f 1 g 1 h 1 f 2 g 2 h 2 f 3 g 3 h 3 e Show that a Fermionic wavefunction from

F 1 g 1 h 1 f 2 g 2 h 2 f 3 g 3 h 3 e show that a

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f 1 ( ) g 1 ( ) h 1 ( ) f 2 ( ) g 2 ( ) h 2 ( ) f 3 ( ) g 3 ( ) h 3 ( ) (e) Show that a Fermionic wavefunction from part (d) with two identical levels occupied must always correspond to a zero wavefunction (this is essentially proving the form of the Pauli principle that you were taught in earlier classes). 2. Practice with Huckel MO theory (a) Solve for the energy levels of the C3H5 radical (draw its resonance structures for practice as well). There is a 3 by 3 determinant to be solved…. (b) Solve for the eigenvectors and make pictures of them, showing the nodal surfaces. (c) Evaluate the total energy of the C3H5 radical. Compare its energy to that of ethylene and an unpaired 2pz electron. Is it resonance stabilized? (d) Write the Huckel Hamiltonian, and solve for the energy levels of cyclic C5H5(-), the cyclopentadienyl anion. (e) Evaluate the total energy of C5H5(-). (f) To evaluate the resonance stabilization energy (if any) of C5H5(-) within Huckel theory, compare your total energy from (b) to your choice of fragments that separate the pi electron system (there are various possible choices – you are welcome to try various ones. The best one is presumably the one that is closest in stability to C5H5(-) itself.)
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3. Fullerene (!) treated by Huckel theory. Use Python (wait for your hard-working TAs to provide a software scaffold unless you are too enthusiastic and/or too expert to wait!)
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  • Summer '16
  • Alistair Sinclair
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