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minor corrections on slides

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Pierre-Francois Loos 2020-06-28 21:35:41 +02:00
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SlideToulouse/main.tex
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@ -150,7 +150,7 @@ In physics perturbation theory is often a good way to improve the obtained resul
\begin{beamerboxesrounded}[scheme=foncé]{}
\centering
Full Configuration Interaction gives us access to high order terms of the perturbation series !
Full Configuration Interaction gives access to high-order terms of the perturbation series!
\end{beamerboxesrounded}
\end{frame}
@ -159,8 +159,8 @@ Full Configuration Interaction gives us access to high order terms of the pertur
\begin{figure}
\centering
\includegraphics[width=0.4\textwidth]{gill1986.png}
\caption{\centering Barriers to homolytic fission of \ce{He2^2+} using STO-3G basis set MPn theory (n~=~1-20).}
\includegraphics[width=0.5\textwidth]{gill1986.png}
\caption{\centering Barriers to homolytic fission of \ce{He2^2+} at MPn/STO-3G level ($n = 1$--$20$).}
\label{fig:my_label}
\end{figure}
@ -184,7 +184,7 @@ Full Configuration Interaction gives us access to high order terms of the pertur
\label{tab:my_label}
\end{table}
\footnotetext{\tiny{Gill et al. Why does unrestricted Møller–Plesset perturbation theory converge so slowly for spin-contaminated wave functions, \textit{Journal of chemical physics}, 1988}}
\footnotetext{\tiny{Gill et al. Why does unrestricted M{\o}ller-Plesset perturbation theory converge so slowly for spin-contaminated wave functions, \textit{Journal of chemical physics}, 1988}}
\end{frame}
@ -222,7 +222,7 @@ Full Configuration Interaction gives us access to high order terms of the pertur
\begin{itemize}
\item Smooth for $x \in \mathbb{R}$
\item Infinitely differentiable on $\mathbb{R}$
\item Infinitely differentiable in $\mathbb{R}$
\end{itemize}
\column{0.48\textwidth}
@ -242,13 +242,13 @@ But the Taylor expansion of this function does not converge for $x\geq1$...
\end{frame}
\begin{frame}{And if we look in the complex plane ?}
\begin{frame}{And if we look in the complex plane?}
\begin{columns}
\column{0.48\textwidth}
\centering The function has 4 singularities in the complex plane !
\centering The function has 4 singularities in the complex plane!
\vspace{1cm}
@ -305,11 +305,11 @@ The \textcolor{red}{radius of convergence} of the Taylor expansion of a function
\section{Classifying the singularity}
\begin{frame}{Which features of the system localize the singularities ?}
\begin{frame}{Which features of the system localize the singularities?}
\begin{itemize}
\item Partitioning of the Hamiltonian: Møller-Plesset, Epstein-Nesbet,...
\item Zeroth order reference: weak correlation or strongly correlated electrons.
\item Partitioning of the Hamiltonian: Møller-Plesset, Epstein-Nesbet, \ldots
\item Zeroth-order reference: weak or strong correlation.
\item Finite or complete basis set.
\item Localized or delocalized basis functions.
\end{itemize}
@ -409,7 +409,7 @@ We can separate singularities in two parts.
\begin{itemize}
\item Large avoided crossing
\item Non-zero imaginary part
\item Interaction with a low lying doubly excited states
\item Interaction with a low-lying doubly excited states
\end{itemize}
\end{beamerboxesrounded}
@ -468,7 +468,7 @@ Proof of the existence of this group of sharp avoided crossings for Ne, He and H
\vspace{0.5cm}
\begin{itemize}
\item $E_{kin} >> E_p$
\item $E_\text{kin} \gg E_\text{pot}$
\item Uniform density of electrons
\item \textcolor{red}{Weak correlation}
\end{itemize}
@ -481,7 +481,7 @@ Proof of the existence of this group of sharp avoided crossings for Ne, He and H
\vspace{0.5cm}
\begin{itemize}
\item $E_{kin} << E_p$
\item $E_\text{kin} \ll E_\text{pot}$
\item Electrons on the opposite sides of the sphere
\item \textcolor{red}{Strong correlation}
\end{itemize}