  We describe a first-principles method for calculating electronic structure,
vibrational modes and frequencies, electron-phonon couplings, and inelastic
electron transport properties of an atomic-scale device bridging two metallic
contacts under nonequilibrium conditions. The method extends the
density-functional codes SIESTA and TranSIESTA that use atomic basis sets. The
inelastic conductance characteristics are calculated using the nonequilibrium
Green's function formalism, and the electron-phonon interaction is addressed
with perturbation theory up to the level of the self-consistent Born
approximation. While these calculations often are computationally demanding, we
show how they can be approximated by a simple and efficient lowest order
expansion. Our method also addresses effects of energy dissipation and local
heating of the junction via detailed calculations of the power flow. We
demonstrate the developed procedures by considering inelastic transport through
atomic gold wires of various lengths, thereby extending the results presented
in [Frederiksen et al., Phys. Rev. Lett. 93, 256601 (2004)]. To illustrate that
the method applies more generally to molecular devices, we also calculate the
inelastic current through different hydrocarbon molecules between gold
electrodes. Both for the wires and the molecules our theory is in quantitative
agreement with experiments, and characterizes the system-specific mode
selectivity and local heating.
