Benzene and Cyclohexatriene

This suggests, that in the delocalised calculation the formal single bonds still have some double bond character, as they have in 1,3,5-hexatriene. They lose this in the purely localised calculation. This throws some doubt on the clear interpretability of the delocalised calculation. However if a two-structure calculation is performed at the optimised geometry of cyclohexatriene, the weights according to Eq. (3) of the structures are quite similar in both models, viz. 0.74/0.26 for the delocalised calculations vs. 0.79/0.21 for the strictly localised ones. 

The calculations show that the resonance energy is the driving force behind the symmetrisation of benzene (cf. [62]). Indeed benzene is easy to distort to e.g. a cyclohexatriene geometry [61]. This, however, should not be construed to be an indication of the unimportance of resonance but, on the contrary, to be taken as a sign of its persistence (cf. [69]). 

A calculation using the delocalised orbital model yields a rectangular structure as expected [78], both with the two-structure and with the one-structure calculation. The bond lengths are 1.552 A and 1.367 A for the two-structure calculation and hardly different for the one-structure calculation. The resonance energy is quite small (-0.98 kcal/mol). 

In order to see if it is possible to neutralise this effect of the a-system we performed a second calculation which used localised orbitals for the a-system as well as for the Tt-system. In this calculation one perfect-pairing structure was used for the C-C bonds of the a-system. All orbitals were localised on the C-H fragments. Doubly occupied orbitals were used for the C-H bonds, and strictly localised singly occupied orbitals for the C-C bonds. This calculation again yields a rectangular geometry with a much lower resonance energy. The bond 

We may conclude that the relative strengths of the a- and the rc-bonds determine the geometry of cyclobutadiene. For relatively weak rc-bonds, the resonance, together with the a-bonds, prevails to yield a square geometry. With stronger rc-bonds or weaker a-bonds the, expected, rectangular structure is produced. 

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See also in sourсe #XX -- [ , ]

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