Significance of Classical Valence Structures

The rules for aromaticity in the previous section do need qualification in one respect. We have throughout this chapter assumed implicitly that it is possible to write at least one classical structure, i.e., a structure obeying the rules of valence and stereochemistry, for each molecule. Now this is not necessarily the case. Consider, for example, triangulene (28). However one struggles, one cannot write a structure in which all the carbon atoms are linked in pairs by double bonds. There are always two nonadjacent atoms left over. The reason for this can be seen at once if we star the molecule (29). There are two more starred atoms (total 12) than unstarred ones (total 10). Since each double bond in a classical structure must by definition link a starred atom to an unstarred one, it is clearly impossible to pair up the atoms into doubly bonded pairs unless the numbers of starred and unstarred atoms are the same. 

It is not immediately apparent that this should make any difference, since we have shown that aromatic compounds are not in any case represented by classical structures. The bonds in them do not alternate in length in the way that the bonds in a polyene do and the n electrons in them cannot at all be regarded as localized in specific bonds. Yet in practice no stable hydro- 

The answer is given in the following theorem, which we will now prove  

An even AH for which no classical structure can be written is much less stable than a classicar isomer and also will exist as a biradical with two unpaired electrons. 

Since an NBMO has zero density at unstarred atoms, one would expect it to be unaffected by union at such points. This is in fact the case. In a perturbation treatment of union, all the terms for perturbations involving an 

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