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 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, 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. 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 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: , 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 and bond order potentials. The magnitude of the bond order is associated with the bond length. According to Linus Pauling in 1947, the