We use a density-functional-based tight-binding method to study diamond gro
wth steps by depositing dicarbon species onto a hydrogen-free diamond (110)
surface. Subsequent C-2 molecules are deposited on an initially clean surf
ace, in the vicinity of a growing adsorbate cluster, and finally near vacan
cies just before completion of a full new monolayer. The preferred growth s
tages arise from C-2n clusters in near ideal lattice positions forming zigz
ag chains running along the [(1$) over bar 10] direction parallel to the su
rface. 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 clus
ters using a constrained conjugate gradient method. We find migration barri
ers in excess of 3 eV on the clean surface, and 0.6-1.0 eV on top bf graphe
nelike adsorbates. The barrier heights and pathways indicate that the growt
h from gaseous dicarbon proceeds either by direct adsorption onto clean sit
es or after migration on top of the existing C-2n chains.