Valence bond theory Kekule structures

X-ray crystallographic analysis indicated that benzene is a planar, regular hexagon in which all the carbon-carbon bond lengths are 139 pm, intermediate between the single C-C bond in ethane (154 pm) and the C=C bond in ethene (134 pm), and therefore all have some double bond character. Thus the representation of benzene by one Kekule structure is unsatisfactory. The picture of benzene according to valence bond theory is a resonance hybrid of the two Kekule or canonical forms 4 and 9, conventionally shown as in Figure 1.2, and so each carbon-carbon bond apparently has a bond order of 1.5. 

Resonance between imaginary structures having localised bond (valence bond theory) or delocalization of it orbitals (molecular orbital theory) have both been found to explain the bonding state of benzene. The benzene molecule may be represented either as a hybrid of Kekule structures (valence bond theory) or as a regular carbon hexagon having an inscribed circle or dotted circle that symbolizes the three delocalized n orbitals. 

More than anyone else it has been Linus Pauling (b. 1901) who has been responsible for the development and application of the valence bond theory. In the early 1930s he deduced from quantum mechanics the tetrahedrally directed valencies of carbon, and he introduced the concept of the hybridisation of atomic orbitals. He introduced the idea of resonance as the quantum-mechanical counterpart of mesomerism. The wavefiinction for the molecule must contain terms for all possible structures, and the molecule is said to resonate between them. In 1933 Pauling described the benzene molecule as a resonance hybrid between the two Kekule structures and the three possible Dewar structures (Figure 11.22). 

The fact that there may exist several equally plausible Kekule-type structural formulas for a chemical compound, has long pt there may exist several equally plausibleuzzled the chemical community. A more-or-less acceptable solution was found only after quantum-theoretical arguments were used for the description and explanation of chemical bonding [3-8]. One direction of development of quantum chemistry (usually referred to as valence bond theory ) explicitly used mathematical objects resembling Kekule stmctural formulas. 

Maccoll 3 and Simonetta applied valence bond theory (neglecting all but Kekule structures) to some heterocycles. A number of these results are collected in Table 2.2. 

The resonance theory is very useful in accounting for, and in many cases predicting, the behavior of substances with tt bonds. However, it is not omnipotent. One example where it fails is cyclobutadiene, for which we can write two equivalent valence-bond structures corresponding to the Kekule structures for benzene ... 

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... 

In practice, the valence bond picture has probably exerted more influence on how chemists actually think than the HMO picture. However most early applications were primarily qualitative in nature. This qualitative VB picture can be summarized under die name of resonance theory [10]. The basic concept is that in general the more ways one has of arranging the spin pairing in the VB wave function, the more stable the molecule is likely to be. Thus, VB theory predicts that phenanthrene with 14 carbon atoms and 5 Kekule structures should be more stable than anthracene with 14 carbon atoms but just 4 Kekule structures, in complete accord with the experimental evidence. It also predicts that benzenoid hydrocarbons with no Kekule structures should be unstable and highly reactive, and in fact no such compounds are knowa Extensions of this qualitative picture appear, for example, in Clar s ideas of resonant sextets [11], which seem to be very powerful in rationalizing much of the chemistry of benzenoid aromatic hydrocarbons. The early ascendancy of HMO theory was thus largely based on the ease with which it could be used for quantitative computations rather than on any inherent superiority of its fundamental assumptions. 

Individual formal valence structures of conjugated hydrocarbons are excellent substrates for research in chemical graph theory, whereby many of the concepts of discrete mathematics and combinatorics may be applied to chemical problems. The lecture note published by Cyvin and Gutman (Cy-vin, Gutman 1988)) outlines the main features of this type of research mostly from enumeration viewpoint. In addition to their combinatorial properties, chemists were also interested in relative importance of Kekule valence-bond structures of benzenoid hydrocarbons. In fact, as early as 1973, Graovac et al. (1973) published their Kekule index, which seems to be one of the earliest results on the ordering of Kekule structures These authors used ideas from molecular orbital theory to calculate their indices... 

We will not explore the computational details of VB theory, but it is worth noting some results that can be obtained with it. Recall that one of the features of HMO theory is that it is possible to make useful predictions, such as the relative stabilities of cyclic n systems or the locations of impaired electron density in a conjugated radical, without actually doing the HMO calculations. Similarly, it is not necessary to carry out a complete valence bond calculation to obtain useful quantitative predictions of resonance energies and some other properties of conjugated n systems. Herndon described a structure-resonance theory (SRT) method that enables one to calculate resonance energies using only Kekule structures The methods described in the references present... 

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