The Kekule Basis

Full Cl ground state energy of the Heisenberg model (Eq. I-) in units of J 

Molecule Complete basis Kekule basis oercent 

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. 

A hydrocarbon is said to be alternant if the carbon atoms can be separated into two groups, usually designated starred and unstarred, such that starred atoms are bonded only to unstarred atoms and vice versa. All benzenoid 

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As we can see by comparing the HH-Clar structures and k-Clar structures they offer a distinctive basis for representation of benzenoid hydrocarbons. Each of the two approaches have their own merits, and as we will see in the next section, although the structures arising in the two models are quite different, the two approaches can be related in some respect. Both approaches use the same basis Kekule structures and differ... 

It is perhaps worth remarking that had we chosen, instead of the standard basis, the Rumer basis of spin functions, then the five VB singlet covalent functions are just the two well-known Kekule Structures and the three Dewar structures. 

The Rumer basis turns out to be particularly useful for interpreting the total spin functions for aromatic systems. In the case of Af=6 and S=0, there are just five linearly independent modes of spin coupling [29], which may be represented as in Figure 1, in which an arrow i—>j signifies a factor in the total spin function of 2 (a(j)P(/)-a(/)p(0). The similarity to Kekule and para-bonded structures for benzene is obvious. 

In the Rumer basis [29] (see Figure 1), the total spin function corresponds to weights of 40.6% each for the two Kekule structures (RirR4) and of 6.3% each for the three para-bonded ( Dewar ) structures These values are very close... 

The modem dye industry is built upon the coal tar industry as its source of material, and upon the Kekule benzene theory as its scientific basis. Without these foundations, the dye industry could not have been developed. 

The changes in the shapes of the orbitals are accompanied by a re-coupling of the electron spins. For this reaction, it proves most convenient to express the total active-space spin function oo in the Rumer basis. As shown in Fig. 5(b), the two Kekule-like functions (1-2, 3-4, 5-6) and (1-6, 2-3, 4-5) are dominant over the... 

The molecular basis for the left- and right-handedness of distinct crystals of the same chemical substance and the associated differences in optical rotation was developed from the hypothesis of Paterno (1869) and Kekule that the geometry about a carbon atom bound to four ligands is tetrahedral. Based on the concept of tetrahedral geometry, Van t Hoff and LeBel concluded that when four different groups or atoms are bound to a carbon atom, two distinct tetrahedral molecular forms are possible, and these bear a non-superimposable mirror-image relationship to one another (Fig. 3). This hypothesis provided the link between three-dimensional molecular structure and optical activity, and as such represents the foundation of stereoisomerism and stereochemistry. 

Hiebert, Erwin. "The Experimental Basis for Kekule s Valence Theory." Journal of Chemical Education 36 (1959) 320-27. 

We have seen that benzene shows unusual behavior by undergoing substitution reactions when, on the basis of its Kekule structure, we should expect it to undergo addition. Benzene is unusual in another sense it is more stable thermodynamically than the Kekule structure su ests. To see how, consider the following thermochemical results. 

When these results are represented as in Fig. 14.1, it becomes clear that benzene is much more stable than we calculated it to be. Indeed, it is more stable than the hypothetical 1,3,5-cyclohexatriene by 152 kJ moP. This difference between the amount of heat actually released and that calculated on the basis of the Kekule structure is now called the resonance energy of the compound. 

Kekule showed that itaconic and citraconic acids, and an isomer mesaconic acid obtained by J. Gottlieb by boiling citraconic acid with dilute nitric acid, are unsaturated when reduced with sodium amalgam they all form pyro-tartaric acid but with bromine they form three different dibromotartaric acids. He knew that they were methyl-substituted maleic or fumaric acids. R. Fittig, at the end of a long memoir on the unsaturated acids, remarked that no constitutional formulae exist which explain all the facts, if the dogma that in unsaturated compounds the carbon is always multiply linked is retained but he was unaware that two years before the whole problem had been solved, on the basis of a very simple assumption, by van t Hoff (see p. 757), and that of citraconic acid, etc., was cleared up on the same basis by Wislicenus (p. 762). 

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