Chapter 14, Problem 14.38P

Interpretation Introduction

(a)

Interpretation:

The $\text{π}$ MO energy diagram for the given line structure of cyclic ion is to be drawn and whether the ion is aromatic or antiaromatic is to be determined.

Concept introduction:

The relative energies of fully conjugated cyclic $\text{π}$ MOs can be derived using Frost method. The steps involved in Frost method are as follows:

• The polygon representing the line structure of the cyclic compound is drawn by pointing one of the vertices directly downward.
• The horizontal dashed line is drawn through the center of the polygon.
• A short horizontal solid line is drawn at each vertex, and the $\text{π}$ electrons are distributed among them, indicating the energies of $\text{π}$ MOs.
• The distribution of $\text{π}$ electrons starts from the lowest energy $\text{π}$ MO and continues to the highest energy $\text{π}$ MO.
• According to Hund’s rule, each MO is occupied by two electrons with opposite spin before moving to a higher energy MO.

The short solid lines below the central dashed line represent the bonding $\text{π}$ MOs; those above the central dashed line represent the antibonding $\text{π}$ MOs, and those right on the central dashed line represent the nonbonding $\text{π}$ MOs. If the bonding $\text{π}$ MOs are completely filled, each with two electrons while the antibonding and nonbonding $\text{π}$ MOs are empty, then the molecule is said to be an aromatic.

Answer to Problem 14.38P

The given line structure of the cyclic ion is aromatic according to the $\text{π}$ MO energy diagram as shown below:

Explanation of Solution

The given line structure of the cyclic ion is:

The given ion is trigonal and has three vertices with $\text{2π}$ electrons. The trigonal line structure is drawn by pointing one vertex directly downward and placing the horizontal dashed line through the center.

The short solid horizontal lines are drawn at each vertex representing the energies of $\text{π}$ MOs as bonding and antibonding. Then these $\text{π}$ MOs are filled by $\text{2π}$ electrons according to Hund’s rule.

As the bonding $\text{π}$ MO is fully occupied and antibonding $\text{π}$ MOs are fully unoccupied, the ion is said to be aromatic.

Conclusion

The given cyclic ion is determined as aromatic based on $\text{π}$ MO energy diagram.

Interpretation Introduction

(b)

Interpretation:

The $\text{π}$ MO energy diagram for the given line structure of a cyclic ion is to be drawn and whether the ion is aromatic or antiaromatic is to be determined.

Concept introduction:

The relative energies of fully conjugated, cyclic $\text{π}$ MOs can be derived using Frost method. The steps involved in Frost method are as follows:

• The polygon representing the line structure of cyclic compound is drawn by pointing one of the vertices directly downward.
• The horizontal dashed line is drawn through the center of polygon.
• A short horizontal solid line is drawn at each vertex, and the $\text{π}$ electrons are distributed among them indicating the energies of $\text{π}$ MOs.
• The distribution of $\text{π}$ electrons starts from the lowest energy $\text{π}$ MO and continues to highest energy $\text{π}$ MO.
• According to Hund’s rule, each MO is occupied by two electrons with opposite spin before moving to higher energy MO.

The short solid lines below the central dashed line represent the bonding $\text{π}$ MOs; those above the central dashed line represent the antibonding $\text{π}$ MOs, and those right on the central dashed line, represent the nonbonding $\text{π}$ MOs. If the bonding $\text{π}$ MOs are completely filled, each with two electrons while the antibonding and nonbonding $\text{π}$ MOs are empty, then the molecule is said to be aromatic.

Answer to Problem 14.38P

The given line structure of the cyclic ion is antiaromatic according to the $\text{π}$ MO energy diagram as shown below:

Explanation of Solution

The given line structure of the cyclic ion is:

The given ion is trigonal and has three vertices with $\text{4π}$ electrons (two from the lone pair on negatively charged carbon). The trigonal line structure is drawn by pointing one vertex directly downward and placing a horizontal dashed line through the center.

The short solid horizontal lines are drawn at each vertex representing the energies of $\text{π}$ MOs as bonding and antibonding. Then these $\text{π}$ MOs are filled by $\text{4π}$ electrons according to Hund’s rule.

As the bonding $\text{π}$ MO is fully occupied and antibonding $\text{π}$ MOs are partially occupied, the ion is said to be antiaromatic.

