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Unformatted text preview: Chem 120A Polyatomic molecules: H¨uckel theory 05/05/06 Spring 2006 Lecture 41 READING: Engel (QCS): 14.614.7 McQuarrie and Simon: Ch. 10 Approximations to the HFLCAO method We saw in Lecture 40 that the HartreeFock method can be used to solve the Schr¨odinger 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 H¨uckel theory. In the H¨uckel 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 α which is the ionization energy for a given atom in the molecule, while the offdiagonal terms are equal to β for nearest neighbors, and 0 otherwise. β is called the ’resonance integral’ and is a measure of the delocalization of electrons between nearest neighbors. Note that both α and β 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 H¨uckel theory is the sum of the single electron energies. We will illustrate how this method is used with several examples....
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 Spring '07
 Whaley
 Physical chemistry, Atom, Electron, Mole, pH, Quantum Chemistry, Molecule, H¨ ckel theory

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