+Mattoni~et~al.~\cite{mattoni2002} predict the ground-state configuration of \ci{} \hkl<1 0 0>-type defect pairs for a \hkl[1 0 0] or equivalently a \hkl[0 1 0] defect created at position 1 with both defects basically maintaining the as-isolated DB structure, resulting in a binding energy of \unit[-2.1]{eV}.
+In the present study, a further relaxation of this defect structure is observed.
+The C atom of the second and the Si atom of the initial DB move towards each other forming a bond, which results in a somewhat lower binding energy of \unit[-2.25]{eV}.
+The corresponding defect structure is displayed in Fig.~\ref{fig:defects:225}.
+In this configuration the initial Si and C DB atoms are displaced along \hkl[1 0 0] and \hkl[-1 0 0] in such a way that the Si atom is forming tetrahedral bonds with two Si and two C atoms.
+The C and Si atom constituting the second defect are as well displaced in such a way that the C atom forms tetrahedral bonds with four Si neighbors, a configuration expected in SiC.
+The two carbon atoms, which are spaced by \unit[2.70]{\AA}, do not form a bond but anyhow reside in a shorter distance than expected in SiC.
+Si atom number 2 is pushed towards the C atom, which results in the breaking of the bond to Si atom number 4.
+Breaking of the $\sigma$ bond is indeed confirmed by investigating the charge density isosurface of this configuration.
+
+Apart from that, a more favorable configuration is found for the combination with a \hkl[0 -1 0] and \hkl[-1 0 0] DB respectively, which is assumed to constitute the actual ground-state configuration of two \ci{} DBs in Si.
+The atomic arrangement is shown in Fig.~\ref{fig:defects:239}.
+The initial configuration is still evident in the relaxed configuration.
+The two \ci{} atoms form a strong C-C bond, which is responsible for the large gain in energy resulting in a binding energy of \unit[-2.39]{eV}.
+This bond has a length of \unit[1.38]{\AA} close to the next neighbor distance in diamond or graphite, which is approximately \unit[1.54]{\AA}.
+The minimum of the binding energy observed for this configuration suggests preferred C clustering as a competing mechanism to the \ci{} DB interstitial agglomeration inevitable for the SiC precipitation.
+However, the second most favorable configuration ($E_{\text{f}}=-2.25\,\text{eV}$) is represented four times, i.e.\ two times more often than the ground-state configuration, within the systematically investigated configuration space.
+Thus, particularly at high temperatures that cause an increase of the entropic contribution, this structure constitutes a serious opponent to the ground state.
+In fact, following results on migration simulations will reinforce the assumption of a low probability for C clustering by thermally activated processes.
+
+\begin{figure}[tp]
+\begin{center}
+\subfigure[\underline{$E_{\text{b}}=-2.16\,\text{eV}$}]{\label{fig:defects:216}\includegraphics[width=0.25\textwidth]{00-1dc/2-16.eps}}
+\hspace{0.2cm}
+\subfigure[\underline{$E_{\text{b}}=-1.90\,\text{eV}$}]{\label{fig:defects:190}\includegraphics[width=0.25\textwidth]{00-1dc/1-90.eps}}
+\hspace{0.2cm}
+\subfigure[\underline{$E_{\text{b}}=-2.05\,\text{eV}$}]{\label{fig:defects:205}\includegraphics[width=0.25\textwidth]{00-1dc/2-05.eps}}
+\end{center}
+\caption[Relaxed structures of defect combinations obtained by creating {\hkl[1 0 0]} and {\hkl[0 1 0]} DBs at position 2 and a {\hkl[0 0 1]} DB at position 3.]{Relaxed structures of defect combinations obtained by creating \hkl[1 0 0] (a) and \hkl[0 1 0] (b) DBs at position 2 and a \hkl[0 0 1] (c) DB at position 3.}
+\label{fig:defects:comb_db_02}
+\end{figure}
+Fig.~\ref{fig:defects:comb_db_02} shows the next three energetically favorable configurations.
+The relaxed configuration obtained by creating a \hkl[1 0 0] DB at position 2 is shown in Fig.~\ref{fig:defects:216}.
+A binding energy of \unit[-2.16]{eV} is observed.
+After relaxation, the second DB is aligned along \hkl[1 1 0].
