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Problem 6. The Hückel molecular orbital theory can be applied to trans-1,3-butadiene as a simplified model for conjugated polyenes like \(\beta\)-carotene. The chemical structure of trans-1,3- butadiene is depicted below: \(H_2C=CH-CH=CH_2\) For trans-1,3-butadiene the Hückel method yields the following values for the energies of the various molecular orbitals: \(E = \alpha \pm 0.62\beta\) \(E = \alpha \pm 1.62\beta\) Let us assume a somewhat high value for the resonance integral of \(\beta = -450\text{ kJ mole}^{-1}\). Apply the Bohr frequency condition to calculate the wavelength of light that is absorbed in the HOMO to LUMO transition.

          Problem 6. The Hückel molecular orbital theory can be applied to trans-1,3-butadiene as a
simplified model for conjugated polyenes like \(\beta\)-carotene. The chemical structure of trans-1,3-
butadiene is depicted below:
\(H_2C=CH-CH=CH_2\)
For trans-1,3-butadiene the Hückel method yields the following values for the energies of the
various molecular orbitals:
\(E = \alpha \pm 0.62\beta\)
\(E = \alpha \pm 1.62\beta\)
Let us assume a somewhat high value for the resonance integral of \(\beta = -450\text{ kJ mole}^{-1}\).
Apply the Bohr frequency condition to calculate the wavelength of light that is absorbed in the
HOMO to LUMO transition.

Problem 6. The Hückel molecular orbital theory can be applied to trans-1,3-butadiene as a
simplified model for conjugated polyenes like β-carotene. The chemical structure of trans-1,3-
butadiene is depicted below:
H2C=CH-CH=CH2
For trans-1,3-butadiene the Hückel method yields the following values for the energies of the
various molecular orbitals:
E = α± 0.62β
E = α± 1.62β
Let us assume a somewhat high value for the resonance integral of β = -450 kJ mole^-1.
Apply the Bohr frequency condition to calculate the wavelength of light that is absorbed in the
HOMO to LUMO transition.

Added by Charles M.

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