From: hackbard Date: Sat, 5 Nov 2011 20:47:39 +0000 (+0100) Subject: formulas ... X-Git-Url: https://hackdaworld.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=d0ff895e76b30891a3fcd4b9a037eada196e9f95;p=lectures%2Flatex.git formulas ... --- diff --git a/posic/talks/mpi_app.tex b/posic/talks/mpi_app.tex index f588e1d..67a4d40 100644 --- 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} @@ -1071,6 +1062,18 @@ $ \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}