https://doi.org/10.1351/goldbook.BT07005
The electron population in the region between atoms A and B of a molecular entity at the expense of @E01986@ in the immediate vicinity of the individual atomic centers. Different schemes of partitioning @E01986@ give rise to different definitions of bond orders. In the framework of the Mulliken population analysis, bond order is associated with the total overlap population, \[\text{q}_{\text{AB}}=2\ \sum _{\begin{array}{c} \mu \end{array}}^{\text{A}}\sum _{\begin{array}{c} \nu \end{array}}^{\text{B}}\text{P}_{\unicode[Times]{x3BC} \unicode[Times]{x3BD} }\ \text{S}_{\unicode[Times]{x3BC} \unicode[Times]{x3BD} }\] where \(\text{P}_{\unicode[Times]{x3BC}\unicode[Times]{x3BD}}\) and \(\text{S}_{\unicode[Times]{x3BC}\unicode[Times]{x3BD}}\) are respectively the elements of the density matrix and overlap matrix (see @O04357@). A large positive value of bond order signifies strong bonding between the atoms of the molecular entity, whereas negative values of \(\text{q}_{\text{AB}}\) imply that electrons are displaced away from the inter-atomic region and point to an @A00381@-bonding interaction. In @V06588@ bond theory, bond order is given by a weighted average of the formal bond orders (i.e. by the number of electron pairs in a given Lewis structure) between the atoms in the @R05326@ structures (see @RT07094@).
Source:
PAC, 1999, 71, 1919. (Glossary of terms used in theoretical organic chemistry) on page 1927 [Terms] [Paper]