What are electron-precise hydrogen compounds

Covalent bond - Covalent bond

Chemical bond in which pairs of electrons are shared between atoms

A Covalent bond is a chemical bond in which pairs of electrons are shared between atoms. These electron pairs are as common couples or Binding pairs known , and the stable balance of forces of attraction and repulsion between atoms when they share electrons is called a covalent bond. For many molecules, electron sharing allows each atom to achieve the equivalent of a complete outer shell, which corresponds to a stable electronic configuration. In organic chemistry, covalent bonds are much more common than ionic bonds.

The covalent bond also encompasses many types of interactions including σ-bond, π-bond, metal-metal bond, agostic interactions, bent bonds, three-center-two-electron bonds, and three-center-four-electron bonds . The term Covalent bond dates from 1939. The prefix co- medium connected together, in action, to a lesser extent together, Etc .; Thus, a "co-valent bond" essentially means that the atoms share a "valence" as discussed in valence bond theory.

In the H.
2 The hydrogen atoms share the two electrons via covalent bonds. The covalency between atoms with similar electronegativities is greatest. A covalent bond therefore does not necessarily require that the two atoms have the same elements, only that they have comparable electronegativity. A covalent bond in which electrons are distributed over more than two atoms is called delocalized.


Early concepts of covalent bonding arose from this type of image of the methane molecule. The covalent bond is implied in the Lewis structure by indicating electrons that are shared between atoms.

The term Covalency Regarding binding, it was first mentioned in an article by Irving Langmuir in 1919 American American Society magazine with entitled "The arrangement of electrons in atoms and molecules" is used. Langmuir wrote: "We'll be using the term Covalency denote the number of electron pairs that a given atom shares with its neighbors. "

The idea of ​​covalent bonding can be traced back a few years before 1919 to Gilbert N. Lewis, who described the sharing of electron pairs between atoms in 1916. He led the Lewis notation or Electron dot notation or Lewis point structure , in which valence electrons (those in the outer shell) are represented as dots around the atomic symbols. Electron pairs between atoms represent covalent bonds. Multiple pairs represent multiple bonds, such as double bonds and triple bonds. An alternative form of representation, which is not shown here, has bond-forming electron pairs, which are shown as solid lines.

Lewis suggested that an atom forms enough covalent bonds to form a complete (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 by the carbon itself and four by the hydrogen atoms attached to it. Every hydrogen has a valence of one and is surrounded by two electrons (a duet rule) - one of its own plus one from the carbon. The number of electrons corresponds to the full shells in the quantum theory of the atom; The outer shell of a carbon atom is that n = 2 shell that can hold eight electrons, while the outer (and only) shell of a hydrogen atom is the n = 1 shell that can only accommodate two.

While the idea of ​​shared electron pairs provides an effective qualitative picture of covalent bonding, quantum mechanics is required to understand the nature of these bonds and to 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. 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 the atoms involved.

Types of covalent bonds

Atomic orbitals (with the exception of s orbitals) have specific directional properties that lead to different types of covalent bonds. Sigma (σ) bonds are the strongest covalent bonds and are based on the frontal overlap of orbitals on two different atoms. A single bond is usually a σ-bond. Pi (π) bonds are weaker and are based on a 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 consists of one σ and two π bonds.

Covalent bonds are also influenced by the electronegativity of the connected atoms, which determines the chemical polarity of the bond. Two atoms with the same electronegativity form non-polar covalent bonds like H - H. An unequal relationship creates a polar covalent bond like H-Cl. However, the polarity also requires a geometric asymmetry, since otherwise dipoles can cancel each other out, which leads to a non-polar molecule.

Covalent structures

There are several types of structures for covalent substances, including single molecules, molecular structures, macromolecular structures, and giant covalent structures. Individual molecules have strong bonds that hold atoms together, but there are negligible forces of attraction between molecules. Such covalent substances are usually gases, for example HCl, SO 2 , CO 2 and CH 4 . There are weak forces of attraction in molecular structures. Such covalent substances are liquids with a low boiling temperature (such as ethanol) and solids with a low melting temperature (such as iodine and solid CO 2 ). 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 connected in layers (like graphite) or three-dimensional structures (like diamond and quartz). These substances have high melting and boiling points, are often brittle and tend to have a high specific electrical resistance. Elements with high electronegativity and the ability to form three or four electron pair bonds often form such large macromolecular structures.

One and three electron bonds

One or three electron bonds can be found in radical species that have an odd number of electrons. The simplest example of a 1-electron bond in the dihydrogen cation found, H +
2 . One-electron bonds often have about half the bond energy of a two-electron bond and are therefore referred to as "half bonds". There are exceptions, however: In the case of dilithium, the bond for the 1-electron Li is actually stronger +
2 than for the 2-electron Li 2 . This exception can be explained by hybridization and inner shell effects.

The simplest example of a three-electron bond is found in the helium dimer cation He +
2 . It is considered a "half bond" because it consists of only one common electron (rather than two); In molecular orbit, the third electron is in an anti-bond orbital that breaks half of the bond formed by the other two electrons. Another example of a molecule that contains two 2-electron bonds and a 3-electron bond is nitric oxide NO. It can also be assumed that the oxygen molecule O 2 has two 3-electron bonds and one 2-electron bond, which is responsible for its paramagnetism and its formal bond order of 2. 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 bonds are only stable between atoms with similar electronegativities.

