2. (40 points) In class we talked about a linear chain of equidistant H atoms, with lattice constant "a" as a simplified model to understand band structures. However, most chemists would tell you that the H atoms would not be equidistant, but instead would be more stable as a chain of dimerized H2 molecules. Let's derive a new band structure for this linear chain of H2 molecules. (Physicists would call this a "Peirels distortion", chemists might call this a "Jahn-Teller" distortion). a) Draw what you would expect the repeating unit cell to be for this new chain structure. b) The new 1D lattice constant for the H2 unit cell we will call " a ". Do you expect aH to be approximately double, half, or the same as the lattice constant "a" for the equidistant chain of atoms? c) Based on your answer in b, do you expect the horizontal length of the 1st Brillouin zone edge for the referred to as "reciprocal" space) d) How many 1 s orbital bands should appear in the H2 band diagram from k=0 to k=/aH2 ? In a single unit cell, draw the different molecular orbitals (linear combinations of atomic orbitals), you would expect to see