The FEMO theory of conjugated molecules is crude and marginally better results are obtained with simple Huckel theory. (a) For a linear conjugated polyene with each of N carbon atoms contributing an electron in a 2porbital, the energies Ek of the resulting π molecular orbitals are given by: Ek = α + 2β cos kπ/N+1 k = 1,2,3, ... N Use this expression to estimate the resonance integral β for the series consisting of ethene, butadiene, hexatriene, and octatetraene given that ult raviolet absorptions from the HOMO, which is a bonding π orbital, to the LUMO, which is an antibonding π* orbital, occur at 61 500, 46 080, 39 750,and 32 900 cm- 1, respectively. (b) Calculate the π-electron delocalization energy, Edelcc = Eπ -n(α + β). of octatetraene, where Eπ, is the total π-electron binding energy and n is the total number of π-electrons.
The FEMO theory of conjugated molecules is crude and marginally better results are obtained with simple Huckel theory. (a) For a linear conjugated polyene with each of N carbon atoms contributing an electron in a 2p
orbital, the energies Ek of the resulting π molecular orbitals are given by:
Ek = α + 2β cos kπ/N+1 k = 1,2,3, ... N
Use this expression to estimate the resonance integral β for the series consisting of ethene, butadiene, hexatriene, and octatetraene given that ult raviolet absorptions from the HOMO, which is a bonding π orbital, to the LUMO, which is an antibonding π* orbital, occur at 61 500, 46 080, 39 750,
and 32 900 cm- 1, respectively. (b) Calculate the π-electron delocalization energy, Edelcc = Eπ -n(α + β). of octatetraene, where Eπ, is the total π-electron binding energy and n is the total number of π-electrons.
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