2 Huckel Theory for Conjugated Polymers Conjugated polymers are a class of polymers that leverage an extended π-electron system to absorb visible light and be electrically conductive. The simplest conjugated polymer is shown above, where "n" indicates the number of repeating units of the chemical structure, and you can assume that the ends of the chain are terminated with hydrogens. For all calculations that follow you can use a = -11.4eV and B = −2.8eV. (A) Calculate the wavelength of light absorption corresponding to the HOMO-LUMO transition in this molecule for n = = 1. (B) Calculate the wavelength of light absorption corresponding to the HOMO-LUMO transition in this molecule for n = = 3. (C) Using the eigenvectors from C, draw the lowest energy eigenstate for the n = 3 case. (D) Let's imagine that you wish to perturb the electronic structure of the conjugated polymer backbone by substituting a pendant Fluorine atom onto every other Carbon atom in the n = 3 chain. By doing this, it changes the a value for that carbon from −11.4eV to -13.0eV. Calculate the wavelength of light absorption corresponding to the HOMO-LUMO transition in this molecule. (E) Using first order perturbation theory, treat the modifcation to the Hamiltonian you made in (D) as a perturbation to the original Hamiltonian from (B). Using 1st order perturbation theory, calculate the energy of the highest occupied molecular orbital energy from (B). n