Question

Construct MO energy diagrams for the cyclopropenyl cation, radical, and anion. Which of these species is aromatic according to the Hückel criteria?

Short answer

Answer: The cyclopropenyl cation is aromatic according to the Hückel criteria.

Step-by-step solution

Determine the number of π-electrons

Cyclopropenyl cation has two π-electrons, the radical has three π-electrons, and the anion has four π-electrons.

Construct the MO energy diagram for the cyclopropenyl cation

Draw an energy diagram with two energy levels (1 and -1). Place two electrons in the lower energy level (-1). The MO energy diagram for cyclopropenyl cation is: E =------------- | ↑↓ --------- (1) | ↑↓ E =------------- -------- (-1)

Construct the MO energy diagram for the cyclopropenyl radical

Draw an energy diagram with three energy levels (1,0, and -1). Place three electrons in the energy levels: two in the lower level (-1) and one in the highest level (1). The MO energy diagram for the cyclopropenyl radical is: E =------------- | ↑ --------- (1) | E =------------- | ↑↓ -------- (-1)

Construct the MO energy diagram for the cyclopropenyl anion

Draw an energy diagram with three energy levels (1,0, and -1). Place four electrons in the energy levels: two in the lower level (-1) and two in the highest level (1). The MO energy diagram for the cyclopropenyl anion is: E =------------- | ↑↓ --------- (1) | E =------------- | ↑↓ -------- (-1)

Apply the Hückel criteria and determine aromaticity

- Cyclopropenyl cation: The Hückel criteria require (4n+2) π-electrons. With two π-electrons, this corresponds to n=0, and thus the cation is aromatic. - Cyclopropenyl radical: With three π-electrons, the Hückel criteria are not met, and thus the radical is not aromatic. - Cyclopropenyl anion: With four π-electrons, the Hückel criteria are not met, as it doesn't follow the (4n+2) rule. Therefore the anion is not aromatic. In conclusion, only the cyclopropenyl cation is aromatic, according to the Hückel criteria.

Key concepts

Hückel criteria

The Hückel criteria is a fundamental concept in determining the aromaticity of organic compounds. It provides a rule based on the number of π-electrons present in a compound. The criteria state that a molecule can be considered aromatic if it has \( (4n + 2) \) π-electrons, where \( n \) is a non-negative integer (0, 1, 2, etc.).

• This rule helps identify if a compound has a delocalized π-electron system that contributes to a lower energy structure, characteristic of aromaticity.


• Examples of commonly known aromatic compounds include benzene with 6 π-electrons (n = 1), perfectly fitting the Hückel rule.

Applying the Hückel criteria to solve exercises usually involves counting the π-electrons present in the system and determining if the electron count fits the formula. It's crucial to understand that a structure also needs to be cyclic and planar for these criteria to be applied successfully. This provides guidance not only in understanding aromaticity but also in predicting the stability and reactivity of molecules in organic chemistry.

Aromaticity

Aromaticity is a concept central to the stability and chemical behavior of certain cyclic compounds. Aromatic compounds are known for their remarkable stability, distinct from non-aromatic and anti-aromatic compounds.

• Aromatic compounds have a fully conjugated π-electron system in a ring that is cyclic, planar, and adheres to the Hückel rule.


• The electrons in these compounds are delocalized, which leads to additional stabilization. This delocalization can often be visualized through resonance structures.

In practical terms, aromaticity can influence properties such as reactivity, making some compounds more desirable for reactions or applications. For instance, the aromatic ring provides stabilization through a phenomenon known as resonance energy; this makes the compound's π-electron system more stable than any single resonance structure could predict. Understanding aromaticity is foundational in organic chemistry, especially when predicting the behavior of molecules in synthetic pathways.

Cyclopropenyl cation

The cyclopropenyl cation is an interesting example of a positively-charged aromatic molecule. It serves as a perfect case study in applying the Hückel criteria to determine aromaticity.

• The cation consists of a three-membered carbon ring with one of the carbons carrying a positive charge. This configuration results in a total of two π-electrons.


• According to the Hückel criteria, these two π-electrons satisfy the \( (4n + 2) \) rule with \( n = 0 \), confirming its aromatic nature.

Despite the inherent strain of a three-membered cycle, the cyclopropenyl cation's aromaticity accounts for its unexpected stability. In comparison to its radical and anion counterparts, neither satisfies the aromaticity requirements posed by the Hückel criteria. Thus, the cyclopropenyl cation is notably distinct in possessing aromatic character, which is both insightful and crucial for understanding its unique properties in chemical reactions.