Kekule distortion

The gap parameter or lattice distortion vanishes in the critical AB flux (jt which opens the gap as large as that due to the distortion. For <]) = 0, the gap decreases exponentially as a funetion of the cireumferenee Lla. Table 2 gives some examples for an in-plane Kekul distortion. 

Table 2. Calculated energy gap due to an in-plane Kekul distortion for CNTs having chiral vector L/a = (m, 2m). The critical magnetic flux (p. and the corresponding magnetic field are also shown. The coupling constant is A, = 1.62.

One benzene and two CO s per unit cell. CO is L to the surface, adsorbed 1.30 A above 3-fold hep sites. Benzene is parallel to the surface, centered 2.20 A over a 3-fold hep site. Slight in-plane Kekule distortion of the benzene molecule. 

Rh (111) C6Hg+CO c(2V/3x4) rect Benzene is coadsorbed with CO, each with one molecule per unit cell, both centered over 3-fold hep sites, benzene is parallel to and 2.25 0.05 A above the surface. CO is 1 to the surface and the metal-carbon spacing is 1.50 0.05 A. The benzene molecule has an in-plane Kekule distortion, with alternating long and short bonds. LEED/14/... 

A above the surface. CO is perpendicular to the surface, and the metal-carbon spacing is 1.50 0.05 A. The benzene molecule has an in-plane Kekule distortion, with alternating long and short bonds. 

The effect of facial coordination of benzene to a trinuclear cluster has been studied by statistical analysis of their crystal structures and by DFT calculations. The arene ligand was thus found to be considerably expanded with respect to the free arene and it showed a small but significant Kekule distortion. DFT calculation led to the conclusion that facial benzene exhibits substantial cyclic electron delocalization. ... 

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. 

Owing to the 7tCc-ocrc CT interactions, the usual equivalence between the two Kekule structures of benzene is broken and the ring distorts strongly to D3h symmetry, with pronounced alternation (by 0.02 A) of C=C bond lengths. Complexes of this type are evidently closely related to the metallocene sandwich compounds discussed elsewhere in this book (Section 4.9.5), with the benzene molecule described as a tridentate ligand in the language of metal coordination chemistry. 

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... 

Finally, one uses low-temperature techniques for ESR measurements of non-Kekule species not only because of the inherent high reactivity of the species, but also because unless the sample is immobilized or at least hampered in its motion by viscous solvent, rapid tumbling will cause the spectrum to suffer line shape distortions that impede the extraction of the zero-field splitting parameters. 

A recent summary of the history and dynamics of the theoretical models of benzene39 cites a view that even though the current molecular orbital (MO) view of benzene seems complete and ultimate while the valence bond (VB) view seems obsolete, the recent findings about zr-distortivity in benzene indicate that the benzene story is likely to take additional twists and turns that will revive the VB viewpoint (see footnote 96 in ref 39). What the present review will show is that the notion of delocalized zr-systems in Scheme 1 is an outcome of both VB and MO theories, and the chemical manifestations are reproduced at all levels. The use of VB theory leads, however, to a more natural appreciation of the zr-distortivity, while the manifestations of this ground state s zr-distortivity in the excited state of delocalized species provides for the first time a physical probe of a Kekule structure .3... 

Part a of Figure 12 shows the situation in benzene, where the Kekule structures cross and establish a distortive zr-curve with a maximum at the l t, symmetry (the origin of the AR coordinate). Parts b and c describe two opposite effects of -interaction between the annelating ring and the endo-double bonds in K2. 

Despite our natural satisfaction with this explanation, we noted that it nevertheless does not provide a clear physical mechanism for the effect. For example, it was not evident why the frequency exaltation is state selective, i.e., it is not observed in any other state, and the frequency of all other modes are reduced upon excitation. It was deemed necessary, therefore, to articulate the avoided crossing model, derive a clear physical origin of the frequency exaltation of the Kekule mode, its state, and mode specificity, and establish the connection of the phenomenon to the jr-distortivity in the ground state. This was achieved in 1996.209... 

The frequency exaltation of the Kekule mode is mirrored by the structural manifestations in the twin states, discussed with reference to Figures 16 and 17. Thus, the repulsive jr-curve in the ground state softens the potential and thereby enables the ground-state molecule to distort along the Kekule mode when angular strain is exerted. In contrast, the attractive jr-curve in the twin excited state stiffens the potential and restores the local Deh symmetry of the benzene nucleus. The two physical effects are in perfect harmony and find a natural reflection in the VB model. 

Despite the quantitative difference between aromatics and antiaromatics, the qualitative picture is the same The combination of a, T-distortive ground state and a -attractive excited state along the Kekule modes is manifested in soft potentials in the ground state and steep ones in the twin excited state. This in turn is expressed as exalted frequencies and symmetrized geometries in the twin excited state. 

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