Resonance energy Hiickel method

One of the more useful predicative applications of the relatively crude Hiickel method has been to illustrate quantitatively the effect of benzenoid annelation on the resonance energies of furan and thiophene. The results are summarized in Figure 1. As expected, thiophenes are more stable than the corresponding furans and 3,4-fusion results in less stable compounds than 2,3-fusion (77CR(C)(285)42l). 

In agreement with the Hiickel rule those annulenes and dehydroannulenes which contain (4 n + 2) 77 electrons and a reasonably planar carbon skeleton appear to be aromatic. Aromaticity in annulenes is usually equated with positive resonance energy and the absence of bond alternation. The most direct method of measuring bond alternation is by single crystal X-ray diffraction. Unfortunately this method has been applied in only a few cases. 

Earlier definition of resonance energies comes down to an evaluation of the QMRE within the framework of the Hiickel MO method (HMO) (61MI1 75MI1 86MI1). Hiickel resonance energy (HRE) is defined as... 

Finally, if we abandon Hiickel s topological approach altogether and consider more elaborate quantum-mechanical approaches, the concept of aromaticity derived purely from a consideration of -electrons becomes blurred and tends to disappear completely. In fact, allelectron methods allow the calculation of aromatic properties (Section V,B) of a given substance without introducing explicitly the concept of aromaticity. Certain authors, notably Dewar,19 have published resonance energies derived from self-consistent field molecular-orbital (SCF-MO) calculations, and these could be used as a measure of aromaticity. 

The only satisfactory approach to this problem at present involves the use of perturbations methods. Attempts to calculate resonance energies indirectly, by comparing calculated total energies of a compound with that of a single classical structure for it, have proved ineffective. Thus calculations of this kind have failed to account for the special stability of monocyclic compounds containing 4n + 2 electrons (Hiickel s rule), and they predict that all the compounds XVII-XXIII should be aromatic whereas the only one that is aromatic is azulene (XXII). 

To synthesize a new electronic system, tri-heteroatom-substituted cyclopropenium, we thought it useful to examine beforehand the stability of the proposed trisubstituted cyclopropenium system by quantum mechanical methods (or, in other ways). A simple Hiickel molecular orbital calculation for the tri-heteroatom-substituted cyclopropenimn cation 3) gave the results shown in Table 1, where qc and -pc-c denote the n electron density on the ring carbon atom and the n bond order between ring carbon atoms, respectively. Ai it (additional resonance energy) as the measure of stability of 3) is a value obtained as a resonance energy difference between 3 a) and 3 b). 

Two major contributions to the 7t-energy change in the ring-cleavage reaction leading to a PAHTC need to be included in the model. In a simplified Pariser-Parr-Pople (PPP) method with Hiickel orbitals as the basis [33], the PAHTC is an arylmethyl cation, with resonance energy... 

---