to solve for the energy levels and eigenvalues of the famous C 60 molecule

To solve for the energy levels and eigenvalues of the

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provide a software scaffold unless you are too enthusiastic and/or too expert to wait!) to solve for the energy levels and eigenvalues of the famous C 60 molecule using the Huckel model, involving the following steps. (a) Choose a suitable numerical value of the two parameters α and β . Discuss how you chose them, giving some physical justification. (b) Build the 60X60 matrix of the Hamiltonian in the Python software scaffold, using a molecular model to get the connectivity right. For example, using IQmol ( ), you can load C60 as a molecule, and display the atom labels, and then rotate to find the nearest neighbors of each atom. Here’s how: Add Fragment (it’s a button in the interface) -> Molecules -> Fullerenes -> Buckminsterfullerene Then, Display -> Atom Labels -> Index (c) Obtain the eigenvalues as an energy level diagram, and then use the Pauli Principle, Aufbau Principle, and Hunds rules to predict the ground state energy, and the spin state. (d) Evaluate the resonance stabilization (relative to 30 separate C2H4 molecules) per C atom, and compare with the resonance stabilization of benzene per C atom. Which species shows the greater stabilization?
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  • Summer '16
  • Alistair Sinclair
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