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chemistry Chemistry is the scientific study of the properties and behavior of matter. It is a natural science that covers the elements that make up matter to the compounds made of atoms, molecules and ions: their composition, structure, proper ...
, bond order, as introduced by Linus Pauling, is defined as the difference between the number of bonds and anti-bonds. The bond order itself is the number of
electron pair In chemistry, an electron pair or Lewis pair consists of two electrons that occupy the same molecular orbital but have opposite spins. Gilbert N. Lewis introduced the concepts of both the electron pair and the covalent bond in a landmark paper he ...
s ( covalent bonds) between two
atom Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons. Every solid, liquid, gas, a ...
s. For example, in diatomic
nitrogen Nitrogen is the chemical element with the symbol N and atomic number 7. Nitrogen is a nonmetal and the lightest member of group 15 of the periodic table, often called the pnictogens. It is a common element in the universe, estimated at se ...
N≡N, the bond order between the two nitrogen atoms is 3 (
triple bond A triple bond in chemistry is a chemical bond between two atoms involving six bonding electrons instead of the usual two in a covalent single bond. Triple bonds are stronger than the equivalent single bonds or double bonds, with a bond order o ...
). In acetylene H–C≡C–H, the bond order between the two
carbon Carbon () is a chemical element with the symbol C and atomic number 6. It is nonmetallic and tetravalent—its atom making four electrons available to form covalent chemical bonds. It belongs to group 14 of the periodic table. Carbon ma ...
atoms is also 3, and the C–H bond order is 1 ( single bond). In
carbon monoxide Carbon monoxide ( chemical formula CO) is a colorless, poisonous, odorless, tasteless, flammable gas that is slightly less dense than air. Carbon monoxide consists of one carbon atom and one oxygen atom connected by a triple bond. It is the simpl ...
, the bond order between carbon and oxygen is 3. In thiazyl trifluoride , the bond order between
sulfur Sulfur (or sulphur in British English) is a chemical element with the symbol S and atomic number 16. It is abundant, multivalent and nonmetallic. Under normal conditions, sulfur atoms form cyclic octatomic molecules with a chemical formul ...
and nitrogen is 3, and between sulfur and
fluorine Fluorine is a chemical element with the symbol F and atomic number 9. It is the lightest halogen and exists at standard conditions as a highly toxic, pale yellow diatomic gas. As the most electronegative reactive element, it is extremely reactiv ...
is 1. In diatomic
oxygen Oxygen is the chemical element with the symbol O and atomic number 8. It is a member of the chalcogen group in the periodic table, a highly reactive nonmetal, and an oxidizing agent that readily forms oxides with most elements ...
O=O the bond order is 2 ( double bond). In
ethylene Ethylene (IUPAC name: ethene) is a hydrocarbon which has the formula or . It is a colourless, flammable gas with a faint "sweet and musky" odour when pure. It is the simplest alkene (a hydrocarbon with carbon-carbon double bonds). Ethylene ...
the bond order between the two carbon atoms is also 2. The bond order between carbon and oxygen in
carbon dioxide Carbon dioxide ( chemical formula ) is a chemical compound made up of molecules that each have one carbon atom covalently double bonded to two oxygen atoms. It is found in the gas state at room temperature. In the air, carbon dioxide is t ...
O=C=O is also 2. In
phosgene Phosgene is the organic chemical compound with the formula COCl2. It is a toxic, colorless gas; in low concentrations, its musty odor resembles that of freshly cut hay or grass. Phosgene is a valued and important industrial building block, esp ...
, the bond order between carbon and oxygen is 2, and between carbon and
chlorine Chlorine is a chemical element with the symbol Cl and atomic number 17. The second-lightest of the halogens, it appears between fluorine and bromine in the periodic table and its properties are mostly intermediate between them. Chlorine i ...
is 1. In some molecules, bond orders can be 4 ( quadruple bond), 5 ( quintuple bond) or even 6 ( sextuple bond). For example, potassium octachlorodimolybdate salt () contains the
anion An ion () is an atom or molecule with a net electrical charge. The charge of an electron is considered to be negative by convention and this charge is equal and opposite to the charge of a proton, which is considered to be positive by conve ...
, in which the two Mo atoms are linked to each other by a bond with order of 4. Each Mo atom is linked to four
ligands In coordination chemistry, a ligand is an ion or molecule (functional group) that binds to a central metal atom to form a coordination complex. The bonding with the metal generally involves formal donation of one or more of the ligand's electr ...
by a bond with order of 1. The compound ( terphenyl)– CrCr–(terphenyl) contains two
chromium Chromium is a chemical element with the symbol Cr and atomic number 24. It is the first element in group 6. It is a steely-grey, lustrous, hard, and brittle transition metal. Chromium metal is valued for its high corrosion resistance and hard ...
atoms linked to each other by a bond with order of 5, and each chromium atom is linked to one terphenyl ligand by a single bond. A bond of order 6 is detected in ditungsten molecules , which exist only in a
gaseous phase Gas is one of the four fundamental states of matter (the others being solid, liquid, and plasma). A pure gas may be made up of individual atoms (e.g. a noble gas like neon), elemental molecules made from one type of atom (e.g. oxygen), or co ...
. Bond order gives an indication of the stability of a bond. Isoelectronic species have the same bond order. In molecules which have
resonance Resonance describes the phenomenon of increased amplitude that occurs when the frequency of an applied periodic force (or a Fourier component of it) is equal or close to a natural frequency of the system on which it acts. When an oscil ...
or nonclassical bonding, bond order may not be an
integer An integer is the number zero (), a positive natural number (, , , etc.) or a negative integer with a minus sign ( −1, −2, −3, etc.). The negative numbers are the additive inverses of the corresponding positive numbers. In the languag ...
. In
benzene Benzene is an organic chemical compound with the molecular formula C6H6. The benzene molecule is composed of six carbon atoms joined in a planar ring with one hydrogen atom attached to each. Because it contains only carbon and hydrogen atoms ...
, the delocalized
molecular orbital In chemistry, a molecular orbital is a mathematical function describing the location and wave-like behavior of an electron in a molecule. This function can be used to calculate chemical and physical properties such as the probability of find ...
s contain 6 pi electrons over six carbons, essentially yielding half a pi bond together with the sigma bond for each pair of carbon atoms, giving a calculated bond order of 1.5 (one and a half bond). Furthermore, bond orders of 1.1 (eleven tenths bond), 4/3 (or 1.333333..., four thirds bond) or 0.5 (
half bond A covalent bond is a chemical bond that involves the sharing of electrons to form electron pairs between atoms. These electron pairs are known as shared pairs or bonding pairs. The stable balance of attractive and repulsive forces between atom ...
), for example, can occur in some molecules and essentially refer to bond strength relative to bonds with order 1. In the nitrate anion (), the bond order for each bond between nitrogen and oxygen is 4/3 (or 1.333333...). Bonding in
dihydrogen cation The dihydrogen cation or hydrogen molecular ion is a cation (positive ion) with formula . It consists of two hydrogen nuclei ( protons) sharing a single electron. It is the simplest molecular ion. The ion can be formed from the ionization of ...
can be described as a covalent one-electron bond, thus the bonding between the two hydrogen atoms has bond order of 0.5.


