We investigate the microscopic processes leading to graphene growth by the chemical vapor deposition of propane in an argon atmosphere at the SiC surface. Experimentally, it is known that the presence of argon fastens the dehydrogenation processes at the surface, at high temperatures of about 2000 K. We perform ab initio calculations, at zero temperature, to check whether chemical reactions can explain this phenomenon. Density functional theory and supporting quantum chemistry methods qualitatively describe formation of the graphene wafers. We find that the 4H-SiC(0001) surface exhibits a large catalytic effect in the adsorption process of hydrocarbon molecules, this is also supported by preliminary molecular dynamics results. The existence of the ArH(+) molecule, and an observation from the Raman spectra that the negative charge transfers into the SiC surface, would suggest that presence of argon atoms leads to a deprotonization on the surface, which is necessary to obtain a pure carbon adlayer. But the zero-temperature description shows that the cold environment is insufficient to promote argon-assisted surface cleaning.