Abstract
We investigated the changes in the electronic structure of Cu, Ag, and Au in going from three-dimensional (3D) to two-dimensional to one-dimensional structure. Compared to 3D case, the interatomic distance (cohesive energy per bond) shows significant drop (rise) as dimensionality decreases. The shallow $d$ bands of 3D become sharper and shallower, and for Cu (Au) reach just below (above) the Fermi level. This picture is very sensitive to the accuracy of the calculations and may affect the calculated properties of nanowires. The spin-orbit interaction is found to play a significant role in Au, altering the electronic structure considerably and increasing the number of conducting channels in 1D Au.
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