dft basics ...

[lectures/latex.git] / posic / talks / mpi_app.tex

diff --git a/posic/talks/mpi_app.tex b/posic/talks/mpi_app.tex
index f588e1d..c05db6d 100644 (file)
--- a/posic/talks/mpi_app.tex
+++ b/posic/talks/mpi_app.tex
@@ -1008,7 +1008,6 @@ r = \unit[2--4]{nm}
 {\bf Molecular dynamics (MD)}\\
 \scriptsize
 \begin{tabular}{p{4.5cm} p{7.5cm}}
-%\hline
 Basics & Details\\
 \hline
 System of $N$ particles &
@@ -1026,16 +1025,8 @@ E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad
     \left[ f_R(r_{ij}) + {\color{blue}b_{ij}} f_A(r_{ij}) \right]
 $\\
 \hline
-%\multicolumn{2}{c}{}\\
 Observables: time/ensemble averages &
 NpT (isothermal-isobaric) | Berendsen thermostat/barostat\\
-%\begin{itemize}
-%\item Berendsen thermostat:
-%      $\tau_{\text{T}}=100\text{ fs}$
-%\item Berendsen barostat:\\
-%      $\tau_{\text{P}}=100\text{ fs}$,
-%      $\beta^{-1}=100\text{ GPa}$
-%\end{itemize}\\
 \hline
 \end{tabular}
 
@@ -1050,11 +1041,13 @@ NpT (isothermal-isobaric) | Berendsen thermostat/barostat\\
 \begin{minipage}[t]{6cm}
 \underline{Basics}
 \begin{itemize}
- \item Born-Oppenheimer approximation:\\
-       Decouple electronic \& ionic motion
- \item Hohenberg-Kohn theorem:\\
-       $n_0(r) \stackrel{\text{uniquely}}{\rightarrow}$
-       $V_0$ / $H$ / $\Phi_i$ / \underline{$E_0$}
+ \item $\Psi_0(r_1,r_2,\ldots,r_N)=\Psi[n_0(r)]$, $E_0=E[n_0]$
+ \item Single-particle effective theory
+% \item Born-Oppenheimer approximation:\\
+%       Decouple electronic \& ionic motion
+% \item Hohenberg-Kohn theorem:\\
+%       $n_0(r) \stackrel{\text{uniquely}}{\rightarrow}$
+%       $V_0$ / $H$ / $\Phi_i$ / \underline{$E_0$}
 \end{itemize}
 \underline{Details}
 \begin{itemize}
@@ -1067,10 +1060,23 @@ $\displaystyle
 E_{\text{cut}}=\frac{\hbar^2}{2m}G^2_{\text{cut}}=\unit[300]{eV}
 $
 \item Ultrasoft pseudopotential
+\item Exchange \& correlation: GGA
 \item Brillouin zone sampling: $\Gamma$-point
 \end{itemize}
 \end{minipage}
 \begin{minipage}[t]{6cm}
+
+\[
+\left[ -\frac{\hbar^2}{2m}\nabla^2 + V_{\text{eff}}(r) - \epsilon_i \right] \Phi_i(r) = 0
+\]
+\[
+n(r)=\sum_i^N|\Phi_i(r)|^2
+\]
+\[
+V_{\text{eff}}(r)=V_{\text{ext}}(r)+\int\frac{e^2 n(r')}{|r-r'|}d^3r'
+                 +V_{\text{XC}}[n(r)]
+\]
+
 \end{minipage}
 
 \end{slide}