Distortions in One-Dimensional Systems

The polymeric material of 13.24, polyacetylene, with one orbital per atom has a TT-band structure which is identical to the one we have spent so much time discussing in Section 13.1. With one electron per atom this band is half-full and if the electrons 

In addition to giving rise to different values of Rp in equation 13.6, different values of the resonance integrals will also be found. y9 and Pi may be assigned to the interaction integrals between two neighboring orbitals separated byxd and (I x) /, respectively. Sincexo is smaller than (I —x)owe note that S Pi. Note also that 1 and/ 2 0 for the case of pjr orbital overlap. The secular determinant then becomes 

Note that as in equation 13.31 one off-diagonal element is the complex conjugate of the other. Solution of this determinant leads to 

Plots of e(k) versus k and DOS for a hydrogen chain. The solid lines refer to 13.26 where all H-H nearest neighbor distances are equal. The dashed lines are for the paired situation in 13.27. 

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