  We describe an ab initio method for calculating the electronic structure,
electronic transport, and forces acting on the atoms, for atomic scale systems
connected to semi-infinite electrodes and with an applied voltage bias. Our
method is based on the density functional theory (DFT) as implemented in the
well tested Siesta approach (which uses non-local norm-conserving
pseudopotentials to describe the effect of the core electrons, and linear
combination of finite-range numerical atomic orbitals to describe the valence
states). We fully deal with the atomistic structure of the whole system,
treating both the contact and the electrodes on the same footing. The effect of
the finite bias (including selfconsistency and the solution of the
electrostatic problem) is taken into account using nonequilibrium Green's
functions. We relate the nonequilibrium Green's function expressions to the
more transparent scheme involving the scattering states. As an illustration,
the method is applied to three systems where we are able to compare our results
to earlier ab initio DFT calculations or experiments, and we point out
differences between this method and existing schemes. The systems considered
are: (1) single atom carbon wires connected to aluminum electrodes with
extended or finite cross section, (2) single atom gold wires, and finally (3)
large carbon nanotube systems with point defects.
