Chapter 28, Problem 28.4P

Interpretation Introduction

(a)

Interpretation:

In $2,4,6-\text{heptatrienyl cation}$ molecule the nonbonding MO is to be stated.

Concept introduction:

The molecular orbital is a combination of two atomic orbitals. It is used to represent the regions in a molecule where the electron is likely to be present in an orbital. It represents the wave-like nature of an electron in a molecule. It may be symmetric or antisymmetric. It may be bonding, antibonding or non-bonding. It may be HOMO or LUMO.

Answer to Problem 28.4P

In $2,4,6-\text{heptatrienyl cation}$ molecule ${\text{π}}_{\text{4}}$ is a nonbonding molecular orbital.

Explanation of Solution

The structure of $2,4,6-\text{heptatrienyl cation}$ is shown below.

${\text{H}}_{\text{2}}\text{C}=\text{CH }—\text{CH}=\text{CH}—\text{CH}=\text{CH}-\stackrel{+}{{\text{CH}}_{\text{2}}}$

This molecule contains seven carbon atoms. In case of the odd number of carbon atoms chain which is in conjugation, the molecular orbitals do not separate out into two equal halves in bonding and antibonding molecular orbitals. Along with that it gives rise to one molecular orbital whose energy is equal to that of $\text{2p}$ orbitals. It is known as nonbonding molecular orbitals. Therefore, one orbital is nonbonding and rest is then divided into two equal halves as bonding and antibonding molecular orbitals. In $2,4,6-\text{heptatrienyl cation}$, a total of seven carbon atoms are present which give rise to seven $\text{π}$ molecular orbitals. The first three are bonding molecular orbitals and the last three are antibonding molecular orbitals. The middle molecular orbital that is ${\text{π}}_{\text{4}}$ is a nonbonding molecular orbital.

Conclusion

In $2,4,6-\text{heptatrienyl cation}$ molecule, the nonbonding MO is ${\text{π}}_{\text{4}}$ molecular orbital.

Interpretation Introduction

(b)

Interpretation:

Each molecular orbital of $2,4,6-\text{heptatrienyl cation}$ is to be classified as symmetric and antisymmetric.

Concept introduction:

The molecular orbital is a combination of two atomic orbitals. It is used to represent the regions in a molecule where the electron is likely to be present in an orbital. It represents the wave-like nature of an electron in a molecule. It may be symmetric or antisymmetric. It may be bonding, antibonding or non-bonding. It may be HOMO or LUMO.

Answer to Problem 28.4P

The molecular orbitals ${\text{π}}_1{\text{, π}}_3{\text{, π}}_5^{\ast },{\text{π}}_{\text{7}}^{\text{*}}$ are symmetric and the molecular orbitals ${\text{π}}_2{\text{, π}}_{\text{4}}^{\text{n}}{\text{, π}}_6^{\ast }$ are antisymmetric molecular orbital.

Explanation of Solution

In molecular orbital theory, the MO is said to be symmetric or anti-symmetric depending on the relative phase of the two terminal carbons. In symmetric MO, the peaks reflect across the reference plane into the peaks and troughs reflect into troughs. On the other hand, in antisymmetric MO, the peaks reflect into troughs and vice versa. According to the general principle, the even number molecular orbitals are antisymmetric and odd number molecular orbitals are symmetric. Therefore, the molecular orbitals ${\text{π}}_1{\text{, π}}_3{\text{, π}}_5^{\ast },{\text{π}}_{\text{7}}^{\text{*}}$ are symmetric and the molecular orbitals ${\text{π}}_2{\text{, π}}_{\text{4}}^{\text{n}}{\text{, π}}_6^{\ast }$ are antisymmetric.

Conclusion

The molecular orbitals ${\text{π}}_1{\text{, π}}_3{\text{, π}}_5^{\ast },{\text{π}}_{\text{7}}^{\text{*}}$ are symmetric and the molecular orbitals ${\text{π}}_2{\text{, π}}_{\text{4}}^{\text{n}}{\text{, π}}_6^{\ast }$ are antisymmetric molecular orbital.

Interpretation Introduction

(c)

Interpretation:

The carbon on which the positive charge is delocalized is to be stated. The explanation on the basis of resonance structures and molecular orbital arguments is to be stated.

Concept introduction:

The molecular orbital is a combination of two atomic orbitals. It is used to represent the regions in a molecule where the electron is likely to be present in an orbital. It represents the wave-like nature of an electron in a molecule. Most of the organic structures cannot be represented using a single Lewis structure. Therefore, there exists more than one Lewis structure for representing a molecule or ion. These structures are known as resonance structures. The delocalization of electrons results in the formation of resonance structure.

Answer to Problem 28.4P

The positive charge is delocalized over $\text{C1, C3, C5, C7}$ carbon atoms.

Explanation of Solution

The resonance structure of $2,4,6-\text{heptatrienyl cation}$ is shown below.

Figure 1

The resonance structures of $2,4,6-\text{heptatrienyl cation}$ shows that the positive charge is delocalized over $\text{C1, C3, C5, C7}$ positions. The molecular orbital diagram of $2,4,6-\text{heptatrienyl cation}$ is shown below.

Figure 2

According to the general principle if the node is passing through the carbon then the positive charge is not present on that carbon. In this molecular orbital diagram, the node is passing through the $\text{C2, C4, C6}$ positions that mean positive charge is not present on these positions. Therefore, both resonance and molecular orbital arguments confirm that positive charge resides over $\text{C1, C3, C5, C7}$ positions.

Conclusion

The positive charge is delocalized over $\text{C1, C3, C5, C7}$ positions.