  Electronic structure calculations for atomic wire of metals like Al, Ga and
In are performed for a patterned dihydrogeneted Si(001):1 $\times$ 1 in search
of structures with metallic behavior. The dihydrogeneted Si(001) is patterned
by depassivating hygrozen atoms only from one row of Si atoms along the
[1$\bar{1}$0] direction. Various structures of adsorbed metals and their
electronic properties are examined. It is found that Al and Ga atomic wire
structures with metallic property are strongly unstable towards the formation
of buckled metal dimers leading to semiconducting behavior. Indium atomic wire,
however, displays only marginal preference towards the formation of symmetric
dimers staying close to the metallic limit. The reasons behind the lack of
metallic atomic wires are explored. In addition, a direction is proposed for
the realization of metallic wires on the dihydrogeneted Si(001).
