## Question Restated **Draw all the molecular orbitals of the cation of cyclopentadiene. Discuss, by correlating the appropriate number of electrons in the correct orbitals, whether the molecule is aromatic or antiaromatic.** --- ## Step 1: Cyclopentadiene and Its Cation - **Cyclopentadiene** has the formula C₅H₆. - The **cation** means one electron is removed, forming C₅H₅⁺. --- ## Step 2: π Electron Count - Cyclopentadiene’s π system comes from its double bonds. - **C₅H₆**: 4 π electrons (from two double bonds). - **C₅H₅⁺**: Removing one electron → **3 π electrons**. --- ## Step 3: Molecular Orbitals of Cyclopentadienyl System For a 5-membered ring (like cyclopentadiene): - There are **5 p orbitals** combining to give **5 molecular orbitals**. - These are filled according to energy (from lowest to highest): 1. **ψ₁**: Lowest (bonding, fully symmetric) 2. **ψ₂, ψ₃**: Degenerate (bonding, one node each) 3. **ψ₄, ψ₅**: Degenerate (antibonding, two nodes each) ### Energy Diagram (Frost Circle) ``` ψ₅* (antibonding, 2 nodes) ------ | | ψ₄*, ψ₃* (degenerate antibonding, 1 node each) ------ | | ψ₂, ψ₃ (degenerate bonding, 1 node each) ------ ψ₁ (fully bonding) ------ ``` ### Electron Filling (C₅H₅⁺: 3 π electrons) - **ψ₁**: 2 electrons (filled) - **ψ₂ or ψ₃**: 1 electron (half-filled) - **ψ₄, ψ₅**: electrons --- ## Step 4: Aromatic or Antiaromatic? **Aromaticity rules:** - Follows Hückel’s rule: \(4n+2\) π electrons (n = , 1, 2, ...) - Planar, cyclic, fully conjugated system **Antiaromaticity:** - Has \(4n\) π electrons ### For C₅H₅⁺ (Cyclopentadienyl cation): - **3 π electrons** - **Does NOT satisfy \(4n+2\) rule** - Has an unpaired electron in a non-bonding orbital - **Unstable, highly reactive (antiaromatic)** --- ## Step 5: Drawing the Molecular Orbitals Here’s a schematic (energy increases upwards): ``` ψ₅* ( e⁻) ------ ψ₄*, ψ₃* ( e⁻) ------ ψ₂, ψ₃ (1 e⁻ in one, in other) ------ ψ₁ (2 e⁻) ------ ``` - Total: 3 electrons, with one unpaired in a degenerate orbital. --- ## Step 6: Summary Table | Orbital | Number of electrons | Bonding/Nonbonding/Antibonding | |--------------|--------------------|-------------------------------| | ψ₁ | 2 | Bonding | | ψ₂/ψ₃ | 1 (in one) | Nonbonding | | ψ₄/ψ₅ | | Antibonding | --- ## Conclusion - **Cyclopentadienyl cation (C₅H₅⁺) has 3 π electrons.** - **Its molecular orbital diagram shows an unpaired electron in a non-bonding orbital.** - **Does not satisfy Hückel’s rule for aromaticity (\(4n+2\)), nor is it stable.** - **It is antiaromatic and highly unstable.** --- ### Let me know if you’d like a drawn molecular orbital diagram!