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Unformatted text preview: Chem 120A Polyatomic molecules: Huckel theory 05/05/06 Spring 2006 Lecture 41 READING: Engel (QCS): 14.6-14.7 McQuarrie and Simon: Ch. 10 Approximations to the HF-LCAO method We saw in Lecture 40 that the Hartree-Fock method can be used to solve the Schrodinger equation using a linear combination of atomic orbitals (LCAO) which we commonly express as Slater determinants. This is a powerful method that is widely applied in chemistry, but it is somewhat expensive and so it is still attractive to use other less exact methods for molecules whose electronic states can be suitably represented using some approximation. One of the most drastic approximations of this type is Huckel theory. In the Huckel method one makes the following assumptions: 1. The two electron terms are neglected. 2. The overlap matrix, S , is taken to be equal to the identity matrix. 3. The matrix elements of the Hamiltonian matrix H are given empirical values. The diagonal matrix elements are set equal to which is the ionization energy for a given atom in the molecule, while the off-diagonal terms are equal to for nearest neighbors, and 0 otherwise. is called the resonance integral and is a measure of the delocalization of electrons between nearest neighbors. Note that both and are negative. Once the Hamiltonian matrix has been constructed given these assumptions, we solve the secular determi- nant to find the energy eigenvalues and molecular orbitals. The last step is to place the electrons pairwise into the MOs following the Aufbau principle. The total ground state energy for the system modeled with the Huckel theory is the sum of the single electron energies. We will illustrate how this method is used with several examples....
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