Valence bond theory benzene

T orbital for benzene obtained from spin-coupled valence bond theory. (Figure redrawn from Gerratt ], D L oer, P B Karadakov and M Raimondi 1997. Modem valence bond theory. Chemical Society Reviews 87 100.) figure also shows the two Kekule and three Dewar benzene forms which contribute to the overall wavefunction Kekuleform contributes approximately 40.5% and each Dewar form approximately 6.4%. 

Several methods of quantitative description of molecular structure based on the concepts of valence bond theory have been developed. These methods employ orbitals similar to localized valence bond orbitals, but permitting modest delocalization. These orbitals allow many fewer structures to be considered and remove the need for incorporating many ionic structures, in agreement with chemical intuition. To date, these methods have not been as widely applied in organic chemistry as MO calculations. They have, however, been successfully applied to fundamental structural issues. For example, successful quantitative treatments of the structure and energy of benzene and its heterocyclic analogs have been developed. It remains to be seen whether computations based on DFT and modem valence bond theory will come to rival the widely used MO programs in analysis and interpretation of stmcture and reactivity. 

Benzene is described by valence-bond theory as a resonance hybrid of two equivalent structures. 

McWeeny, R., Proc. Roy. Soc. (London) A227, 288, The valence-bond theory of molecular structure. III. Cyclobutadiene and benzene." f. 

In the case of tt complexes of substituted cyclopentadienones, such as the iron tricarbonyl derivatives prepared by Weiss and H libel (30), qualitative molecular-orbital theory (20) predicted a considerable reduction of the ketonic carbonyl bond order. It was observed that the ketonic carbonyl frequency dropped by as much as 65 cm-1, in agreement with theory. A similar explanation can also be provided in terms of valence bond theory (Fig. 14). It has been suggested that n complexing of arenes such as benzene results in loss of aromaticity of the ring in contrast to the dicyclopentadienyl... 

FIGURE 17. Schematic representation of the symmetry-unique spin-coupling patterns in cyclopropane (above) and benzene (below). In the case of cyclopropane, carbon hybrid orbitals and, in the case of benzene, carbon p n orbitals are shown. For each structure, Gallup-Norbeck occupation numbers as determined by spin-coupled valence bond theory are given. All data from Reference 51... 

We have used the concepts of the resonance methods many times in previous chapters to explain the chemical behavior of compounds and to describe the structures of compounds that cannot be represented satisfactorily by a single valence-bond structure (e.g., benzene, Section 6-5). We shall assume, therefore, that you are familiar with the qualitative ideas of resonance theory, and that you are aware that the so-called resonance and valence-bond methods are in fact synonymous. The further treatment given here emphasizes more directly the quantum-mechanical nature of valence-bond theory. The basis of molecular-orbital theory also is described and compared with valence-bond theory. First, however, we shall discuss general characteristics of simple covalent bonds that we would expect either theory to explain. 

Valence bond theory is somewhat out of favour at present a number of the spectroscopic and magnetic properties of transition-metal complexes are not simply explained by the model. Similarly, there are a number of compounds (with benzene as an organic archetype) which cannot be adequately portrayed by a single two-centre two-electron bonding representation. Valence bond theory explains these compounds in terms of resonance between various forms. This is the origin of the tautomeric forms so frequently encountered in organic chemistry texts. The structures of some common ligands which are represented by a number of resonance forms are shown in Fig. 1-11. 

E. C. da Silva, J. Gerratt, D. L. Cooper, M. Raimondi, J. Chem. Phys. 101, 3866 (1994). Study of the Electronic States of the Benzene Molecule Using Spin-Coupled Valence Bond Theory. 

The benzene derivatives presented an enigma to structural chemists in that although the benzene rings had three double bonds, they underwent substitution rather than addition when treated with reagents such as bromine and nitric acid. No adequate explanation for their behavior was presented prior to the development of quantum mechanics. In the early 1930 s, two explanations were presented. One was by Pauling making use of valence bond theory,2 and the other was by E. Huckel making use of molecular orbital theory.3... 

Pauling s use of valence bond theory had a direct connection with the types of structures commonly used by organic chemists, and was relatively easy to understand, provided one did not delve too deeply into its details. The basic postulate was that compounds having n-electron systems that can be described by more than one structure will be stabilized by "resonance" and will have a lower energy than any of the contributing structures. Thus, for benzene one would write... 

