Ab initio computational methods for electronic transport in nanoscaled systems are an invaluable tool for the design of quantum devices. We have developed a flexible and efficient algorithm for evaluating $I\text{−}V$ characteristics of atomic junctions, which integrates the nonequilibrium Green’s function method with density functional theory. This is currently implemented in the package SMEAGOL. The heart of SMEAGOL is our scheme for constructing the surface Green’s functions describing the current-voltage probes. It consists of a direct summation of both open and closed scattering channels together with a regularization procedure of the Hamiltonian and provides great improvements over standard recursive methods. In particular it allows us to tackle material systems with complicated electronic structures, such as magnetic transition metals. Here we present a detailed description of SMEAGOL together with an extensive range of applications relevant for the two burgeoning fields of spin and molecular electronics.

This tutorial outlines the basic theoretical concepts and tools which underpin the fundamentals of phase-coherent electron transport through single molecules. The key quantity of interest is the transmission coefficient T(E), which yields the electrical conductance, current–voltage relations, the thermopower S and the thermoelectric figure of merit ZT of single-molecule devices. Since T(E) is strongly affected by quantum interference (QI), three manifestations of QI in single-molecules are discussed, namely Mach–Zehnder interferometry, Breit–Wigner resonances and Fano resonances. A simple MATLAB code is provided, which allows the novice reader to explore QI in multi-branched structures described by a tight-binding (Hückel) Hamiltonian. More generally, the strengths and limitations of materials-specific transport modelling based on density functional theory are discussed.