Q15-15-30E - Organic Chemistry (Mcmurry)

Question

Draw an energy diagram for the three molecular orbitals of the cyclopropenyl system  (C₃H₃). How are these three molecular orbitals occupied in the cyclopropenyl anion, cation, and radical? Which of the three substances is aromatic according to Hückel’s rule?

Step-by-Step Solution

Answer

                                                       Energy diagram

Energy diagram

The three atomic p orbitals combine to give three pi molecular orbitals, there are lower energy and higher energy degenerate pair of orbitals. In two pi-electron cation, there are two electrons in ${\mathit{\psi }}_{\mathbf{1}}$and no electrons in ${\mathit{\psi }}_{\mathbf{2}}\mathbf{,}\mathbf{ }{\mathit{\psi }}_{\mathbf{3}}$ .

Energy diagram of cyclopropenyl system

In three pi-electron radicals, there are two electrons in ${\psi }_1$ and one electron in ${\psi }_2$, which is partially filled, thus it is antiaromatic. In the four pi-electron anions, there are two electrons in ${\psi }_1$  and one electron each in 2, the two orbitals are partially filled, thus it is antiaromatic. The energy diagram for the three molecular orbitals of the cyclopropenyl system $\left(C_3{H}_3\right)$is as shown:

                                                         Energy diagram

Therefore, cyclopropenyl cation is aromatic, because it follows $\left(4n+2\right)\mathrm{\pi }$rule and is a planar molecule.