\label{fig:albe_mig}
\end{figure}
Calculations based on the EA potential yield a different picture.
-Fig.~\ref{fig:albe_mig} shows the evolution of structure and energy along the lowest energy migration pathways (path~1) based on the EA potential.
+Fig.~\ref{fig:albe_mig} shows the evolution of structure and energy along the lowest energy migration path (path~1) based on the EA potential.
+Due to symmetry it is sufficient to merely consider the migration from the BC to C$_{\text{I}}$ configuration.
Two different pathways are obtained for different time constants of the Berendsen thermostat.
With a time constant of \unit[1]{fs} the C atom resides in the \hkl(1 1 0) plane resulting in a migration barrier of \unit[2.4]{eV}.
% lower / weaker / less strong ?
-However, lower coupling to the heat bath realized by a an increase of the time constant to \unit[100]{fs} enables the C atom to move out of the \hkl(1 1 0) plane already at the beginning, which is accompanied by a reduction in energy, approaching the final configuration on a curved path.
+However, lower coupling to the heat bath realized by an increase of the time constant to \unit[100]{fs} enables the C atom to move out of the \hkl(1 1 0) plane already at the beginning, which is accompanied by a reduction in energy, approaching the final configuration on a curved path.
The energy barrier of this path is \unit[0.2]{eV} lower in energy than the direct migration within the \hkl(1 1 0) plane.
It should be noted that the BC configuration is actually not a local minimum configuration in EA based calculations since a relaxation into the \hkl<1 1 0> dumbbell configuration occurs.
-However, investigating further migration pathways involving the \hkl<1 1 0> interstitial did not yield to lower migration barriers.
+However, investigating further migration pathways involving the \hkl<1 1 0> interstitial did not yield lower migration barriers.
Thus, the lowest activation energy must be assumed to be higher than or equal to \unit[2.2]{eV}.
% experimental findings much lower, overestimated by a factor of 2.4
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[0.73]{eV} -- \unit[0.87]{eV})\cite{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, adjusts.
+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, adjusts.
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 carbon interstitial can be expected to be mobile at prevailing temperatures in the process under investigation, i.e. IBS.
+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.
The description of the same processes obviously 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.
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