  We have studied Peierls instability in an atomically thin wire of sodium
atoms using first-principles density-functional methods. A Na wire has a stable
uniform linear structure over a range of inter-atomic distances. At smaller
inter-atomic distances it develops a zigzag distortion. At larger inter-atomic
distances, just before breaking, a Na wire undergoes a very weak Peierls
dimerization. This behavior of a Na wire is understood in terms of its
electron-phonon coupling properties.