+The bond of Si atoms 1 and 2 does not persist.
+Instead, the Si atom forms a bond with the initial \ci{} and the second C atom forms a bond with Si atom 1 forming four bonds in total.
+The C atoms are spaced by \unit[3.14]{\AA}, which is very close to the expected C-C next neighbor distance of \unit[3.08]{\AA} in SiC.
+Figure~\ref{fig:defects:205} displays the results of a \hkl[0 0 1] DB inserted at position 3.
+The binding energy is \unit[-2.05]{eV}.
+Both DBs are tilted along the same direction remaining aligned in parallel and the second DB is pushed downwards in such a way that the four DB atoms form a rhomboid.
+Both C atoms form tetrahedral bonds to four Si atoms.
+However, Si atom number 1 and number 3, which are bound to the second \ci{} atom are also bound to the initial C atom.
+These four atoms of the rhomboid reside in a plane and, thus, do not match the situation in SiC.
+The C atoms have a distance of \unit[2.75]{\AA}.
+In Fig.~\ref{fig:defects:190} the relaxed structure of a \hkl[0 1 0] DB constructed at position 2 is displayed.
+An energy of \unit[-1.90]{eV} is observed.
+The initial DB and especially the C atom is pushed towards the Si atom of the second DB forming an additional fourth bond.
+Si atom number 1 is pulled towards the C atoms of the DBs accompanied by the disappearance of its bond to Si number 5 as well as the bond of Si number 5 to its neighbored Si atom in \hkl[1 1 -1] direction.
+The C atom of the second DB forms threefold coordinated bonds to its Si neighbors.
+A distance of \unit[2.80]{\AA} is observed for the two C atoms.
+Again, the two C atoms and its two interconnecting Si atoms form a rhomboid.
+C-C distances of \unit[2.70--2.80]{\AA} seem to be characteristic for such configurations, in which the C atoms and the two interconnecting Si atoms reside in a plane.
+
+Configurations obtained by adding a \ci{} \hkl<1 0 0> DB at position 4 are characterized by minimal changes from their initial creation condition during relaxation.
+There is a low interaction of the DBs, which seem to exist independent of each other.
+This, on the one hand, becomes evident by investigating the final structure, in which both of the DBs essentially retain the structure expected for a single DB and, on the other hand, is supported by the observed binding energies, which vary only slightly around zero.
+This low interaction is due to the large distance and a missing direct connection by bonds along a chain in the crystallographic \hkl<1 1 0> direction.
+Both, C and Si atoms of the DBs form threefold coordinated bonds to their neighbors.
+The energetically most unfavorable configuration ($E_{\text{b}}=0.26\,\text{eV}$) is obtained for the \ci{} \hkl[0 0 1] DB, which is oppositely orientated with respect to the initial one.
+A DB taking the same orientation as the initial one is less unfavorable ($E_{\text{b}}=0.04\,\text{eV}$).
+Both configurations are unfavorable compared to far-off, isolated DBs.
+Nonparallel orientations, i.e.\ the \hkl[0 1 0], \hkl[0 -1 0] and its equivalents, result in binding energies of \unit[-0.12]{eV} and \unit[-0.27]{eV}, thus, constituting energetically favorable configurations.
+The reduction of strain energy is higher in the second case, where the C atom of the second DB is placed in the direction pointing away from the initial C atom.
+
+\begin{figure}[tp]
+\begin{center}
+\subfigure[\underline{$E_{\text{b}}=-1.53\,\text{eV}$}]{\label{fig:defects:153}\includegraphics[width=0.25\textwidth]{00-1dc/1-53.eps}}
+\hspace{0.7cm}
+\subfigure[\underline{$E_{\text{b}}=-1.66\,\text{eV}$}]{\label{fig:defects:166}\includegraphics[width=0.25\textwidth]{00-1dc/1-66.eps}}\\
+\subfigure[\underline{$E_{\text{b}}=-1.88\,\text{eV}$}]{\label{fig:defects:188}\includegraphics[width=0.25\textwidth]{00-1dc/1-88.eps}}
+\hspace{0.7cm}
+\subfigure[\underline{$E_{\text{b}}=-1.38\,\text{eV}$}]{\label{fig:defects:138}\includegraphics[width=0.25\textwidth]{00-1dc/1-38.eps}}
+\end{center}
+\caption[Relaxed structures of defect combinations obtained by creating {\hkl[0 0 1]}, {\hkl[0 0 -1]}, {\hkl[0 -1 0]} and {\hkl[1 0 0]} DBs at position 5.]{Relaxed structures of defect combinations obtained by creating \hkl[0 0 1] (a), \hkl[0 0 -1] (b), \hkl[0 -1 0] (c) and \hkl[1 0 0] (d) DBs at position 5.}
+\label{fig:defects:comb_db_03}
+\end{figure}
+Energetically beneficial configurations of defect combinations are observed for interstitials of all orientations placed at position 5, a position two bonds away from the initial interstitial along the \hkl[1 1 0] direction.
