Question

a. For conjugated systems with two, three, four, five, six, and seven conjugated p-bonds, construct quick MOs (just draw the lobes at the ends of the conjugated system as they are drawn on pages 1220 and 1221) to show whether the HOMO is symmetric or antisymmetric.
b. Using these drawings, convince yourself that the Woodward–Hoffmann rules in Table 28.1 are valid.

Accepted Answer

Step 1: Understand the problem. The question involves constructing molecular orbitals (MOs) for conjugated systems with varying numbers of conjugated π-bonds and determining whether the highest occupied molecular orbital (HOMO) is symmetric or antisymmetric. Additionally, you need to relate this to the Woodward–Hoffmann rules, which describe the symmetry of orbitals in pericyclic reactions. Step 2: Recall the key concept of molecular orbitals in conjugated systems. For a conjugated system with n π-bonds, there are n molecular orbitals. These orbitals are formed by the linear combination of atomic p-orbitals, and their symmetry alternates between symmetric and antisymmetric as you move up in energy levels. The HOMO is the highest energy orbital that is fully occupied. Step 3: Draw the molecular orbitals for each system. For example, for a system with two π-bonds, there are two MOs: one bonding (symmetric) and one antibonding (antisymmetric). For three π-bonds, there are three MOs: one bonding (symmetric), one non-bonding (antisymmetric), and one antibonding (symmetric). Continue this process for systems with four, five, six, and seven π-bonds, ensuring you alternate symmetry as you move up in energy levels. Step 4: Identify the HOMO for each system. The HOMO is the highest energy orbital that is fully occupied. For systems with an even number of π-bonds, the HOMO will be symmetric. For systems with an odd number of π-bonds, the HOMO will be antisymmetric. This pattern arises from the alternating symmetry of the molecular orbitals. Step 5: Relate the findings to the Woodward–Hoffmann rules. The Woodward–Hoffmann rules state that the symmetry of the HOMO determines whether a pericyclic reaction is allowed under thermal or photochemical conditions. By observing the symmetry of the HOMO in each case, you can confirm that the rules in Table 28.1 are consistent with the molecular orbital symmetries you have drawn.

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Key Concepts

Conjugated Systems

Molecular Orbitals (MOs)

Woodward–Hoffmann Rules