Question

Simple molecular orbital theory for the ethylene molecule.

(a) (5 points) Write down a Hamiltonian matrix for the pi electrons of ethylene, using a 2p basis function on each C atom, and assuming that the matrix elements of the Hamiltonian are α for on-site interaction you a 2 by 2 matrix - it is known as the Huckel Hamiltonian s, and B for the interactions between nearest neighbors This should give (b) (10 points) Write down the secular equation for the eigenvalues of this Hamiltonian, and solve this equation to obtain the eigenvalues, and then the eigenvectors. You may assume that the overlap matrix is the identity matrix (since the Hamiltonian is empirical) (c) (5 points) Explain the signs of the values of α for on-site interactions, and β for the interactions between nearest neighbors, explaining your logic. Based on your result explain which of the levels is occupied (d) (5 points) Evaluate the predicted stabilization energy of ethylene relative to 2 C atoms (where each has a single pi electron in a 2pz orbital)

Answer 1

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