The relative stabilities of 1-phenylvinyl cations can be...

The relative stabilities of 1-phenylvinyl cations can be measured by determining the gas phase basicity of the corresponding alkynes. The table below gives data on free energy of protonation for substituted phenyethynes and phenylpropynes. These data give rise to the corresponding Yukawa-Tsuno relationships: $$ \begin{aligned} \text { For } \mathrm{ArC} \equiv \mathrm{CH}: \delta \Delta G^{\circ} &=-14.1\left(\sigma^{\circ}+1.21 \sigma_{\mathrm{R}}^{+}\right) \\ \text {For } \mathrm{ArC} \equiv \mathrm{CCH}_{3}: \delta \Delta G^{\circ} &=-13.3\left(\sigma^{\circ}+1.12 \sigma_{\mathrm{R}}^{+}\right) \end{aligned} $$ How do you interpret the values of $\rho$ and $r$ in these equations? Which system is more sensitive to the aryl substituents? How do you explain the difference in sensitivity? Sketch the resonance, polar, and hyperconjugative interactions that contribute to these substituent effects. What geometric constraints do these interactions place on the ions?

The relative stabilities of 1-phenylvinyl cations can be measured by determining the gas phase basicity of the corresponding alkynes. The table below gives data on free energy of protonation for substituted phenyethynes and phenylpropynes. These data give rise to the corresponding Yukawa-Tsuno relationships:
$$
\begin{aligned}
\text { For } \mathrm{ArC} \equiv \mathrm{CH}: \delta \Delta G^{\circ} &=-14.1\left(\sigma^{\circ}+1.21 \sigma_{\mathrm{R}}^{+}\right) \\
\text {For } \mathrm{ArC} \equiv \mathrm{CCH}_{3}: \delta \Delta G^{\circ} &=-13.3\left(\sigma^{\circ}+1.12 \sigma_{\mathrm{R}}^{+}\right)
\end{aligned}
$$
How do you interpret the values of $\rho$ and $r$ in these equations? Which system is more sensitive to the aryl substituents? How do you explain the difference in sensitivity? Sketch the resonance, polar, and hyperconjugative interactions that contribute to these substituent effects. What geometric constraints do these interactions place on the ions?

Key Concepts

Polar (Inductive) Effects

Polar or inductive effects pertain to the transmission of electron density along sigma bonds due to differences in electronegativity between substituents and the rest of the molecule. Such effects can either stabilize or destabilize reactive intermediates depending on whether electron density is withdrawn from or donated to the reaction centre.

Geometric Constraints

Stabilizing interactions like resonance and hyperconjugation require a specific geometric arrangement, often necessitating planarity for optimal orbital overlap. These constraints limit the possible conformations of the intermediate ions and influence the overall stabilization by dictating how effectively the substituents can interact with the reactive center.

Resonance Interactions

Resonance interactions involve the delocalization of electrons through a conjugated system, which can stabilize cations by distributing positive charge over a larger framework. These interactions depend on the proper alignment of p-orbitals and contribute significantly to the overall energetics of the system.

Hyperconjugation

Hyperconjugation is the stabilization arising from the overlap between filled sigma orbitals (often from alkyl groups) and an adjacent empty or partially filled p-orbital or ? system. This interaction provides additional delocalization of charge, which is especially significant in carbocation stabilization.

Reaction Constant (?)

The reaction constant (?) reflects the sensitivity of a reaction’s free energy to changes in substituent electronic properties. A higher magnitude of ? indicates that the reaction center is more strongly affected by the electron-donating or -withdrawing nature of substituents.

Resonance Sensitivity Parameter (r)

This parameter quantifies the additional influence of resonance interactions beyond the polar effects. It shows how much extra stabilization (or destabilization) a substituent can provide due to delocalization of charge, with larger values pointing to a greater role of conjugative interactions in stabilizing the ionic system.

Yukawa-Tsuno Equation

This equation models how substituents affect reaction energetics by combining a polar (inductive) component (expressed by a sigma constant) with an extra resonance term scaled by an additional parameter. It distinguishes the inherent electron-withdrawing or -donating effects from those arising through resonance stabilization.

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