some new stuff + new todo ...

[lectures/latex.git] / posic / talks / upb-ua-xc.tex

diff --git a/posic/talks/upb-ua-xc.tex b/posic/talks/upb-ua-xc.tex
index e95c0fb..4197c0a 100644 (file)
--- a/posic/talks/upb-ua-xc.tex
+++ b/posic/talks/upb-ua-xc.tex
@@ -218,8 +218,8 @@ POTIM = 0.1
  \begin{itemize}
   \item Calculation of cohesive energies for different lattice constants
   \item No ionic update
  \begin{itemize}
   \item Calculation of cohesive energies for different lattice constants
   \item No ionic update

-  \item tetrahedron method with Blöchl corrections for
-        the partial occupancies $f_{nk}$
+  \item Tetrahedron method with Blöchl corrections for
+        the partial occupancies $f(\{\epsilon_{n{\bf k}}\})$

   \item Supercell 3 (8 atoms, 4 primitive cells)
  \end{itemize}
  \vspace*{0.6cm}
   \item Supercell 3 (8 atoms, 4 primitive cells)
  \end{itemize}
  \vspace*{0.6cm}


@@ -269,8 +269,8 @@ POTIM = 0.1
  \begin{itemize}
   \item Calculation of cohesive energies for different lattice constants
   \item No ionic update
  \begin{itemize}
   \item Calculation of cohesive energies for different lattice constants
   \item No ionic update

-  \item tetrahedron method with Blöchl corrections for
-        the partial occupancies $f_{nk}$
+  \item Tetrahedron method with Blöchl corrections for
+        the partial occupancies $f(\{\epsilon_{n{\bf k}}\})$

  \end{itemize}
  \vspace*{0.6cm}
  \begin{minipage}{6.5cm}
  \end{itemize}
  \vspace*{0.6cm}
  \begin{minipage}{6.5cm}


@@ -283,7 +283,15 @@ POTIM = 0.1
  \begin{center}
  {\color{red}
   Non-continuous energies\\
  \begin{center}
  {\color{red}
   Non-continuous energies\\

-  for $E_{\textrm{cut-off}}<1050\,\textrm{eV}$!
+  for $E_{\textrm{cut-off}}<1050\,\textrm{eV}$!\\
+ }
+ \vspace*{0.5cm}
+ {\footnotesize
+ Does this matter in structural optimizaton simulations?
+ \begin{itemize}
+  \item Derivative might be continuous
+  \item Similar lattice constants where derivative equals zero
+ \end{itemize}

  }
  \end{center}
  \end{minipage}
  }
  \end{center}
  \end{minipage}


@@ -348,25 +356,30 @@ POTIM = 0.1
          \item Spin polarized calculation
          \item Interpolation formula according to Vosko Wilk and Nusair
                for the correlation part of the exchange correlation functional
          \item Spin polarized calculation
          \item Interpolation formula according to Vosko Wilk and Nusair
                for the correlation part of the exchange correlation functional

-         \item Gaussian smearing for the partial occupancies $f_{nk}$
+         \item Gaussian smearing for the partial occupancies
+               $f(\{\epsilon_{n{\bf k}}\})$

                ($\sigma=0.05$)
          \item Magnetic mixing: AMIX = 0.2, BMIX = 0.0001
          \item Supercell: one atom in cubic
                $10\times 10\times 10$ \AA$^3$ box
         \end{itemize}
         {\color{blue}
                ($\sigma=0.05$)
          \item Magnetic mixing: AMIX = 0.2, BMIX = 0.0001
          \item Supercell: one atom in cubic
                $10\times 10\times 10$ \AA$^3$ box
         \end{itemize}
         {\color{blue}

-        $E_{\textrm{free,sp}}(\textrm{Si},250\, \textrm{eV})=
+        $E_{\textrm{free,sp}}(\textrm{Si},{\color{green}250}\, \textrm{eV})=

          -0.70036911\,\textrm{eV}$
          -0.70036911\,\textrm{eV}$

+        }\\
+        {\color{blue}
+        $E_{\textrm{free,sp}}(\textrm{Si},{\color{red}650}\, \textrm{eV})=
+         -0.70021403\,\textrm{eV}$

         },
         {\color{gray}
         },
         {\color{gray}

-        $E_{\textrm{free,sp}}(\textrm{C},xxx\, \textrm{eV})=
-         yyy\,\textrm{eV}$
+        $E_{\textrm{free,sp}}(\textrm{C},{\color{red}650}\, \textrm{eV})=
+         -1.3535731\,\textrm{eV}$

         }
   \item $E$:
         energy (non-polarized) of system of interest composed of\\
         n atoms of type N, m atoms of type M, \ldots
  \end{itemize}
         }
   \item $E$:
         energy (non-polarized) of system of interest composed of\\
         n atoms of type N, m atoms of type M, \ldots
  \end{itemize}

