We present a comprehensive theoretical investigation of the structures formed by self-assembly of tetrahydroxybenzene (THB)-derivatives on Cu(111). The THB molecule is known to dehydrogenate completely during annealing, forming a reactive radical which assembles into a close-packed structure or a porous metal-coordinated network depending on the coverage of the system. Here, we present details on how the structures are determined by density functional theory calculations, using scanning tunneling microscopy-derived information on the periodicity. The porous network is based on adatom trimers. By analysing the charge distribution of the structure, it is found that this unusual coordination motif is preferred because it simultaneously provides a good coordination of all oxygen atoms and allows for the formation of a two-dimensional network on the surface.