+Relaxed structures of these combinations are displayed in Fig.~\ref{fig:defects:comb_db_03}.
+Fig.~\ref{fig:defects:153} and~\ref{fig:defects:166} show the relaxed structures of \hkl[0 0 1] and \hkl[0 0 -1] DBs.
+The upper DB atoms are pushed towards each other forming fourfold coordinated bonds.
+While the displacements of the Si atoms in case (b) are symmetric to the \hkl(1 1 0) plane, in case (a) the Si atom of the initial DB is pushed a little further in the direction of the C atom of the second DB than the C atom is pushed towards the Si atom.
+The bottom atoms of the DBs remain in threefold coordination.
+The symmetric configuration is energetically more favorable ($E_{\text{b}}=-1.66\,\text{eV}$) since the displacements of the atoms is less than in the antiparallel case ($E_{\text{b}}=-1.53\,\text{eV}$).
+In Fig.~\ref{fig:defects:188} and~\ref{fig:defects:138} the non-parallel orientations, namely the \hkl[0 -1 0] and \hkl[1 0 0] DBs, are shown.
+Binding energies of \unit[-1.88]{eV} and \unit[-1.38]{eV} are obtained for the relaxed structures.
+In both cases the Si atom of the initial interstitial is pulled towards the near by atom of the second DB.
+Both atoms form fourfold coordinated bonds to their neighbors.
+In case (c) it is the C and in case (d) the Si atom of the second interstitial, which forms the additional bond with the Si atom of the initial interstitial.
+The respective atom of the second DB, the \ci{} atom of the initial DB and the two interconnecting Si atoms again reside in a plane.
+As observed before, a typical C-C distance of \unit[2.79]{\AA} is, thus, observed for case (c).
+In both configurations, the far-off atom of the second DB resides in threefold coordination.
+
+The interaction of \ci{} \hkl<1 0 0> DBs is investigated along the \hkl[1 1 0] bond chain assuming a possible reorientation of the DB atom at each position to minimize its configurational energy.
+Therefore, the binding energies of the energetically most favorable configurations with the second DB located along the \hkl[1 1 0] direction and resulting C-C distances of the relaxed structures are summarized in Table~\ref{tab:defects:comb_db110}.
+\begin{table}[tp]
+\begin{center}
+\begin{tabular}{l c c c c c c}
+\hline
+\hline
+ & 1 & 2 & 3 & 4 & 5 & 6\\
+\hline
+$E_{\text{b}}$ [eV] & -2.39 & -1.88 & -0.59 & -0.31 & -0.24 & -0.21 \\
+C-C distance [\AA] & 1.4 & 4.6 & 6.5 & 8.6 & 10.5 & 10.8 \\
+Type & \hkl[-1 0 0] & \hkl[1 0 0] & \hkl[1 0 0] & \hkl[1 0 0] & \hkl[1 0 0] & \hkl[1 0 0], \hkl[0 -1 0]\\
+\hline
+\hline
+\end{tabular}
+\end{center}
+\caption{Binding energies $E_{\text{b}}$, C-C distance and types of energetically most favorable \ci{} \hkl<1 0 0>-type defect pairs separated along the \hkl[1 1 0] bond chain.}
+\label{tab:defects:comb_db110}
+\end{table}
+%
+\begin{figure}[tp]
+\begin{center}
+\includegraphics[width=0.7\textwidth]{db_along_110_cc_n.ps}
+\end{center}
+\caption[Minimum binding energy of DB combinations separated along {\hkl[1 1 0]} with respect to the C-C distance.]{Minimum binding energy of dumbbell combinations separated along \hkl[1 1 0] with respect to the C-C distance. The blue line is a guide for the eye and the green curve corresponds to the most suitable fit function consisting of all but the first data point.}
+\label{fig:defects:comb_db110}
+\end{figure}
+The binding energy of these configurations with respect to the C-C distance is plotted in Fig.~\ref{fig:defects:comb_db110}.
