Question

Describe the ground-state electron configuration of the cyclopentadienyl cation and radical. Assuming each species is planar, would you expect it to be aromatic or antiaromatic?

Short answer

Question: Describe the ground-state electron configuration of the cyclopentadienyl cation and radical and determine if each species is planar, aromatic, or antiaromatic. Answer: The cyclopentadienyl cation is planar and aromatic with 6 π electrons, while the cyclopentadienyl radical is planar and non-aromatic with 9 π electrons.

Step-by-step solution

Draw the structures of the cyclopentadienyl cation and radical

First, we need to draw the structures of the cyclopentadienyl cation and radical. The cyclopentadienyl cation is a five-membered ring with alternating single and double bonds, and a positive charge on one of the carbons. The cyclopentadienyl radical is a five-membered ring with four double bonds and one unpaired electron.

Determine the number of π electrons

Each double bond contributes 2 π electrons, and the unpaired electron contributes 1 π electron. So, the cyclopentadienyl cation has (3 double bonds x 2) = 6 π electrons, and the cyclopentadienyl radical has (4 double bonds x 2) + 1 = 9 π electrons.

Apply Hückel's rule

Hückel's rule states that a planar, cyclic, and conjugated molecule is aromatic if it has (4n+2) π electrons, where n is a non-negative integer. If a molecule has 4n π electrons, it is considered antiaromatic. Applying Hückel's rule to the cyclopentadienyl cation (6 π electrons): n=1 is a non-negative integer (6=4(1)+2), so it is aromatic. For the cyclopentadienyl radical (9 π electrons), there is no non-negative integer n that would satisfy Hückel's rule, so it is non-aromatic.

Determine the planarity of the species

Both the cyclopentadienyl cation and radical are considered planar due to their sp2 hybridization and conjugated π electron system.

Conclusion

The cyclopentadienyl cation has 6 π electrons, is planar, and is therefore aromatic according to Hückel's rule. The cyclopentadienyl radical has 9 π electrons, is also planar, but does not fulfill Hückel's rule, making it non-aromatic.

Key concepts

Electron Configuration

Understanding the electron configuration of molecules is crucial in chemistry as it helps predict the molecule's reactivity, bonding patterns, and even aromaticity. In the case of the cyclopentadienyl cation, it contains six π electrons arising from three double bonds within a five-membered ring. Specifically, its electron configuration includes a positively charged carbon atom, which affects the distribution of π electrons. On the other hand, the cyclopentadienyl radical holds nine π electrons due to an additional unpaired electron which brings a distinctive arrangement that does not conform to the pattern required for aromaticity.

Aromaticity

Aromaticity is a concept referring to a cyclic, planar molecule exhibiting unusual stability due to the delocalization of π electrons across the ring. These π electrons form a continuous loop above and below the plane of the atoms, creating a region of electron density that stabilizes the molecule. The cyclopentadienyl cation is considered aromatic because it has a closed-loop of six π electrons that can delocalize, which meets the criteria for aromaticity. However, the cyclopentadienyl radical does not enjoy this stability as its nine π electrons disrupt the continuous loop required for a molecule to be classified as aromatic.

Hückel's Rule

Hückel's rule is a simple yet powerful tool used to determine the aromaticity of cyclic compounds. According to this rule, a molecule can be classified as aromatic if it contains a planar ring of continuously overlapping p-orbitals and possesses a certain number of π electrons, specifically given by the formula (4n+2), where 'n' is an integer. The cyclopentadienyl cation, with six π electrons, fits perfectly with n=1, making it aromatic. Conversely, the cyclopentadienyl radical, with nine π electrons, does not satisfy this requirement for any value of n and is therefore non-aromatic.

π Electrons

π electrons play a key role in the chemical characteristics of molecules, especially in the context of aromaticity. They are electrons in molecular orbitals formed by the sideways overlap of p-orbitals, allowing for electron delocalization which contributes to molecular stability. In the structure of the cyclopentadienyl cation, six π electrons, which come from three double bonds, contribute to its aromaticity. However, the cyclopentadienyl radical has an odd number of nine π electrons, which disrupts potential aromatic stability. Thus, the number and arrangement of π electrons are central to predicting whether a molecule will display the extra stability associated with aromatic compounds.