3. Hueckel Theory. We discuss the effect of replacing one carbon atom of cyclopen- tadien by oxygen to make the furan molecule. In this problem, either use software or a calculator to get eigenvalues and eigenvectors. (a) Write down the Huckel Hamiltonian for cyclopentadien and for furan in terms of parameters ac, do and 3, where we have assumed that Boc = Bco = B. (b) Reasonable choices for these parameters are B = -75kcal/mol, and do = ac + 3/2. Justify why these choices are (or are not) reasonable. (c) Solve for the eigenvalues of both systems. Make plots of the energy diagrams for cyclopentadien and furan side by side. (d) Explain why we did or did not need to know the value of ac to properly obtain the energy level diagrams above