Recent work by Thess et al. suggests that (10,10) carbon nanotubes wit
h diameters of 1.38 nm have been observed with high conductivities. Ot
her experimental results have directly measured the density of states
of single-wall carbon nanotubes with diameters in the range 1-1.5nm. H
erein we examine the expected electronic properties of armchair single
-wall nanotubes with diameters in this range, and present first-princi
ples local-density functional results for band structure and density o
f states of these SWNTs. We find our results support the validity of t
he simple graphene sheet model, and are in close agreement with experi
mental measurements of the density of states of these materials.