We present detailed ab initio density functional calculations of equilibrium atomic geometry, electronic states, and chemical bonding for the adsorption of elemental S on Si(001). Following recently reported room temperature low-energy electron diffraction, Auger electron spectroscopy, thermal desorption spectroscopy, and work function measurements by Papageorgopoulos et al. [Phys. Rev. B 55, 4435 (1997)], three different adsorption models have been studied: hemisulfide (2X1) structure, monosulfide (1X1) structure, and disulfide (1X1) structure. For hemisulfide and monosulfide structures, the calculated location of S above the Si(001) surface is in excellent agreement with the experiment. An analysis of surface free energy suggests that, in the allowed range of S chemical potential, the monosulfide structure is more stable than the hemisulfide and disulfide structures. A signature of desorption of the SiS unit is obtained from the study of the disulfide structure. (C) 1998 American Institute of Physics. [S0021-8979(98)03123-5].