X-Git-Url: https://hackdaworld.org/gitweb/?a=blobdiff_plain;f=posic%2Ftalks%2Fupb-ua-xc.tex;h=4197c0ab1ecbc77e0621617e5486c72275814a7e;hb=071e7bdd84bc69d2dde1835c2693fc1375d2bfb2;hp=e95c0fb64ce6488fd76c19a89902aaad9c85d829;hpb=fee777e5d2af71751eddd51826ede4945aea40e7;p=lectures%2Flatex.git diff --git a/posic/talks/upb-ua-xc.tex b/posic/talks/upb-ua-xc.tex index e95c0fb..4197c0a 100644 --- 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 - \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} @@ -269,8 +269,8 @@ POTIM = 0.1 \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} @@ -283,7 +283,15 @@ POTIM = 0.1 \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} @@ -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 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} - $E_{\textrm{free,sp}}(\textrm{Si},250\, \textrm{eV})= + $E_{\textrm{free,sp}}(\textrm{Si},{\color{green}250}\, \textrm{eV})= -0.70036911\,\textrm{eV}$ + }\\ + {\color{blue} + $E_{\textrm{free,sp}}(\textrm{Si},{\color{red}650}\, \textrm{eV})= + -0.70021403\,\textrm{eV}$ }, {\color{gray} - $E_{\textrm{free,sp}}(\textrm{C},xxx\, \textrm{eV})= - yyy\,\textrm{eV}$ + $E_{\textrm{free,sp}}(\textrm{C},{\color{red}650}\, \textrm{eV})= + -1.3535731\,\textrm{eV}$ } \item $E$: energy (non-polarized) of system of interest composed of\\ n atoms of type N, m atoms of type M, \ldots \end{itemize} - \vspace*{0.3cm} + \vspace*{0.2cm} {\color{red} \[ \Rightarrow @@ -379,6 +392,49 @@ POTIM = 0.1 \end{slide} +\begin{slide} + + {\large\bf + Used types of supercells\\ + } + + \footnotesize + + \begin{minipage}{4.3cm} + \includegraphics[width=4cm]{sc_type0.eps}\\[0.3cm] + \underline{Type 0}\\[0.2cm] + Basis: fcc\\ + $x_1=(0.5,0.5,0)$\\ + $x_2=(0,0.5,0.5)$\\ + $x_3=(0.5,0,0.5)$\\ + 1 primitive cell / 2 atoms + \end{minipage} + \begin{minipage}{4.3cm} + \includegraphics[width=4cm]{sc_type1.eps}\\[0.3cm] + \underline{Type 1}\\[0.2cm] + Basis:\\ + $x_1=(0.5,-0.5,0)$\\ + $x_2=(0.5,0.5,0)$\\ + $x_3=(0,0,1)$\\ + 2 primitive cells / 4 atoms + \end{minipage} + \begin{minipage}{4.3cm} + \includegraphics[width=4cm]{sc_type2.eps}\\[0.3cm] + \underline{Type 2}\\[0.2cm] + Basis: sc\\ + $x_1=(1,0,0)$\\ + $x_2=(0,1,0)$\\ + $x_3=(0,0,1)$\\ + 4 primitive cells / 8 atoms + \end{minipage}\\[0.4cm] + + {\bf\color{blue} + In the following these types of supercells are used and + are possibly scaled by integers in the different directions! + } + +\end{slide} + \begin{slide} {\large\bf @@ -403,11 +459,137 @@ POTIM = 0.1 -E_{\textrm{coh}}^{\textrm{initial conf}}\Big) N \] } + 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} - \includegraphics[width=7.0cm]{si_self_int.ps} + Continue\\ + with\\ + US LDA? \end{center} +\vspace{1.5cm} + \end{slide} \end{document}