Question

a) Use the HMO model to calculate the resonance energy ε_R for butadiene. Use the graphical solution for the energies of the MO's involved. Show your work. Assume β = -2.0 eV. b) Given that the hydrogenation energy of ethene is −2.16 × 10⁻¹⁹ J and the hydrogenation energy of butadiene is −3.72 × 10⁻¹⁹ J, compute an experimental resonance energy for butadiene and compare it to your predicted value.

Answer 1

In the Hückel treatment for butadiene, the MO is a linear combination of the 4p AO's at carbon with their ratios :

The secular equation is:

which leads to

and:

Butadiene molecular orbitals

Here β = -2.0 eV., E = hydrogenation energy of butadiene is −3.72 × 10⁻¹⁹ J,

From which alpha can be calculated