applying suggested changes

theory/presentation/presentation.tex

@@ -48,66 +48,74 @@
 % I guess you always want a titleframe
 \titleframe
 
-% Have this if you'd like a frame containing the 
-% table of content
-\begin{frame}{Overview}
-    \tableofcontents[hideallsubsections]
-\end{frame}
-
 % Start of the first section
 \section{Introduction}
 
 \begin{frame}
     \frametitle{The Hartree-Fock approximation}
+The Schrödinger equation
     \begin{equation}
         \hat{H}\Psi = E\Psi
     \end{equation}
+The Roothaan-Hall equation
+\begin{equation}
+    \mathbf{FC} = \epsilon \mathbf{SC}
+\end{equation}
+One constraint $\Longrightarrow$ energy minimum
     \begin{equation}
-        \hat{f} = \hat{h}(1) + \sum_j^N\hat{J}_j - \hat{K}_j
-    \end{equation}
-    \begin{equation}
-        \langle \psi + \delta\psi | \hat{H} | \psi + \delta\psi \rangle = E + \delta E^* + \delta E + \delta E^2
+        \langle \psi + \delta\psi | \hat{H} | \psi + \delta\psi \rangle = E + \delta E^* + \delta E + \delta E^2 = E
     \end{equation}
+
 \end{frame}
 
 \begin{frame}
-    \frametitle{Löwdin's symmetry dilema}
+    \frametitle{Restricted Hartree-Fock}
     \begin{itemize}
-        \item Restricted Hartree-Fock
-        \begin{itemize}
-            \item Higher energy
-            \item Symmetry intact
-        \end{itemize}
-        \item Unrestricted Hartree-Fock
-        \begin{itemize}
-            \item Lower energy
-            \item Spin quantum numbers lost
-        \end{itemize}
+        \item Electrons forced into pairs
+        \item Higher energy
+        \item Symmetry intact
     \end{itemize}
+    \begin{minipage}[b]{0.6\linewidth}
+        \includegraphics[width=\linewidth]{./figures/rhf.pdf}
+    \end{minipage}
 
 \end{frame}
 
 
+\begin{frame}
+    \frametitle{Unrestricted Hartree-Fock}
+    \begin{itemize}
+        \item No electron pairs
+        \item Lower energy
+        \item $\langle\hat{S}^2\rangle$ lost as quantum number
+    \end{itemize}
+    \begin{minipage}[b]{0.6\linewidth}
+        \includegraphics[width=\linewidth]{./figures/uhf.pdf}
+    \end{minipage}
+    \begin{minipage}[b]{0.35\linewidth}
+        \begin{equation}
+            \delta s = \langle \hat{S}^2 \rangle - S_z(S_z + 1)
+        \end{equation}
+    \end{minipage}
+\end{frame}
 
 
 \begin{frame}
-    \frametitle{Spin contamination}
-    \begin{equation}
-        \langle \hat{S}^2 \rangle = S_z^2 + S_z + q - \sum_{ij}^{pq}S_{ij}^2
-    \end{equation}
+    \frametitle{Löwdin's symmetry dillema}
+    \begin{itemize}
+        \item Low energy $\Longrightarrow$ loss of symmetry
+        \item Keeping symmetry $\Longrightarrow$ high symmetry
+        \item Do we always lose?
+    \end{itemize}
 
-    \begin{equation}
-        \delta s = \langle \hat{S}^2 \rangle - S_z(S_z + 1)
-    \end{equation}
-
-\begin{figure}
-    \begin{minipage}[b]{0.45\linewidth}
-        \includegraphics[width=\linewidth]{./figures/rhf.png}
-    \end{minipage}
-    \begin{minipage}[b]{0.45\linewidth}
-        \includegraphics[width=\linewidth]{./figures/uhf.png}
-    \end{minipage}
-\end{figure}
+
+\begin{itemize}
+    \item Can we keep both symmetry and lower energies?
+    \begin{itemize}
+        \item ROHF
+        \item CUHF
+    \end{itemize}
+\end{itemize}
 
