Question

The C₅H₅⁺ and C₅Cl₅⁺ cations, which have never been isolated, are known to be ground state triplets - that is, they have 2 unpaired electrons, thus are diradicals. But the C₅(CH₃)₅⁺ cation has no unpaired electrons - it is a singlet.

Construct a schematic molecular diagram of C₅H₅⁺ (pi system only) in D₅h point group using p_z-orbitals of C. Sketch the shape of each orbital next to the irreducible representation of the MO. Does your MO diagram support the singlet or triplet ground state?

Result from X-ray crystallography, NMR, and theory..... C₅(CH₃)₅⁺ is an irregular pentagon.... the ring is nonplanar... the pi electrons are found to be largely localized on opposite sides of the ring - in an allyl cation fragment and in a double bond.

Now, construct a schematic molecular diagram of C₅(CH₃)₅⁺ (pi system only) using p_x-orbitals of C, assuming allyl group and a double bond separately and simply put them on the same stack). Sketch the shape of each orbital next to the irreducible representation of the MO. Does your MO diagram support the singlet or triplet ground state?

Please help!! Super hard homework question!

Answer 1

The out of plane motions destroy the planarityof cyclopentadienyl cation leading to rehybridization of their sigma and pi orbitals. It is a failure of simple resonance theory, not of valence bond theory. Taking into account the sign of the matrix element (overlap) between five valence bond structures show that singlet of C5H5+ is jahn-teller unstable and the ground state is infact the triplet state. It is possible for antiaromatic ionic species having 4n electrons having over 4n+1 and 4n-1 centers.