# Covalent bond

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A covalent bond, also called a molecular bond, is a chemical bond that involves the sharing of electron pairs between atoms. These electron pairs are known as shared pairs or bonding pairs, and the stable balance of attractive and repulsive forces between atoms, when they share electrons, is known as covalent bonding. [1] [2] For many molecules, the sharing of electrons allows each atom to attain the equivalent of a full outer shell, corresponding to a stable electronic configuration. In organic chemistry, covalent bonds are much more common than ionic bonds. [3]

## Contents

Covalent bonding includes many kinds of interactions, including σ-bonding, π-bonding, metal-to-metal bonding,agostic interactions, bent bonds, and three-center two-electron bonds. [4] [5] The term covalent bond dates from 1939. [6] The prefix co- means jointly, associated in action, partnered to a lesser degree, etc.; thus a "co-valent bond", in essence, means that the atoms share "valence", such as is discussed in valence bond theory.

In the molecule H
2
, the hydrogen atoms share the two electrons via covalent bonding. [7] Covalency is greatest between atoms of similar electronegativities. Thus, covalent bonding does not necessarily require that the two atoms be of the same elements, only that they be of comparable electronegativity. Covalent bonding that entails sharing of electrons over more than two atoms is said to be delocalized.

## History

The term covalence in regard to bonding was first used in 1919 by Irving Langmuir in a Journal of the American Chemical Society article entitled "The Arrangement of Electrons in Atoms and Molecules". Langmuir wrote that "we shall denote by the term covalence the number of pairs of electrons that a given atom shares with its neighbors." [8]

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. [9] He introduced the Lewis notation or electron dot notation or Lewis dot structure, in which valence electrons (those in the outer shell) are represented as dots around the atomic symbols. Pairs of electrons located between atoms represent covalent bonds. Multiple pairs represent multiple bonds, such as double bonds and triple bonds. An alternative form of representation, not shown here, has bond-forming electron pairs represented as solid lines.

Lewis proposed that an atom forms enough covalent bonds to form a full (or closed) outer electron shell. In the diagram of methane shown here, the carbon atom has a valence of four and is, therefore, surrounded by eight electrons (the octet rule), four from the carbon itself and four from the hydrogens bonded to it. Each hydrogen has a valence of one and is surrounded by two electrons (a duet rule) – its own one electron plus one from the carbon. The numbers of electrons correspond to full shells in the quantum theory of the atom; the outer shell of a carbon atom is the n = 2 shell, which can hold eight electrons, whereas the outer (and only) shell of a hydrogen atom is the n = 1 shell, which can hold only two.

While the idea of shared electron pairs provides an effective qualitative picture of covalent bonding, quantum mechanics is needed to understand the nature of these bonds and predict the structures and properties of simple molecules. Walter Heitler and Fritz London are credited with the first successful quantum mechanical explanation of a chemical bond (molecular hydrogen) in 1927. [10] Their work was based on the valence bond model, which assumes that a chemical bond is formed when there is good overlap between the atomic orbitals of 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) bonds are the strongest covalent bonds and are due to head-on overlapping of orbitals on two different atoms. A single bond is usually a σ bond. Pi (π) bonds are weaker and are due to lateral overlap between p (or d) orbitals. A double bond between two given atoms consists of one σ and one π bond, and a triple bond is one σ and two π bonds.

Covalent bonds are also affected by the electronegativity of the connected atoms which determines the chemical polarity of the bond. Two atoms with equal electronegativity will make nonpolar covalent bonds such as H–H. An unequal relationship creates a polar covalent bond such as with H−Cl. However polarity also requires geometric asymmetry, or else dipoles may cancel out resulting in a non-polar molecule.

## Covalent structures

There are several types of structures for covalent substances, including individual molecules, molecular structures, macromolecular structures and giant covalent structures. Individual molecules have strong bonds that hold the atoms together, but there are negligible forces of attraction between molecules. Such covalent substances are usually gases, for example, HCl, SO2, CO2, and CH4. In molecular structures, there are weak forces of attraction. Such covalent substances are low-boiling-temperature liquids (such as ethanol), and low-melting-temperature solids (such as iodine and solid CO2). Macromolecular structures have large numbers of atoms linked by covalent bonds in chains, including synthetic polymers such as polyethylene and nylon, and biopolymers such as proteins and starch. Network covalent structures (or giant covalent structures) contain large numbers of atoms linked in sheets (such as graphite), or 3-dimensional structures (such as diamond and quartz). These substances have high melting and boiling points, are frequently brittle, and tend to have high electrical resistivity. Elements that have high electronegativity, and the ability to form three or four electron pair bonds, often form such large macromolecular structures. [11]

