- \begin{itemize}
- \item Microscopic description of N particle system
- \item Analytical interaction potential
- \item Numerical integration using Newtons equation of motion\\
- as a propagation rule in 6N-dimensional phase space
- \item Observables obtained by time and/or ensemble averages
- \end{itemize}
- {\bf Details of the simulation:}
- \begin{itemize}
- \item Integration: Velocity Verlet, timestep: $1\text{ fs}$
- \item Ensemble: NpT (isothermal-isobaric)
- \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}
- \item Erhart/Albe potential: Tersoff-like bond order potential
- \vspace*{12pt}
- \[
- E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad
- \pot_{ij} = {\color{red}f_C(r_{ij})}
- \left[ f_R(r_{ij}) + {\color{blue}b_{ij}} f_A(r_{ij}) \right]
- \]
- \end{itemize}
+\small
+
+\vspace{0.1cm}
+
+{\bf Density functional theory (DFT)}
+
+\scriptsize
+
+\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{$E_0$}
+\end{itemize}
+\underline{Details}
+\begin{itemize}
+\item Code: \textsc{vasp}
+\item Plane wave basis set $\{\phi_j\}$\\[0.1cm]
+$\displaystyle
+\Phi_i=\sum_{|G+k|<G_{\text{cut}}} c_j^i \phi_j(r)
+$\\
+$\displaystyle
+E_{\text{cut}}=\frac{\hbar^2}{2m}G^2_{\text{cut}}=\unit[300]{eV}
+$
+\item Ultrasoft pseudopotential
+\item Brillouin zone sampling: $\Gamma$-point
+\end{itemize}
+\end{minipage}
+\begin{minipage}[t]{6cm}
+\end{minipage}