Both cluster and extended slab models for the bare Si(001) surface and for acetylene chemisorbed on that surface were studied by various theoretical methods. Our calculations point to a buckled Si-Si dimer on the bare reconstructed surface, Acetylene adsorbs onto the dimer to form a four-member disilacyclobutene ring without breaking the Si-Si bond. Upon acetylene chemisorption, the buckled dimers become symmetric. The surface reaction is orbital symmetry-forbidden. A likely pathway for the cycloaddition, via a pi-complex precursor and a biradical intermediate, is suggested.