 \end{frame}
 
@@ -133,14 +141,14 @@ \section{Theory}
 
 \begin{frame}
     \begin{figure}
-        \includegraphics[width=0.6\linewidth]{./figures/cuhf_mix.png}
+        \includegraphics[width=0.6\linewidth]{./figures/cuhf_mix.pdf}
     \end{figure}
 \end{frame}
 
 \begin{frame}
-    \frametitle{Configuration interaction} 
+    \frametitle{Configuration interaction: CIS} 
     \begin{equation}\label{eq:lincomb}
-        |\Psi_0\rangle = c_0|\Phi_0\rangle + \sum_{ar}c_{r}^{a}|\Phi_r^a\rangle + \sum_{a<b,r<s}c_{rs}^{ab}|\Phi^{ab}_{rs} \rangle + \cdots
+        |\Psi_0\rangle = {\color{ugent-re} c_0|\Phi_0\rangle + \sum_{ar}c_{r}^{a}|\Phi_r^a\rangle} + \sum_{a<b,r<s}c_{rs}^{ab}|\Phi^{ab}_{rs} \rangle + \cdots
       \end{equation}
       Brillouin's theorem:
       \begin{equation}\label{eq:overlapsingle}
@@ -154,14 +162,31 @@ \section{Theory}
 
 \section{results}
 
+\begin{frame}
+    \frametitle{Goals}
+    \begin{enumerate}
+        \item Excitation energy levels
+        \item Differences/similarities between methods
+        \begin{itemize}
+            \item UHF
+            \item CUHF
+            \item ROHF
+        \end{itemize}
+        \item Spin contamination in the excited states
+    \end{enumerate}
+
+
+
+\end{frame}
+
 \begin{frame}
     \frametitle{\ce{H3}}
     \begin{figure}
         \begin{minipage}[b]{0.45\linewidth}
-            \includegraphics[width=\linewidth]{./figures/h3_uhf_sto-3g.png}
+            \includegraphics[width=\linewidth]{./figures/h3_uhf_sto-3g.pdf}
         \end{minipage}
         \begin{minipage}[b]{0.45\linewidth}
-            \includegraphics[width=\linewidth]{./figures/h3_cuhf.png}
+            \includegraphics[width=\linewidth]{./figures/h3_cuhf.pdf}
         \end{minipage}
     \end{figure}
 
@@ -171,7 +196,7 @@ \section{results}
 \begin{frame}
     \frametitle{CUHF and UHF}
     \begin{minipage}[b]{0.6\linewidth}
-        \includegraphics[width=\linewidth]{./figures/h3_cis.png}
+        \includegraphics[width=\linewidth]{./figures/h3_cis.pdf}
     \end{minipage}
     \begin{minipage}[b]{0.3\linewidth}
         \begin{table}[h]
@@ -180,8 +205,8 @@ \section{results}
                  & UHF       & CUHF      \\
               \hline
               1  & -2.938139 & -2.922658 \\
-              2  & -2.923512 & -2.915707 \\
-              3  & -2.896022 & -2.915707 \\
+              2  &  {\color{ugent-re}   \textbf{-2.923512}} & {\color{ugent-re}   \textbf{-2.915707}} \\
+              3  & -2.896022 & {\color{ugent-re}   \textbf{-2.915707}} \\
               4  & -2.840079 & -2.895707 \\
               5  & -2.560947 & -2.560947 \\
               6  & -2.428072 & -2.436524 \\
@@ -192,41 +217,12 @@ \section{results}
             \end{tabular}
           \end{table}
     \end{minipage}
+    \begin{itemize}
+        \item degeneracies
+        \item lower energy states
+    \end{itemize}
 \end{frame}
 
