Consider the molecule azulene and a. Setup the secular determinant for azulene within the Hückel approximation and using the out-of-plane C2p orbitals as basis set. b. Estimate π-electron binding energy within the Hückel approximation. c. Approximate the delocalization energy.
The Huckel approximation is used to determine the energies & shapes of the pi molecular orbitals in conjugated systems. Within the Huckel approximation, the covalent bonding in these hydrocarbons can be separated into two different frameworks. The wavefunctions used to describe the bonding orbitals in each framework results from different combinations of atomic orbitals. The method limits itself to addressing conjugated hydrocarbons & specifically only pi electron molecular orbitals are included because these determine the general properties of these molecules; the sigma electrons are ignored. This is referred as sigma - pi separability & is justified by the orthogonality of sigma-sigma & pi-pi orbitals in planar molecules. Due to this reason, Huckel approximation is limited to planar systems. Huckel approximation assumes that the electrons in the pi-pi bonds experience an electrostatic potential due to the entire sigma-sigma bonding framework in the molecule.
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