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 nonlocal 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 self-consistency 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: (i) single atom carbon wires connected to aluminum electrodes with extended or finite cross section, (ii) single atom gold wires, and finally (iii) large carbon nanotube systems with point defects.

We investigate the tight-binding approximation for the dispersion of the $\pi$ and ${\pi }^{*}$ electronic bands in graphene and carbon nanotubes. The nearest-neighbor tight-binding approximation with a fixed ${\gamma }_0$ applies only to a very limited range of wave vectors. We derive an analytic expression for the tight-binding dispersion including up to third-nearest neighbors. Interaction with more distant neighbors qualitatively improves the tight-binding picture, as we show for graphene and three selected carbon nanotubes.

A study based on ab initio calculations is presented on the structural, elastic, and vibrational properties of single-wall carbon nanotubes with different radii and chiralities. These properties are obtained using an implementation of pseudopotential-density-functional theory, which allows calculations on systems with a large number of atoms per cell. Different quantities are monitored versus tube radius. The validity of expectations based on graphite is explored down to small radii, where some deviations appear related to the curvature-induced rehybridization of the carbon orbitals. Young moduli are found to be very similar to graphite and do not exhibit a systematic variation with either the radius or the chirality. The Poisson ratio also retains graphitic values except for a possible slight reduction for small radii. It shows, however, chirality dependence. The behavior of characteristic phonon branches as the breathing mode, twistons, and high-frequency optic modes, is also studied, the latter displaying a small chirality dependence at the top of the band. The results are compared with the predictions of the simple zone-folding approximation. Except for the known deficiencies of the zone-folding procedure in the low-frequency vibrational regions, it offers quite accurate results, even for relatively small radii.