Achieving a better control of the nucleation and growth: of single-walled carbon nanotubes requires understanding of the changes in the catalyst-structure and the interfacial phenomena occurring at the solid surface and the gaseous phase from the early stages of the, synthesis process. Carbon nanotubes produced by chemical-vapor deposition typically use carbon-philic metal catalysts such as Fe, Ni, and Co, in which both surface C and dissolved C atoms contribute to the nanotube formation. We use density functional theory to investigate the interactions of Rh, a noble metal, with carbon both as individual atoms gradually deposited on the catalyst surface from the precursor gas decomposition and as a nucleating seed adhered to the catalyst. Adsorption and limited dissolution of carbon atoms in the subsurface are found to be favorable in unsupported-clusters of various sizes (Rh-38, Rh-55, and: Rh-68) and in Rh-32 cluster supported on MgO(100) and MgO(111) surfaces. Changes in solubility, electron density transfer;, and interactions-of the Rh clusters with the support and the nascent nanotube are explored for increasing contents of carbon adsorbed on or dissolved inside the particles. The adhesion energy of small Rh-38 clusters on the different MgO surfaces studied can differ by as much as 1 eV compared with the same;sized Rh2C particles:Also; the adhesion of graphene differs On the Rh particles by as much as 5.7 eV withrespect to Rh2C supported nanoparticles. This demonstrates the influence that the presence of dissolved carbon Can;have on the catalyst interactions with the support and nucleating nanotube. A discussion on how such factors affect the lattice and electronic structure of the catalyst particles is presented in the interest of obtaining insight that will allow the design of improved catalysts for controlled nanotube synthesis,