Kekule type

Run benzene using HMO. Write out the full bond order matr ix, enter ing zero for any element off the tridiagonal. What is the bond order of benzene Is there any Kekule-type alternation in this model ... 

The circle m a hexagon symbol was first suggested by the British chemist Sir Robert Robinson to represent what he called the aromatic sextet —the six delocalized TT electrons of the three double bonds Robinson s symbol is a convenient time saving shorthand device but Kekule type formulas are better for counting and keeping track of electrons especially m chemical reactions... 

The analytical expression for the Kekule type has also been derived [16] but omitted here for simplicity. 

Another example is provided by [30] anmlene. Longuet-Higgins and Salem have shown that the observed visible and UV absorption spectrum and, in particular, the NMR proton chemical shifts of this molecule are very difficult to reconcile with the symmetrical nuclear configuration (Dg ) suggested by the superposition of the Kekule-type resonance structures. The hypothesis of a bond-length alternation of symmetry removes this difficulty. This indicates that the resonance between Kekule-type structures should be very much impeded also in this molecule. 

A theoretical explanation for such an anomalous phenomenon in certain nonalternant hydrocarbons has first been attempted, in case of pentalene, by Boer-Veenendaal and Boer followed by Boer-Veenen-daal et Snyder and Nakajima and Katagiri for other related nonalternant hydrocarbons. By making allowance for the effects of <7-bond compression, these authors have shown that a distorted structure resembling either of the two Kekule-type structures is actually energetically favored as compared with the apparently-full symmetrical one. 

Further, if a certain distorted structure and its countertype in which the bond-length variation is reversed are not equivalent (e. g., the two Kekule-type structures in IV), these two structures should be differentiated as a starting geometry. 

The effect of substituents on colour in substituted anthraquinones may be rationalised using the valence-bond (resonance) approach, in the same way as has been presented previously for a series of azo dyes (see Chapter 2 for details). For the purpose of explaining the colour of the dyes, it is assumed that the ground electronic state of the dye most closely resembles the most stable resonance forms, the normal Kekule-type structures, and that the first excited state of the dye more closely resembles the less stable, charge-separated forms. Some relevant resonance forms for anthraquinones 52, 52c, 52d and 52f are illustrated in Figure 4.3. The ground state of the parent compound 52 is assumed to resemble closely structures such as I, while charge-separated forms, such as structure II, are assumed to make a major contribution to the first excited state. Structure II is clearly unstable due to the carbocationic centre. In the case of aminoanthraquinones 52c and 52d, donation of the lone pair from the... 

This leads to modifications of the localized it orbitals. In benzene, for example, a Kekule localization which mixes the a and ir orbitals to form double banana bonds is preferred over the other equivalent ir localizations discussed. 60) In naphthalene a Kekule type structure is found similar to the one presently discussed, but different in that the (jtE2) are hybridized with corresponding o-CC bonding orbitals to form banana bonds, whereas the (ttC2 ) remains a pure jt orbital. 61 > While this is of interest in the discussion of the whole molecule, it is clear that certain intrinsic properties of the ir-electrons are more readily recognized by the localization which has been discussed here. We hope to discuss elsewhere localized orbitals involving a bonds in organic molecules. 

Solving the simultaneous equations (2a) and (2b) leads to y = 3 and t = n — 2, implying the presence of three B-B bonds and n — 2 B-B-B bonds in the boron skeleton. Since a deltahedron with n vertices has In — 4 faces, the n — 2 B-B-B bonds cover exactly half of the faces. In this sense a Kekule-type structure for the deltahedral boranes B H 2- has exactly half of the faces covered by B-B-B bonds just as a Kekule structure for benzene has half of its edges covered by C=C double bonds. In 1977 Lipscomb and co-workers [29] reported a variety of such Kekule-type localized bonding structures with the lowest energies for deltahedral boranes. These structures were computed using wave functions in the differential overlap approximation. 

However, in recent years this basis has been somewhat undermined due to a critical reappraisal of experimental data on the benzene structure which, surprisingly, showed that a rigorous experimental proof of the generally accepted D6h structure of benzene is actually nonexistent It turned out that the X-ray structural data for benzene are compatible not only with the crystallographically ordered Dbh structure but also with the disordered Dih model associated with superposition of Kekule-type benzene molecules rotated by 60° with respect to each other about the threefold axis, both static and dynamic types of disorder being conceivable [87AG(E)782]. It has been shown by very simple calculations that if the difference between the C—C and C=C bond lengths in the D3h form is... 

This conclusion, nevertheless, should not be considered categorical but it points to the necessity of careful consideration of the correlation between the AEdis value and the part of it that relates to cyclic electron delocalization. It has been shown by use of TRE calculations of aromatic benzene and antiaromatic cyclobutadiene molecules that in the case of benzene the distortion into a Kekule-type structure is characterized by a change of the aromatic cyclic Tr-electron delocalization energy in an opposite direction... 

Exercise 21-12 Draw the possible Kekule-type structures for biphenylene (five) and naphthalene (three). Assuming the structures may be weighted equally, estimate the double-bond character and bond lengths for both compounds. Indicate which bonds of these hydrocarbons should be attacked preferentially by ozone. 

Write the five Kekule-type resonance structures of phenanthrene and show how these structures can account for the fact that phenanthrene, unlike benzene, adds bromine, but only across the 9,10-positions. 

Exercise 22-31 Draw the Kekule-type valence-bond structures for napthalene, anthracene, and phenanthrene. Estimate the percentage of double-bond character for the 9,10 bond of phenanthrene, assuming that each of the valence-bond structures contributes equally to the hybrid structure. 

The frequency exaltation of the Kekule-type b2u modes of the electronically excited l B state is not limited to benzene and its derivatives. A similar observation was made by Michl and co-workers238 for [ 14]-annulene, who explained the phenomenon in terms of the avoided crossing of the Kekule structures similar to the above. Other hydrocarbons such as naphthalene, anthracene, etc. have been reported to exhibit the same phenomenon. Thus, in naphthalene,239240 the Kekule-type mode undergoes a frequency exaltation of 189 cm 1 in the 11 B2u state relative to the ground state. In anthracene, two Kekule-type modes exist. One was assigned and undergoes an upshift of 231 cm-1.241-243 The second anthracene mode has not been definitely assigned yet. It is calculated to be exalted by 96 cm-1.243... 

VB model, though successful for the interactions between monovalent atoms, breaks down when 71 bonds are considered. The aim of this chapter is to bring a quantitative answer to a question which can be so summarized What is the nature of the driving force which makes benzene more stable in a D6h geometry than in an alternated Dih geometry of Kekule type Exactly the same type of question applies to the allyl radical which will also be investigated and will allow the study of the effects of configuration interaction (Cl) and basis set extension. 

The values of AE , as directly computed in the ground states via the ct-ji partition of Eq. (1), confirm the previous conclusions arising from considerations of the high spin states A localizing distortion leading to an alternated geometry of Kekule type stabilizes the n bonds of benzene by 9.1-9.7 kcal/mol, and those of allyl radical by 0.9 kcal/mol. 

The difference in energy between one of the Kekule-type structures (RJ and the full spin-coupled wavefunction, with all five Rumer structures, can reasonably be termed the resonance energy. In this way, we obtain a value of 88 kJ mol-1. If we allow also for the spin-coupled ionic structures, this value is increased to 106 kJ mol"l. 

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