Problem 19 - Advanced Organic Chemistry. Part A. Structure and Mechanisms

Question

Using isodesmic reactions and the G2(MP2) energies given below, determine if \(1,2,3\)-trichlorocyclopropenium ion is more or less stable than the tert-butyl carbocation. Are the chlorine substituents stabilizing or destabilizing with respect to cyclopropenium ion? $$ \begin{array}{lc} \hline {\text { Substance }} & \begin{array}{c} \text { G2(MP2) energy } \\ \text { (hartrees) } \end{array} \\ \hline \text { Trichlorocyclopropenium } & -1492.916633 \\ \text { Cyclopropenium ion } & -115.492839 \\ \text { tert } \text {-Butyl carbocation } & -157.169332 \\ 1,2,3,3 \text {-tetrachlorocyclopropene } & -1952.950661 \\ 3 \text {-Chlorocyclopropene } & -575.525577 \\ \text { tert } \text {-Butyl chloride } & -617.226718 \end{array} $$

Step-by-Step Solution

Answer

1,2,3-Trichlorocyclopropenium ion is less stable; chlorine is stabilizing.

Step 1: Identify the Isodesmic Reactions

In an isodesmic reaction, the number and types of chemical bonds are conserved. To compare stabilities using isodesmic reactions, construct two reactions: one comparing 1,2,3-trichlorocyclopropenium ion to a known stable compound (like tert-butyl carbocation), and another comparing substituted and unsubstituted versions of the same base structure, such as chlorinated versus non-chlorinated cyclopropenes.

Step 2: Construct Reaction Equations

For this comparison, define two isodesmic reaction equations:1. \[\text{Trichlorocyclopropenium ion} + \text{tert-butyl chloride} \rightarrow \text{tert-butyl carbocation} + 1,2,3,3\text{-tetrachlorocyclopropene}\]2. \[\text{Trichlorocyclopropenium ion} + \text{3-chlorocyclopropene} \rightarrow \text{Cyclopropenium ion} + 1,2,3,3\text{-tetrachlorocyclopropene} \]

Step 3: Calculate Reaction Energies

For each reaction, calculate the energy change (\(\Delta E \)) using the G2(MP2) energies:**Reaction 1:** \[\Delta E_1 = (-1492.916633 + -617.226718) - (-157.169332 + -1952.950661) = 0.209288 \] **Reaction 2:**\[\Delta E_2 = (-1492.916633 + -575.525577) - (-115.492839 + -1952.950661) = -0.998710 \]

Step 4: Analyze the Energies

Interpret the energy changes. A positive \(\Delta E\) indicates the products are higher in energy (less stable) compared to the reactants, while a negative \(\Delta E\) indicates a more stable product formation:1. Reaction 1 (\(\Delta E_1 = 0.209288\)): Positive, suggesting that tert-butyl carbocation is more stable than the trichlorocyclopropenium ion.2. Reaction 2 (\(\Delta E_2 = -0.998710\)): Negative, suggesting that chlorine substituents have a stabilizing effect on the cyclopropenium ion structure.

Key Concepts

G2(MP2) energies

G2(MP2) energies are a sophisticated type of quantum chemical calculations.
They give very accurate energy values in hartrees for molecules and ions.
Hartree is a unit of energy often used in quantum chemistry.

• G2(MP2) stands for Gaussian-2 theory with second-order Møller-Plesset perturbation theory.
• These calculations account for many-body effects and electron correlation, making them a reliable choice for establishing relative stabilities in molecules.

In the exercise above, these energies are used to evaluate the stability of molecules.
By comparing energies from reactions, we determine which species are more stable, such as between 1,2,3-trichlorocyclopropenium ion and tert-butyl carbocation.
Understanding and using these energies involves calculating energy changes (\( \Delta E \)) in reactions, helping predict compound stability.

Trichlorocyclopropenium ion stability

The trichlorocyclopropenium ion is a cyclopropenium ring with three chlorine atoms.
Stability in ions like this can be influenced by substituents, such as chlorine.

• In the given reactions, the trichlorocyclopropenium ion is compared to more and less stable compounds.
• This helps to see if the chlorine atoms make it more or less stable.

By using isodesmic reactions, the exercise determines if the ion is more stable than the tert-butyl carbocation.
Isodesmic reactions help in maintaining the types and numbers of bonds so comparisons focus on the effects of substituents, like chlorine.
Calculations show that trichlorocyclopropenium is less stable when compared to the tert-butyl carbocation (\( \Delta E_1 = 0.209288 \)).

tert-Butyl carbocation

The tert-butyl carbocation is a positively charged ion with four substituents coming from a central carbon atom.
It is known for its relatively high stability among carbocations due to hyperconjugation and branching.

• In comparing its stability using the energy changes from reactions, the tert-butyl carbocation serves as a benchmark.
• It is used to see how stable the trichlorocyclopropenium ion is.

The calculations show that the tert-butyl carbocation is more stable than the trichlorocyclopropenium ion since reaction one has a positive \( \Delta E \).
This is due to its inherent structure, where electron donations from alkyl groups stabilize the positively charged carbon.

Chlorine substituent effects

Chlorine atoms can significantly impact the stability of organic ions and molecules, often through inductive effects and resonance.

• Inductive effects involve the electron-withdrawing nature of chlorine, which can stabilize positive charges by delocalizing them over a molecule.
• Resonance involves the sharing of electrons across multiple atoms, further stabilizing the molecule.

In this exercise, trichlorocyclopropenium ion and other chlorinated compounds benefit from chlorine's stabilizing influence.
This is evident in the second reaction, where \( \Delta E_2 = -0.998710 \) indicates that the chlorine atoms lead to a more stable product.
The presence of chlorine allows for greater charge delocalization, making these ions more stable than their non-chlorinated counterparts.