Set up the secular determinants for the homologous series consisting of ethene, butadiene, hexatriene, and octatetraene and diagonalize them by using mathematical software. Use your results to show that the π molecular orbitals of linear polyenes obey the following rules: • The π molecular orbital with lowest energy is delocalized over all carbon atoms in the chain. • The number of nodal planes between C2p orbitals increases with the energy of the π molecular orbital.

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Chapter12: The Solid State
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Problem 19PS: Considering only the molecular orbitals formed by combinations of the 2s atomic orbitals, how many...
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Set up the secular determinants for the homologous series consisting of ethene, butadiene, hexatriene, and octatetraene and diagonalize them by using mathematical software. Use your results to show that the π molecular orbitals of linear polyenes obey the following rules:
• The π molecular orbital with lowest energy is delocalized over all carbon atoms in the chain.
• The number of nodal planes between C2p orbitals increases with the energy of the π molecular orbital.

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