Bond order, defined

Stabilities of molecules can be qualitatively related to the bond order, defined as... 

The Pauling bond order (PBO) concept was introduced by L. Pauling, L. O. Brockway, and J. Y. Beach [1] (1935). The determination of the PBOs requires counting Kekule structures in GBSs. N. S. Ham [16] (1958) proved that, for a KBS, Pauling s bond order pu for neighbouring carbon atoms i, j equals the bond order defined by K. Ruedenberg [17] (1954) which results from LCAO-MO considerations further, he showed that ptJ is equal to the entry in position (i, j) of the inverse A 1 of the adjacency matrix A of the system (note that, by Eq. (2), det A = K2 > 0). 

The definition of free valence was originally given in terms of bond orders defined by resonance theory for a general account see ref. 7. 

Instead of the bond character of the V.B. method we have in this case the mobile bond order or double bond order defined by Coulson41 as p= - mcmicmj t ie bond between the atoms i andj again summed over all electrons in the occupied levels m. The double bond order runs from o for the pure single bond to 1 for a pure double bond. For benzene we find 0.667. We obtain with a factor 2 on account of the occupation of each level by two electrons (p. 277) ... 

These are descriptors for molecule bonds proposed with the aim of estimating the bond order defined in quantum-chemical theory or of generally defining bond weights so as to distinguish the bonds in a - molecular graph. 

Analogous to the topological atomic charge definition is that of topological bond orders, defined as the limit of... 

The bond order defined as half the difference between the number of bonding (A b) and the number of anti-bonding (iVa) electrons... 

There have been many attempts to build a link between modern electronic structure calculations and various intuitive models of chemical bonding. Among the concepts that proved to be especially useful in this respect is the idea of bond order and/or the bond index as a theoretical counterpart of the classical concept of bond multiplicity that reflects the number of shared electron pairs involved according to Lewis model in the bonding between the given pair of atoms. There is a plethora of various definitions of bond order but of speeial relevance for our purposes is the so-called Wiberg-Mayer bond order defined by eqn (l)... 

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