Bond order, as introduced by Linus Pauling, is defined as the difference between the number of bonds and anti-bonds.

The bond number itself is the number of electron pairs (bonds) between a pair of atoms. [1] For example, the bond number in diatomic nitrogen N≡N is 3, in ethene H− C≡C −H, the bond number between the two carbon atoms is also 3, and the C−H bonds order is 1. The number indicates the stability of a bond. Isoelectronic species have the same bond number. [2]

In molecules that contain resonance or non-classical bonds, the bond number may not be an integer. In benzene, the delocalized molecular orbital 6 involving pi electrons on six carbons essentially yields a pi bond by half, giving a calculated bond count of 1.5 to a pair of carbon atoms together with a sigma bond. Furthermore, a bond number of 1.1, for example, can arise under complex scenarios and essentially refers to the bonds strength relative to bonds with order 1.

## Bond order in molecular orbital theory

In molecular orbital theory, the bond order is defined as half the difference between the number of bonding electrons and the number of antibonding electrons according to the equation below. [3] [4] This often does not give the same result for bonds close to their equilibrium lengths, but it does work for stretched bonds. [5] Bond orders is also an index of bond strength and is also used extensively in valence bond theory.

\text{B.O.} = \frac{\text{number of bonding electrons} - \text{number of antibonding electrons}}{2}\

Generally, the higher the bond order, the stronger the bond. The bond orders of half can be stable, as shown by the stability of H+

2(bond length 106 pm, bond energy 269 kJ/mol) and He+2(bond length 108 pm, bond energy 251 kJ/mol). [6]

Hückel MO theory provides another approach to define bond orders based on MO coefficients, for planar molecules with delocalized bonding. The theory divides the bond into a sigma structure and a pi system. The -bond orders between atoms r and s derived from Hückel theory was defined by Charles Coulson using the orbital coefficients of Hückel MOs:

{\displaystyle p_{rs}=\sum _{i}n_{i}c_{ri}c_{si}},

Here the summation extends only to the π molecular orbitals, and n i is the number of electrons that occupy orbital i with coefficients crisis and c si on atoms r and s, respectively. Assuming a bond order contribution of 1 from the sigma component, this gives a total bond orders (σ+) of 5/3 = 1.67 for benzene instead of the commonly quoted 1.5, showing some degree of ambiguity as to whether the bond order How is the concept defined.

For more elaborate forms of MO theory involving a larger basis set, other definitions have been proposed. [9] A standard quantum mechanical definition for bond orders has long been debated. [10] A comprehensive method to calculate bond orders from quantum chemistry calculations was published in 2017.

## Other definitions

Bond order concepts as used in molecular dynamics and bond orders potential. The magnitude of bond orders is related to the length of the bond. According to Linus Pauling in 1947, the bond order between atoms i and j has been described experimentally by

s_{ij} = \exp{\left[ \frac{d_{1} - d_{ij}}{b} \right]}

where is the single bond length, the bond length is measured experimentally, and b is a constant, which depends on the atoms. Pauling suggested a value of 0.353 for b for the carbon-carbon bond in the original equation:

d_{1}d_{ij}

{\displaystyle d_{1}-d_{ij}=0.353~{\text{ln}}s_{ij}}

The value of the constant b depends on the atoms. This definition of bond orders is somewhat ad hoc and easy to apply only to diatomic molecules.

**frequently Asked question**

**What is bond order and what is its importance?**

Bond orders is a measure of the number of electrons involved in bonds between two atoms in a molecule. It is used as an indicator of the stability of a chemical bond. Generally, the higher the bond orders, the stronger the chemical bond. Most of the time, the bond orders is equal to the number of bonds between two atoms.

**What is meant by the term bond order?**

Bond order is defined as half of the difference in the number of electrons present in the bonding and anti-bonding orbitals of a molecule. If Na is equal to the number of electrons in one anti-bonding orbital, then Nb is equal to the number of electrons in one bonding orbital. Bond orders = 12(Nb−Na).

**What does bond order of 0.5 mean?**

The bond in the dihydrogen cation H+2 can be described as a covalent one-electron bond, thus the bond between two hydrogen atoms has a bond order of 0.5.

**Can bond order be negative?**

Since the number of anti-bonding electrons cannot exceed the number of bonding electrons, the bond orders can never be negative.

**Which is the strongest bond?**

Chemical bonds are much stronger than chemical bonds. Chemical bonds are difficult to break whereas hydrogen bonds are easily and rapidly formed and broken under normal biological conditions.

**What is a bond? Explain the types of bonds?**

Bonds are debt instruments, allowing various entities such as corporates and governments to raise funds from the market. These funds can be used for expansion of business or infrastructure development. In addition, entities can use the funds to meet the cost of long-term investments or to finance current expenditures.

**What is a bond, explain its characteristics and types?**

Bonds are fixed-income instruments that represent the value of a loan by an investor to a borrower. The issuer promises to pay specific interest for the life of the bond and the principal amount or face value at maturity. Bonds are usually issued by governments, corporations, municipalities and other sovereign bodies.

**How to place bond order?**

In molecular orbital theory, bond order is also expressed as half the difference between the bonding and antibonding electrons. For a direct answer, use this formula: Bond order = [(Number of electrons in bonding molecules) – (Number of electrons in antibonding molecules)]/2.