Bond order in molecular orbital theory

In
molecular orbital theory In chemistry, molecular orbital theory (MO theory or MOT) is a method for describing the electronic structure of molecules using quantum mechanics. It was proposed early in the 20th century. In molecular orbital theory, electrons in a molec ...
, bond order is defined as half the difference between the number of bonding electrons and the number of
antibonding electron In chemical bonding theory, an antibonding orbital is a type of molecular orbital 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 n ...
s as per the equation below. This often but not always yields similar results for bonds near their equilibrium lengths, but it does not work for stretched bonds. Bond order is also an index of bond strength and is also used extensively in valence bond theory. :''bond order'' = Generally, the higher the bond order, the stronger the bond. Bond orders of one-half may be stable, as shown by the stability of (bond length 106 pm, bond energy 269 kJ/mol) and (bond length 108 pm, bond energy 251 kJ/mol).
Hückel molecular orbital theory Hückel or Huckel may refer to: * Erich Hückel (1896-1980), German physicist and chemist ** Debye–Hückel equation (named after Peter Debye and Erich Hückel), in chemistry, a method of calculating activity coefficients ** Hückel method (nam ...
offers another approach for defining bond orders based on molecular orbital coefficients, for planar molecules with delocalized π bonding. The theory divides bonding into a sigma framework and a pi system. The π-bond order between atoms ''r'' and ''s'' derived from Hückel theory was defined by Charles Coulson by using the orbital coefficients of the Hückel MOs: :p_ = \sum_i n_ic_c_, Here the sum extends over π molecular orbitals only, and ''ni'' is the number of electrons occupying orbital ''i'' with coefficients ''cri'' and ''csi'' on atoms ''r'' and ''s'' respectively. Assuming a bond order contribution of 1 from the sigma component this gives a total bond order (σ + π) of 5/3 = 1.67 for benzene, rather than the commonly cited bond order of 1.5, showing some degree of ambiguity in how the concept of bond order is defined. For more elaborate forms of molecular orbital theory involving larger basis sets, still other definitions have been proposed. A standard quantum mechanical definition for bond order has been debated for a long time. A comprehensive method to compute bond orders from quantum chemistry calculations was published in 2017.


Other definitions

The bond order concept is used in
molecular dynamics Molecular dynamics (MD) is a computer simulation method for analyzing the physical movements of atoms and molecules. The atoms and molecules are allowed to interact for a fixed period of time, giving a view of the dynamic "evolution" of th ...
and
bond order potential Bond order potential is a class of empirical (analytical) interatomic potentials which is used in molecular dynamics and molecular statics simulations. Examples include the Tersoff potential, the EDIP potential, the Brenner potential, the Finni ...
s. The magnitude of the bond order is associated with the bond length. According to Linus Pauling in 1947, the bond order between atoms ''i'' and ''j'' is experimentally described as :s_ = \exp where ''d''1 is the single bond length, ''dij'' is the bond length experimentally measured, and ''b'' is a constant, depending on the atoms. Pauling suggested a value of 0.353 Å for ''b'', for carbon-carbon bonds in the original equation: :d_ - d_ = 0.353~\text(s_) The value of the constant ''b'' depends on the atoms. This definition of bond order is somewhat ''
ad hoc Ad hoc is a Latin phrase meaning literally 'to this'. In English, it typically signifies a solution for a specific purpose, problem, or task rather than a generalized solution adaptable to collateral instances. (Compare with ''a priori''.) Com ...
'' and only easy to apply for diatomic molecules.


References

{{Chemical bonding theory
Order Order, ORDER or Orders may refer to: * Categorization, the process in which ideas and objects are recognized, differentiated, and understood * Heterarchy, a system of organization wherein the elements have the potential to be ranked a number of ...