Extensive electronic structure calculations are performed to obtain the
stable geometries of metals like Al, Ga and In on the Si(001) surface at 0.5 ML
and 1 ML coverages. Our results coupled with previous theoretical findings
explain the recent experimental data in a comprehensive fashion. At low
coverages, as shown by previous works, Para' dimers give the lowest energy structure. With increasing coverage beyond 0.5 ML, Ortho’ dimers become part
of low energy configurations leading toward a Para' to Ortho’ transition at 1
ML coverage. For In mixed staggered dimers (Ortho' and Para’) give the lowest
energy configuration. For Ga, mixed dimers are non-staggered, while for Al
Para' to Ortho’ transition of dimers is complete. Thus at intermediate
coverages between 0.5 and 1 ML, the Ortho' and Para’ dimers may coexist on
the surface. Consequently, this may be an explanation of the fact that the
experimental observations can be successfully interpreted using either
orientation. A supported zigzag structure at 0.5 ML, which resembles ${\rm
(CH)_x}$, does not undergo a dimerization transition, and hence stays
semi-metallic. Also, unlike the soliton formation is ruled out
for this structure.

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