  We calculate the effect of electron-vibration coupling on conduction through
atomic gold wires, which was measured in the experiments of Agra\"it et al.
[Phys. Rev. Lett. 88, 216803 (2002)]. The vibrational modes, the coupling
constants, and the inelastic transport are all calculated using a tight-binding
parametrization and the non-equilibrium Green function formalism. The
electron-vibration coupling gives rise to small drops in the conductance at
voltages corresponding to energies of some of the vibrational modes. We study
systematically how the position and height of these steps vary as a linear wire
is stretched and more atoms are added to it, and find a good agreement with the
experiments. We also consider two different types of geometries, which are
found to yield qualitatively similar results. In contrast to previous
calculations, we find that typically there are several close-lying drops due to
different longitudinal modes. In the experiments, only a single drop is usually
visible, but its width is too large to be accounted for by temperature.
Therefore, to explain the experimental results, we find it necessary to
introduce a finite broadening to the vibrational modes, which makes the
separate drops merge into a single, wide one. In addition, we predict how the
signatures of vibrational modes in the conductance curves differ between linear
and zigzag-type wires.