## One- and three-electron bonds

Bonds with one or three electrons can be found in radical species, which have an odd number of electrons. The simplest example of a 1-electron bond is found in the dihydrogen cation, H+
2
. One-electron bonds often have about half the bond energy of a 2-electron bond, and are therefore called "half bonds". However, there are exceptions: in the case of dilithium, the bond is actually stronger for the 1-electron Li+
2
than for the 2-electron Li2. This exception can be explained in terms of hybridization and inner-shell effects. [12]

The simplest example of three-electron bonding can be found in the helium dimer cation, He+
2
. It is considered a "half bond" because it consists of only one shared electron (rather than two); [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, 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. [14] Chlorine dioxide and its heavier analogues bromine dioxide and iodine dioxide also contain three-electron bonds.

Molecules with odd-electron bonds are usually highly reactive. These types of bond are only stable between atoms with similar electronegativities. [14]

Modified Lewis structures with 3e bonds
Nitric oxide
Dioxygen

## Resonance

There are situations whereby a single Lewis structure is insufficient to explain the electron configuration in a molecule, hence a superposition of structures are needed. The same two atoms in such molecules can be bonded differently in different structures (a single bond in one, a double bond in another, or even none at all), resulting in a non-integer bond order. The nitrate ion is one such example with three equivalent structures. The bond between the nitrogen and each oxygen is a double bond in one structure and a single bond in the other two, so that the average bond order for each N–O interaction is 2 + 1 + 1/3 = 4/3.

### Aromaticity

In organic chemistry, when a molecule with a planar ring obeys Hückel's rule, where the number of π electrons fit the formula 4n + 2 (where n is an integer), it attains extra stability and symmetry. In benzene, the prototypical aromatic compound, there are 6 π bonding electrons (n = 1, 4n + 2 = 6). These occupy three delocalized π molecular orbitals (molecular orbital theory) or form conjugate π bonds in two resonance structures that linearly combine (valence bond theory), creating a regular hexagon exhibiting a greater stabilization than the hypothetical 1,3,5-cyclohexatriene.

In the case of heterocyclic aromatics and substituted benzenes, the electronegativity differences between different parts of the ring may dominate the chemical behaviour of aromatic ring bonds, which otherwise are equivalent.

### Hypervalence

Certain molecules such as xenon difluoride and sulfur hexafluoride have higher co-ordination numbers than would be possible due to strictly covalent bonding according to the octet rule. This is explained by the three-center four-electron bond ("3c–4e") model which interprets the molecular wavefunction in terms of non-bonding highest occupied molecular orbitals in molecular orbital theory and resonance of sigma bonds in valence bond theory.

### Electron deficiency

In three-center two-electron bonds ("3c–2e") three atoms share two electrons in bonding. This type of bonding occurs in electron deficient compounds like diborane. Each such bond (2 per molecule in diborane) contains a pair of electrons which connect the boron atoms to each other in a banana shape, with a proton (nucleus of a hydrogen atom) in the middle of the bond, sharing electrons with both boron atoms. In certain cluster compounds, so-called four-center two-electron bonds also have been postulated.

## Quantum mechanical description

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 [15] 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 of the molecule. [16] For valence bond theory, the atomic hybrid 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 a linear combination of atomic orbitals is performed first, followed by filling of the resulting molecular orbitals 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 and the understanding of reaction mechanisms. 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 of aromaticity, while simple valence bond theory incorrectly predicts that cyclobutadiene has a 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. [16] 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 while the simple valence bond approach overestimates it. [16]

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. Molecular orbitals are orthogonal, which significantly increases feasibility and speed of computer calculations compared to nonorthogonal valence bond orbitals. However, better valence bond programs are now available.

### Covalency from atomic contribution to the electronic density of states

In COOP, [17] COHP [18] and BCOOP, [19] evaluation of bond covalency is dependent on the basis set. To overcome this issue, an alternative formulation of the bond covalency can be provided in this way.

The center mass cm(n,l,ml,ms) of an atomic orbital |n,l,ml,ms, with quantum numbers n, l, ml, ms, for atom A is defined as

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

where gA
|n,l,ml,ms
(E)
is the contribution of the atomic orbital |n,l,ml,ms of the atom A to the total electronic density of states g(E) of the solid

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

where the outer sum runs over all atoms A of the unit cell. The energy window [E0,E1] is chosen in such a way that it encompasses all relevant bands participating in the bond. If the range to select is unclear, it can be identified in practice by examining the molecular orbitals that describe the electron density along the considered bond.

