We present converged first-principles calculations for the atomic and electronic structure of the diamond(111)-(2 x 1) face adsorbed with C-2 or C2H2 based on the periodic density functional theory (DFT) in the general gradient approximation. The unique geometry of the C(111)-(2 x 1) Pandey chain provides the ideal molecular template for the self-assembly of C-2. Depending on the initial bonding configuration of the,C-2 biradical on the Pandey chain, self-assembly via mutual interactions can result in different superstructures. The most stable C-2 binding site on the C(111)-(2 x 1) surface is the straddled bridging site between adjacent Pandey chains. Van der Waals Epitaxy of graphite can proceed on the C(111)-(2 x 1) template following the self-assembly of C-2 biradical, with consequent gain in surface energy. The self-assembly of C2H2 on top of the Pandey chain results in the formation of polyethylene that follows the zigzag course of the chain. The adsorption of C2H2 can passivate the surface states on C(111)-(2 x 1) and result in an opening of the surface band gap.