+ Spin polarized calculations
+
+ {\small
+ \begin{minipage}[t]{5.8cm}
+ \underline{Kohn-Sham eigenvalues}\\
+ \begin{minipage}{2.8cm}
+ Spin up:\\
+ 430: 4.2639 - 1\newline
+ 431: 4.7332 - 1\newline
+ 432: 4.7354 - 1\newline
+ 433: 4.7700 - 1\newline
+ 434: 4.8116 - 1\newline
+ 435: 4.8118 - 1\newline
+ 436: 5.5360 - 0\newline
+ 437: 5.5623 - 0
+ \end{minipage}
+ \begin{minipage}{2.8cm}
+ Spin down:\\
+ 430: 4.2682 - 1\newline
+ 431: 4.7738 - 1\newline
+ 432: 4.8150 - 1\newline
+ 433: 4.8151 - 1\newline
+ 434: 5.3475 - 0\newline
+ 435: 5.3476 - 0\newline
+ 436: 5.5455 - 0\newline
+ 437: 5.5652 - 0
+ \end{minipage}\\[0.3cm]
+ \begin{itemize}
+ \item linear Si-C-Si bond
+ \item Each Si has another 3 Si neighbours
+ \end{itemize}
+ \begin{center}
+ {\color{blue}Spin polarized calculations necessary!}\\[0.3cm]
+ \end{center}
+ {\scriptsize Charge density isosurface of
+ {\color{gray}spin up}, {\color{green}spin down} and
+ the {\color{blue}resulting spin up} electrons.\\
+ Two {\color{yellow} Si} atoms and one {\color{red}C}
+ atom are shown.
+ }
+ \end{minipage}
+ \begin{minipage}[t]{6.5cm}
+ \underline{MO diagram}\\
+ \begin{minipage}[t]{1.2cm}
+ {\color{red}Si}\\
+ {\tiny sp$^3$}\\[0.8cm]
+ \underline{${\color{red}\uparrow}$}
+ \underline{${\color{red}\uparrow}$}
+ \underline{${\color{red}\uparrow}$}
+ \underline{${\color{red}\uparrow}$}\\
+ sp$^3$
+ \end{minipage}
+ \begin{minipage}[t]{1.4cm}
+ \begin{center}
+ {\color{red}M}{\color{blue}O}\\[1.0cm]
+ \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
+ $\sigma_{\text{ab}}$\\[0.5cm]
+ \underline{${\color{red}\uparrow}{\color{blue}\downarrow}$}\\
+ $\sigma_{\text{b}}$
+ \end{center}
+ \end{minipage}
+ \begin{minipage}[t]{1.0cm}
+ \begin{center}
+ {\color{blue}C}\\
+ {\tiny sp}\\[0.2cm]
+ \underline{${\color{white}\uparrow\uparrow}$}
+ \underline{${\color{white}\uparrow\uparrow}$}\\
+ 2p\\[0.4cm]
+ \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}
+ \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}\\
+ sp
+ \end{center}
+ \end{minipage}
+ \begin{minipage}[t]{1.4cm}
+ \begin{center}
+ {\color{blue}M}{\color{green}O}\\[1.0cm]
+ \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
+ $\sigma_{\text{ab}}$\\[0.5cm]
+ \underline{${\color{green}\uparrow}{\color{blue}\downarrow}$}\\
+ $\sigma_{\text{b}}$
+ \end{center}
+ \end{minipage}
+ \begin{minipage}[t]{1.2cm}
+ \begin{flushright}
+ {\color{green}Si}\\
+ {\tiny sp$^3$}\\[0.8cm]
+ \underline{${\color{green}\uparrow}$}
+ \underline{${\color{green}\uparrow}$}
+ \underline{${\color{green}\uparrow}$}
+ \underline{${\color{green}\uparrow}$}\\
+ sp$^3$
+ \end{flushright}
+ \end{minipage}\\[0.4cm]
+ \begin{flushright}
+ \includegraphics[width=6cm]{c_100_mig_vasp/im_spin_diff.eps}
+ \end{flushright}
+ \end{minipage}
+ }
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+ \hkl<0 0 -1> configuration revisited ($3\times 3\times 3$ Type 2)
+ }
+
+ Spin polarized calculations
+
+ {\small
+ \begin{minipage}[t]{5.8cm}
+ \underline{Kohn-Sham eigenvalues}\\
+ \begin{minipage}{2.8cm}
+ Spin up:\\
+ 430: 4.3317 - 1\newline
+ 431: 4.7418 - 1\newline
+ 432: 4.8014 - 1\newline
+ 433: 4.8060 - 1\newline
+ 434: 4.9033 - 1\newline
+ 435: 5.2544 - 0\newline
+ 436: 5.5723 - 0\newline
+ 437: 5.5848 - 0
+ \end{minipage}
+ \begin{minipage}{2.8cm}
+ Spin down:\\
+ 430: 4.3317 - 1\newline