The relative position CnAlA,nBlB of the center mass of |nA,lA levels of atom A with respect to the center mass of |nB,lB levels of atom B is given as

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

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

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

where, for simplicity, we may omit the dependence from the principal quantum number n in the notation referring to CnAlA,nBlB.

In this formalism, the greater the value of CA,B, the higher the overlap of the selected atomic bands, and thus the electron density described by those orbitals gives a more covalent A–B bond. The quantity CA,B is denoted as the covalency of the A–B bond, which is specified in the same units of the energy E.

## Related Research Articles

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 electrostatic force of attraction between oppositely charged ions as in ionic bonds or through the sharing of electrons as in covalent bonds. The strength of chemical bonds varies considerably; there are "strong bonds" or "primary bonds" such as covalent, ionic and metallic bonds, and "weak bonds" or "secondary bonds" such as dipole–dipole interactions, the London dispersion force and hydrogen bonding.

Electronegativity, symbol χ, is a concept that describes the tendency of an atom to attract a shared pair of electrons towards itself. An atom's electronegativity is affected by both its atomic number and the distance at which its valence electrons reside from the charged nucleus. The higher the associated electronegativity number, the more an atom or a substituent group attracts electrons towards itself.

Ionic bonding is a type of chemical bonding that involves the electrostatic attraction between oppositely charged ions, and is the primary interaction occurring in ionic compounds. It is one of the main types of bonding along with covalent bonding and metallic bonding. Ions are atoms with an electrostatic charge. Atoms that gain electrons make negatively charged ions. Atoms that lose electrons make positively charged ions. This transfer of electrons is known as electrovalence in contrast to covalence. In the simplest case, the cation is a metal atom and the anion is a nonmetal atom, but these ions can be of a more complex nature, e.g. molecular ions like NH+
4
or SO2−
4
. In simpler words, an ionic bond results from the transfer of electrons from a metal to a non-metal in order to obtain a full valence shell for both atoms.

A quantum mechanical system or particle that is bound—that is, confined spatially—can only take on certain discrete values of energy, called energy levels. This contrasts with classical particles, which can have any amount of energy. The term is commonly used for the energy levels of electrons in atoms, ions, or molecules, which are bound by the electric field of the nucleus, but can also refer to energy levels of nuclei or vibrational or rotational energy levels in molecules. The energy spectrum of a system with such discrete energy levels is said to be quantized.

The octet rule is a chemical rule of thumb that reflects the observation that elements tend to bond in such a way that each atom has eight electrons in its valence shell, giving it the same electronic configuration as a noble gas. The rule is especially applicable to carbon, nitrogen, oxygen, and the halogens, but also to metals such as sodium or magnesium.

In chemistry, resonance is a way of describing bonding in certain molecules or ions by the combination of several contributing structures into a resonance hybrid in valence bond theory. It has particular value for describing delocalized electrons within certain molecules or polyatomic ions where the bonding cannot be expressed by one single Lewis structure.

Lewis structures, also known as Lewis dot diagrams, Lewis dot formulas,Lewis dot structures, electron dot structures, or Lewis electron dot structures (LEDS), are diagrams that show the bonding between atoms of a molecule and the lone pairs of electrons that may exist in the molecule. A Lewis structure can be drawn for any covalently bonded molecule, as well as coordination compounds. The Lewis structure was named after Gilbert N. Lewis, who introduced it in his 1916 article The Atom and the Molecule. Lewis structures extend the concept of the electron dot diagram by adding lines between atoms to represent shared pairs in a chemical bond.

In chemistry, Molecular orbital (MO) theory is a method for describing the electronic structure of molecules using quantum mechanics. Electrons are not assigned to individual bonds between atoms, but are treated as moving under the influence of the nuclei in the whole molecule. The spatial and energetic properties of electrons are described by quantum mechanics as molecular orbitals surround two or more atoms in a molecule and contain valence electrons between atoms. Molecular orbital theory, which was proposed in the early 20th century, revolutionized the study of bonding by approximating the states of bonded electrons—the molecular orbitals—as linear combinations of atomic orbitals (LCAO). These approximations are now made by applying the density functional theory (DFT) or Hartree–Fock (HF) models to the Schrödinger equation.

In chemistry, delocalized electrons are electrons in a molecule, ion or solid metal that are not associated with a single atom or a covalent bond. The term delocalization is general and can have slightly different meanings in different fields. In organic chemistry, this refers to resonance in conjugated systems and aromatic compounds. In solid-state physics, this refers to free electrons that facilitate electrical conduction. In quantum chemistry, this refers to molecular orbital electrons that have extended over several adjacent atoms.

