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in the ring structure. Since six π electrons in the molecule are delocalized along the ring via the sideway overlap of six p orbitals forming a conjugate π bond and all the C─C bonds are of equal length, neither of the Lewis structures alone can truly describe the geometry and the real electronic configuration of the benzene molecule. Due to delocalization of the π electrons, the real electronic configuration can be considered resonating between the Lewis structures I and II, which are called resonance structures. In other words, the real structure and electronic configuration of benzene contain characters of both resonance structures and can be thought the average of the two. The bond order of each of the C─C bonds is 1.5, which is between a single bond (b.o. = 1) and a double bond (b.o. = 2). This way of characterization of benzene using two resonance structures I and II is consistent with the consequence of the π electrons delocalization as described by structure III. Therefore, the real wavefunction of the benzene molecule ΨIII can be formulated as the linear combination of the wavefunctions of structures I and II (ΨI and ΨII, respectively) [4]:

equation

      Since the structures I and II are equivalent, the contributions of both Lewis structures to the real structure of the benzene molecule should be equal. Therefore, we have a = b. Due to the electron delocalization, the real structure III has lower energy than that of structure I or II. Such stabilization by electron delocalization is called resonance stabilization.

Chemical reaction depicts the possible resonance structures for the carbonyl group. Chemical reaction depicts the resonance stabilization of the anolate anion. equation

      Due to a charge separation, the structure B possesses a higher energy than does the structure A. The contributions of structures A and B to the real structure of carbonyl are not the same. In general, a resonance structure possessing a lower energy has greater contribution than that which possesses a higher energy [4]. Therefore, the structure A is the major contributing Lewis structure to carbonyl, while the structure B only makes a minor contribution.

equation

      The covalent contributor (HCl) possesses lower energy. Thus, it is more important than the ionic contributor (H+Cl). In other words, the true structure of HCl is neither pure covalent nor pure ionic. It resonates between the two structures, consistent with the observed bond polarity.

      Figure 1.15b describes the nature of a brominium ion, the intermediate of electrophilic bromination of an alkene (see Chapter 3 for more details). The positive charge can be delocalized to all the three cyclic atoms giving rise to three contributing resonance structures. Overall, the real wavefunction of the species (Ψ) can be expressed in terms of linear combination of the wavefunctions of the individual resonance structures as shown below:

equation

      The relative importance of the contributing resonance structures depends on the nature of the R groups. We will have more discussions on this situation in the individual chapters.

      1.8.4 Frontier Molecular Orbitals

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