1. (15 pts) Nitrogenase is an enzyme that converts N2 to NH3. Extraction procedures have shown that nitrogenase contains an iron-sulfur cluster, Fe4S4, where the atoms of each type are arranged alternately at the corners of a cube. We wish to attempt to model the bonding in this iron-sulfur cube with the wavefunctions derived for an electron in a cubical (three dimensional) box whose dimension is a x a x a. (a) Construct an energy-level diagram showing the relative energy ordering of the lowest 17 molecular orbitals when this cube is aaa. Label the levels in terms of their quantum numbers and E0(E0=h2/8ma2). Be alert for degeneracies