The Mobile Bond Order

The relative a binding between pairs of adjacent nuclei is expected to be related to the coefficients of the atomic orbitals on the atoms between which the bond is formed. For butadiene we can qualitatively assess the binding between adjacent nuclei by inspection of the occupied orbitals as follows  

This approach has been put on a quantitative basis by Coulson through p j, the mobile bond order between adjacent atoms i and j. This is defined by the equation 

If we take the o- bonds as 1.0 bonds, then we can write for the total C-G bond orders  

37 A and rzj = 1.47 A. Rather good agreement has been reported between calculated and experimental bond lengths in polynuclear aromatic hydrocarbons. Typical results are shown on the next page for naphthalene and anthracene (with 

The Coulson ir-bond orders provide a useful check on the calculation of E, through the relation 

---

A typical example is given in the case of aromatic substitutions. The sum of the mobile bond orders of the bonds between the reaction center... 

An MO study of triplet coumarin has indicated that the mobile bond order for the 3,4-double bond decreases significantly on excitation (73MI22201). Furthermore, the electron density at C-3 is decreased but is increased at C-4 and hence an explanation of the orientational specificity of the photoaddition of coumarin to 1,1-diethoxyethylene is available (equation 1) (66TL1419). The reactivity of the 3- and 4-positions of triplet coumarin is also substantiated by the high spin-densities calculated for these positions (70JPC4234). 

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) ... 

Ruedenberg, K. (1958). Theorem on the Mobile Bond Orders of Alternant Conjugated Systems. J.Chem.Phys., 29,1232-1233. 

The number of electrons in the system is dEJdfi n/2, while a measure of the mobile bond order is ( ln)cEJc VC/2. This value is close to the accurate one, 0.79, for the graphene sheet with a coordination number 3. 

The skeletal configuration of polyphenyl molecules, that is, biphenyl, para-terphenyl, pora-quaterphenyl, and me/a-terphenyl, and the numbering of atoms in those molecules are shown in Fig. 1. In our previous papers we calculated the mobile bond orders and discussed the related phenomena for... 

Calculate the mobile bond orders for bicvclobuta-diene. (A check on the answers is available in Appendix I.)... 

---