  We present an ab initio inelastic quantum transport approach based on
maximally localized Wannier functions. Electronic-structure properties are
calculated with density-functional theory in a planewave basis, and
electron-vibration coupling strengths and vibrational properties are determined
with density-functional perturbation theory. Vibration-induced inelastic
transport properties are calculated with non-equilibrium Green's function
techniques, which are based on localized orbitals. For this purpose we
construct maximally localized Wannier functions. Our formalism is applied to
investigate inelastic transport in a benzene molecular junction connected to
mono-atomic carbon chains. In this benchmark system the electron-vibration
self-energy is calculated either in the self-consistent Born approximation or
by lowest-order perturbation theory. It is observed that upward and downward
conductance steps occur, which can be understood using multi-eigenchannel
scattering theory and symmetry conditions. In a second example where the
mono-atomic carbon chain electrode is replaced by a (3; 3) carbon nanotube, we
focus on the non-equilibrium vibration populations driven by the conducting
electrons using a semi-classical rate equation.