Conclusion

The given cyclic ion is determined as antiaromatic based on $\text{π}$ MO energy diagram.

Interpretation Introduction

(c)

Interpretation:

The $\text{π}$ MO energy diagram for the given line structure of cyclic ion is to be drawn and whether the ion is aromatic or antiaromatic is to be determined.

Concept introduction:

The relative energies of fully conjugated, cyclic $\text{π}$ MOs can be derived using Frost method. The steps involved in Frost method are as follows:

• The polygon representing the line structure of cyclic compound is drawn by pointing one of the vertices directly downward.
• The horizontal dashed line is drawn through the center of the polygon.
• A short horizontal solid line is drawn at each vertex, and the $\text{π}$ electrons are distributed among them, indicating the energies of $\text{π}$ MOs.
• The distribution of $\text{π}$ electrons starts from the lowest energy $\text{π}$ MO and continues to highest energy $\text{π}$ MO.
• According to Hund’s rule, each MO is occupied by two electrons with opposite spin before moving to higher energy MO.

The short solid lines below the central dashed line represent the bonding $\text{π}$ MOs; those above the central dashed line represent the antibonding $\text{π}$ MOs, and those right on the central dashed line represent the nonbonding $\text{π}$ MOs. If the bonding $\text{π}$ MOs are completely filled, each with two electrons while the antibonding and nonbonding $\text{π}$ MOs are empty, then the molecule is said to be aromatic.

Answer to Problem 14.38P

The given line structure of the cyclic ion is antiaromatic according to the $\text{π}$ MO energy diagram as shown below:

Explanation of Solution

The given line structure of cyclic ion is:

The given ion is pentagonal and has five vertices with $\text{4π}$ electrons. The pentagonal line structure is drawn by pointing one vertex directly downward and placing the horizontal dashed line through the center.

The short solid horizontal lines are drawn at each vertex representing the energies of $\text{π}$ MOs as bonding and antibonding. Then these $\text{π}$ MOs are filled by $\text{4π}$ electrons according to Hund’s rule.

As the bonding $\text{π}$ MOs are partially occupied, the ion is said to be an antiaromatic.

Conclusion

The given cyclic ion is determined as antiaromatic based on $\text{π}$ MO energy diagram.

Interpretation Introduction

(d)

Interpretation:

The $\text{π}$ MO energy diagram for the given line structure of cyclic ion is to be drawn and whether the ion is aromatic or antiaromatic is to be determined.

Concept introduction:

The relative energies of fully conjugated, cyclic $\text{π}$ MOs can be derived using Frost method. The steps involved in Frost method are as follows:

• The polygon representing the line structure of cyclic compound is drawn by pointing one of the vertices directly downward.
• The horizontal dashed line is drawn through the center of polygon.
• A short horizontal solid line is drawn at each vertex, and the $\text{π}$ electrons are distributed among them, indicating the energies of $\text{π}$ MOs.
• The distribution of $\text{π}$ electrons starts from the lowest energy $\text{π}$ MO and continues to highest energy $\text{π}$ MO.
• According to Hund’s rule, each MO is occupied by two electrons with opposite spin before moving to higher energy MO.

The short solid lines below the central dashed line represent the bonding $\text{π}$ MOs; those above the central dashed line represent the antibonding $\text{π}$ MOs, and those right on the central dashed line represent the nonbonding $\text{π}$ MOs. If the bonding $\text{π}$ MOs are completely filled, each with two electrons while the antibonding and nonbonding $\text{π}$ MOs are empty, then the molecule is said to be aromatic.

Answer to Problem 14.38P

The given line structure of cyclic ion is aromatic according to the $\text{π}$ MO energy diagram as shown below:

Explanation of Solution

The given line structure of cyclic ion is:

The given ion is pentagonal and has five vertices with $\text{6π}$ electrons (two from lone pair on negatively charged carbon). The pentagonal line structure is drawn by pointing one vertex directly downward and placing the horizontal dashed line through the center.

The short solid horizontal lines are drawn at each vertex representing the energies of $\text{π}$ MOs as bonding and antibonding. Then, these $\text{π}$ MOs are filled by $\text{6π}$ electrons according to Hund’s rule.

As the bonding $\text{π}$ MOs are fully occupied and antibonding $\text{π}$ MOs are fully unoccupied, the ion is said to be aromatic.

Conclusion

The given cyclic ion is determined as aromatic based on $\text{π}$ MO energy diagram.

