Delocalization Model for PA

The Peierls distortion is confirmed in accurate models. If Pol is given the value of 3 eV in a bond-length-dependent coupling model, the band gap has the value Ipl = 1.57 eV. 

3 Behavior of Three-Quarter or One-Quarter Fieeed Bands 

If the bond-length-dependent Hiickel model is used for three-quarter or one-quarter filled bands, the result is surprising at first. A one-dimensional chain with 104 atoms, each bonded by a single bond is used. Three-quarter occupancy can be achieved by occupying the lowest 78 MOs by two electrons and leaving the rest empty. A band gap at the Fermi level opens up, but it is smaller than in the case of half-filled bands p = 0.12 eV, if Ipol = 3 eV. 

If the occupancy is changed so that 77 orbitals are filled, while orbitals 78 and 79 have one electron each, we obtain a state that corresponds to an excited singlet or triplet state. After convergence, a completely different resnlt is obtained compared to the previous occupation. All bonds are now of the same length (1.444 A) and all sites have the same % charge (l.Slel). 

FIGURE 18.20 Degenerate wave functions for one-quarter filling. 

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