Effective hamiltonian for pi electrons in linear carbon chains

The electronic structure of conjugated linear carbon chains (polyynes) is described on the basis of a common Hu¨ckel hamiltonian. The experimental energy gaps of polyynes of increasing chain lengths are analyzed in this frame and the limiting case of the infinite polymer is discussed. The treatment is based on two empirical parameters which share common values in the hamiltonian of polyynes of any length. This proves that the relevant red shift of the optical absorption with chain length can be fully explained on common physical grounds. Moreover this approach allows to obtain a reliable extrapolation for the optical gap of the infinite linear carbon chain. A precise relationship between the band structure of the polymer and the p electronic states of any polyyne of finite length can be established on the same grounds.