+The interaction is found to be proportional to the reciprocal cube of the C-C distance for extended separations of the \ci{} DBs and saturates for the smallest possible separation, i.e.\ the ground-state configuration.
+The ground-state configuration was ignored in the fitting process.
+Not considering the previously mentioned elevated barriers for migration, an attractive interaction between the \ci{} \hkl<1 0 0> DB defects indeed is detected with a capture radius that clearly exceeds \unit[1]{nm}.
+The interpolated graph suggests the disappearance of attractive interaction forces, which are proportional to the slope of the graph, in between the two lowest separation distances of the defects.
+This finding, in turn, supports the previously established assumption of C agglomeration and absence of C clustering.
+
+%\subsection{Diffusion processes among configurations of \ci{} pairs}
+
+To draw further conclusions on the probability of C clustering, transitions into the ground-state configuration are investigated.
+Based on the lowest energy migration path of a single \ci{} \hkl<1 0 0> DB, the configuration, in which the second \ci{} DB is oriented along \hkl[0 1 0] at position 2 is assumed to constitute an ideal starting point for a transition into the ground state.
+In addition, the starting configuration exhibits a low binding energy (\unit[-1.90]{eV}) and is, thus, very likely to occur.
+However, a smooth transition path is not found.
+Intermediate configurations within the investigated turbulent pathway identify barrier heights of more than \unit[4]{eV} resulting in a low probability for the transition.
+The high activation energy is attributed to the stability of such a low energy configuration, in which the C atom of the second DB is located close to the initial DB.
+Due to an effective stress compensation realized in the respective low energy configuration, which will necessarily be lost during migration, a high energy configuration needs to get passed, which is responsible for the high barrier.
+Low barriers are only identified for transitions starting from energetically less favorable configurations, e.g. the configuration of a \hkl[-1 0 0] DB located at position 2 (\unit[-0.36]{eV}).
+Starting from this configuration, an activation energy of only \unit[1.2]{eV} is necessary for the transition into the ground state configuration.
+The corresponding migration energies and atomic configurations are displayed in Fig.~\ref{fig:036-239}.
+\begin{figure}[tp]
+\begin{center}
+\includegraphics[width=0.7\textwidth]{036-239.ps}
+\end{center}
+\caption[Migration barrier and structures of the transition of a C$_{\text{i}}$ {\hkl[-1 0 0]} DB at position 2 into a C$_{\text{i}}$ {\hkl[0 -1 0]} DB at position 1.]{Migration barrier and structures of the transition of a C$_{\text{i}}$ \hkl[-1 0 0] DB at position 2 (left) into a C$_{\text{i}}$ \hkl[0 -1 0] DB at position 1 (right). An activation energy of \unit[1.2]{eV} is observed.}
+\label{fig:036-239}
+\end{figure}
+Since thermally activated C clustering is, thus, only possible by traversing energetically unfavored configurations, extensive C clustering is not expected.
+Furthermore, the migration barrier of \unit[1.2]{eV} is still higher than the activation energy of \unit[0.9]{eV} observed for a single C$_{\text{i}}$ \hkl<1 0 0> DB in c-Si.
+The migration barrier of a C$_{\text{i}}$ DB in a complex system is assumed to approximate the barrier of a DB in a separated system with increasing defect separation.
+Accordingly, lower migration barriers are expected for pathways resulting in larger separations of the C$_{\text{i}}$ DBs.
+% acknowledged by 188-225 (reverse order) calc
+However, if the increase of separation is accompanied by an increase in binding energy, this difference is needed in addition to the activation energy for the respective migration process.
+Configurations, which exhibit both, a low binding energy as well as afferent transitions with low activation energies are, thus, most probable C$_{\text{i}}$ complex structures.
+On the other hand, if elevated temperatures enable migrations with huge activation energies, comparably small differences in configurational energy can be neglected resulting in an almost equal occupation of such configurations.