-\begin{frame}
-    \begin{figure}[h]
-        \begin{center}
-          \begin{tikzpicture}
-            \draw (-1.25, 0.5) -- (-0.75, 0.5);
-            \draw (-1.25, 0) -- (-0.75, 0);
-            \draw (-1.25, -0.5) -- (-0.75, -0.5);
-            \draw [-{Straight Barb[left]}] (-1.1, -0.60) -- (-1.1, -0.20);
-            \draw [-{Straight Barb[left]}] (-1.1, -0.10) -- (-1.1, 0.30);
-            \draw [-{Straight Barb[left]}] (-0.9, -0.20) -- (-0.9, -0.60);
-
-            \draw (1.25, 0.5) -- (0.75, 0.5);
-            \draw (1.25, 0) -- (0.75, 0);
-            \draw (1.25, -0.5) -- (0.75, -0.5);
-            \draw [-{Straight Barb[left]}] (0.9, -0.60) -- (0.9, -0.20);
-            \draw [-{Straight Barb[left]}] (1.1, 0.30) -- (1.1, -0.10);
-            \draw [-{Straight Barb[left]}] (1.1, -0.20) -- (1.1, -0.60);
-          \end{tikzpicture}
-        \end{center}
-      \end{figure}
-    \begin{table}[h]
-        \label{tab:excits_no_triplets}
-        \begin{tabular}{l|l|l}
-            & UHF       & CUHF      \\
-          \hline
-          1 & -2.923515 & -2.915707 \\
-          2 & -2.840101 & -2.895707 \\
-          3 & -2.428086 & -2.436524 \\
-          4 & -2.160319 & -2.176620 \\
-          5 & -2.137039 & -2.139049
-        \end{tabular}
-      \end{table}
-\end{frame}
 \begin{frame}
     \frametitle{CUHF and ROHF}
 
@@ -265,16 +261,19 @@ \section{results}
 \end{frame}
 \section{Conclusions and prospects}
 \begin{frame}
+    \frametitle{Conclusions and prospects}
     \begin{itemize}
-        \item Things to look out for:
+        \item CUHF takes care of spin contamination in the ground state
+        \item Things to look out for in CIS
         \begin{itemize}
-            \item triplet excitations with lower energy
+            \item triplet excitations with lower energy (for some systems)
             \item spin contamination
         \end{itemize}
         \item Prospects
         \begin{itemize}
             \item triplet systems
-            \item Full CI $\Longrightarrow$ other constraints?
+            \item Higher order CI
+            \item Other constraints $\Longrightarrow$ excited states?
         \end{itemize}
     \end{itemize}
 
@@ -283,4 +282,39 @@ \section{Conclusions and prospects}
 % End presentation with titleframe
 \titleframe
 
+\begin{frame}
+    \begin{figure}[h]
+        \begin{center}
+          \begin{tikzpicture}
+            \draw (-1.25, 0.5) -- (-0.75, 0.5);
+            \draw (-1.25, 0) -- (-0.75, 0);
+            \draw (-1.25, -0.5) -- (-0.75, -0.5);
+            \draw [-{Straight Barb[left]}] (-1.1, -0.60) -- (-1.1, -0.20);
+            \draw [-{Straight Barb[left]}] (-1.1, -0.10) -- (-1.1, 0.30);
+            \draw [-{Straight Barb[left]}] (-0.9, -0.20) -- (-0.9, -0.60);
+
+            \draw (1.25, 0.5) -- (0.75, 0.5);
+            \draw (1.25, 0) -- (0.75, 0);
+            \draw (1.25, -0.5) -- (0.75, -0.5);
+            \draw [-{Straight Barb[left]}] (0.9, -0.60) -- (0.9, -0.20);
+            \draw [-{Straight Barb[left]}] (1.1, 0.30) -- (1.1, -0.10);
+            \draw [-{Straight Barb[left]}] (1.1, -0.20) -- (1.1, -0.60);
+          \end{tikzpicture}
+        \end{center}
+      \end{figure}
+      $\Longrightarrow$ The ground state is degenerate
+    \begin{table}[h]
+        \label{tab:excits_no_triplets}
+        \begin{tabular}{l|l|l}
+            & UHF       & CUHF      \\
+          \hline
+          1 & {\color{ugent-re}   \textbf{-2.923512}} & {\color{ugent-re}   \textbf{-2.915707}} \\
+          2 & -2.840101 & -2.895707 \\
+          3 & -2.428086 & -2.436524 \\
+          4 & -2.160319 & -2.176620 \\
+          5 & -2.137039 & -2.139049
+        \end{tabular}
+      \end{table}
+\end{frame}
+
 \end{document}