ABSTRACT
A significant distinguishing feature of π -electron systems is the relatively strong interaction between the electrons and phonons. For example, the carbon-carbon bond length in an olefinic C=C bond is generally taken to be 1.35 ˚A, whereas an olefinic C--C bond is somewhat larger at 1.45 ˚A. In aromatic systems, the C=C bond length is 1.40 ˚A. This is, of course, due to the modulation of bond order as one moves down the olefinic chain. For aromatic systems, we know that the resonance structures account for the homogenous delocalization of the electron density about the ring. Here we present the classic model developed by Su, Schrieffer, and Heeger (SSH) that accounts for semiconducting properties of olefinic chains.102,103
From the Hu¨ckel model, we found that if all the sites along the chain are equivalent, then the energy for the infinite chain is given by
Ek = α − 2β cos(ka) (9.1)
where a is the bond distance between neighboring C atoms. For a π -electron system that is half-filled (that is, each C atom contributes one e-to the π system), then the band gap at the Fermi energy is exactly 0. This is the case if all the C--C bonds are the same length, as in aromatic rings.