+ 431: 4.7420 - 1\newline
+ 432: 4.8013 - 1\newline
+ 433: 4.8059 - 1\newline
+ 434: 4.9035 - 1\newline
+ 435: 5.2550 - 0\newline
+ 436: 5.5724 - 0\newline
+ 437: 5.5846 - 0
+ \end{minipage}
+ \end{minipage}
+ \begin{minipage}[t]{6.5cm}
+ \underline{MO diagram}\\
+ \begin{minipage}[t]{1.2cm}
+ {\color{red}Si}\\
+ {\tiny sp$^2$}\\[0.1cm]
+ \underline{${\color{white}\uparrow}$}\\
+ p\\[0.4cm]
+ \underline{${\color{red}\uparrow\downarrow}$}
+ \underline{${\color{red}\uparrow}{\color{white}\downarrow}$}
+ \underline{${\color{red}\uparrow}{\color{white}\downarrow}$}\\
+ sp$^2$
+ \end{minipage}
+ \begin{minipage}[t]{1.2cm}
+ \begin{flushright}
+ {\color{red}M}\\[1.0cm]
+ \underline{${\color{white}\uparrow}{\color{white}\downarrow}$}\\
+ $\sigma_{\text{ab}}$\\[0.5cm]
+ \underline{${\color{red}\uparrow}{\color{blue}\downarrow}$}\\
+ $\sigma_{\text{b}}$
+ \end{flushright}
+ \end{minipage}
+ \begin{minipage}[t]{1.2cm}
+ \begin{flushleft}
+ {\color{blue}O}\\[0.4cm]
+ \underline{${\color{white}\uparrow}{\color{white}\downarrow}$}\\
+ $\pi_{\text{ab}}$\\[0.5cm]
+ \underline{${\color{red}\uparrow}{\color{blue}\downarrow}$}\\
+ $\pi_{\text{b}}$
+ \end{flushleft}
+ \end{minipage}
+ \begin{minipage}[t]{2.0cm}
+ \begin{center}
+ {\color{blue}C}\\
+ {\tiny sp$^2$}\\[0.5cm]
+ \underline{${\color{white}\uparrow\uparrow}$}\\
+ p\\[0.4cm]
+ \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}
+ \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}
+ \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
+ sp$^2$
+ \end{center}
+ \end{minipage}
+ \end{minipage}
+ }
+
+ \vspace*{0.4cm}
+
+ \begin{itemize}
+ \item Si-C double bond
+ \item Si and C atom have another 2 Si neighbours
+ \end{itemize}
+
+ \begin{center}
+ {\color{blue}Spin polarized calculations {\color{red}not} necessary!}
+ \end{center}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+ Kohn-Sham levels visualized
+ }
+
+ \begin{minipage}{6cm}
+ \underline{\hkl<0 0 -1> configuration}
+ \begin{center}
+ \includegraphics[height=8cm]{c_100_mig_vasp/100_ksl.ps}
+ \end{center}
+ \end{minipage}
+ \begin{minipage}{6cm}
+ \underline{Saddle point configuration}
+ \begin{center}
+ \includegraphics[height=8cm]{c_100_mig_vasp/im_ksl.ps}
+ \end{center}
+ \end{minipage}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+ New default parameter set\\[1cm]
+ }
+
+ Since some defect configurations need spin polarized calculations ...\\[1cm]
+
+ from now on the default parameter set\\
+ {\bf\color{blue}
+ $+$ no symmetry\\
+ $+$ spin polarized\\
+ }
+ \ldots is used!\\[1cm]
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf\boldmath
+ \hkl<0 0 -1> to \hkl<0 0 1> migration
+ in the $3\times 3\times 3$ Type 2 supercell
+ }
+
+ \begin{minipage}{6cm}
+ Method:
+ \begin{itemize}
+ \item Starting configuration:\\
+ C bond centered
+ \item CRT towards \hkl<0 0 -1> configuration
+ \item Spin polarized calculations
+ \end{itemize}
+ Results:\\
+ Video \href{../video/c_im_00-1_vasp.avi}{$\rhd_{\text{local}}$ } $|$
+ \href{http://www.physik.uni-augsburg.de/~zirkelfr/download/posic/c_im_00-1_vasp.avi}{$\rhd_{\text{remote url}}$}
+ \begin{itemize}
+ \item Still abrupt changes in configuration and energy
+ \item Migration barrier $>$ 1 eV
+ \item I bet it's not reversible!
+ \item {\color{red}Final run in progress}
+ \end{itemize}
+ \end{minipage}