# Chemical bond

The chemical bond is a physical-chemical phenomenon by which two or more atoms or ions firmly to chemical compounds are bound to each other. This is based on the fact that it is energetically more favorable for most atoms or ions to be bound to suitable binding partners instead of being present as a single (unbound) particle.

The basis of the bond are electrostatic interactions or interactions between the electrons of two or more atoms. In many cases, both binding mechanisms play a role. Parameters which are important for describing a bond and which can be investigated experimentally are the bond length as a measure of the distance between two atomic nuclei and the bond energy , which indicates the strength of a bond. The chemical bond is the basis for molecules and thus chemical compounds to be able to form, and is therefore one of the most important foundations of chemistry .

Chemical bonds can be divided into different types. In ionic crystals the ionic bond based on electrostatic interactions predominates, in metals the metallic bond based on freely moving electrons . The formation of molecules and complexes , on the other hand, is based on localized bonds that are based on the formation of electron pairs . Within the localized electron pair bonds , a distinction is often made between the covalent bond , in which each atom contributes one electron to the bond, and the coordinative bond in complexes, in which an electron pair of a ligand interacts with an empty orbital of the central atom. In special cases, multi-center bonds can occur. Metallic, ionic and covalent bonds are idealizations of chemical bonds.

Sometimes weak interactions, such as the Van der Waals interactions , dipole interactions and the hydrogen bond are counted among the chemical bonds. However, these are not strong chemical bonds, but rather weak forces of attraction that act between individual molecules.

For the description of the bonds in molecules, various theories have been put forward in theoretical chemistry , but they are all only as exact as possible approximations of the actual bond situation. They include the valence structure and molecular orbital theory .

Bonds can be split by supplying energy, for example in the form of heat or light . The resulting individual atoms or molecules often have a high tendency to bond again. The rebonding can take place at the previously cleaved site, or it takes place at other atoms or molecules. This is a basis for chemical reactions .

## history

Linus Pauling received the Nobel Prize in Chemistry in 1954, among other things, for his work on chemical bonding.

The development of various theories on chemical bonding is closely related to the development of theories and experiments on the shape of the individual atom . The first concrete theories have been after the discovery of the electron by JJ Thomson established the 1897th In his atomic model , Thomson imagined that the chemical bonds are based on electrostatic forces that are created by the transfer from one atom to another. This initially led to the assumption that chemical bonds must always have a polar structure.

Due to the properties of organic compounds, which could not be explained by polar bonds, and experiments with channel rays , it soon became clear that there must also be a non-polar bond. Gilbert Lewis first hypothesized in 1916 that the non-polar bond is based on paired electrons. This theory was also compatible with the Rutherford and Bohr atomic models , which had since replaced Thomson's model.

With the development of quantum mechanics and above all the formulation of the Schrödinger equation by Erwin Schrödinger in 1926, more precise theories of bonding could be established. The first quantum mechanical theory was developed with the valence structure theory in 1927 by Walter Heitler and Fritz London . The original theory was initially only valid for the simplest molecule, the H 2 + ion made up of two protons and one electron. Linus Pauling expanded the theory extensively by introducing the orbital and hybridization so that the theory could be applied to more complicated molecules.

Also in 1927, Friedrich Hund and Robert Mulliken established the more precise molecular orbital theory . This, too, was initially only applicable to simple molecules, but was gradually expanded, for example in 1930 by Erich Hückel by a more detailed explanation of multiple bonds with the explanation of the π bond.

After the basic quantum mechanical theories were established, various researchers tried to explain phenomena observed in organic or inorganic chemistry through these theories. Important examples are the ligand field theory for complexes , which was published in 1951 by Hermann Hartmann and FE Ilse and 1968 by Robert B. Woodward and Roald Hoffmann established Woodward-Hoffmann rules that allow a specific type of organic reactions, pericyclic reactions based on the Molecular orbital theory could be understood.

With the development of the computer from around 1950, more complicated theoretical calculations about chemical bonds became possible. An important development for this was, among others, the Roothaan-Hall equations by Clemens CJ Roothaan and George G. Hall in 1951, which are important in the Hartree-Fock method . From 1964 Walter Kohn finally developed another possibility for the theoretical calculation of the chemical bond with the density functional theory . For this he received the Nobel Prize in Chemistry in 1998.

