Electronic Structure of All-Trans Polyacetylene

We finish our discussion of this polymer by examining the band structure for the o linear, all trans structure with alternating bond lengths (Fig. 15-18a) as calculated by the extended Huckel method. 

The EHMO band structure appears in Fig. 15-18b. There are 10 valence AO basis functions per unit cell (two carbons and two hydrogens) so we get 10 lines in the band diagram. Note that, since the chain is no longer linear, the 2p and 2p bands are no longer degenerate. One of these is still perpendicular to the molecular plane, hence is still of 7T symmetry, but the other now lies in the plane and has a symmetry. 

Chapter 15 Molecular Orbital Theory of Periodic Systems 

A gap resulting from bond-length alternation occurs at the right edge for each of the bands, though it is quite small in bands associated with MOs that have small C-C overlap. A density-of-states plot for the occupied valence a bands and the it bands shows the gap to be just above the highest-energy jr-band level. 

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