Nanoscale silver particles have growing applications in biomedical and other technologies due to their unique antibacterial, optical, and electrical properties. The preparation of metal nanoparticles requires the action of a capping agent, such as thiol-containing compounds, to provide colloidal stability, prevent agglomeration, stop uncontrolled growth, and attenuate oxidative damage. However, despite the extensive use of these thiol-based capping agents, the structure of the capping agent layers on the metal surface and the thermodynamics of the formation of these layers remains poorly understood. Here, we leverage molecular dynamics simulations and free energy calculation techniques, to study the behavior of citrate and four thiol-containing capping agents commonly used to protect silver nanoparticles from oxidation. We have studied the single-molecule adsorption of these capping agents to the metal-water interface, their coalescence into clusters, and the formation of complete monolayers covering the metal nanoparticle. At sufficiently high concentrations, we find that allylmercaptan, lipoic acid, and mercaptohexanol spontaneously self-assemble into ordered layers with the thiol group in contact with the metal surface. The high density and ordered structure is presumably responsible for their improved protective characteristics relative to the other compounds studied.