Some Linear Polyenes Of Which

Some linear polyenes, of which ,6-carotene is an example, are important biological co-factors that participate in processes as diverse as the absorption of solar energy in photosynthesis (Impact 123.2) and protection against harmful biological oxidations. Use as a model of, 6-carotene a linear polyene containing 22 conjugated C atoms.
(a) To what point group does this model of, 6-carotene belong?
(b) Classify the irreducible representations spanned by the carbon 2pz orbitals and find their symmetry-adapted linear combinations.
(c) Use your results from part (b) to calculate the Huckel secular determinant.
(d) What states of this model of, 6-carotene may be reached by electric dipole transitions from its (totally symmetrical) ground state?

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