Butadiene orbital mixing diagram

Rationalize the low band gap seen in polyisothianaphthalene. Begin with the band structure of polythiophene (PT) developed in Exercise 9. Next, create an orbital mixing diagram in which the appropriate MOs of butadiene are combined with the highest occupied and lowest unoccupied crystal orbitals of PT. 

The photochemical disrotatory closure of butadiene to cyclobutene has been described with a state-correlation diagram, like that shown in Figure 21.4. It is based on the familiar orbital-correlation diagram of Woodward and Hoffmann," from which the intended correlations indicated by the dashed lines can readily be deduced. The solid lines indicate that there is an avoided crossing, which is put in as a result of the quantum mechanical noncrossing rule. It says that two states of the same total symmetry cannot cross. Instead, as they approach each other in energy, they will mix and separate, as the solid lines indicate. 

The mixing diagram for creating the tt MOs of butadiene from ethylene group orbitals and the calculated orbitals for the tt system of butadiene. 

In this correlation diagram, the orbitals that mix upon disrotatory ring opening have been included in the orbital description of cyclobutene. In fact, little or no interaction exists between this a and n set in the planar cyclobutene. Since mixing between the indicated couples begins with incipient butadiene formation, they have been included for continuity. 

The 7t system MO diagram for 1,3-butadiene is made by mixing the fourp orbitals in all possible ways. 

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