+For a possible clarification of the controversial views on the participation of C$_{\text{s}}$ in the precipitation mechanism by classical potential simulations, test calculations need to ensure the proper description of the relative formation energies of combined structures of C$_{\text{s}}$ and Si$_{\text{i}}$ compared to C$_{\text{i}}$.
+This is particularly important since the energy of formation of C$_{\text{s}}$ is drastically underestimated by the EA potential.
+A possible occurrence of C$_{\text{s}}$ could then be attributed to a lower energy of formation of the C$_{\text{s}}$-Si$_{\text{i}}$ combination due to the low formation energy of C$_{\text{s}}$, which is obviously wrong.
+
+Since quantum-mechanical calculations reveal the Si$_{\text{i}}$ \hkl<1 1 0> DB as the ground-state configuration of Si$_{\text{i}}$ in Si, it was assumed to provide the energetically most favorable configuration in combination with C$_{\text{s}}$ in the calculations carried out in section~\ref{subsection:si-cs}.
+Empirical potentials, however, predict Si$_{\text{i}}$ T to be the energetically most favorable configuration.
+Thus, investigations of the relative energies of formation of defect pairs need to include combinations of C$_{\text{s}}$ with Si$_{\text{i}}$ T.
+Results of {\em ab initio} and classical potential calculations are summarized in Table~\ref{tab:defect_combos}.
+\begin{table}[tp]
+\begin{center}
+\begin{tabular}{l c c c}
+\hline
+\hline
+ & C$_{\text{i}}$ \hkl<1 0 0> & C$_{\text{s}}$ \& Si$_{\text{i}}$ \hkl<1 1 0> & C$_{\text{s}}$ \& Si$_{\text{i}}$ T\\
+\hline
+ \textsc{vasp} & 3.72 & 4.37 & 4.17$^{\text{a}}$/4.99$^{\text{b}}$/4.96$^{\text{c}}$ \\
+ \textsc{posic} & 3.88 & 4.93 & 5.25$^{\text{a}}$/5.08$^{\text{b}}$/4.43$^{\text{c}}$\\
+\hline
+\hline
+\end{tabular}
+\end{center}
+\caption{Formation energies of defect configurations of a single C impurity in otherwise perfect c-Si determined by classical potential and {\em ab initio} methods. The formation energies are given in eV. T denotes the tetrahedral and the subscripts i and s indicate the interstitial and substitutional configuration. Superscripts a, b and c denote configurations of C$_{\text{s}}$ located at the first, second and third nearest neighbored lattice site with respect to the Si$_{\text{i}}$ atom.}
+\label{tab:defect_combos}
+\end{table}
+Obviously, the EA potential properly describes the relative energies of formation.
+Combined structures of C$_{\text{s}}$ and Si$_{\text{i}}$ T are energetically less favorable than the ground state C$_{\text{i}}$ \hkl<1 0 0> DB configuration.
+With increasing separation distance, the energies of formation decrease.
+However, even for non-interacting defects, the energy of formation, which is then given by the sum of the formation energies of the separated defects (\unit[4.15]{eV}) is still higher than that of the C$_{\text{i}}$ \hkl<1 0 0> DB.
+Unexpectedly, the structure of a Si$_{\text{i}}$ \hkl<1 1 0> DB and a neighbored C$_{\text{s}}$, which is the most favored configuration of a C$_{\text{s}}$ and Si$_{\text{i}}$ DB according to quantum-mechanical calculations, likewise constitutes an energetically favorable configuration within the EA description, which is even preferred over the two least separated configurations of C$_{\text{s}}$ and Si$_{\text{i}}$ T.
+This is attributed to an effective reduction in strain enabled by the respective combination.
+Quantum-mechanical results reveal a more favorable energy of formation for the C$_{\text{s}}$ and Si$_{\text{i}}$ T (a) configuration.
+However, this configuration is unstable involving a structural transition into the C$_{\text{i}}$ \hkl<1 1 0> DB interstitial, thus, not maintaining the tetrahedral Si nor the \cs{} defect.
+
+Thus, the underestimated energy of formation of C$_{\text{s}}$ within the EA calculation does not pose a serious limitation in the present context.
+Since C is introduced into a perfect Si crystal and the number of particles is conserved in simulation, the creation of C$_{\text{s}}$ is accompanied by the creation of Si$_{\text{i}}$, which is energetically less favorable than the ground state, i.e.\ the C$_{\text{i}}$ \hkl<1 0 0> DB configuration, for both, the EA and {\em ab initio} treatment.
+In either case, no configuration more favorable than the C$_{\text{i}}$ \hkl<1 0 0> DB has been found.
+Thus, a proper description with respect to the relative energies of formation is assumed for the EA potential.
+
+\section{Conclusions concerning the SiC conversion mechanism}
+
+\ifnum1=0
+
+Obtained results for separated point defects in Si are in good agreement to previous theoretical work on this subject, both for intrinsic defects~\cite{leung99,al-mushadani03} as well as for C point defects~\cite{dal_pino93,capaz94}.
+The ground-state configurations of these defects, i.e.\ the Si$_{\text{i}}$ \hkl<1 1 0> and C$_{\text{i}}$ \hkl<1 0 0> DB, are reproduced and compare well to previous findings of theoretical investigations on Si$_{\text{i}}$~\cite{leung99,al-mushadani03} as well as theoretical~\cite{dal_pino93,capaz94,burnard93,leary97,jones04} and experimental~\cite{watkins76,song90} studies on C$_{\text{i}}$.
+A quantitatively improved activation energy of \unit[0.9]{eV} for a qualitatively equal migration path based on studies by Capaz et~al.~\cite{capaz94} to experimental values~\cite{song90,lindner06,tipping87} ranging from \unit[0.70--0.87]{eV} reinforce their derived mechanism of diffusion for C$_{\text{i}}$ in Si
+However, it turns out that the BC 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.
+Since the \ci{} \hkl<1 0 0> DB is the ground-state configuration and highly mobile, possible migration of these DBs to form defect agglomerates, as demanded by the model introduced in section~\ref{section:assumed_prec}, is considered possible.
+
+Unfortunately, the description of the same processes fails if classical potential methods are used.
+Already the geometry of the most stable DB 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.
+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.
+From this, a description of defect structures by classical potentials looks promising.
+%
+However, focusing on the description of diffusion processes the situation changes 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 to 3.5 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 DB agglomeration as proposed by one of the precipitation models.
+
+Quantum-mechanical investigations of two \ci{} of the \hkl<1 0 0>-type and varying separations and orientations state an attractive interaction between these interstitials.
+Obtained results for the most part compare well with results gained in previous studies~\cite{leary97,capaz98,mattoni2002,liu02} and show an astonishingly good agreement with experiment~\cite{song90}.
+%
+Depending on orientation, energetically favorable configurations are found, in which these two interstitials are located close together instead of the occurrence of largely separated and isolated defects.