## Ionic bond

Stylized ion lattice ( sodium chloride structure)

The ionic bond is an omnidirectional bond with a long range that has the same strength in all spatial directions. It is the predominant type of bond in salts , i.e. compounds of metals and non-metals that are periodically arranged in lattices. When metals and non-metals react, the large electronegativity difference results in a transfer of valence electrons of the metal to the non-metal and thus to electrically charged atoms, the so-called ions . The greater the electronegativity difference, the more the valence electrons are transferred and the more ionic the bond. However, with all ionic bonds there are also covalent parts of the bond. In the case of weak differences, there is only a slight transfer and it is necessary to take both parts into account when describing the bond.

Electrostatic interactions between the differently charged ions are primarily responsible for the bond in ion crystals . In theory, the energetic structure can be described well with the lattice energy . For this purpose, the attractive and repulsive forces between the ions, as well as the repulsion of the penetrating electron shells, are included and the Coulomb's law is taken into account. The type of grid is also included via the Madelung constant .

The ionic bond is a strong bond. Typical values ​​for lattice energies of ionic substances are 787 kJ / mol (8.2  eV ) for sodium chloride and 3850 kJ / mol (39.9 eV) for the more highly charged magnesium oxide (determined using the Born-Haber cycle ). This causes the high melting temperatures of many ionically structured substances. Since the bond is undirected, it is not stronger than many covalent bonds that only work within a molecule and not between the molecules of a substance. The electrostatic nature of the ionic bond causes the brittleness of many ion crystals, since when there is a shift between the ions, ions with the same charge easily adjoin each other, which repel each other and thus burst the crystal apart.

## Covalent bond

Typical structural formula (here acetone )

The covalent bond is the bond that predominates in non-metal compounds and complexes . In contrast to the ionic bond, it is directed and bound to a specific point between two individual atoms. Exceptions are the multicenter bonds , in which three or more atoms are covalently bonded, and the delocalized π-bonds , in which several bonds are fused into a single cloud of electrons.

Covalent bonds are usually based on a so-called electron pair , which is formed from the valence electrons of the atoms involved. To represent a covalent bond in a chemical formula, it is symbolized in the Lewis formula by a line, sometimes by two dots. Theoretically, the covalent bond is explained with two different theories, the molecular orbital and the valence structure theory. Older theories for complexes are the crystal field and ligand field theory , but the bonding relationships in complex compounds can be more precisely predicted by the molecular orbital theory.

The strength of a covalent bond depends on the type of bond, the atoms involved and the bond length . The strongest covalent bonds are the short triple bonds of elements of the second period such as carbon , nitrogen or oxygen , so the dissociation energy of a nitrogen-nitrogen triple bond is 941.7 kJ / mol (9.8 eV). Binding energies for single bonds are generally between 150 and 500 kJ / mol (about 1.5-5 eV), for double bonds binding energies are typically 500-800 kJ / mol (5-8 eV) for the second period (OO double bond : 493.6 kJ / mol, CO double bond: 798.9 kJ / mol), for the weaker double bonds of the higher periods below.

### Valence structure theory

The valence structure theory tries to describe a bond quantum mechanically . It is first for the hydrogen molecule with two protons and two electrons with different spin have been prepared and can be applied by additions and simplifications for complex molecules. For precise calculations, the wave functions of the electrons involved must first be established. These differ depending on the orbital in which the electron is located. In contrast to molecular orbital theory , the bonds are usually viewed individually and not the molecule as a whole.

In the simplest approximation, the total wave function Ψ of the H 2 molecule is seen as the product of the two wave functions of the two electrons.

