Molecular dynamics (MD) simulations have been carried out for self-assembled monolayers (SAMs) of alkanethiol molecules chemisorbed on the Au(111) surface using a model with full atomic representation of methyl and methylene groups. The system consisted of flexible alkanethiol chains, S(CH2)(n)CH3, whose sulfur head groups were arranged to form a (root 3x root 3)R30 degrees commensurate structure, with periodic boundary conditions in the plane of the surface. Various properties of the system have been monitored as functions of temperature. Particular attention is given to the monolayer structure at low temperature. To this end, the configurational energies of several possible crystalline structures have been examined. The present interaction potentials are found to favor a herringbone structure with two molecules per unit cell, a finding that disagrees with the four-chain per unit cell structure proposed on the basis of recent X-ray and He diffraction data. Among many possible structures with four molecules per unit cell, three are reasonably competitive with the energy of the herringbone arrangement. Although the current study seems to provide a better description of the SAM than the so-called united-atom model, the disagreement with the X-ray data suggests that more work needs to be done in refining the treatment of the substrate.