- \vspace*{0.3cm}
+ \vspace*{0.2cm}

  {\color{red}
  \[
  \Rightarrow
  {\color{red}
  \[
  \Rightarrow


@@ -379,6 +392,49 @@ POTIM = 0.1
 
 \end{slide}
 
 
 \end{slide}
 

+\begin{slide}
+
+ {\large\bf
+  Used types of supercells\\
+ }
+
+ \footnotesize
+
+ \begin{minipage}{4.3cm}
+  \includegraphics[width=4cm]{sc_type0.eps}\\[0.3cm]
+  \underline{Type 0}\\[0.2cm]
+  Basis: fcc\\
+  $x_1=(0.5,0.5,0)$\\
+  $x_2=(0,0.5,0.5)$\\
+  $x_3=(0.5,0,0.5)$\\
+  1 primitive cell / 2 atoms
+ \end{minipage}
+ \begin{minipage}{4.3cm}
+  \includegraphics[width=4cm]{sc_type1.eps}\\[0.3cm]
+  \underline{Type 1}\\[0.2cm]
+  Basis:\\
+  $x_1=(0.5,-0.5,0)$\\
+  $x_2=(0.5,0.5,0)$\\
+  $x_3=(0,0,1)$\\
+  2 primitive cells / 4 atoms
+ \end{minipage}
+ \begin{minipage}{4.3cm}
+  \includegraphics[width=4cm]{sc_type2.eps}\\[0.3cm]
+  \underline{Type 2}\\[0.2cm]
+  Basis: sc\\
+  $x_1=(1,0,0)$\\
+  $x_2=(0,1,0)$\\
+  $x_3=(0,0,1)$\\
+  4 primitive cells / 8 atoms
+ \end{minipage}\\[0.4cm]
+
+ {\bf\color{blue}
+ In the following these types of supercells are used and
+ are possibly scaled by integers in the different directions!
+ }
+
+\end{slide}
+

 \begin{slide}
 
  {\large\bf
 \begin{slide}
 
  {\large\bf


@@ -403,11 +459,137 @@ POTIM = 0.1
                -E_{\textrm{coh}}^{\textrm{initial conf}}\Big) N
  \]
  }
                -E_{\textrm{coh}}^{\textrm{initial conf}}\Big) N
  \]
  }

+ Influence of supercell size\\
+ \begin{minipage}{8cm}
+ \includegraphics[width=7.0cm]{si_self_int.ps}
+ \end{minipage}
+ \begin{minipage}{5cm}
+ $E_{\textrm{f}}^{\textrm{110},\,{\color{red}32}\textrm{pc}}=3.38\textrm{ eV}$\\
+ $E_{\textrm{f}}^{\textrm{hex},\,54\textrm{pc}}=3.42\textrm{ eV}$\\
+ $E_{\textrm{f}}^{\textrm{tet},\,54\textrm{pc}}=3.45\textrm{ eV}$\\
+ $E_{\textrm{f}}^{\textrm{vac},\,54\textrm{pc}}=3.47\textrm{ eV}$
+ \end{minipage}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+  Questions so far ...\\
+ }
+
+ What configuration to chose for C in Si simulations?
+ \begin{itemize}
+  \item Switch to another method for the XC approximation (GGA, PAW)?
+  \item Reasonable cut-off energy
+  \item Switch off symmetry? (especially for defect simulations)
+  \item $k$-points
+        (Monkhorst? $\Gamma$-point only if cell is large enough?)
+  \item Switch to tetrahedron method or Gaussian smearing ($\sigma$?)
+  \item Size and type of supercell
+        \begin{itemize}
+         \item connected to choice of $k$-point mesh?
+         \item hence also connected to choice of smearing method?
+         \item constraints can only be applied to the lattice vectors!
+        \end{itemize}
+  \item Use of real space projection operators?
+  \item \ldots
+ \end{itemize}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+  Review (so far) ...\\
+ }
+
+ Smearing method for the partial occupancies $f(\{\epsilon_{n{\bf k}}\})$
+ and $k$-point mesh
+
+ \begin{itemize}
+  \item $1\times 1\times 1$ Type 0 simulations
+        \begin{itemize}
+         \item No difference in tetrahedron method and Gauss smearing
+         \item ...
+        \end{itemize}
+  \item $1\times 1\times 1$ Type 2 simulations
+        \begin{itemize}
+         \item Again, no difference in tetrahedron method and Gauss smearing
+         \item ...
+        \end{itemize}
+ \end{itemize}
+
+ {\LARGE\bf\color{red}
+ More simulations running ...
+ }
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+  Review (so far) ...\\
+ }
+
+ Symmetry (in defect simulations)
+
+ {\LARGE\bf\color{red}
+ Simulations running ...
+ }
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+  Review (so far) ...\\
+ }
+
+ Real space projection
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+  Review (so far) ...\\
+ }
+
+ Energy cut-off
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+  Review (so far) ...\\
+ }
+
+ Size and type of supercell
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+  Not answered (so far) ...\\
+ }
+
+\vspace{1.5cm}
+
+ \LARGE
+ \bf
+ \color{blue}

 
  \begin{center}
 
  \begin{center}

- \includegraphics[width=7.0cm]{si_self_int.ps}
+ Continue\\
+ with\\
+ US LDA?

  \end{center}
 
  \end{center}
 

+\vspace{1.5cm}
+

 \end{slide}
 
 \end{document}
 \end{slide}
 
 \end{document}