${\ displaystyle \ Psi = \ Psi _ {\ mathrm {A (1)}} \ cdot \ Psi _ {\ mathrm {B (2)}}}$
A: 1st atom, B: 2nd atom, 1: 1st electron, 2: 2nd electron

This does not yet take into account the influence of the electrons on one another and therefore only applies to two isolated hydrogen atoms. For more precise results for bound atoms, the exchange energy must be included, which is due to the fact that the electrons are not localized on one atom, but rather have a probability of being located on both . The wave function is then called

${\ displaystyle \ Psi = \ Psi _ {\ mathrm {A (1)}} \ cdot \ Psi _ {\ mathrm {B (2)}} + \ Psi _ {\ mathrm {A (2)}} \ cdot \ Psi _ {\ mathrm {B (1)}}}$

written. With refinements, such as the inclusion of the shielding , a further approximation of the theory to the experimental value can be achieved.

Hybridization is an important concept that can be used to extend valence structure theory to more complex molecules . For this purpose, hybrid orbitals are formed from different types of orbitals. The best known are the sp 3 hybrid orbitals formed from one s and three p orbitals , which are mainly used to explain the bonding situation in carbon atoms . From the three p orbitals in the carbon atom and the 2s orbital, four identical sp 3 hybrid orbitals are formed, which are arranged in a tetrahedral manner and form bonds to neighboring atoms. It is also possible that only one or two of the p orbitals are involved in the hybridization. Then sp or sp 2 hybrid orbitals are formed. However, the concept of hybridization is not suitable for making predictions for compounds with a previously unknown spatial structure, since it was developed by starting from the spatial structure and mixing suitable orbitals in such a way that they describe the real structure. Therefore, conclusions about the hybrid orbitals can only be drawn from the spatial structure, but not vice versa.

Different types of bonding are distinguished depending on which orbitals are involved. If a bond is rotationally symmetrical about the core-core connection axis, it is a σ bond . This usually only consists of s and / or sp hybrid orbitals. In rare cases, a σ-bond is formed by two d orbitals. σ-bonds lie directly on the connecting axis between the atoms and have no nodal plane . p orbitals form π bonds that lie above and below the core connection axis and have a nodal plane. They are important for describing double and triple bonds . Very rarely, quadruple or quintuple bonds also occur which, in addition to σ and π bonds, have δ bonds formed from d orbitals .

### Molecular orbital theory

Molecular orbital scheme of  hydrogen  H 2
Molecular orbital scheme of  helium  He 2

Like valence structure theory, molecular orbital theory is a theory based on quantum mechanical principles. In this approach, however, the atoms are not considered separately, but a molecular orbital is first formed from the individual atomic orbitals, into which the electrons are classified according to Hund's rule and the Pauli principle .

Molecular orbitals are formed by a linear combination of the atomic orbitals involved ("LCAO method"). The linear combination always creates two molecular orbitals, one binding and one antibonding, which correspond to the addition or subtraction of the wave functions of the two atomic orbitals.

${\ displaystyle \ mathrm {\ \ Psi _ {b} = \ Psi _ {A} + \ Psi _ {B}}}$
Formation of the binding orbital
${\ displaystyle \ mathrm {\ \ Psi _ {a} = \ Psi _ {A} - \ Psi _ {B}}}$
Formation of the antibonding orbital

In the binding molecular orbital, the overlap integral is positive, which increases the electron density between the atoms. Due to the increased electron density, the nuclei are better shielded from one another, which is energetically favorable. A bond is therefore formed. In the antibonding, however, the overlap integral is negative, there is a nodal plane and a lower electron density between the nuclei. Since this is energetically unfavorable, no bond can form.

The energetically most favorable distance between two atoms and the energy gain in the bond compared to the unbound state, which determines the strength of the bond, can be determined in simple systems such as the H 2 and the H 2 + molecule according to the LCAO approximation (Linear Combination of Atomic Orbitals) can be calculated approximately using the potential . To do this, various attractive and repulsive factors must be taken into account. On the one hand, this is the mutual repulsion of the nuclei with the same charge and, in multi-electron systems such as the H 2 molecule, also the electrons among themselves. In contrast, the interactions between the positively charged nuclei and the negatively charged electrons have an attractive effect and thus result in an energy gain. A bond can only be stable if the potential curve calculated from these factors shows a minimum.

If the binding and antibonding orbitals in a molecular orbital are occupied by electrons, the bond order can be determined. For this purpose, the number of electrons in the antibonding molecular orbitals is subtracted from that in the binding molecular orbitals. If the theoretical bond order is zero , as in the case of the He 2 molecule, the molecule is unstable and the molecule is only held together by the weak Van der Waals interactions.

