On the spin gaps of conjugated hydrocarbon polymers

Many of the (ideal) infinite conjugated hydrocarbon polymers do not present a gap at the Fermi level in tight-binding calculations. However, due to the bielectronic interaction the excitation energy from the ground state to the lowest triplet state may be nonzero for some lattices (called spin gapped), while other lattices will keep a singlet-triplet degeneracy (spin-gapless lattices). This difference results in qualitative differences in their magnetic properties. Making use of the relevance of Heisenberg Hamiltonians for the study of the lowest states of conjugated hydrocarbons, this paper presents some qualitative arguments to predict the spin-gap character of various classes of such polymers. The arguments are based on real space renormalization group procedures, which considers fragments of the polymers as effective spins. Numerical evaluations, based on a renormalized excitonic method, confirm the qualitative predictions. (C) 2007 American Institute of Physics.