Interpretation Introduction

(e)

Interpretation:

The $\text{π}$ MO energy diagram for the given line structure of cyclic ion is to be drawn and whether the ion is aromatic or antiaromatic is to be determined.

Concept introduction:

The relative energies of fully conjugated, cyclic $\text{π}$ MOs can be derived using Frost method. The steps involved in Frost method are as follows:

• The polygon representing the line structure of cyclic compound is drawn by pointing one of the vertices directly downward.
• The horizontal dashed line is drawn through the center of the polygon.
• A short horizontal solid line is drawn at each vertex, and the $\text{π}$ electrons are distributed among them, indicating the energies of $\text{π}$ MOs.
• The distribution of $\text{π}$ electrons starts from the lowest energy $\text{π}$ MO and continues to highest energy $\text{π}$ MO.
• According to Hund’s rule, each MO is occupied by two electrons with opposite spin before moving to higher energy MO.

The short solid lines below the central dashed line represent the bonding $\text{π}$ MOs; those above the central dashed line represent the antibonding $\text{π}$ MOs and those right on the central dashed line represent the nonbonding $\text{π}$ MOs. If the bonding $\text{π}$ MOs are completely filled, each with two electrons while the antibonding and nonbonding $\text{π}$ MOs are empty, then the molecule is said to be aromatic.

Answer to Problem 14.38P

The given line structure of cyclic ion is aromatic according to the $\text{π}$ MO energy diagram as shown below:

Explanation of Solution

The given line structure of the cyclic ion is:

The given ion is heptagonal and has seven vertices with $\text{6π}$ electrons. The heptagonal line structure is drawn by pointing one vertex directly downward and placing the horizontal dashed line through the center.

The short solid horizontal lines are drawn at each vertex representing the energies of $\text{π}$ MOs as bonding and antibonding. Then, these $\text{π}$ MOs are filled by $\text{6π}$ electrons according to Hund’s rule.

As the bonding $\text{π}$ MOs are fully occupied and antibonding $\text{π}$ MOs are fully unoccupied, the ion is said to be aromatic.

Conclusion

The given cyclic ion is determined as aromatic based on $\text{π}$ MO energy diagram.

Interpretation Introduction

(f)

Interpretation:

The $\text{π}$ MO energy diagram for the given line structure of cyclic ion is to be drawn and whether the ion is aromatic or antiaromatic is to be determined.

Concept introduction:

The relative energies of fully conjugated, cyclic $\text{π}$ MOs can be derived using Frost method. The steps involved in Frost method are as follows:

• The polygon representing the line structure of cyclic compound is drawn by pointing one of the vertices directly downward.
• The horizontal dashed line is drawn through the center of the polygon.
• A short horizontal solid line is drawn at each vertex and the $\text{π}$ electrons are distributed among them, indicating the energies of $\text{π}$ MOs.
• The distribution of $\text{π}$ electrons starts from the lowest energy $\text{π}$ MO and continues to the highest energy $\text{π}$ MO.
• According to Hund’s rule, each MO is occupied by two electrons with opposite spin before moving to higher energy MO.

The short solid lines below the central dashed line represent the bonding $\text{π}$ MOs; those above the central dashed line represent the antibonding $\text{π}$ MOs, and those right on the central dashed line represent the nonbonding $\text{π}$ MOs. If the bonding $\text{π}$ MOs are completely filled, each with two electrons while the antibonding and nonbonding $\text{π}$ MOs are empty then the molecule is said to be aromatic.

Answer to Problem 14.38P

The given line structure of the cyclic ion is antiaromatic according to the $\text{π}$ MO energy diagram as shown below:

Explanation of Solution

The given line structure of cyclic ion is:

The given ion is heptagonal and has seven vertices with $\text{8π}$ electrons. The heptagonal line structure is drawn by pointing one vertex directly downward and placing the horizontal dashed line through the center.

The short solid horizontal lines are drawn at each vertex representing the energies of $\text{π}$ MOs as bonding and antibonding. Then, these $\text{π}$ MOs are filled by $\text{6π}$ electrons according to Hund’s rule.

As the bonding $\text{π}$ MOs are fully occupied and antibonding $\text{π}$ MOs are partially occupied, the ion is said to be antiaromatic.

Conclusion

The given cyclic ion is determined as antiaromatic based on $\text{π}$ MO energy diagram.