Exchange effects on the inner valence and core energy bands and density of states of metallic chains

It is pointed out that the restricted Hartree-Fock singularity at the Fermi wave-number for a metallic chain is not limited to the partially filled uppermost band(s), but occurs in all bands. Thus the density of states vanishes in all bands at the energy corresponding to the Fermi wavenumber. Possible implications for the characterisation of the Peierls' instability are discussed.