+In both cases the configuration yielding a binding energy of \unit[-2.25]{eV} is promising.
+First of all, it constitutes the second most energetically favorable structure.
+Secondly, a migration path with a barrier as low as \unit[0.47]{eV} exists starting from a configuration of largely separated defects exhibiting a low binding energy (\unit[-1.88]{eV}).
+The migration barrier and corresponding structures are shown in Fig.~\ref{fig:188-225}.
+\begin{figure}[tp]
+\begin{center}
+\includegraphics[width=0.7\textwidth]{188-225.ps}
+\end{center}
+\caption[Migration barrier and structures of the transition of a C$_{\text{i}}$ {\hkl[0 -1 0]} DB at position 5 into a C$_{\text{i}}$ {\hkl[1 0 0]} DB at position 1.]{Migration barrier and structures of the transition of a C$_{\text{i}}$ \hkl[0 -1 0] DB at position 5 (left) into a C$_{\text{i}}$ \hkl[1 0 0] DB at position 1 (right). An activation energy of \unit[0.47]{eV} is observed.}
+\label{fig:188-225}
+\end{figure}
+Finally, as already mentioned above, this type of defect pair is represented two times more often than the ground-state configuration.
+The latter is considered very important at high temperatures, accompanied by an increase in the entropic contribution to structure formation.
+As a result, C defect agglomeration indeed is expected, but only a low probability is assumed for C-C clustering by thermally activated processes with regard to the considered process time in IBS.
+
+\subsection[Combinations of the \ci{} \hkl<1 0 0> and \cs{} type]{\boldmath Combinations of the \ci{} \hkl<1 0 0> and \cs{} type}
+\label{subsection:defects:c-csub}
+
+\begin{table}[tp]
+\begin{center}
+\begin{tabular}{c c c c c c}
+\hline
+\hline
+1 & 2 & 3 & 4 & 5 & R \\
+\hline
+0.26$^a$/-1.28$^b$ & -0.51 & -0.93$^A$/-0.95$^B$ & -0.15 & 0.49
+ & -0.05\\
+\hline
+\hline
+\end{tabular}
+\end{center}
+\caption[Binding energies of combinations of the \ci{} {\hkl[0 0 -1]} defect with a \cs{} atom located at positions 1 to 5 according to Fig.~\ref{fig:defects:combos_ci}.]{Binding energies of combinations of the \ci{} \hkl[0 0 -1] defect with a \cs{} atom located at positions 1 to 5 according to Fig.~\ref{fig:defects:combos_ci}. R corresponds to the position located at $\frac{a_{\text{Si}}}{2}\hkl[3 2 3]$ relative to the initial defect position, which is the maximum realizable distance due to periodic boundary conditions.}
+\label{tab:defects:c-s}
+\end{table}
+%\begin{figure}[tp]
+%\begin{center}
+%\begin{minipage}[t]{5cm}
+%a) \underline{Pos: 1, $E_{\text{b}}=0.26\text{ eV}$}
+%\begin{center}
+%\includegraphics[width=4.8cm]{00-1dc/0-26.eps}
+%\end{center}
+%\end{minipage}
+%\begin{minipage}[t]{5cm}
+%b) \underline{Pos: 3, $E_{\text{b}}=-0.93\text{ eV}$}
+%\begin{center}
+%\includegraphics[width=4.8cm]{00-1dc/0-93.eps}
+%\end{center}
+%\end{minipage}
+%\begin{minipage}[t]{5cm}
+%c) \underline{Pos: 5, $E_{\text{b}}=0.49\text{ eV}$}
+%\begin{center}
+%\includegraphics[width=4.8cm]{00-1dc/0-49.eps}
+%\end{center}
+%\end{minipage}
+%\end{center}
+%\caption{Relaxed structures of defect complexes obtained by creating a carbon substitutional at position 1 (a)), 3 (b)) and 5 (c)).}
+%\label{fig:defects:comb_db_04}
+%\end{figure}
+%\begin{figure}[tp]
+%\begin{center}
+%\begin{minipage}[t]{7cm}
+%a) \underline{Pos: 2, $E_{\text{b}}=-0.51\text{ eV}$}
+%\begin{center}
+%\includegraphics[width=6cm]{00-1dc/0-51.eps}
+%\end{center}
+%\end{minipage}
+%\begin{minipage}[t]{7cm}
+%b) \underline{Pos: 4, $E_{\text{b}}=-0.15\text{ eV}$}
+%\begin{center}
+%\includegraphics[width=6cm]{00-1dc/0-15.eps}
+%\end{center}
+%\end{minipage}
+%\end{center}
+%\caption{Relaxed structures of defect complexes obtained by creating a carbon substitutional at position 2 (a)) and 4 (b)).}
+%\label{fig:defects:comb_db_05}
+%\end{figure}
+%
+Table~\ref{tab:defects:c-s} lists the energetic results of \cs{} combinations with the initial \ci{} \hkl[0 0 -1] DB.
