Ring Bond Orders

There have been few modifications of the Pauling bond order, but in contrast to hybrid orbitals, it took 80 years for the arrival in 2014 of the ring bond order, which is an important and simple generalization of the Pauling bond order. As we will see. 

FIGURE 11.7 Ring bond orders for smaller benzenoid hydrocarbons. 

FIGURE 11.8 Calculation of the average C=C ring content for tetracene. 

---

From Reference 167, using the CI/SINDOl method. Bond lengths in A, bond angles in degrees. Aromaticity index determined by the lowest ring bond order. 

Bird aromaticity index (I) - An index of aromatic character based on a statistical evaluation of the extent of variation of ring bond orders compared to those of the nondelocalized Kekule structure. Bond orders are determined from experimentally determined bond lengths, or from accurate calculated values. The index was introduced for five-membered ring (7S) in 1985 by Clive Bird and subsequently extended to six-membered rings If) and bicyclic systems (7S,6 and 766). A universal index 7a unifies the approach (7a = 76 = 1.235 7s = 1.840 76,6 = 2.085 I tf) <1992T335>. For examples see Sections 2.24.2.3, 2.34.2.3, and 244.2.3. 

A Bird aromaticity index (7 ), introduced in 1992, based on the extent of variation of ring bond orders, is directly proportional to resonance energy <92T335>. 

BO = bond order of ring s bond SBO = sum of bond orders BOD = sum of bond order deviation from an average ring bond order. The second re-bond is not a part of the ring re-bonds and should be excluded if BOi = 1.359 then SBO = 8.292 and BOD = 0.19... 

ABO = average pyrrole ring bond order X = some of the ring bond orders or sum of deviation from average ring bond order. 

The aromatic character of benzo[6]-fused heterocycles was evaluated through uniformity of their ring bond order (Table 19). It is very interesting to mention that little aromatic stability for benzene is lost by [6] fusing with furan, pyrrole. 

BO = bond order BOD = bond orders or sum bond ring bond order. 

For the benzo[c]-fused heterocycles presented in Table 20, the same interesting features are possessed. All the heterocycles have a much more uniform ring bond order than their benzo[6] isomers. Benzene bond order uniformity here is considerably more disrupted by the presence of the five-membered heterocycle (Table 20). According to the ring s bond orders, the most uniform heterocycle is benzo[c]pyrrole with a total bond order deviation of 1.718. 

Now we would like to use a transition state ring bond order uniformity (n-molecular orbital delocalization) as a measure of its stability, and therefore the selectivity between two or more isometric transition state structures. A view that transition state structures can be classified as aromatic and antiaromatic is widely accepted in organic chemistry [54], A stabilized aromatic transition state will lead to a lower activation barrier. Also, it can be said that a more uniform bond order transition state will have lower activation barriers and will be allowed. An ideal uniform bond order transition state structure for a six-membered transition state structure is presented in Scheme 4. According to this definition, a six-electron transition state can be defined through a bond order distribution with an average bond order X. Less deviation from these ideally distributed bond orders is present in a transition state which is more stable. Therefore, it is energetically preferred over the other transition state structures. 

This bond order deviation from an ideal transition state structure to an example of cyclopropene added to a benzo-fused heterocycle may now be applied. Before we exEunine bond order deviation from an ideal transition state, we can take a look at the sums of rings bond order in the transition state structures. To simplify this picture, we will focus only on exo transition state structures between cyclopropene and benzo[c]heterocycles. Previously, we mentioned that the Diels-Alder reaction with benzo[c]heterocycles as dienes is a HOMO controlled diene reaction, therefore, an electron rich (higher sum of bond order) transition state structure should be energetically preferred. If this is the case, the order of reactivity should be benzo[c]furan, benzo[c]thiophene, and then benzo[c]pyrrole, which is exactly the same as determined on the basis FMO energy change (Table 23). 

Another static approach that can give us the relative reactivity of heterocycles as dienes for Diels-Alder reactions is evaluation of their aromatic stability through the ring bond order uniformity. If, for a moment, we examine reactivity of the heterocycle on the basis of FMO energy gap with cyclopropene as a dienophile, it is obvious that the most reactive heterocycle is 1,3-thiazole. It had a FMO energy gap of only 9.609 eV (Table 26). That finding is almost... 

Table 27. The ring bond orders and bond order deviation for heterocycles with two...

CPD = cyclopentadiene BOx-Y = bond order between atoms X and Y in the heterocycle ring SBO = sum of ring bond orders ABO = average bond order BOD = sum of bond order deviation from the average ring bond order. 

A new approach that we would like to introduce here to evaluate the reactivity of aromatic heterocycles that have asymmetric transition state structures is a comparison of the changes of the ring bond order between the heterocycle and... 

Average bond order deviation is computed from the formula 6X + 4 = sum of the ring bond orders as explained in Scheme 4 BOCx-Y = bond order change of bonds between atoms X and Y in the heterocycle ring required to achieve transition state structures SBOD = sum of the bond order deviations. 

The ring bond order deviation from uniformity partially agreed with the order of reactivity computed on the basis of FMO energy gaps. The least aromatic was 1,2,5-oxadiazole, while 1,2,3-thiadiazole should be most aromatic (Table 36). The order of reactivity was oxadiazole, triazole, thiadiazole in all 1,2,3-, 1,2,5- and 1,3,4-series of the three heteroatom heterocycles. Except for 1,3,4-oxadiazole, the two other 1,3,4- five-membered heterocycles were predicted to be more reactive than their 1,2,3- isomers (Table 36). The prediction that 1,2,5-oxadiazole was the most reactive heterocycle as a diene for Diels-Alder reaction was unacceptable due to the fact that two C-N bonds should be formed in the course of the reaction, which usually requires an exceptionally high activation barrier. 

---