fundamentally and quantitatively correct, but the mathematical methods used could not be extended to molecules containing more than one electron. A more practical, albeit less quantitative, approach was put forward in the same year by Walter Heitler and Fritz London. The Heitler-London method forms the basis of what is now called valence bond theory. In 1929, the linear combination of atomic orbitals molecular orbital method (LCAO) approximation was introduced by Sir John Lennard-Jones, who also suggested methods to derive electronic structures of molecules of F2 (fluorine) and O2 (oxygen) molecules, from basic quantum principles. This molecular orbital theory represented a covalent bond as a orbitals formed by combining the quantum mechanical Schrödinger atomic orbitals which had been hypothesized for electrons in single atoms. The equations for bonding electrons in multi-electron atoms could not be solved to mathematical perfection (i.e., analytically), but approximations for them still gave many good qualitative preditions and results. Most quantitative calculations in modern quantum chemistry use either valence bond or molecular orbital theory as a starting point, although a third approach, Density Functional Theory, has become increasingly popular in recent years.

In 1935, H. H. James and A. S. Coolidge carried out a calculation on the dihydrogen molecule that, unlike all previous calculation which used functions only of the distance of the electron from the atomic nucleus, used functions which also explicitly added the distance between the two electrons.[2] With up to 13 adjustable parameters they obtained a result very close to the experimental result for the dissociation energy. Later extensions have used up to 54 parameters and give excellent agreement with experiment. This calculation convinced the scientific community that quantum theory could give agreement with experiment. However this approach has none of the physical pictures of the valence bond and molecular orbital theories and is difficult to extend to larger molecules.

Valence bond theory

In the year 1927, valence bond theory was formulated which argued essentially that a chemical bond forms when two valence electrons, in their respective atomic orbitals, work or function to hold two nuclei together, by virtue of system energy lowering effects. In 1931, building on this theory, chemist Linus Pauling published what some consider one of the most important papers in the history of chemistry: “On the Nature of the Chemical Bond”. In this paper, building on the works of Lewis, and the valence bond theory (VB) of Heitler and London, and his own earlier work, he presented six rules for the shared electron bond, the first three of which were already generally known:

1. The electron-pair bond forms through the interaction of an unpaired electron on each of two atoms.
2. The spins of the electrons have to be opposed.
3. Once paired, the two electrons cannot take part in additional bonds.

His last three rules were new:

4. The electron-exchange terms for the bond involves only one wave function from each atom.
5. The available electrons in the lowest energy level form the strongest bonds.
6. Of two orbitals in an atom, the one that can overlap the most with an orbital from another atom will form the strongest bond, and this bond will tend to lie in the direction of the concentrated orbital.

Building on this article, Pauling’s 1939 textbook: On the Nature of the Chemical Bond would become what some have called the “bible” of modern chemistry. This book helped experimental chemists to understand the impact of quantum theory on chemistry. However, the later edition in 1959 failed to address adequately the problems that appeared to be better understood by molecular orbital theory. The impact of valence theory declined during the 1960's and 1970's as molecular orbital theory grew in popularity and was implemented in many large computer programs. Since the 1980s, the more difficult problems of implementing valence bond theory into computer programs have been largely solved and valence bond theory has seen a resurgence.

Molecular orbital theory

Molecular orbital theory (MO) uses a linear combination of atomic orbitals to form molecular orbitals which cover the whole molecule. These are often divided into bonding orbitals, anti-bonding orbitals, and non-bonding orbitals. A molecular orbital is merely a Schrödinger orbital which includes several, but often only two nuclei. If this orbital is of type in which the electron(s) in the orbital have a higher probability of being between nuclei than elsewhere, the orbital will be a bonding orbital, and will tend to hold the nuclei together. If the electrons tend to be present in a molecular orbital in which they spend more time elsewhere than between the nuclei, the orbital will function as an anti-bonding orbital and will actually weaken the bond. Electrons in non-bonding orbitals tend to be in deep orbitals (nearly atomic orbitals) associated almost entirely with one nucleus or the other, and thus they spend equal time between nuclei or not. These electrons neither contribute nor detract from bond strength.

