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.
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