The ultimate miniaturization in electronics is realized when single molecules and nanowires are used as rectifiers, transistors and interconnects. Wer have developed a scheme in which the conductance of a nanowire bonded between two metal electrodes is calculated from first principles, taking into account the atomic structure of electrodes and wire . Electron transport is treated as a quantum mechanical scattering problem, where electron waves coming from one electrode are (partially) transmitted through the wire into the second electrode . The smallest possible nanowire has a cross section of one atom and experiments indicate that the conductance oscillates as a function of the length of the wire. Calculations show that sodium atomic wires consisting of an odd number of atoms have a conductance close to the maximum of one conductance quantum, whereas even numbered wires have a 15% lower conductance. This behavior is explained in terms of the bonding/anti-bonding resonances of the wires [1,2].
 P.A. Khomyakov and G. Brocks, Real-space finite-difference method for conductance calculations, Phys. Rev. B 70, 146405 (2004).
 P.A. Khomyakov, G. Brocks, V. Karpan, M. Zwierzycki and P.J. Kelly, Conductance calculations for quantum wires and interfaces: Mode matching and Green’s functions, Phys. Rev. B72 035450 (2005).
Figure 1. Left: sodium nanowire consisting of four atoms between two sodium bulk electrodes. Right: the calculated conductance G = dI/dV (in units of the conductance quantum 2e2/h ) at low bias voltage V as function of the number of atoms in the wire. In the lower curve the direct tunneling between the electrodes through the vacuum is subtracted.