The origin of the polytypes of SiC has been investigated from the viewpoint of surface reactions by the density functional theory (DFT) within the Projector Augmented Wave-Generalized Gradient Approximation. Three radicals were considered here as the major species in the crystal growth process: Si, Si2C and SiC2. We supposed that these radicals contribute to the crystal growth directly through the adsorption on the 4H-SiC (000-1) C-face surface. The DFT calculations showed that the Si2C, which relatively has a similar structure with the SiC crystal, had no activation barrier to be adsorbed chemically to the 4H-SiC C-face surface. On the other hand, SiC2 with Si showed an activation barrier of 0.79eV to form the 4H-SiC crystal. In order to investigate the arrangements to decide polytypism in SiC, we compared the adsorption energies between the different sites, which correspond to the 4H-SiC crystal and a disordered arrangement. The activation energies had almost no difference. Our calculations indicated that these radicals do not contribute to the origin of the polytypes of SiC.