## Theoretical and Computational Aspects of electronic transport at the Nanoscale

Alexandre Reily Rocha

The problem of electronic transport in systems comprising only a handful of atoms is one of the most exciting branches of nanoscience. The aim of this work is to address the issue of non-equilibrium transport at the nanoscale. At first, we lay down the theoretical framework based on Keldysh's non-equilibrium Green function formalism. We show how this formalism relates to the Landauer-Buttiker formalism for the linear regime and how the current through a nanoscopic system can be related to a rate equation for which a steady state solution can be found. This formalism can be applied with different choices of Hamiltonian. In this work we choose to work with the Hamiltonian obtained from density functional theory which provides an accurate description of the electronic structure of nanoscopic systems. The combination of NEGFs and DFT results in {\it Smeagol}, a state-of-the-art tool for calculating materials-specific electronic transport properties of molecular devices as well as interfaces and junctions.

Smeagol is then used to study the magnetoresistance in magnetic point contacts and whether asymmetries in the $I-V$ characteristics can be explained solely by electronic effects. We show how new exchange and correlation functionals must be used to accurately portray the electronic transport properties of point contacts with adsorbed impurities. We also introduce the new concept of molecular spin valves. In other words we investigate the possibility of using organic molecules sandwiched between magnetic electrodes to create novel GMR devices which combine spintronics and the relatively new field of molecular electronics. We show that organic molecules can be engineered to produce large magnetoresistance ratios and by further choosing the end-groups even greater enhancement of these ratios can be achieved. We also show how to accurately model spin-polarised scanning tunnelling microscopy using Smeagol.

Finally we show how computer simulations can give powerful insights into the transport properties of macromolecules (most notably DNA). We show the main mechanism for transport in DNA molecules attached to gold electrodes and conclude that it is a wide-gap semiconductor.