Resonance between three 7r-complex structures might lead to stabilization of 1 in the sense of 7r-aromatic stabilization involving the six CC bond electrons. Therefore, Dewar has discussed the stability of in terms of a c-aromatic stabilization (Section V). However, spin-coupled valence bond theory clearly shows that 1 cannot be considered as the cr-aro-matic analogue to 7r-aromatic benzene The 7r-complex description of 1 is a (very formal) model description, which should be discarded as soon as it leads to conflicting descriptions of the properties of 1. This will be discussed in Section V. 

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. 

Aromaticity is one of a number of remarkably important but fuzzy concepts in chemistry that does not lend itself easily to widely applicable clear-cut definitions. One of the more recent attempts to summarise what chemists with dilferent backgrounds see in this term was made by Schleyer. Valence bond theory has been, since Kekule s times, a major source of qualitative and quantitative interpretations of aromaticity, and it is surprising that it has not been mentioned, even once, in Schleyer s editorial. Of course, this omission does not diminish the importance that VB methods have had and still have in providing easy-to-understand ideas about aromatic behaviour which are often markedly superior to those coming from other theoretical sources. In order to justify this claim from a current perspective, in this section we look at the recent VB studies of the aromaticity of a series of benzenelike rings, and of clamped benzenes. 

Bond order A theoretical index of the degree of bonding between two atoms relative to that for a normal single bond, that is, one localized electron pair. In valence bond theory it is expressed by the weighted average of the bond numbers between the respective atoms in the contributing structures. By this criterion each C—C bond in benzene has a bond order of 1.5. 

The weak reactivity of benzene is in part attributed to this additional stabiliza- j tion. That stabilization energy is often called the delocalization energy or reso- nance energy of benzene and is taken as a measure of the aromaticity of the j molecule. The expression resonance energy comes from the description of] the delocalized tt system in valence-bond theory in terms of the resonant hybrid... 

One of the arguments for retaining valence bond theory has been the ease with which things like the nucleophilicity of the allyl anion at C-l and C-3 are explained by drawing the canonical structures. Even as simple a version of MO theory as the one presented here does the job just as well. The drawings chemists use for their structures will inevitably be crude representations we shall always have to make some kind of localized drawing, whether it be of a benzene ring,... 

Figure 9-11 Representations of the bonding in the benzene molecule, CgHg. (a) Lewis formulas of the two valence bond resonance structures, (b) The six p orbitals of the benzene ring, shown overlapping to form the (hypothetical) double bonds of the two resonance forms of valence bond theory, (c) In the MO description the six electrons in the pi-bonded region are dehcalized, meaning they occupy an extended pi-bonding region above and below the plane of the six C atoms.

The three Dewar structures 5, 11 and 12 (Dewar benzene) are also considered to contribute to the resonance hybrid (according to valence bond theory, approximately 20% in total) and to the extra stability. Dewar benzene has now been prepared. It is a bent, non-planar molecule and is not aromatic. It gradually reverts to benzene at room temperature. The Ladenburg structure, prismane i6), is an explosive liquid. Dewar benzene and prismane are valence isomers of benzene. 

In 1927, Heitler and London used valence bond theory to treat the H2 molecule but to treat larger molecules, further simplifications were needed. In 1931, Erich Hiickel introduced an extremely simple approximation which could be used to treat the 7i-electrons in flat organic molecules such as benzene, napthaline, and so on. This approximation yielded matrices to be diagonalized, and it is a measure of the state of computers at that time to remember that during World War II, Alberte Pullman sat in a basement room in Paris diagonalizing Hiickel matrices with a mechanical desk calculator, while her husband-to-be Bernard drove a tank with the Free French Forces in North Africa. Alberte s hand-work led to the publication of the Pullmans early book Quantum Biochemistry. ... 

It is generally conceded that simple valence bond theory cannot adequately explain the bonds between the carbon atoms in benzene. This classic conundrum is often resolved by stating that there is a sort of... 

We can now state that each carbon-to-carbon linkage in benzene contains a sigma bond and a partial pi bond. The bond order between any two adjacent carbon atoms is therefore between 1 and 2. Thus molecular orbital theory offers an alternative to the resonance approach, which is based on valence bond theory. (The resonance structures of benzene are shown on p. 349.)... 

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