The possibility of manipulating atoms and individual molecules to establish electrical contact between two metallic electrodes has evolved into a fascinating field in nanoscience termed as molecular electronics. Today, nanowires are devised not only as an alternative to silicon in post-CMOS devices, but also have a tremendous potential in applications as biosensors, in catalysis, optoelectronics, just to mention a few examples. This progress has not only been possible due to the development of scanning probe techniques and other technologies available today to build nanosized devices, but has also been pushed forward by novel theoretical approaches and an increase in computational power. In fact, computational simulations have become indispensable to get an in-depth understanding on the size-dependant properties of matter and of cooperative phenomena at this scale length. A recent development in this field that is relevant to nanowires, and nanoscale modeling in general, is that of linear scaling (or O(N)) methods. The aim of this chapter is to provide the reader with a comprehensive review of the latest advances in the development of computational tools to study the stability of nanowires. Two classes of nanowires are considered: metallic monatomic strands and single molecules bridging two metallic electrodes. A brief introduction on the fabrication methods for these types of nanocontacts is given. In the case of monatomic metallic wires, the computational methods used to study the mechanism of formation and the subsequent stability of these systems are addressed. These typically include molecular dynamics, ab initio calculations, a combination of both methods and ab initio molecular dynamics. The relevant parameters that can be obtained from these studies are, for instance, binding energies, and forces of rupture, besides a detailed picture of the bonding situation. These quantities, although relevant to the question of stability, provide only with a static picture of the system. To add a realistic temporal dimension one should consider studying the energy landscape for the system of interest. This can be accomplished, for example, using a combination of ab initio calculations along with the Nudged Elastic Band (NEB) method for exploring reaction pathways. Computational simulations of contaminated metallic nanowires, and comparison with relevant experimental results are also discussed. In the case of single-molecule junctions, the lifetime of the nanowire is determined mainly by the chemical identity of the linker. Most computational studies performed for these systems have been devoted to the transport properties of the molecular junctions. These studies are not covered in this chapter, but we rather focus on the investigation of the mechanisms of rupture of the nanocontacts, either thermally or force induced. Interestingly, it is found that in the case of molecular nanowires these two situations can lead to different reaction pathways, since some bonds that are thermally stable can be mechanically activated.
