Si(1 1 1)-Au surfaces with around one monolayer of Au exhibit many ordered structures and structures containing disordered domain walls. Hybrid density functional theory (DFT) calculations presented here reveal the origin of these complex structures and tendency to form domain walls. The conjugate honeycomb chain trimer (CHCT) structure of the [Formula: see text]-Au phase contains Si atoms with non-bonding surface states which can bind Au atoms in pairs in interstices of the CHCT structure and make this surface metallic. Si adatoms adsorbed on the [Formula: see text]-Au surface induce a gapped surface through interaction with the non-bonding states. Adsorption of extra Au atoms in interstitial sites of the [Formula: see text]-Au surface is stabilized by interaction with the non-bonding orbitals and leads to higher coverage ordered structures including the [Formula: see text]-Au phase. Extra Au atoms bound in interstitial sites of the [Formula: see text]-Au surface result in top layer Si atoms with an SiAu4 butterfly wing configuration. The structure of a [Formula: see text]-Au phase, whose in-plane top atomic layer positions were previously determined by an electron holography technique (Grozea et al 1998 Surf. Sci. 418 32), is calculated using total energy minimization. The Patterson function for this structure is calculated and is in good agreement with data from an in-plane x-ray diffraction study (Dornisch et al 1991 Phys. Rev. B 44 11221). Filled and empty state scanning tunneling microscopy (STM) images are calculated for domain walls and the [Formula: see text]-Au structure. The [Formula: see text]-Au phase is 2D chiral and this is evident in computed and actual STM images. [Formula: see text]-Au and domain wall structures contain the SiAu4 motif with a butterfly wing shape. Chemical bonding within the Si-Au top layers of the [Formula: see text]-Au and [Formula: see text]-Au surfaces is analyzed and an explanation for the SiAu4 motif structure is given.