### Crystal field and ligand field theory

Splitting in the octahedral ligand field

The crystal field theory and its extension, the ligand field theory, try to explain the bonding situation in complexes , i.e. compounds with a metal center, usually a transition metal , and surrounding ligands , non-metal atoms or small molecules such as chloride or water.

In contrast to most molecules, the d orbitals of the metal atom play a decisive role in the bond in complexes. These are influenced in their energy by electrostatic interactions with the ligands. Depending on the geometry of the complex, the energy of the individual orbitals is increased to different degrees. Therefore, the degeneracy of the various orbitals is abolished and the orbital energies are split up, which is typical for each complex geometry. The strength of the splitting depends on the type of central ion, its oxidation state , the geometry of the complex and the type of ligands. Their different ability to split energy is specified in the spectrochemical series .

Many properties of complexes can be explained well with crystal field theory. In this way, the color, the magnetic properties and the stability of complexes can be predicted. The theory is limited, however, as the special strength of carbon monoxide as a ligand and the nephelauxetic effect cannot be explained using crystal field theory. More precise results are provided by the molecular orbital theory, in which not only the d orbitals of the central atom, but all orbitals involved are included in the calculations.

### Cohesion

The cohesiveness, i.e. the number of bonds that an atom can form, is determined by the orbitals. According to the noble gas rule, it is beneficial to form fully occupied or empty orbitals. In addition, the larger d and f orbitals form energetically favorable half-occupied orbitals (d 5 and f 7 configuration) in which all orbitals are occupied by an electron with a parallel spin . This is why an atom usually accepts as many electrons from neighboring atoms and forms bonds until it has reached the noble gas configuration . Since the maximum number of valence electrons that an atom of the second period can reach is eight, the octet rule is often used . For example, oxygen itself has six valence electrons and can absorb two more. Accordingly, it usually forms two bonds with other atoms; the stable oxide ion is doubly negatively charged by accepting two additional electrons.

## Metallic bond

In the metallic bond, in contrast to the ionic or covalent bond, there are freely moving electrons that are not bound to a specific atom. A simple model is that of the electron gas , in which the valence electrons form a negatively charged “gas” that completely surrounds the positively charged “atomic cores” of a metal lattice and takes care of the charge balance. The energy gain when a metallic bond is formed results mainly from the strong reduction in the kinetic energy of the particles in the electron gas. A stable metallic lattice results from the superposition and summation of the repulsion between the atomic cores and the attraction between the electron gas and the positively charged metal cations in an equilibrium distance between the atomic cores. In the solid state, these are arranged in the closest possible packing; about 60% of all metals crystallize in the hexagonal or cubic closest packing of spheres .

Ribbon model for conductors, semiconductors and non-conductors

A more precise model of the metallic bond is the band model derived from molecular orbital theory , which is mainly used to describe metals, but can also explain the properties of salts and semiconductors . In the process, binding and antibonding molecular orbitals are formed from the valence orbitals. Due to the Pauli principle , each atomic orbital has a slightly different energy, so that the molecular orbitals in the metal form broad bands. The bands formed from different molecular orbitals can overlap or band gaps are formed between them.

The electrons fill the bands up to a certain level, the Fermi level . If this lies within a band, almost no energy is required for an electron to transition from the occupied to the unoccupied level and a metal with the typical conductivity is present. If the Fermi level is at a band gap, this simple transition of an electron into the conduction band is no longer possible, the substance is not conductive. In the case of small band gaps, however, it is possible that the electrons can still overcome the gap due to an external supply of energy, for example in the form of heat, and such a substance becomes conductive. These substances are therefore called semiconductors.

## Weak ties

Weak bonds are sometimes also counted among the bonds, but are not actually bonds within molecules, but interactions that act between different molecules and can be broken with a low input of energy. As a rule, the kinetic energy of the atoms and molecules is sufficient to break such a bond again after a very short time.

