-The first-principles results are in good agreement to previous work on this subject\cite{burnard93,leary97,dal_pino93,capaz94}.
-The C-Si \hkl<1 0 0> dumbbell interstitial is found to be the ground state configuration of a C defect in Si.
-The lowest migration path already proposed by Capaz et~al.\cite{capaz94} is reinforced by an additional improvement of the quantitative conformance of the barrier height calculated in this work (\unit[0.9]{eV}) with experimentally observed values (\unit[0.70]{eV} -- \unit[0.87]{eV})\cite{lindner06,song90,tipping87}.
-However, it turns out that the bond-centered configuration is not a saddle point configuration as proposed by Capaz et~al.\cite{capaz94} but constitutes a real local minimum if the electron spin is properly accounted for.
-A net magnetization of two electrons, which is already clear by simple molecular orbital theory considerations on the bonding of the sp hybridized C atom, is settled.
-By investigating the charge density isosurface it turns out that the two resulting spin up electrons are localized in a torus around the C atom.
-With an activation energy of \unit[0.9]{eV} the C$_{\text{i}}$ carbon interstitial can be expected to be highly mobile at prevailing temperatures in the process under investigation, i.e. IBS.
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-We found that the description of the same processes fails if classical potential methods are used.
-Already the geometry of the most stable dumbbell configuration differs considerably from that obtained by first-principles calculations.
-The classical approach is unable to reproduce the correct character of bonding due to the deficiency of quantum-mechanical effects in the potential.
-%ref mod: language - energy / order
-%Nevertheless, both methods predict the same type of interstitial as the ground state configuration, and also the order in energy of the remaining defects is reproduced fairly well.
-Nevertheless, both methods predict the same type of interstitial as the ground state configuration.
-Furthermore, the relative energies of the other defects are reproduced fairly well.
-From this, a description of defect structures by classical potentials looks promising.
-% ref mod: language - changed
-%However, focussing on the description of diffusion processes the situation is changing completely.
-However, focussing on the description of diffusion processes the situation has changed completely.
-Qualitative and quantitative differences exist.
-First of all, a different pathway is suggested as the lowest energy path, which again might be attributed to the absence of quantum-mechanical effects in the classical interaction model.
-Secondly, the activation energy is overestimated by a factor of 2.4 compared to the more accurate quantum-mechanical methods and experimental findings.
-This is attributed to the sharp cut-off of the short range potential.
-As already pointed out in a previous study\cite{mattoni2007} the short cut-off is responsible for overestimated and unphysical high forces of next neighbor atoms.
-The overestimated migration barrier, however, affects the diffusion behavior of the C interstitials.
-By this artifact the mobility of the C atoms is tremendously decreased resulting in an inaccurate description or even absence of the dumbbell agglomeration as proposed by the precipitation model.