Question

Problem:Give a molecular orbital description for each of the following:

a. 1,3-pentadiene b. 1,4-pentadiene c. 1,3,5-heptatriene d. 1,3,5,8-nonatetraene

Short answer

a.

b.

c.

d.

Step-by-step solution

Step 1: Molecular orbital description for 1,3-pentadiene

1,3-Pentadiene has “two conjugated pie bonds,” so it has four p atomic orbitals. Four atomic orbitals combine to produce four molecular orbitals :${\mathbf{\psi }}_1\mathbf{,}{\mathbf{\psi }}_2\mathbf{,}{\mathbf{\psi }}_3\mathbf{and}{\mathbf{\psi }}_4$

Half are bonding Molecular orbital (${\mathbf{\psi }}_1\mathbf{,}{\mathbf{\psi }}_2$), and the other Half are antibonding molecular orbital (${\mathbf{\psi }}_3\mathbf{and}{\mathbf{\psi }}_4$).

The molecular orbital description for 1,3-pentadiene is drawn as follows:

Molecular orbitals of1,3-pentadiene

Step 2: Molecular orbital description for 1,4-pentadiene

1,4-Pentadiene has four electrons (pie electrons). However, unlike the delocalized electrons in 1,3-butadiene, the electrons in 1,4-pentadiene are entirely separate. In other words, the electrons are localized. The molecular orbitals of 1,4-pentadiene have the same energy as ethene(a compound with one pair of localized electrons).

The molecular orbital description of 1,4-pentadiene has two p atomic orbitals that produce two molecular orbitals. The in-phase interaction of the two p atomic orbitals forms a $\mathbf{\pi }$bonding MO, designated by ${\mathbf{\psi }}_1$, and the out-of-phase interaction forms an ${\mathbf{\pi }}^{*}$antibonding MO, designated by ${\mathbf{\psi }}_2$drawn as follows:

Molecular orbitals of1,4-Pentadiene

Step 3: Molecular orbital description for 1,3,5-heptatriene

1,3,5-heptatriene has “three conjugated pie bonds” with six p atomic orbitals. six atomic orbitals combine to produce six molecular orbitals :${\mathbf{\psi }}_1\mathbf{,}{\mathbf{\psi }}_2\mathbf{,}{\mathbf{\psi }}_3\mathbf{,}{\mathbf{\psi }}_4\mathbf{,}{\mathbf{\psi }}_5\mathbf{and}{\mathbf{\psi }}_6$

Half are bonding Molecular orbital (${\mathbf{\psi }}_1\mathbf{,}{\mathbf{\psi }}_2\mathbf{,}{\mathbf{\psi }}_3$), and the other Half are antibonding molecular orbital (${\mathbf{\psi }}_4{\mathbf{\psi }}_5\mathbf{and}{\mathbf{\psi }}_6$).

The molecular orbital description for 1,3,5-heptatriene is drawn as follows:

Molecular orbitals of1,3,5-heptatriene

Step 4: Molecular orbital description for 1,3,5,8-nonatetraene

1,3,5,8-nonatetraene has “three conjugated pie” and “one “isolated pie” bonds.

Three conjugated double bonds have a molecular orbital description with six p atomic orbitals. Six atomic orbitals combine to produce six molecular orbitals:${\mathbf{\psi }}_1\mathbf{,}{\mathbf{\psi }}_2\mathbf{,}{\mathbf{\psi }}_3\mathbf{,}{\mathbf{\psi }}_4\mathbf{,}{\mathbf{\psi }}_5\mathbf{and}{\mathbf{\psi }}_6$ , Half are bonding Molecular orbitals (${\mathbf{\psi }}_1\mathbf{,}{\mathbf{\psi }}_2\mathbf{,}{\mathbf{\psi }}_3$), and the other Half is antibonding molecular orbitals (${\mathbf{\psi }}_4{\mathbf{\psi }}_5\mathbf{and}{\mathbf{\psi }}_6$).

The molecular orbital description ofThree conjugated double of 1,3,5,8-nonatetraene is drawn as follows:

Molecular orbitals ofthree conjugated double of 1,3,5,8-nonatetraene

The molecular orbital description isolated pie bond of 1,3,5,8-nonatetraene has two p atomic orbitals that produce two molecular orbitals. The in-phase interaction of the two p atomic orbitals forms a bonding $\mathbf{\pi }$MO, designated by ${\mathbf{\psi }}_1$, and the out-of-phase interaction forms an${\mathbf{\pi }}^{*}$ antibonding MO, designated by ${\mathbf{\psi }}_2$ drawn as follows:

Molecular orbital of isolated pie bond of 1,3,5,8-nonatetraenem