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We performed an {\it ab initio} investigation on the properties of rutile tinoxide (SnO$_{x}$) nanowires. We computed the wire properties determining theequilibrium geometries, binding energies and electronic band structures forseveral wire dimensions and surface facet configurations. The results allowedto establish scaling laws for the structural properties, in terms of thenanowire perimeters. The results also showed that the surface states controlmost of the electronic properties of the nanowires. Oxygen incorporation in thenanowire surfaces passivated the surface-related electronic states, and theresulting quantum properties and scaling laws were fully consistent withelectrons confined inside the nanowire. Additionally, oxygen incorporation inthe wire surfaces generated an unbalanced concentration of spin up and downelectrons, leading to magnetic states for the nanowires.

The structural and electronic properties of tin oxide nanowires: an {\it ab initio} investigation