update sec 5.1

RapportStage/Rapport.tex

@@ -540,13 +540,27 @@ In addition, we can also consider the symmetry-broken solutions beyond their res
 
 \subsection{Evolution of the radius of convergence}
 
-Different partitioning
+In this part, we will try to investigate how some parameters of $\bH(\lambda)$ influence the radius of convergence of the perturbation series. The radius of convergence is equal to the closest singularity to the origin of $E(\lambda)$. The exceptional points are simultaneous solution of \eqref{eq:PolChar} and \eqref{eq:DPolChar} so we solve this system to find their position.
 
-$Y_{l0}$ vs $P_l(\cos(\theta))$
+\begin{equation}\label{eq:PolChar}
+\text{det}[E-\bH(\lambda)]=0
+\end{equation}
+
+\begin{equation}\label{eq:DPolChar}
+\pdv{E}\text{det}[E-\bH(\lambda)]=0
+\end{equation}
+
+We will take the simple case of the M{\o}ller-Plesset partitioning with a restricted Hartree-Fock minimal basis set as our starting point for this analysis. \\
+
+Puis on rajoute les 3 autres partitionnements \\
+
+Puis différence entre $Y_{l0}$ et $P_l(\cos(\theta))$ (CSF). Parler de la possibilité de la base strong coupling. \\
+
+Différence RHF/UHF, Hamiltonien non-bloc diagonal, coefficients complexe pour R<3/2 \\
+
+Influence de la taille de la base en RHF et UHF \\
 
-Size of the basis set
 
-Strong coupling ???
 
 \subsection{Exceptional points in the UHF formalism}
 
@@ -562,7 +576,7 @@ PT broken symmetry sb UHF
 
 \begin{itemize}
 \item Corriger les erreurs dans la biblio
-\item tableau nrj uhf, citation spin density wave et charge density wave
+\item citation spin density wave et charge density wave
 \end{itemize}
 
 \section{Conclusion}