Chapter 14, Problem 14.33P

Interpretation Introduction

(a)

Interpretation:

The bond length of the indicated $\text{C - C}$ single bond in $\text{hexa-1, 3, 5-triene}$ is about 146 pm, which is considerably shorter than that in ethane, ${\text{H}}_{\text{3}}{\text{C-CH}}_{\text{3}}$. It is to be determined how much shorter it is.

Concept introduction:

Weak resonance contributors give some single-bond character to the two terminal $\text{C = C}$ bonds, resulting in the lengthening of those bonds. Resonance contributors also give some double-bond character to the $\text{C - C}$ bond adjacent to the $\text{C = C}$ bond, resulting in the shortening of that bond.

Answer to Problem 14.33P

In $\text{hexa-1, 3, 5-triene}$, the indicated $\text{C - C}$ single bond is shortened by about $5\%$.

Explanation of Solution

The bond length of $\text{C - C}$ single bond in $\text{hexa-1, 3, 5-triene}$ is 146 pm is shown below:

The normal $\text{C - C}$ in ethane is 154 pm. Resonance contributors give some double-bond character to the $\text{C - C}$ bond shown above, resulting in the shortening of that bond. The bond length of $\text{C - C}$ single bond in $\text{hexa-1, 3, 5-triene}$ is shortened by 8 pm when compared to ethane. Therefore, in $\text{hexa-1, 3, 5-triene}$, the indicated $\text{C - C}$ single bond is shortened by about $5\%$.

Conclusion

The amount of shortening of $\text{C - C}$ single bond in $\text{hexa-1, 3, 5-triene}$ is determined by comparing it with the $\text{C - C}$ single bond in ethane.

Interpretation Introduction

(b)

Interpretation:

The bond length of the indicated $\text{C - C}$ single bond in $\text{hexa-1, 3, 5-triene}$ is about 146 pm, which is considerably shorter than that in ethane, ${\text{H}}_{\text{3}}{\text{C-CH}}_{\text{3}}$. It is to be determined which occupied $\text{π}$ MOs help decrease this bond length.

Concept introduction:

Resonance contributors give some double-bond character to the $\text{C - C}$ bond adjacent to the $\text{C = C}$ bond, resulting in the shortening of that bond. The occupied $\text{π}$ MOs that help decrease the $\text{C - C}$ bond length are the ones in which bonding interaction occurs.

Answer to Problem 14.33P

The occupied $\text{π}$ MOs that help decrease the indicated $\text{C - C}$ bond length in $\text{hexa-1, 3, 5-triene}$ are ${\text{π}}_1$ and ${\text{π}}_2$ are shown below:

Explanation of Solution

The bond length of $\text{C - C}$ single bond of $\text{hexa-1, 3, 5-triene}$ is 146 pm is shown below:

The occupied $\text{π}$ MOs that help decrease the $\text{C - C}$ bond length are the ones in which there is a bonding interaction between C2 and C3, as shown above. The three highest energy MOs do not contribute as they are not occupied. The occupied $\text{π}$ MOs in $\text{hexa-1, 3, 5-triene}$ are

Out of these, the occupied $\text{π}$ MOs that contribute to shortening of bond between C2 and C3 include ${\text{π}}_1$ and ${\text{π}}_2$, as shown below:

Conclusion

The occupied $\text{π}$ MOs that help decrease the indicated $\text{C - C}$ bond length in $\text{hexa-1, 3, 5-triene}$ are determined from the MO picture of $\text{hexa-1, 3, 5-triene}$.

Interpretation Introduction

(c)

Interpretation:

The bond length of the indicated $\text{C - C}$ single bond in $\text{hexa-1, 3, 5-triene}$ is about 146 pm, which is considerably shorter than that in ethane, ${\text{H}}_{\text{3}}{\text{C-CH}}_{\text{3}}$. It is to be explained if the length of the $\text{C - C}$ single bond will increase, decrease, or stay roughly the same if an electron were promoted from the HOMO to the LUMO.

Concept introduction:

The highest energy MO of $\text{π}$ bonding MOs, which are completely filled up, is generally the HOMO. The LUMO is the next highest energy unoccupied MO. The occupancy of LUMO essentially has no effect on the $\text{C - C}$ bond if the internuclear region of the atoms of the given $\text{C - C}$ bond shows neither a bonding nor an antibonding interaction. If the internuclear region of the HOMO shows the antibonding interaction on the removal of an electron from that orbital, the length of that $\text{C - C}$ bond decreases.

Answer to Problem 14.33P

If an electron were promoted from the HOMO to the LUMO, the length of the $\text{C - C}$ single bond of $\text{hexa-1, 3, 5-triene}$ would decrease.

Explanation of Solution

The $\text{π}$ MOs of ${\text{hexa-1, 3, 5-triene (H}}_{\text{2}}{\text{C = CH - CH = CH - CH = CH}}_{\text{2}}\text{)}$ are

If an electron is promoted from HOMO (${\text{π}}_3$) to LUMO (${\text{π}}_4$), the C2-C3 bond will shorten slightly. As C2-C3 internuclear region shows neither bonding nor antibonding interaction, the occupancy of LUMO has no essential effect on the bond length of the $\text{C - C}$ single bond. The C2-C3 internuclear region of HOMO shows an antibonding interaction.

Therefore, the removal of an electron from the HOMO contributes to a shorter C2-C3 bond.

Conclusion

If an electron were promoted from the HOMO to the LUMO, the length of the $\text{C - C}$ single bond would decrease as the C2-C3 internuclear region of HOMO is an antibonding interaction.