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b/theory/presentation/presentation.synctex(busy) deleted file mode 100644 index e69de29..0000000 diff --git a/theory/presentation/presentation.tex b/theory/presentation/presentation.tex index 3fa0fbf..ad3f8b9 100644 --- a/theory/presentation/presentation.tex +++ b/theory/presentation/presentation.tex @@ -48,66 +48,82 @@ % 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 Fock operator \begin{equation} \hat{f} = \hat{h}(1) + \sum_j^N\hat{J}_j - \hat{K}_j \end{equation} +The Roothaan-Hall equation +\begin{equation} + \mathbf{FC} = \epsilon \mathbf{SC} +\end{equation} +One constraint $\Longrightarrow$ energy minimum \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.png} + \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.png} + \end{minipage} + \begin{minipage}[b]{0.35\linewidth} + \begin{equation} + \langle \hat{S}^2 \rangle = S_z^2 + S_z + q - \sum_{ij}^{pq}S_{ij}^2 + \end{equation} + + \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 symetry 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} @@ -154,6 +170,23 @@ \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} @@ -171,7 +204,7 @@ \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_copy.png} \end{minipage} \begin{minipage}[b]{0.3\linewidth} \begin{table}[h] @@ -180,8 +213,8 @@ \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 \\ @@ -192,6 +225,10 @@ \section{results} \end{tabular} \end{table} \end{minipage} + \begin{itemize} + \item degeneracies + \item lower energy states + \end{itemize} \end{frame} \begin{frame} @@ -214,12 +251,13 @@ \section{results} \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 & -2.923515 & -2.915707 \\ + 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 \\ @@ -266,7 +304,7 @@ \section{results} \section{Conclusions and prospects} \begin{frame} \begin{itemize} - \item Things to look out for: + \item Things to look out for \begin{itemize} \item triplet excitations with lower energy \item spin contamination @@ -274,7 +312,8 @@ \section{Conclusions and prospects} \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} From e5179ab642b6c9c95d82d049bd5176b0289062e5 Mon Sep 17 00:00:00 2001 From: ruvdrsti Date: Wed, 19 May 2021 15:20:53 +0000 Subject: [PATCH 2/7] rounding out the story --- theory/presentation/presentation.tex | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/theory/presentation/presentation.tex b/theory/presentation/presentation.tex index ad3f8b9..651500f 100644 --- a/theory/presentation/presentation.tex +++ b/theory/presentation/presentation.tex @@ -303,8 +303,10 @@ \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 spin contamination From 3ecf3d1d32a3a01d58cf9ec2510ea673f9294fa9 Mon Sep 17 00:00:00 2001 From: ruvdrsti Date: Thu, 20 May 2021 07:50:01 +0000 Subject: [PATCH 3/7] correcting typo --- theory/presentation/presentation.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/theory/presentation/presentation.tex b/theory/presentation/presentation.tex index 651500f..d9d3a4e 100644 --- a/theory/presentation/presentation.tex +++ b/theory/presentation/presentation.tex @@ -109,7 +109,7 @@ \section{Introduction} \begin{frame} - \frametitle{Löwdin's symetry dillema} + \frametitle{Löwdin's symmetry dillema} \begin{itemize} \item Low energy $\Longrightarrow$ loss of symmetry \item Keeping symmetry $\Longrightarrow$ high symmetry From 08134f298d68234ff0795e29e7dab52f2c83c798 Mon Sep 17 00:00:00 2001 From: ruvdrsti Date: Thu, 20 May 2021 09:11:37 +0000 Subject: [PATCH 4/7] applying suggesteed changes --- theory/presentation/presentation.tex | 89 +++++++++++++--------------- 1 file changed, 41 insertions(+), 48 deletions(-) diff --git a/theory/presentation/presentation.tex b/theory/presentation/presentation.tex index d9d3a4e..7cae971 100644 --- a/theory/presentation/presentation.tex +++ b/theory/presentation/presentation.tex @@ -57,10 +57,6 @@ \section{Introduction} \begin{equation} \hat{H}\Psi = E\Psi \end{equation} -The Fock operator - \begin{equation} - \hat{f} = \hat{h}(1) + \sum_j^N\hat{J}_j - \hat{K}_j - \end{equation} The Roothaan-Hall equation \begin{equation} \mathbf{FC} = \epsilon \mathbf{SC} @@ -80,7 +76,7 @@ \section{Introduction} \item Symmetry intact \end{itemize} \begin{minipage}[b]{0.6\linewidth} - \includegraphics[width=\linewidth]{./figures/rhf.png} + \includegraphics[width=\linewidth]{./figures/rhf.pdf} \end{minipage} \end{frame} @@ -94,13 +90,9 @@ \section{Introduction} \item $\langle\hat{S}^2\rangle$ lost as quantum number \end{itemize} \begin{minipage}[b]{0.6\linewidth} - \includegraphics[width=\linewidth]{./figures/uhf.png} + \includegraphics[width=\linewidth]{./figures/uhf.pdf} \end{minipage} \begin{minipage}[b]{0.35\linewidth} - \begin{equation} - \langle \hat{S}^2 \rangle = S_z^2 + S_z + q - \sum_{ij}^{pq}S_{ij}^2 - \end{equation} - \begin{equation} \delta s = \langle \hat{S}^2 \rangle - S_z(S_z + 1) \end{equation} @@ -149,7 +141,7 @@ \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} @@ -191,10 +183,10 @@ \section{results} \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} @@ -204,7 +196,7 @@ \section{results} \begin{frame} \frametitle{CUHF and UHF} \begin{minipage}[b]{0.6\linewidth} - \includegraphics[width=\linewidth]{./figures/h3_cis_copy.png} + \includegraphics[width=\linewidth]{./figures/h3_cis.pdf} \end{minipage} \begin{minipage}[b]{0.3\linewidth} \begin{table}[h] @@ -231,40 +223,6 @@ \section{results} \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} - $\Longrightarrow$ 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} \begin{frame} \frametitle{CUHF and ROHF} @@ -324,4 +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} From caaf6a8a1c1321714a94143cc78ffd8d4897c47b Mon Sep 17 00:00:00 2001 From: ruvdrsti Date: Thu, 20 May 2021 09:13:40 +0000 Subject: [PATCH 5/7] finalising --- theory/presentation/presentation.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/theory/presentation/presentation.tex b/theory/presentation/presentation.tex index 7cae971..91d7f08 100644 --- a/theory/presentation/presentation.tex +++ b/theory/presentation/presentation.tex @@ -266,7 +266,7 @@ \section{Conclusions and prospects} \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 From 21e057fdb1a88218a6f73317fbe04aef1a1bd491 Mon Sep 17 00:00:00 2001 From: ruvdrsti Date: Thu, 20 May 2021 09:20:16 +0000 Subject: [PATCH 6/7] adding figures --- theory/presentation/figures/cuhf_mix.pdf | Bin 0 -> 14017 bytes theory/presentation/figures/h3_cis.pdf | Bin 0 -> 8723 bytes theory/presentation/figures/h3_cuhf.pdf | Bin 0 -> 13980 bytes theory/presentation/figures/h3_uhf_sto-3g.pdf | Bin 0 -> 14297 bytes theory/presentation/figures/rhf.pdf | Bin 0 -> 13745 bytes theory/presentation/figures/uhf.pdf | Bin 0 -> 14271 bytes 6 files changed, 0 insertions(+), 0 deletions(-) create mode 100644 theory/presentation/figures/cuhf_mix.pdf create mode 100644 theory/presentation/figures/h3_cis.pdf create mode 100644 theory/presentation/figures/h3_cuhf.pdf create mode 100644 theory/presentation/figures/h3_uhf_sto-3g.pdf create mode 100644 theory/presentation/figures/rhf.pdf create mode 100644 theory/presentation/figures/uhf.pdf diff --git a/theory/presentation/figures/cuhf_mix.pdf b/theory/presentation/figures/cuhf_mix.pdf new file mode 100644 index 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theory/presentation/presentation.tex | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/theory/presentation/presentation.tex b/theory/presentation/presentation.tex index 91d7f08..5187912 100644 --- a/theory/presentation/presentation.tex +++ b/theory/presentation/presentation.tex @@ -146,9 +146,9 @@ \section{Theory} \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