Organic Mechanisms. Xiaoping Sun

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 Ψ_III can be formulated as the linear combination of the wavefunctions of structures I and II (Ψ_I and Ψ_II, respectively) [4]:

      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.

Figure 1.13 shows that the real structure of the carbonyl (C=O) group can be characterized by two resonance structures A and B owing to delocalization of the π electrons in the C=O bond domain. Each of the structures A and B makes certain contribution to the real structure of the carbonyl group, consistent with its overall bond polarity as shown in structure C. The real wavefunction of carbonyl Ψ_C can be formulated as the linear combination of the wavefunctions of structures A and B (Ψ_A and Ψ_B, respectively).

FIGURE 1.13 Possible resonance structures for the carbonyl (C=O) group.

FIGURE 1.14 Resonance stabilization of the anolate anion.

      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.

Similarly, due to delocalization of the negative charge via a conjugate π bond, an enolate anion resonates between two anionic structures as shown in Figure 1.14. As a result, each of the oxygen and α‐carbon atoms is partially negatively charged, giving rise to the resonance stabilization. Further discussions on the structure of enolate and its reactivity will be presented in Chapter 9.

Since bonding electrons in a σ‐bond are also delocalized in the bonded atoms, a compound that only contains σ‐bonds can also be characterized by different Lewis structures (resonance structures). Figure 1.15a shows that the σ bond in hydrogen chloride (Ψ_HCl) contains both covalent (Ψ_covalent) and ionic (Ψ_ionic) characters [5], which can be expressed mathematically as

FIGURE 1.15 Possible resonance structures for (a) hydrogen chloride (HCl) and (b) a brominium cation.

      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:

      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

In a molecule, AOs of the constituent atoms overlap (LCAOs) giving rise to the formation of a set of MOs. As a result, all the electrons will move in the entire molecule. Some MOs with lower energies will be filled (occupied) by the electrons. Other MOs with higher energies will remain empty (unoccupied). The highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) in a molecular are particularly important, and they are referred to as frontier molecular orbitals (FMOs). In H₂, there are only two MOs (Fig. 1.8). Both of them, σ_1s (HOMO) and σ_1s^* (LUMO), are FMOs. In the C=C double bond, there are one σ‐bond and one π‐bond (Fig. 1.10a). The FMOs are π_p (HOMO) and π_p^* (LUMO). In 1,3‐butadiene (CH₂=CHCH=CH₂), the FMOs are ψ₂ (HOMO) and ψ₃ (LUMO) [Fig. 1.11b]. In general, only the FMOs (HOMO and LUMO) participate in reactions and the other orbitals (lower‐lying or upper‐lying MOs) remain approximately intact during a chemical reaction [6]. Many concerted reactions are effected by interaction of the HOMO of one reactant with the LUMO of the other. This requires that the reacting FMOs must have symmetry‐match [1]. This case will be further addressed in the individual chapters, particularly in Chapter 4. In addition, when the energy of a photon (hν) at certain wavelength (frequency) matches the HOMO–LUMO energy gap, the photon can be absorbed by the molecule resulting in electronic transition from HOMO to LUMO. This type of absorption is common to many compounds whose molecules contain π‐bonds. π (ΗΟMΟ)–π* (LUMO) transition occurs when the light with matching energy is absorbed. The transition gives rise to certain colors for the compounds containing π‐bonds. In addition, the