Configurations a, A and B are not affected by spin polarization and show zero magnetization.\r
Mattoni et~al.\cite{mattoni2002}, in contrast, find configuration b less favorable than configuration A by \unit[0.2]{eV}.\r
Next to differences in the XC-functional and plane-wave energy cut-off this discrepancy might be attributed to the missing accounting for spin polarization in their calculations, which -- as has been shown for the C$_{\text{i}}$ BC configuration -- results in an increase of configurational energy.\r
+Indeed, investigating the migration path from configurations a to b and, in doing so, reusing the wave functions of the previous migration step the final structure, i.e. configuration b, was obtained with zero magnetization and an increase in configurational energy \unit[0.2]{eV}.\r
+Obviously a different energy minimum of the electronic system is obatined in that case showing a hysterisis behavior.\r
+However, since the total energy is lower for the magnetic result it is believed to constitute the real, i.e. global, minimum of the electronic minimization.\r
\r
A low activation energy of \unit[0.1]{eV} is observed for the a$\rightarrow$b transition.\r
Thus, configuration a is very unlikely to occur in favor of configuration b.\r