Ongoing experimental research effort is devoted to further the understanding of the adsorption of dithiol molecules on gold surfaces with promising technological applications. To elucidate the subject from a theoretical perspective, we study the submonolayer adsorption of 1,4-butanedithiol molecules and radicals on the unreconstructed Au(111) and Au(100) surfaces using density-functional theory. From the calculated local energy minima the lowest-energy configurations are selected. The alkane chains are roughly parallel to the surface, such that two sulfur-gold adsorbate-substrate bonds can form. On the unreconstructed Au(100) surface dissociation of butanedithiol molecules into ${\text{H}}_{2}$ in the gas phase and butanedithiol radicals chemisorbed on the surface is energetically preferred. The two sulfur atoms of the radical adopt hollow-bridge-like positions. On the unreconstructed Au(111) surface the S-H bonds are predicted to be cleaved due to entropic effects. In the ground-state configuration the two sulfur atoms of the butanedithiol radical adopt an fcc hollow and an fcc hollow-bridge position on the surface. Hence, we expect butanedithiol radicals to be the prevailing adsorbed species on both investigated gold surfaces. STM-images of the ground-state configuration of butanedithiol radicals chemisorbed on Au(111) have been simulated within the Tersoff-Hamann model. They show elongated bright features above the location of the alkane chain. The long axis is slightly tilted with respect to the $⟨1\overline{1}0⟩$ directions. Finally, a semiempirical approach has been evaluated to investigate the effect of van der Waals interactions to the binding energies calculated within GGA-DFT.