  The electronic structure of a single monatomic gold wire is presented for the
first time. It has been obtained with state-of-the-art ab-initio full-potential
density-functional (DFT) LMTO (linearized muffin-tin orbital) calculations
taking into account relativistic effects. For stretched structures in the
experimentally accessible range the conduction band is exactly half-filled,
whereas the band structures are more complex for the optimized structure. By
studying the total energy as a function of unit-cell length and of a possible
bond-length alternation we find that the system can lower its total energy by
letting the bond lengths alternate leading to a structure containing separated
dimers with bond lengths of about 2.5 \AA, largely independent of the
stretching. However, first for fairly large unit cells (above roughly 7 \AA),
is the total-energy gain upon this dimerization comparable with the energy
costs upon stretching. We propose that this together with band-structure
effects is the reason for the larger interatomic distances observed in recent
experiments. We find also that although spin-orbit couplings lead to
significant effects on the band structure, the overall conclusions are not
altered, and that finite Au_2, Au_4, and Au_6 chains possess electronic
properties very similar to those of the infinite chain.
