513.001 Molecular and Solid State Physics

Absorption in 1,3-butadiene

1,3-butadiene is a planar molecule. What types of bonds occur in this molecule?

The Hückel model can be used to express four molecular orbitals in terms of the four p_z orbitals. Let α = <p_z1|H_MO|p_z1> be the matrix element with both <p_z1| and |p_z1> corresponding to the p_z orbital of the same atom. Let β = <p_z1|H_MO|p_z2> be the matrix element with <p_z1| and |p_z2> corresponding to the p_z orbitals of neighboring atoms. Here β = 0.77 eV. This molecule absorbs a photon and one of the electrons moves from the higest occupied orbital to the lowest unoccupied orbital. What is the wavelength of the photon?