Perform a Hartree-Fock geometry optimization calculation of butadiene using a minimal basis set. Repeat with the 6-311G(d,p) basis set, using the optimized minimal basis set geometry as the starting point.

(a) Compare the results of the two calculations with each other and any available experimental geometry data. Discuss the extent of agreement and the nature of any differences.

(b) Considering the 6-311G(d,p) calculation, state the symmetry and ground state electronic configuration of butadiene.

(c) Using Koopmans' theorem, predict the core electron binding energies. Include qualitative descriptions of the corresponding core molecular orbitals. Comment on the level of (dis)agreement between the two calculations.

(d) Considering the 6-311G(d,p) calculation, describe the four lowest energy unoccupied orbitals. Include the correct symmetry labels, energies, and qualitative descriptions.

(e) Which core-to-valence excitations involving the four MOs considered in part (d) are dipole allowed?