10.38 For monocyclic conjugated polyenes (such as cyclobutadiene and benzene) with each of Nc carbon atoms contributing

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10 38 For Monocyclic Conjugated Polyenes Such As Cyclobutadiene And Benzene With Each Of Nc Carbon Atoms Contributing 1 (74.58 KiB) Viewed 31 times

10.38 For monocyclic conjugated polyenes (such as cyclobutadiene and benzene) with each of Nc carbon atoms contributing an electron in a 2p orbital, simple Hückel theory gives the following expression for the energies Ex of the resulting a molecular orbitals: 2k1 Ex= a + 2B cos- k=0, +1, +2,..., #N/2 (even N) NC k=0, #1, #2, ..., E(N-1)/2 (odd N) (a) Calculate the energies of the a 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 Exercise 10.36). 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)?