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 between a pair of atoms. For example, in diatomicnitrogen N≡N the bond number is 3, in acetylene the bond number between the two carbon atoms is also 3, and the bond order is 1. Bond number gives an indication of the stability of a bond. Isoelectronic species have same bond number. In molecules which have resonance or nonclassical bonding, bond number may not be an integer. In benzene, the delocalized molecular orbitals 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 number of 1.5. Furthermore, bond numbers of 1.1, for example, can arise under complex scenarios and essentially refer tobond strength relative to bonds with order 1.
In molecular orbital theory, bond order is defined as half the difference between the number of bonding electrons and the number of antibonding electrons 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. Generally, the higher the bond order, the stronger the bond. Bond orders of one-half may be stable, as shown by the stability of and .
The bond order concept used in molecular dynamics and bond order potentials. The magnitude of the bond order is associated with the bond length. According to Linus Pauling in 1947, the bond order is experimentally described as where is the single bond length, 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: The value of the constant b depends on the atoms. The above definition of bond order is somewhat ad hoc and only easy to apply for diatomic molecules. Hückel MO theory offers another approach for defining bond orders based on MO coefficients. Since the theory divides bonding into a sigma framework and a pi system, the Hückel definition is only applicable to planar molecules with delocalized π bonding. Assuming a bond order contribution of 1 from the sigma component it gives a total bond order of 1.67 for benzene rather than the commonly cited 1.5, showing some degree of ambiguity in how the concept of bond order is defined. 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.
