Chapter D, Problem D.1P

Interpretation Introduction

Interpretation:

The orbital interaction that represents hyperconjugation in ${\text{CF}}_{\text{3}}{\text{CH}}_{\text{2}}{}^{\text{+}}$ is to be drawn. The hyperconjugation lead to greater stabilization in this ${\text{CF}}_{\text{3}}{\text{CH}}_{\text{2}}{}^{\text{+}}$ or in ${\text{CH}}_{\text{3}}{\text{CH}}_{\text{2}}{}^{\text{+}}$ would expect is to be explained.

Concept introduction:

Relative stabilities of carbocations are explained by hyperconjugation. In the case of primary carbocations like ${\text{RCH}}_{\text{2}}{}^{\text{+}}$, $\text{ρ}$ AO is aligned with one of the $\text{C-H}$ bonds in the adjacent R group, which represents a pair of electrons occupying a $\text{C-H}$$\text{σ}$ bonding orbital. The empty $\text{ρ}$ AO and the $\text{σ}$ bonding orbital therefore interact. In this case, constructive interference results in a new orbital that is more stable than the $\text{σ}$ bonding orbital. The two electrons from the $\text{σ}$ bonding MO end up in the lower-energy of the two new orbitals and are thus stabilized. The mixing of these orbitals effectively transfers some electron density from the alkyl group into the empty $\text{ρ}$ AO.

Answer to Problem D.1P

The orbital interaction that represents hyperconjugation in ${\text{CF}}_{\text{3}}{\text{CH}}_{\text{2}}{}^{\text{+}}$ is,

The hyperconjugation leads to greater stabilization for the ${\text{CH}}_{\text{3}}{\text{CH}}_{\text{2}}{}^{\text{+}}$ ion.

Explanation of Solution

In ${\text{CF}}_{\text{3}}{\text{CH}}_{\text{2}}{}^{\text{+}}$ ion, the filled $\text{σ}$ bonding orbital is of the adjacent $\text{C-F}$ bond of ${\text{CF}}_{\text{3}}$ which can interact with the empty $\text{ρ}$ AO of ${\text{CH}}_{\text{2}}{}^{+}$ as the empty $\text{ρ}$ AO overlaps with $\text{σ}$ bonding orbital of the $\text{C-F}$ bond. It is shown below:

Also, in ${\text{CH}}_{\text{3}}{\text{CH}}_{\text{2}}{}^{\text{+}}$, the empty $\text{ρ}$ AO overlaps with $\text{σ}$ bonding orbital of ${\text{CH}}_{\text{3}}$ bond of ${\text{CH}}_{\text{3}}$, so the two orbitals can interact. The two electrons from the $\text{σ}$ bonding MO end up in the lower-energy of the two new orbitals and are thus stabilized.

The orbital interactions for both ${\text{CF}}_{\text{3}}{\text{CH}}_{\text{2}}{}^{\text{+}}$ and ${\text{CH}}_{\text{3}}{\text{CH}}_{\text{2}}{}^{\text{+}}$ are shown below,

The F atom is more electronegative than H, therefore the $\text{C-F}$$\text{σ}$ bonding orbital is in lower energy than that of the ${\text{CH}}_{\text{3}}$ bond of ${\text{CH}}_{\text{3}}{\text{CH}}_{\text{2}}{}^{\text{+}}$. Therefore, the $\text{ΔE}$ for the overlap of the empty $\text{ρ}$ AO with $\text{C-F}$$\text{σ}$ bonding orbital is smaller than that for overlap of the empty $\text{ρ}$ AO and ${\text{CH}}_{\text{3}}$$\text{σ}$ bonding orbital. Thus, hyperconjugation leads to greater stabilization for the ${\text{CH}}_{\text{3}}{\text{CH}}_{\text{2}}{}^{\text{+}}$ ion.

Conclusion

The cation in which hyperconjugation would leads to greater stabilization is determined on the basis of orbital interactions shown above.