Comparison of valence bond and molecular orbital theory

In some respects valence bond theory is superior to molecular orbital theory. When applied to the simplest two-electron molecule, H2, valence bond theory, even at the simplest Heitler-London approach, gives a much closer approximation to the bond energy, and it provides a much more accurate representation of the behavior of the electrons as chemical bonds are formed and broken. In contrast simple molecular orbital theory predicts that the hydrogen molecule dissociates into a linear superposition of hydrogen atoms and positive and negative hydrogen ions, a completely unphysical result. This explains in part why the curve of total energy against interatomic distance for the valence bond method lies above the curve for the molecular orbital method at all distances and most particularly so for large distances. This situation arises for all homonuclear diatomic molecules and is particularly a problem for F2, where the minimum energy of the curve with molecular orbital theory is still higher in energy than the energy of two F atoms.

The concepts of hybridization are so versatile, and the variability in bonding in most organic compounds is so modest, that valence bond theory remains an integral part of the vocabulary of organic chemistry. However, the work of Friedrich Hund, Robert Mulliken, and Gerhard Herzberg showed that molecular orbital theory provided a more appropriate description of the spectroscopic, ionization and magnetic properties of molecules. The deficiencies of valence bond theory became apparent when hypervalent molecules (e.g. PF5) were explained without the use of d orbitals that were crucial to the bonding hybridisation scheme proposed for such molecules by Pauling. Metal complexes and electron deficient compounds (e.g. diborane) also appeared to be well described by molecular orbital theory, although valence bond descriptions have been made.

In the 1930s the two methods strongly competed until it was realised that they are both approximations to a better theory. If we take the simple valence bond structure and mix in all possible covalent and ionic structures arising from a particular set of atomic orbitals, we reach what is called the full configuration interaction wave function. If we take the simple molecular orbital description of the ground state and combine that function with the functions describing all possible excited states using unoccupied orbitals arising from the same set of atomic orbitals, we also reach the full configuration interaction wavefunction. It can be then seen that the simple molecular orbital approach gives too much weight to the ionic structures, while the simple valence bond approach gives too little. This can also be described as saying that the molecular orbital approach is too delocalised, while the valence bond approach is too localised.

The two approaches are now regarded as complementary, each providing its own insights into the problem of chemical bonding. Modern calculations in quantum 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. However better valence bond programs are now available.

Bonds in chemical formulas

The 3-dimensionality of atoms and molecules makes it difficult to use a single technique for indicating orbitals and bonds. In molecular formulas the chemical bonds (binding orbitals) between atoms are indicated by various different methods according to the type of discussion. Sometimes, they are completely neglected. For example, in organic chemistry chemists are sometimes concerned only with the functional groups of the molecule. Thus, the molecular formula of ethanol (a compound in alcoholic beverages) may be written in a paper in conformational, 3-dimensional, full 2-dimensional (indicating every bond with no 3-dimensional directions), compressed 2-dimensional (CH3–CH2–OH), separating the functional group from another part of the molecule (C2H5OH), or by its atomic constituents (C2H6O), according to what is discussed. Sometimes, even the non-bonding valence shell electrons ( with the 2-dimensionalized approximate directions) are marked, i.e. for elemental carbon .'C'. Some chemists may also mark the respective orbitals, i.e. the hypothetical ethene−4 anion (\/C=C/\ −4) indicating the possibility of bond formation.

Strong chemical bonds

Typical bond lengths in pm
and bond energies in kJ/mol.

Bond lengths can be converted to Å
by division by 100 (1 Å = 100 pm).
Data taken from [1].
Bond Length
H — Hydrogen
H–H 74 436
H–C 109 413
H–N 101 391
H–O 96 366
H–F 92 568
H–Cl 127 432
H–Br 141 366
C — Carbon
C–H 109 413
C–C 154 348
C=C 134 614
C≡C 120 839
C–N 147 308
C–O 143 360
C–F 135 488
C–Cl 177 330
C–Br 194 288
C–I 214 216
C–S 182 272
N — Nitrogen
N–H 101 391
N–C 147 308
N–N 145 170
N≡N 110 945
O — Oxygen
O–H 96 366
O–C 143 360
O–O 148 145
O=O 121 498
F, Cl, Br, I — Halogens
F–H 92 568
F–F 142 158
F–C 135 488
Cl–H 127 432
Cl–C 177 330
Cl–Cl 199 243
Br–H 141 366
Br–C 194 288
Br–Br 228 193
I–H 161 298
I–C 214 216
I–I 267 151
S — Sulfur
C–S 182 272