Modified Lewis structures with 3e bonds


There are situations in which a single Lewis structure is insufficient to explain the electronic configuration in a molecule, which is why an overlay of structures is necessary. The same two atoms in such molecules can be bound differently in different structures (a single bond in one, a double bond in another, or none at all), which leads to 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 the average bond order for each NO interaction is 2 + 1 + 1 /. 3 = 4 /. 3.


If in organic chemistry a molecule with a planar ring follows Hückel's rule, according to which the number of π electrons of the formula 4 n + 2 equals (where n is an integer), it achieves additional stability and symmetry. In benzene, 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) or form conjugated π bonds in two resonance structures that connect linearly (valence bond theory), creating a regular hexagon that is more stabilized than the hypothetical 1,3,5-cyclohexatriene.

In the case of heterocyclic aromatics and substituted benzenes, the differences in electronegativity between different parts of the ring can dominate the chemical behavior of aromatic ring bonds that are otherwise equivalent.


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

Electron deficiency

In three-center two-electron bonds ("3c - 2e"), three atoms share two electrons in the bond. This type of bond occurs in borohydrides such as diborane (B. 2 H 6 ), which are often referred to as electron deficient because there are not enough valence electrons to form localized (2-centered 2-electron) bonds that connect all atoms. The more modern description of 3c-2e bonds, however, provides enough bond orbitals to connect all 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 that bind the boron atoms together in a banana shape, with a proton (the nucleus of a hydrogen atom) in the middle of the bond that shares electrons with both boron atoms. So-called four-center two-electron bonds have also been postulated in certain cluster compounds.

Quantum mechanical description

After the development of quantum mechanics, two basic theories were proposed to provide a quantum description of chemical bonding: valence bond theory (VB) and molecular orbital theory (MO). 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 of building the electron configuration of the molecule. For valence bond theory, the hybrid atomic orbitals are first filled with electrons to create a fully bonded valence configuration, followed by 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 the resulting molecular orbitals with electrons.

The two approaches are viewed as complementary and each offer their own insights into the problem of chemical bonding. Since valence bond theory builds the molecular wave function out of localized bonds, it is better suited for calculating bond energies and understanding reaction mechanisms. Since molecular orbital theory builds the molecular wave function from delocalized orbitals, it is better suited for calculating ionization energies and understanding spectral absorption bands.

On a qualitative level, both theories contain false predictions. The simple (Heitler-London) valence bond theory correctly predicts the dissociation of homonuclear diatomic molecules into separate atoms, while the 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 wave functions generated by both theories do not agree on a qualitative level and experimentally do not agree with the stabilization energy, they can be corrected by configuration interaction. This is done by combining the covalent valence bond function with the functions that describe all possible ionic structures or by combining the ground state function of the molecular orbital with the functions that describe 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 in such a way that the simple molecular orbital approach neglects the electron correlation, while the simple valence bond approach overestimates it.

Modern calculations in quantum chemistry usually assume a molecular orbital rather than a valence bond approach (but ultimately go far beyond that), not because of an intrinsic superiority in the former, but because the MO approach can be more easily adapted to numerical calculations. Molecular orbitals are orthogonal, which greatly increases the feasibility and speed of computational calculations compared to non-orthogonal valence bond orbitals. However, better valence bond programs are now available.

Covalency of the atomic contribution to the electronic density of states

For COOP, COHP and BCOOP, the assessment of the bond covalency depends on the basic set. In order to solve this problem, an alternative formulation of the binding covalency can be provided in this way.

The middle ground cm ( n , l , m l , m s ) of an atomic orbital | n , l , m l , m s ⟩ With quantum numbers n , l , m l , m s , for atom A is defined as

Where G A.
| n , l , m l , m s ( E. ) is the contribution of the atomic orbital | n , l , m l , m s ⟩ Of the atom A to the total electronic density of states G ( E. ) of the fixed

where the outer sum runs over all atoms A of the unit cell. The energy window [ E. 0 , E. 1 ] is chosen to include all relevant ligaments involved in the binding. If the region to choose is unclear, it can be identified in practice by examining the molecular orbitals, which describe the electron density together with the bond under consideration.

The relative position C. n A. l A. , n B. l B. the central mass of | n A. , l A. ⟩ Plane atom A with respect to the mean mass of | n B. , L. B. ⟩ Level atom B is given as

where the contributions of the magnetic and spin quantum numbers are summed up. According to this definition is the relative position of the A-planes with respect to the B-planes

where, for the sake of simplicity, we use the dependence on the principal quantum number n in the notation based on C. n A. l A. , n B. l B. refers, can omit.

In this formalism, the greater the value of, the greater the overlap of the selected atomic bands C. A, B and therefore the electron density described by these orbitals results in a more covalent AB bond. The size C. A, B is called Covalency the FROM Bond, which is given in the same units of energy E.

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