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. The cyclopropenyl radical and anion do not satisfy the Hückel criteria for aromaticity.

Step-by-step solution

Review the Hückel criteria

The Hückel criteria for aromaticity are: 1. The molecule must be planar. 2. The molecule must be cyclic. 3. The molecule must have a continuous ring of overlapping p-orbitals, where each atom in the ring has an unpaired electron in a p-orbital perpendicular to the plane of the ring. 4. The molecule must have 4n+2 π-electrons, where n is a non-negative integer (n = 0, 1, 2, ...). Now, let's analyze each species (cation, radical, and anion) based on these criteria.

Construct the MO energy diagram for the cyclopropenyl cation

The cyclopropenyl cation has 3 carbons in the ring and a positive charge. Therefore, the cation has 2 π-electrons, as each carbon atom contributes 1 π-electron and the positive charge removes 1 π-electron. We need to construct the MO energy diagram for this species. 1. Each carbon atom contributes a p-orbital, so there are 3 p-orbitals in total. 2. Construct the MO diagram by combining these 3 p-orbitals. There will be 3 molecular orbitals as a result, one is bonding (lowest energy), one is non-bonding (middle energy), and one is antibonding (highest energy). 3. Fill the 2 π-electrons into the molecular orbitals, starting with the lowest energy. The 2 π-electrons will fill the bonding MO. The cyclopropenyl cation has a planar, cyclic structure with a continuous ring of overlapping p-orbitals, satisfying the Hückel criteria (1-3). Moreover, the number of π-electrons (2) follows the 4n+2 rule for n=0, which satisfies Hückel criterion 4. Therefore, the cyclopropenyl cation is aromatic.

Construct the MO energy diagram for the cyclopropenyl radical

The cyclopropenyl radical has 3 carbons in the ring and 1 unpaired electron. This species has 3 π-electrons in total, as each carbon atom contributes 1 π-electron. Follow the same steps as in Step 2 to construct the MO energy diagram for the cyclopropenyl radical. Fill the 3 π-electrons into the molecular orbitals, starting with the lowest energy. The 3 π-electrons fill the bonding MO and one electron goes to the non-bonding MO. The cyclopropenyl radical fulfills the Hückel criteria (1-3), but it does not follow the 4n+2 rule, as the number of π-electrons (3) does not fit the rule. Hence, the cyclopropenyl radical is not aromatic.

Construct the MO energy diagram for the cyclopropenyl anion

The cyclopropenyl anion has 3 carbons in the ring and a negative charge. The anion has a total of 4 π-electrons, as each carbon atom contributes 1 π-electron and the negative charge adds 1 π-electron. Construct the MO energy diagram for the cyclopropenyl anion following the same procedure as in Steps 2 and 3. Fill the 4 π-electrons into the molecular orbitals, starting with the lowest energy. The 4 π-electrons fill both the bonding MO and the non-bonding MO. The cyclopropenyl anion satisfies the Hückel criteria (1-3). However, the number of π-electrons (4) does not follow the 4n+2 rule, so the cyclopropenyl anion is not aromatic.

Final Results

Based on the molecular orbital energy diagrams and Hückel criteria analysis, only the cyclopropenyl cation is aromatic among the three species. The cyclopropenyl radical and anion do not satisfy the Hückel criteria for aromaticity.