In this chapter we will tackle the problem of describing electron transport at the nanoscale. Transport spectroscopy, i.e., the measurement of physical quantities related to electron transport such as, e.g., the conductivity, provides an important experimental tool to investigate mesoscale or nanoscale system. In recent years, transport measurements through single molecules attached to two metallic leads have become feasible. In fact, electronic devices based on single molecules form the basis for the vision of a “molecular electronics” (Cuniberti et al. 2005).
In order to properly describe electron transport at the nanoscale, a quantum theory of transport is of paramount importance. This theory should ideally be able to take into account the atomistic details of the junction since transport properties of molecules certainly depend strongly on the details of, e.g., the geometry of the junction or the chemical bonding between molecule and metallic leads. Ground state DFT...