Kekuld

Fig. 5. Possible bond-alternation patterns of CNTs (a) Isodistant (Iso), (b) bond-altemant 1 (Alt 1), (c) bond-alternant 2 (Alt 2) and (d) Kekuld patterns.

It is known that a metallic ID system is unstable against lattice distortion and turns into an insulator. In CNTs instabilities associated two kinds of distortions are possible, in-plane and out-of-plane distortions as shown in Fig. 8. The inplane or Kekuld distortion has the form that the hexagon network has alternating short and long bonds (-u and 2u, respectively) like in the classical benzene molecule [8,9,10]. Due to the distortion the first Brillouin zone reduees to one-third of the original one and both K and K points are folded onto the F point in a new Brillouin zone. For an out-of-plane distortion the sites A and B are displaced up and down ( 2) with respect to the cylindrical surface [11]. Because of a finite curvature of a CNT the mirror symmetry about its surface are broken and thus the energy of sites A and B shift in the opposite direction. 

The results of the electron diffraction investigation reported in this paper are collected in Table X. The re-investigation of benzene confirms the value 1.39 A. for the C-C distance and provides a rough experimental value for the C-H distance. In pyridine and pyrazine the C-N distance is greater than expected for Kekuld resonance the effect is attributed to extra reso-... 

Kekuld von Stradonitz, August 31 fin Kirchhoff, Gustav Robert 93n Kronecker, Leopold 7 In... 

The first row represents an alternative set of equivalent localized orbitals which is as strongly localized as the one just discussed. 56) They extend essentially over three atoms. Whereas the Kekuld type localized orbitals are symmetric with respect to the plane bisecting a bond, the localized orbitals in the first row are symmetric with respect to a plane containing two opposite atoms. The negative lobe extends only over one atom, and the... 

Fig. 29. Localized 7T-MO s in catacondensed molecules for which the LMO s do not correspond to Kekuld structures. Fifth strongest contour is shown... 

About the same time, Kekuld 15> discovered the quadrivalency of C-atoms laying the foundations for constitutional chemistry. 

The resonance energy for the two Kekuld structures in benzene can be calculated in terms of a by neglecting all interactions except those... 

II, plus some additional terms hence, according to the fundamental ideas of quantum mechanics, if it were possible to carry out an experimental test of the electronic structure Oust would identify structure I or structure II, each structure would be found for the molecule to the extent determined by the waee function. The difficulty for benzene and for other molecules showing electronic resonance is to devise an experimental test that could be carried out quickly enough and that would distinguish among the structures under discussion. In benzene the frequency of Kekuld resonance is only a little less than the frequency of the bonding resonance of electron pairs, so that the time required for the experiment is closely limited. 

Zhang FJ, Guo XF, Chen RS (1990) The Existence of Kekuld Structures in a Benzenoid System. 153 181-194... 

Chen, R.S., Cyvin, S.J., Cyvin, B.N., Brunvoll, J., and Klein, D.J. Methods of Enumerating Kekuld Structures. Exemplified by Applified by Applications of Rectangle-Shaped Benzenoids. 153, 227-254 (1990). 

Kekuld + Dewar = covalent singly doubly remainder... 

Kekule valence structures all the combination of Kekule valence structures of interest. The same is also true for finding combinations of Kekule valence structures involved in HH-Clar structures. A better way to obtain the correct combinations of Kekule valence structures instead of construction of various superpositions is to first write down k-Clar structures (or HH-Clar structures) and then decompose them into underlying Kekule valence structures. The apparent difficulty that remains in such an approach, that cannot be avoided, is the case of benzenoids having a large number of Kekuld valence structures which results in large number of decomposition. 

The Kekuld wave function also yields considerable insight into the structure of buckminsterfullerene. Since buckminsterfullerene is a Clar sextet molecule, it has the special Kekule structure which places double bonds on all 30 of the 6-6 edges. Since the pi electrons tend to localize to these positions, this Kekule function should be the most important single contributor to the ground state wave function, while Kekuld functions with many double bonds in 6-5 positions should be less important. Fig. 3 shows the absolute value of the wave function coefficient for each Kekuld structure as a function of the number of double bonds in 6-5 positions. The expected decreasing trend is clearly observed, but something else stands out as well. The Kekule functions divide into two classes, separated by the solid line in the figure. This separation is a reflection of the nonaltemant character of a fiillerene. 

The molecular orbital answer to this problem, as you may well know, is that all six p orbitals can combine to form (six) new molecular orbitals, one of which (the one lowest in enery ) consists of a ring of electron density above and below the plane of the molecule. Benzene does not resonate between the two Kekuld structures—the electrons are in molecular orbitals spread equally over all the carbon atoms. However the term resonance is still sometimes used (but not in this book) to describe this mixing of molecular orbitals. 

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