Density functional theory (DFT) calculations show that dimers and longer carbon strings are more stable than individual atoms on Fe(111) surfaces. It is therefore necessary to consider the formation of these species on the metal surfaces and their effect on the mechanism of single-walled nanotube (SWNT) growth. The good agreement between the trends (energies and structures) obtained using DFT and those based on the Brenner and AIREBO models indicate that these analytic models provide adequate descriptions of the supported carbon systems needed for valid molecular dynamics simulations of SWNT growth. In contrast, the AIREBO model provides a better description of the relative energies for isolated carbon species, and this model is preferred over the Brenner potential when simulating SWNT growth in the absence of metal particles. However, the PM3 semiempirical model appears to provide an even better description for these systems and, given sufficient computer resources, direct dynamics methods based on this model may be preferred.