For monocyclic conjugated polyenes (such as cyclobutadiene and benzene) with each of N

Chapter 11, Problem 11.16

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For monocyclic conjugated polyenes (such as cyclobutadiene and benzene) with each of N carbon atoms contributing an electron in a 2p orbital, simple Hckel theory gives the following expression for the energies Ek of the resulting molecular orbitals: Ek = + 2 cos k = 0, 1, 2, . . . , N/2 (even N) k = 0, 1, 2, . . . , (N 1)/2 (odd N) (a) Calculate the energies of the molecular orbitals of benzene and cyclooctatetraene. Comment on the presence or absence of degenerate energy levels. (b) Calculate and compare the delocalization energies of benzene (using the expression above) and hexatriene (see 11.15a). What do you conclude from your results? (c) Calculate and compare the delocalization energies of cyclooctaene and octatetraene. Are your conclusions for this pair of molecules the same as for the pair of molecules investigated in part (b)?