We use a density-functional-based tight-binding method to study diamond growth steps by depositing dicarbon species onto a hydrogen-free diamond ͑110͒ surface. Subsequent C 2 molecules are deposited on an initially clean surface, in the vicinity of a growing adsorbate cluster, and finally near vacancies just before completion of a full new monolayer. The preferred growth stages arise from C 2n clusters in near ideal lattice positions forming zigzag chains running along the ͓1 10͔ direction parallel to the surface. The adsorption energies are consistently exothermic by 8-10 eV per C 2 , depending on the size of the cluster. The deposition barriers for these processes are in the range of 0.0-0.6 eV. For deposition sites above C 2n clusters the adsorption energies are smaller by 3 eV, but diffusion to more stable positions is feasible. We also perform simulations of the diffusion of C 2 molecules on the surface in the vicinity of existing adsorbate clusters using a constrained conjugate gradient method. We find migration barriers in excess of 3 eV on the clean surface, and 0.6-1.0 eV on top of graphenelike adsorbates. The barrier heights and pathways indicate that the growth from gaseous dicarbon proceeds either by direct adsorption onto clean sites or after migration on top of the existing C 2n chains.