Bond order

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In chemistry, bond order is a formal measure of the multiplicity of a covalent bond between two atoms. As introduced by Linus Pauling, bond order is defined as the difference between the numbers of electron pairs in bonding and antibonding molecular orbitals.

Bond order gives a rough indication of the stability of a bond. Isoelectronic species have the same bond order.[1]

Examples

The bond order itself is the number of

C–H bond order is 1 (single bond). In carbon monoxide, −C≡O+, the bond order between carbon and oxygen is 3. In thiazyl trifluoride N≡SF3, the bond order between sulfur and nitrogen is 3, and between sulfur and fluorine is 1. In diatomic oxygen O=O the bond order is 2 (double bond). In ethylene H2C=CH2 the bond order between the two carbon atoms is also 2. The bond order between carbon and oxygen in carbon dioxide O=C=O is also 2. In phosgene O=CCl2, the bond order between carbon and oxygen is 2, and between carbon and chlorine
is 1.

In some molecules, bond orders can be 4 (

gaseous phase
.

Non-integer bond orders

In molecules which have

one-electron bond, thus the bonding between the two hydrogen atoms has bond order of 0.5.[3]

Bond order in molecular orbital theory

In

bond strength and is also used extensively in valence bond theory
.

bond order = number of bonding electrons - number of antibonding electrons/2

Generally, the higher the bond order, the stronger the bond. Bond orders of one-half may 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).[7]

Hückel molecular orbital theory 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:[8][9][clarification needed
]

,

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

quantum mechanical definition for bond order has been debated for a long time.[11] A comprehensive method to compute bond orders from quantum chemistry calculations was published in 2017.[6]

Other definitions

The bond order concept is 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 between atoms i and j is experimentally described as

where d1 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:[12]

The value of the constant b depends on the atoms. This definition of bond order is somewhat

diatomic
molecules.

References

  1. ^ Dr. S.P. Jauhar. Modern's abc Chemistry.
  2. doi:10.1351/goldbook.B00705
  3. ISBN 978-0-521-83128-4
    .
  4. ISBN 978-0-19-927029-3
    .
  5. ISBN 978-0-273-74275-3
    .
  6. ^
    doi:10.1039/c7ra07400j
    .
  7. ^ Bruce Averill and Patricia Eldredge, Chemistry: Principles, Patterns, and Applications (Pearson/Prentice Hall, 2007), 409.
  8. ISBN 0-205-12770-3
    .
  9. doi:10.1098/rspa.1939.0006
    .
  10. doi:10.1021/ed065p674
    . Retrieved 5 December 2020.
  11. IUPAC Gold Book bond order
  12. doi:10.1021/ja01195a024
    .
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