Organic Mechanisms. Xiaoping Sun

formation of the bonding MO (σ_2p = 2p_z,A + 2p_z,B) and antibonding MO (σ_2p^* = 2p_z,A − 2p_z,B), respectively.

In the category of nonmetallic main group elements, a π bond is formed by overlap of two p orbitals (LCAOs) in sideways (Fig. 1.10). If both p orbitals are identical (such as p orbitals in a C=C π bond), each of the p orbitals has the same contribution to the bonding (π_p) and antibonding (π_p^*) MOs (Fig. 1.10a). They are formed by constructive and destructive sideway orbital overlaps, respectively: π_p = p₁ + p₂ (fused lobes due to a positive linear combination—constructive orbital overlap) and π_p^* = p₁ − p₂ (separated lobes due to a negative linear combination—destructive orbital overlap). If the two p orbitals are from atoms of different elements (such as p orbitals in a C=O π bond), the contribution of each p orbital to the bonding (π_p) and antibonding (π_p^*) MOs is different (Fig. 1.10b). Usually, the p orbital in the more electronegative atom has greater contribution to the bonding MO (π_p), and the p orbital in the less electronegative atom has greater contribution to the antibonding MO (π_p^*). In the C=O π bond, the bonding (π_p) and antibonding (π_p^*) MOs can be expressed as

FIGURE 1.9 Formation of the fluorine molecule (F₂) from two fluorine (F) atoms.

FIGURE 1.10 Formation of (a) the C=C π bond from two equivalent p orbitals and (b) the C=O π bond from two nonequivalent p orbitals.

      The above equations show that for the formation of π_p, the p orbital in oxygen (more electronegative) makes a greater contribution than does the p orbital in carbon (less electronegative). For the formation of π_p^*, the p orbital in carbon (less electronegative) makes a greater contribution than does the p orbital in oxygen (more electronegative). In each case, the bonding π_p MO is responsible for the formation of a π bond, and antibonding orbital π_p^* is responsible for dissociation of the π bond.

When more than two p orbitals overlap sideways, it results in the formation of a conjugate π bond. Similar to the separate π bonds (formed by sideway overlap of two p orbitals), a conjugate π bond consists of series of MOs formed by linear combinations of the contributing p orbitals. The number of constituent MOs is equal to the number of contributing p orbitals. For example, the conjugate π‐bond of allyl radical (CH₂=CHCH₂˙), formed by sideway overlap of three p orbitals in the carbon atoms, consists of the following three MOs (Fig. 1.11a):

      The conjugate π‐bond of 1,3‐butadiene (CH₂=CHCH=CH₂), formed by sideway overlap of four p orbitals in the carbon atoms, consists of the following four MOs (Fig. 1.11b):

      In each of the molecules, since all the p orbitals are from carbon atoms, their contributions to each of the MOs are equal.

      1.8.2 Molecular Orbital Diagrams

When two AOs combine linearly (overlap) to form MOs (Figs ), the bonding MO formed by positive LCAO has lower energy than each of the starting AOs, while the antibonding MO formed by negative LCAO possesses higher energy than the AOs [4, 5]. As a result, the electrons from the starting AOs flow into the lower‐energy‐level bonding MO upon the formation of the molecule and the antibonding MO with a higher energy level remains empty. The overall energy decreases. The diagrams showing correlations of AOs and the resulting MOs and their relative energy levels are called molecular orbital diagrams. Figs show the MO diagrams for the formation of H₂ from hydrogen atoms, the formation of F₂ from fluorine atoms, and the formation of a π‐bond from p orbitals. All the MO diagrams clearly indicate the energy gains (driving forces) for the formation of a molecule (or a bond) from individual atoms. Figure 1.11 shows MO diagrams for the formation of a conjugate π‐bond from p orbitals. The MO diagrams also indicate that any MOs whose energies are lower than those of the starting AOs are bonding orbitals, responsible for the formation of the molecule. If an MO has the same energy as that of a starting AO, it is a nonbonding orbital which does not make any contribution to the formation of the molecule. Any MOs whose energies are higher than those of the starting AOs are antibonding orbitals, responsible for the dissociation of the molecule if they are populated with electrons [5].

FIGURE 1.11 Formation of conjugate π bonds from p orbitals in (a) the allyl radical (CH₂=CHCH₂˙) and (b) the 1,3‐butadiene (CH₂=CHCH=CH₂) molecule.

FIGURE 1.12 Resonance stabilization of benzene.

      1.8.3 Resonance Stabilization

      By the nature, resonance stabilization is a result of electron delocalization in a molecule, which leads to decrease in energy and stabilizes the molecule. It typically occurs in the p_π systems. First, we will use the benzene molecule as an example to demonstrate the nature of resonance stabilization.

Figure 1.12 shows two valid Lewis structures (I and II) for benzene