For a linear conjugated polyene with each of N carbon atoms contributing an elec

Question

For a linear conjugated polyene with each of N carbon atoms contributing an electron in a 2p orbital, the energies E_k of the resulting pi molecular orbitals are given by Use this expression to determine a reasonable empirical estimate of the resonance integral beta for the homologous senes consisting of ethene. butadiene, hexatnene. and octatetraene. given that ultraviolet absorptions from the HOMO to the LUMO occur at 61 500.46 080. 39 750. and 32 900 cm respectively, (b) Calculate the X electron delocalization energy. of octatetraene. where E_x is the total pi-electron binding energy and n is the total number of x electron*, (c) In the context of this Huckel model. the x molecubr orbitals are wntten as linear combinations of the carbon 2p orbitals. The coefficient of the/th atomic orbital in the ftth molecular orbital is given by Determine the values of the coefficients of each of the six 2p orbitals in each of the six x molecular orbitals of hexatnene. Match each set of coefficients (that is. each molecular orbital) with a value of the energy calculated with the expression given in part (a) of the molecular orbital. Comment on trends that relate the energy of a molecular orbital with its 'shape', which can be inferred trom the magnitudes and signs of the coefficients in the linear combination that describes the molecular orbital.

Explanation / Answer

The Hückel method or Hückel molecular orbital method (HMO), proposed by Erich Hückel in 1930, is a very simple linear combination of atomic orbitals molecular orbitals (LCAO MO) method for the determination of energies of molecular orbitals of pi electrons in conjugated hydrocarbon systems, such as ethene, benzene and butadiene.

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