In chemistry, valence bond (VB) theory is one of the two basic theories, along with molecular orbital (MO) theory, that were developed to use the methods of quantum mechanics to explain chemical bonding. It focuses on how the atomic orbitals of the dissociated atoms combine to give individual chemical bonds when a molecule is formed. In contrast, molecular orbital theory has orbitals that cover the whole molecule.

A hypervalent molecule (the phenomenon is sometimes colloquially known as expanded octet) is a molecule that contains one or more main group elements apparently bearing more than eight electrons in their valence shells. Phosphorus pentachloride (PCl5), sulfur hexafluoride (SF6), chlorine trifluoride (ClF3), the chlorite (ClO2) ion, and the triiodide (I3) ion are examples of hypervalent molecules.

In chemistry, orbital hybridisation is the concept of mixing atomic orbitals into new hybrid orbitals suitable for the pairing of electrons to form chemical bonds in valence bond theory. Hybrid orbitals are very useful in the explanation of molecular geometry and atomic bonding properties and are symmetrically disposed in space. Although sometimes taught together with the valence shell electron-pair repulsion (VSEPR) theory, valence bond and hybridisation are in fact not related to the VSEPR model.

In chemistry, the valence or valency of an element is a measure of its combining power with other atoms when it forms chemical compounds or molecules.

In chemistry, a formal charge (FC) is the charge assigned to an atom in a molecule, assuming that electrons in all chemical bonds are shared equally between atoms, regardless of relative electronegativity. When determining the best Lewis structure for a molecule, the structure is chosen such that the formal charge on each of the atoms is as close to zero as possible.

A non-covalent interaction differs from a covalent bond in that it does not involve the sharing of electrons, but rather involves more dispersed variations of electromagnetic interactions between molecules or within a molecule. The chemical energy released in the formation of non-covalent interactions is typically on the order of 1–5 kcal/mol (1000–5000 calories per 6.02 × 1023 molecules). Non-covalent interactions can be classified into different categories, such as electrostatic, π-effects, van der Waals forces, and hydrophobic effects.

In chemical bonding theory, an antibonding orbital is a type of molecular orbital (MO) that weakens the chemical bond between two atoms and helps to raise the energy of the molecule relative to the separated atoms. Such an orbital has one or more nodes in the bonding region between the nuclei. The density of the electrons in the orbital is concentrated outside the bonding region and acts to pull one nucleus away from the other and tends to cause mutual repulsion between the two atoms. This is in contrast to a bonding molecular orbital, which has a lower energy than that of the separate atoms, and is responsible for chemical bonds.

In chemistry, Bent's rule describes and explains the relationship between the orbital hybridization of central atoms in molecules and the electronegativities of substituents. The rule was stated by Henry A. Bent as follows:

Atomic s character concentrates in orbitals directed toward electropositive substituents.

The covalent radius of fluorine is a measure of the size of a fluorine atom; it is approximated at about 60 picometres.

A molecular orbital diagram, or MO diagram, is a qualitative descriptive tool explaining chemical bonding in molecules in terms of molecular orbital theory in general and the linear combination of atomic orbitals (LCAO) method in particular. A fundamental principle of these theories is that as atoms bond to form molecules, a certain number of atomic orbitals combine to form the same number of molecular orbitals, although the electrons involved may be redistributed among the orbitals. This tool is very well suited for simple diatomic molecules such as dihydrogen, dioxygen, and carbon monoxide but becomes more complex when discussing even comparatively simple polyatomic molecules, such as methane. MO diagrams can explain why some molecules exist and others do not. They can also predict bond strength, as well as the electronic transitions that can take place.

The charge-shift bond has been proposed as a new class of chemical bond that sits alongside the three familiar families of covalent, ionic bonds, and metallic bonds where electrons are shared or transferred respectively. The charge shift bond derives its stability from the resonance of ionic forms rather than the covalent sharing of electrons which are often depicted as having electron density between the bonded atoms. A feature of the charge shift bond is that the predicted electron density between the bonded atoms is low. It has long been known from experiment that the accumulation of electronic charge between the bonded atoms is not necessarily a feature of covalent bonds. An example where charge shift bonding has been used to explain the low electron density found experimentally is in the central bond between the inverted tetrahedral carbons in [1.1.1]propellanes. Theoretical calculations on a range of molecules have indicated that a charge shift bond is present, a striking example being fluorine, F2, which is normally described as having a typical covalent bond.

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