Ground State Stability Criteria

The graphical representation of specific 7r-bond energies Eb/N) for the different types of (pd) systems in Fig. 9 clearly shows the differences in stability. 

In Mobius-type 7r systems II, maximum values of Eb/N are observed for three-, four- and five-membered rings containing four 7r electrons and seven-, 

For Craig-type (pd systems III, all values of the specific delocalization energy are below the borderline separating aromatic and olefinic behaviour. 

The Mason-type (pd)n systems IV represent energetically the most favourable situation. Only the values for the odd-membered rings, which are the same as in Craig systems, are below the aromaticity limit. All the even-membered rings exhibit the favourable values of either the Hiickel or Mobius-type it systems. 

The case of (N+ 1) polyene chains by use of the linear combinations of the two d orbitals (6) may be read off from the graphical representation of the specific jr-bond energy of linear polyenes in Fig. 9, but shifted by one unit to the left. The pattern of behaviour is similar to the case of Craig-type it systems but with slightly lower numerical values. So in this kind of bonding there is also no special aromatic stabilization to be expected. 

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In the aromatic transition state approach, the basic criterion was that a reaction is allowed in the ground state if and only if there occurs in the transition state aromatic stabilization. This criterion led to the Dewar-Zimmerman selection rule (Equation 11.36), where p. i. = 0 signifies an even number of phase inversions, p. i. = 1 signifies an odd number of phase inversions, and N is the total number of electrons. 

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