+For \cs{} located at position 1 and 3, the configurations $\alpha$ and A correspond to the naive relaxation of the structure by substituting the Si atom by a C atom in the initial \ci{} \hkl[0 0 -1] DB structure at positions 1 and 3 respectively.
+However, small displacements of the involved atoms near the defect result in different stable structures labeled $\beta$ and B respectively.
+Fig.~\ref{fig:093-095} and~\ref{fig:026-128} show structures A, B and $\alpha$, $\beta$ together with the barrier of migration for the A to B and $\alpha$ to $\beta$ transition respectively.
+
+% A B
+%./visualize_contcar -w 640 -h 480 -d results/c_00-1_c3_csub_B -nll -0.20 -0.4 -0.1 -fur 0.9 0.6 0.9 -c 0.5 -1.5 0.375 -L 0.5 0 0.3 -r 0.6 -A -1 2.465
+\begin{figure}[tp]
+\begin{center}
+\includegraphics[width=0.7\textwidth]{093-095.ps}
+\end{center}
+\caption[Migration barrier and structures of the transition of the initial \ci{} {\hkl[0 0 -1]} DB and C$_{\text{s}}$ at position 3 into a configuration of a twofold coordinated Si$_{\text{i}}$ located in between two C$_{\text{s}}$ atoms occupying the lattice sites of the initial DB and position 3.]{Migration barrier and structures of the transition of the initial \ci{} \hkl[0 0 -1] DB and C$_{\text{s}}$ at position 3 (left) into a configuration of a twofold coordinated Si$_{\text{i}}$ located in between two C$_{\text{s}}$ atoms occupying the lattice sites of the initial DB and position 3 (right). An activation energy of \unit[0.44]{eV} is observed.}
+\label{fig:093-095}
+\end{figure}
+Configuration A consists of a C$_{\text{i}}$ \hkl[0 0 -1] DB with threefold coordinated Si and C DB atoms slightly disturbed by the C$_{\text{s}}$ at position 3, facing the Si DB atom as a neighbor.
+By a single bond switch, i.e.\ the breaking of a Si-Si in favor of a Si-C bond, configuration B is obtained, which shows a twofold coordinated Si atom located in between two substitutional C atoms residing on regular Si lattice sites.
+This configuration has been identified and described by spectroscopic experimental techniques~\cite{song90_2} as well as theoretical studies~\cite{leary97,capaz98}.
+Configuration B is found to constitute the energetically slightly more favorable configuration.
+However, the gain in energy due to the significantly lower energy of a Si-C compared to a Si-Si bond turns out to be smaller than expected due to a large compensation by introduced strain as a result of the Si interstitial structure.
+Present results show a difference in energy of states A and B, which exactly matches the experimental value of \unit[0.02]{eV}~\cite{song90_2}, reinforcing qualitatively correct results of previous theoretical studies on these structures.
+% mattoni: A favored by 0.4 eV - NO, it is indeed B (reinforce Song and Capaz)!
+%
+% AB transition
+The migration barrier is identified to be \unit[0.44]{eV}, almost three times higher than the experimental value of \unit[0.16]{eV}~\cite{song90_2} estimated for the neutral charge state transition in p- and n-type Si.
+Keeping in mind the formidable agreement of the energy difference with experiment, the overestimated activation energy is quite unexpected.
+Obviously, either the CRT algorithm fails to seize the actual saddle point structure or the influence of dopants has exceptional effect in the experimentally covered diffusion process being responsible for the low migration barrier.