These chemical bonds are intramolecular forces, which hold atoms together in molecules. In the simplistic localized view of bonding, the number of electrons participating in a bond (or located in a bonding orbital) is typically multiples of two, four, or six, respectively. Even numbers are common because electrons enjoy lower energy states, if paired. Substantially more advanced bonding theories have shown that bond strength is not always a whole number, depending on the distribution of electrons to each atom involved in a bond. For example, the carbons in benzene are connected to each other with about 1.5 bonds, and the two atoms in nitric oxide NO, are connected with about 2.5 bonds. Quadruple bonds are also well known. The type of strong bond depends on the difference in electronegativity and the distribution of the electron orbital paths available to the atoms that are bonded. The larger the difference in electronegativity, the more an electron is attracted to a particular atom involved in the bond, and the more "ionic" properties the bond is said to have ("ionic" means the bond electron(s) are unequally shared). The smaller the difference in electronegativity, the more covalent properties (full sharing) the bond has.

Covalent bond

Covalent bonding is a common type of bonding, in which the electronegativity difference between the bonded atoms is small or non-existent. Bonds within most organic compounds are described as covalent. See sigma bonds and pi bonds for LCAO-description of such bonding.

Polar covalent bond

Polar covalent bonding is intermediate in character between a covalent and an ionic bond.

Ionic bond

Ionic bonding is a type of electrostatic interaction between atoms which have a large electronegativity difference. There is no precise value that distinguishes ionic from covalent bonding but a difference of electronegativity of over 2.0 is likely to be ionic and a difference of less than 1.5 is likely to be covalent.[3] Ionic bonding leads to separate positive and negative ions. Ionic charges are commonly between −3e to +3e.

Coordinate covalent bond

Coordinate covalent bonding, sometimes referred to as dative bonding, is a kind of covalent bonding, in which the covalent bonding electrons originate solely from one of the atoms, the electron-pair donor or Lewis base but are approximately equally shared in the formation of a covalent bond. This concept is somewhat fading as chemists increasingly embrace molecular orbital theory. Examples of coordinate covalent bonding occur in nitrones and ammonia borane. The arrangement is different from an ionic bond in that the electronegativity difference is small, resulting in covalency. They are shown by an arrow unlike other bonds . This arrow shows its head towards the electron acceptor or lewis acid and its tail towards the lewis base. This bond is seen in ammonium.

Bent bonds

Bent bonds, also known as banana bonds, are bonds in strained or otherwise sterically hindered molecules those binding orbitals are forced into a banana-like form. Bent bonds are often more susceptible to reactions than ordinary bonds.

3c-2e and 3c-4e bonds

In three-center two-electron bonds 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 (shown as a more sharply angled section in the stick model at right), with a proton (nucleus of a hydrogen atom) in the middle of the bond, sharing electrons with both boron atoms. Three-center four-electron bonds also exist which explain the bonding in hypervalent molecules. In certain cluster compounds so-called four-center two-electron bonds also have been postulated. These double bonds are also referred to as π (pi) bonds with the usual single bonds being referred to as σ bonds.

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 hydrogen molecular 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. [4]

The simplest example of three-electron bonding can be found in the helium dimer cation, He2+, and can also be considered a "half bond" because, 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.[5]

Molecules with odd-electron bonds are usually highly reactive. These types of bond are only stable between atoms with similar electronegativities.[5]

Aromatic bond

In most cases, the locations of electrons cannot be simplified to simple lines (place for two electrons) or dots (a single electron). In aromatic bonds which occur in planar rings of atoms where the 4n+2 rule determines whether ring molecules would show extra stability.

In benzene, the prototypical aromatic compound, 18 bonding electrons bind 6 carbon atoms together to form a planar ring structure. The bond "order" (average number of bonds) between the different carbon atoms may be said to be (18/6)/2=1.5, but in this case the bonds are all identical from the chemical point of view. They may sometimes be written as single bonds alternating with double bonds, but the view of all ring bonds as being equivalently about 1.5 bonds in strength, is much closer to truth.

