  We present here a comprehensive search for the structure of the Si(553)-Au
reconstruction. More than two hundred different trial structures have been
studied using first-principles density-functional calculations with the SIESTA
code. An iterative procedure, with a step-by-step increase of the accuracy and
computational cost of the calculations, was used to allow for the study of this
large number of configurations. We have considered reconstructions restricted
to the topmost bilayer and studied two types: i) "flat" surface-bilayer models,
where atoms at the topmost bilayer present different coordinations and
registries with the underlying bulk, and ii) nine different models based on the
substitution of a silicon atom by a gold atom in different positions of a
$\pi$-bonded chain reconstruction of the Si(553) surface. We have developed a
compact notation that allows us to label and identify all these structures.
This is very useful for the automatic generation of trial geometries and
counting the number of inequivalent structures, i.e., structures having
different bonding topologies. The most stable models are those that exhibit a
honeycomb-chain structure at the step edge. One of our models (model f2)
reproduces the main features of the room temperature photoemission and
scanning-tunneling microscopy data. Thus we conclude that f2 structure is a
good candidate for the high temperature structure of the Si(553)-Au surface.
