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Structures and electronic properties of rhombohedral [111] and [110] bismuthnanowires are calculated with the use of density functional theory. Theformation of an energy band gap from quantum confinement is studied and toimprove estimates for the band gap the GW approximation is applied. The [111]oriented nanowires require surface bonds to be chemically saturated to avoidformation of metallic surface states whereas the surface of the [110] nanowiresdo not support metallic surface states. It is found that the onset of quantumconfinement in the surface passivated [111] nanowires occurs at larger criticaldimensions than for the [110] nanowires. For the [111] oriented nanowires it ispredicted that a band gap of approximately 0.5 eV can be formed at a diameterof approximately 6 nm, whereas for the [110] oriented nanowires a diameter ofapproximately 3 nm is required to achieve a similar band gap energy. The GWcorrection is also applied to estimates of the electron affinity, ionisationpotentials and work functions for both orientations of the nanowires forvarious diameters below 5 nm. The magnitude of the energy band gaps that arisein bismuth at critical dimensions of a few nanometers are of the same order asfor conventional bulk semiconductors.

Electronic and structural properties of rhombohedral [111] and [110] oriented ultra-thin bismuth nanowires