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.

Metallic bond

In a metallic bond, bonding electrons are delocalized over a lattice of atoms. By contrast, in ionic compounds, the locations of the binding electrons and their charges are static. Because of delocalization or the free moving of electrons, it leads to the metallic properties such as conductivity, ductility and hardness.

Intermolecular bonding

There are four basic types of bonds that can be formed between two or more (otherwise non-associated) molecules, ions or atoms. Intermolecular forces cause molecules to be attracted or repulsed by each other. Often, these define some of the physical characteristics (such as the melting point) of a substance.

Permanent dipole to permanent dipole

A large electronegativity difference between two strongly bonded atoms within a molecule causes a dipole to form (a dipole is a pair of permanent partial charges). Dipoles will attract or repel each other.

Hydrogen bond

In some ways this is an especially strong example of a permanent dipole, as above. However, in the hydrogen bond, the hydrogen proton comes closer to being shared between target and donor atoms, in a three-center two-electron bond like that in diborane. Hydrogen bonds explain the relatively high boiling points of liquids like water, ammonia, and hydrogen fluoride, compared with their heavier counterparts in the same periodic table column.

Instantaneous dipole to induced dipole (van der Waals)

Instantaneous dipole to induced dipole, or van der Waals forces, are the weakest, but also the most prolific—occurring between all chemical substances. Imagine a helium atom: At any one point in time, the electron cloud around the (otherwise neutral) atom can be thought to be slightly imbalanced, with momentarily more negative charge on one side. This is referred to as an instantaneous dipole. This dipole, with its slight charge imbalance, may attract or repel the electrons within a neighbouring helium atom, setting up another dipole. The two atoms will be attracted for an instant, before the charge rebalances and the atoms move on.

Cation-pi interaction

Cation-pi interactions occur between the localized negative charge of <math>\pi</math> orbital electrons, located above and below the plane of an aromatic ring, and a positive charge. Template:Chemical bonds

Electrons in chemical bonds

Many simple compounds involve covalent bonds. These molecules have structures that can be predicted using valence bond theory, and the properties of atoms involved can be understood using concepts such as oxidation number. Other compounds that involve ionic structures can be understood using theories from classical physics.

In the case of ionic bonding, electrons are mainly localized on the individual atoms, and electrons do not travel between the atoms very much. Each atom is assigned an overall electric charge to help conceptualize the molecular orbital's distribution. The forces between atoms (or ions) are largely characterized by isotropic continuum electrostatic potentials.

By contrast, in covalent bonding, the electron density within a bond is not assigned to individual atoms, but is instead delocalized in the MOs between atoms. The widely accepted theory of the linear combination of atomic orbitals (LCAO) helps describe the molecular orbital structures and energies based on the atomic orbitals of the atoms they came from. Unlike pure ionic bonds, covalent bonds may have directed anisotropic properties. These may have their own names, too, such as Sigma and Pi bond.

Atoms can also form bonds that are intermediates between ionic and covalent. This is because these definitions are based on the extent of electron delocalization. Electrons can be partially delocalized between atoms, but spend more time around one atom than another. This type of bond is often called polar covalent. See electronegativity.

Thus, the electrons in a molecular orbital (or 'in a polar covalent, or in a covalent bond') can be said to be either localized on certain atom(s) or delocalized between two or more atoms. The type of bond between two atoms is defined by how much the electron density is localized or delocalized among the atoms of the bonds


  1. Laidler, K. J. (1993) The World of Physical Chemistry, Oxford University Press, p. 347
  2. James, H. H. (1933). "The Ground State of the Hydrogen Molecule". Journal of Chemical Physics. American Institute of Physics. 1: 825–835. Unknown parameter |coauthors= ignored (help)
  3. Atkins, Peter (1997). Chemistry: Molecules, Matter and Change. New York: W. H. Freeman & Co. pp. 294–295. ISBN 0-7167-3107-X. Unknown parameter |coauthors= ignored (help)
  4. Weinhold, F.; Landis, C. Valency and bonding, Cambridge, 2005; pp. 96-100.
  5. 5.0 5.1 Pauling, L. The Nature of the Chemical Bond. Cornell University Press, 1960.

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