Scalar-relativistic density functional calculations in the zeroth-order regular approximation as well as fully relativistic Dirac-Kohn-Sham calculations have been performed to investigate spectroscopic constants of the eka-gold (element 111) compounds (111) X (X = H, F, Cl, Br, O, Au) and the dimer of element 111. For calibration, we also report results for homologous gold compounds. The bond lengths for the compounds of element 111 are similar but slightly larger than those of the gold compounds. Spin-orbit coupling increases the bond length by a few pm. For the hydride and the halides, the force constants of the eka-gold compounds are generally larger than those of the gold compounds although the dissociation energy is smaller. The oxide of eka-gold is more strongly bound than the gold oxide. The dimer of element 111 has an open shell instead of a closed-shell electronic structure and is less stable than the gold dimer. The effect of spin-orbit coupling on the dissociation energy depends on the extent to which spin-orbit coupling is quenched in the molecule. This effect has been estimated based on a spinor occupation population analysis.