13. This problem refers to the 2 terminal molecular conductor below. T= OK Source and Drain Contacts Molecule Density of States ELUMO -4.0eV Ps =D=-4.5eV source drain VDS Ep = -4.5eV EHOMO -5.0eV Fig. 3.45 Equilibrium between a molecule and a contact requires charge transfer. (a) When T, = 10 fs, T = 5 fs, calculate the actual molecular density of states versus energy. Determine the full width half maximum of HOMO and LUMO. (b) Based on the actual density of states calculated in part c), find the number of electrons and the charging energy when the molecule is brought into contact with the metal electrode and reached equilibrium (no applied voltage). Also sketch the energy diagram at equilibrium. Assume that the charging energy per electron is leV and Ts = 10 fs, T, = 5 fs. Hint: You will need your calculator to solve this. You might use dx: =tan(x). 1+x