The strongest of the weak bonds is the hydrogen bond . This forms between hydrogen atoms bound to nitrogen, oxygen or fluorine and, due to the large electronegativity difference, strongly positively partially charged hydrogen atoms and free electron pairs of these elements. The best-known compound that forms hydrogen bonds is water . But ammonia , hydrogen fluoride and other compounds that have NH or OH bonds, such as amino acids or DNA , are also capable of doing this. Due to its strength, the hydrogen bond strongly influences the properties of a substance. Their effect between water molecules is responsible, among other things, for the unusually high melting point of water.

Significantly weaker are the Van der Waals interactions , under which various phenomena such as the London forces and dipole-dipole interactions are summarized. These forces can be explained with spontaneous and induced dipoles or permanent dipoles that act between the molecules of the respective substances. Therefore, substances that contain non-polar molecules can also be present as liquids or solids under standard conditions.

## Theoretical calculations

For the investigation of bonds, in addition to the measurement of material properties, from which conclusions can be drawn about the properties of the bond, theoretical calculations are of great importance. The attempt is made to solve the Schrödinger equation established for a given system . Since these calculations can not be carried out in closed form even for simple molecular systems (at least without drastic approximations ) and are usually numerically complex, they are generally carried out with the aid of appropriate computer programs. The so -called ab initio methods are often used, which manage without empirical parameters. A method that is also used for more complex systems is the Hartree-Fock method . The aim here is to use the wave functions of the individual electrons to calculate the overall wave function of the electrons in the system, for example a molecule. For this purpose, the product of the individual orbitals is set up in the form of the Slater determinant . According to the Rayleigh-Ritz principle , the energy calculated using the Slater determinant is always greater than or equal to the actual energy of the system. The minimum energy can then be calculated by varying the orbitals. A number of so-called post-Hartree-Fock methods are based on the Hartree-Fock method, which is often insufficiently accurate for quantitative purposes .

Another theory that can be used to study bonds is density functional theory . In contrast to the Hartree-Fock method, it does not calculate with the wave functions of the individual electrons, but with the electron density .

## Measurement of binding properties

The type and strength of chemical bonds cannot be observed directly, but must be derived from the properties of a substance. Material properties that provide information on the nature of a bond are, for example, the melting point , gloss , optical properties or the ductility of a connection. A high melting point, brittleness or optical transparency are indications of an ionic bond, while metallic luster, opacity and ductility indicate metallic bonds. Covalently structured compounds, on the other hand, often have a low melting point and are accordingly often in a liquid or gaseous state. However, these properties are not clear-cut, so diamond has properties such as optical transparency and a high melting point, which indicate ionic bonds, but is made up entirely of covalent bonds.

For a more detailed investigation of the bond, the bond length and the bond energy as well as the geometry of a connection must be determined. Investigation methods for determining these properties differ depending on the type of connection and physical state. The most important methods for determining the bond length in solids are X-ray and neutron diffraction . They can be used to determine the positions of the individual atoms in the crystal and thus the distances and bond angles to one another. However, these methods can only be used with solids, not with liquids or gases. In the case of simply structured gaseous molecules, a bond length can be calculated from rotation spectra using the moment of inertia . Since the geometry also has an influence on the moment of inertia, it can also be derived from the rotational spectra.

The exact binding energy cannot be determined experimentally. It is approximately determined from the dissociation enthalpies of the simplest possible molecules; for exact theoretical values, additional factors such as zero point energy , rotational energies or volume work must be taken into account. Vibration spectroscopy can be used to determine the enthalpy of dissociation . Just like the binding energy of a covalent bond, the lattice energy of an ionic compound cannot be measured directly. It is calculated indirectly using the Born-Haber cycle .

Information about bonds can also be obtained from kinetic studies such as collision and scattering experiments in the molecular beam . These can be used to determine potential surfaces of molecules and thus the strength of a bond and the most favorable distance between two atoms.

## literature

• Chemical bonds. In: The chemistry side. Christoph Tornau, accessed on June 9, 2009 (extensive explanations on chemical bonds). (private side)
• Types of chemical bonds with explanations and illustrations. (private side)
• Video tutorials on chemical bonds - the most important types of bond as well as intermolecular interactions are explained in various videos (private page)

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 This article was added to the list of excellent articles on June 13, 2009 in this version .