+% not satisfactory!
+
+% a b
+\begin{figure}[tp]
+\begin{center}
+\includegraphics[width=0.7\textwidth]{comb_mig_026-128_vasp.ps}
+\end{center}
+\caption[Migration barrier and structures of the transition of the initial C$_{\text{i}}$ {\hkl[0 0 -1]} DB and C$_{\text{s}}$ at position 1 into a C-C {\hkl[1 0 0]} DB occupying the lattice site at position 1.]{Migration barrier and structures of the transition of the initial C$_{\text{i}}$ \hkl[0 0 -1] DB and C$_{\text{s}}$ at position 1 (left) into a C-C \hkl[1 0 0] DB occupying the lattice site at position 1 (right). An activation energy of \unit[0.1]{eV} is observed.}
+\label{fig:026-128}
+\end{figure}
+Configuration $\alpha$ is similar to configuration A, except that the C$_{\text{s}}$ atom at position 1 is facing the C DB atom as a neighbor resulting in the formation of a strong C-C bond and a much more noticeable perturbation of the DB structure.
+Nevertheless, the C and Si DB atoms remain threefold coordinated.
+Although the C-C bond exhibiting a distance of \unit[0.15]{nm} close to the distance expected in diamond or graphite should lead to a huge gain in energy, a repulsive interaction with a binding energy of \unit[0.26]{eV} is observed due to compressive strain of the Si DB atom and its top neighbors (\unit[0.230]{nm}/\unit[0.236]{nm}) along with additional tensile strain of the C$_{\text{s}}$ and its three neighboring Si atoms (\unit[0.198--0.209]{nm}/\unit[0.189]{nm}).
+Again a single bond switch, i.e.\ the breaking of the bond of the Si atom bound to the fourfold coordinated C$_{\text{s}}$ atom and the formation of a double bond between the two C atoms, results in configuration b.
+The two C atoms form a \hkl[1 0 0] DB sharing the initial C$_{\text{s}}$ lattice site while the initial Si DB atom occupies its previously regular lattice site.
+The transition is accompanied by a large gain in energy as can be seen in Fig.~\ref{fig:026-128}, making it the ground-state configuration of a C$_{\text{s}}$ and C$_{\text{i}}$ DB in Si yet \unit[0.33]{eV} lower in energy than configuration B.
+This finding is in good agreement with a combined {\em ab initio} and experimental study of Liu et~al.~\cite{liu02}, who first proposed this structure as the ground state identifying an energy difference compared to configuration B of \unit[0.2]{eV}.
+% mattoni: A favored by 0.2 eV - NO! (again, missing spin polarization?)
+A net magnetization of two spin up electrons, which are equally localized as in the Si$_{\text{i}}$ \hkl<1 0 0> DB structure is observed.
+In fact, these two configurations are very similar and are qualitatively different from the C$_{\text{i}}$ \hkl<1 0 0> DB that does not show magnetization but a nearly collinear bond of the C DB atom to its two neighbored Si atoms while the Si DB atom approximates \unit[120]{$^{\circ}$} angles in between its bonds.
+Configurations $\alpha$, A and B are not affected by spin polarization and show zero magnetization.
+Mattoni et~al.~\cite{mattoni2002}, in contrast, find configuration $\beta$ less favorable than configuration A by \unit[0.2]{eV}.
+Next to differences in the XC functional and plane-wave energy cut-off, this discrepancy might be attributed to the neglect of spin polarization in their calculations, which -- as has been shown for the C$_{\text{i}}$ BC configuration -- results in an increase of configurational energy.
+Indeed, investigating the migration path from configurations $\alpha$ to $\beta$ and, in doing so, reusing the wave functions of the previous migration step the final structure, i.e.\ configuration $\beta$, is obtained with zero magnetization and an increase in configurational energy by \unit[0.2]{eV}.
+Obviously a different energy minimum of the electronic system is obtained indicating hysteresis behavior.
+However, since the total energy is lower for the magnetic result it is believed to constitute the real, i.e.\ global, minimum with respect to electronic minimization.
+%
+% a b transition
+A low activation energy of \unit[0.1]{eV} is observed for the a$\rightarrow$b transition.
+Thus, configuration a is very unlikely to occur in favor of configuration b.