resubmitted version

Manuscript/Ec.tex

@@ -4,7 +4,7 @@
 
 \newcommand{\ie}{\textit{i.e.}}
 \newcommand{\eg}{\textit{e.g.}}
-\newcommand{\alert}[1]{\textcolor{red}{#1}}
+\newcommand{\alert}[1]{\textcolor{black}{#1}}
 \usepackage[normalem]{ulem}
 \newcommand{\titou}[1]{\textcolor{red}{#1}}
 \newcommand{\denis}[1]{\textcolor{blue}{#1}}
@@ -128,8 +128,8 @@ For example, in configuration interaction (CI) methods, the wave function is exp
 
 %%% FIG 1 %%%
 \begin{figure*}
-	\includegraphics[width=0.8\linewidth]{ring5}
-	\includegraphics[width=\linewidth]{ring6}
+	\includegraphics[width=0.8\linewidth]{fig1a}
+	\includegraphics[width=\linewidth]{fig1b}
 	\caption{
 	Five-membered rings (top) and six-membered rings (bottom) considered in this study.
 	\label{fig:mol}}
@@ -318,20 +318,20 @@ More details can be found in Ref.~\onlinecite{Nocedal_1999}.
 
 %%% FIG 2 %%%
 \begin{figure*}
-	\includegraphics[width=0.24\textwidth]{Cyclopentadiene_EvsNdet}
-	\includegraphics[width=0.24\textwidth]{Furan_EvsNdet}
-	\includegraphics[width=0.24\textwidth]{Imidazole_EvsNdet}
-	\includegraphics[width=0.24\textwidth]{Pyrrole_EvsNdet}
+	\includegraphics[width=0.24\textwidth]{fig2a}
+	\includegraphics[width=0.24\textwidth]{fig2b}
+	\includegraphics[width=0.24\textwidth]{fig2c}
+	\includegraphics[width=0.24\textwidth]{fig2d}
 	\\
-	\includegraphics[width=0.24\textwidth]{Thiophene_EvsNdet}
-	\includegraphics[width=0.24\textwidth]{Benzene_EvsNdet}
-	\includegraphics[width=0.24\textwidth]{Pyrazine_EvsNdet}
-	\includegraphics[width=0.24\textwidth]{Pyridazine_EvsNdet}
+	\includegraphics[width=0.24\textwidth]{fig2e}
+	\includegraphics[width=0.24\textwidth]{fig2f}
+	\includegraphics[width=0.24\textwidth]{fig2g}
+	\includegraphics[width=0.24\textwidth]{fig2h}
 	\\
-	\includegraphics[width=0.24\textwidth]{Pyridine_EvsNdet}
-	\includegraphics[width=0.24\textwidth]{Pyrimidine_EvsNdet}
-	\includegraphics[width=0.24\textwidth]{Tetrazine_EvsNdet}
-	\includegraphics[width=0.24\textwidth]{Triazine_EvsNdet}
+	\includegraphics[width=0.24\textwidth]{fig2i}
+	\includegraphics[width=0.24\textwidth]{fig2j}
+	\includegraphics[width=0.24\textwidth]{fig2k}
+	\includegraphics[width=0.24\textwidth]{fig2l}
 	\caption{$\Delta \Evar$ (solid) and $\Delta \Evar + \EPT$ (dashed) computed in the cc-pVDZ basis as functions of the number of determinants $\Ndet$ in the variational space for the twelve cyclic molecules represented in Fig.~\ref{fig:mol}.
 	Two sets of orbitals are considered: natural orbitals (NOs, in red) and optimized orbitals (OOs, in blue).
 	The FCI estimate of the correlation energy is represented as a thick black line.
@@ -342,20 +342,20 @@ More details can be found in Ref.~\onlinecite{Nocedal_1999}.
 
 %%% FIG 3 %%%
 \begin{figure*}
-	\includegraphics[width=0.24\textwidth]{Cyclopentadiene_EvsPT2}
-	\includegraphics[width=0.24\textwidth]{Furan_EvsPT2}
-	\includegraphics[width=0.24\textwidth]{Imidazole_EvsPT2}
-	\includegraphics[width=0.24\textwidth]{Pyrrole_EvsPT2}
+	\includegraphics[width=0.24\textwidth]{fig3a}
+	\includegraphics[width=0.24\textwidth]{fig3b}
+	\includegraphics[width=0.24\textwidth]{fig3c}
+	\includegraphics[width=0.24\textwidth]{fig3d}
 	\\
-	\includegraphics[width=0.24\textwidth]{Thiophene_EvsPT2}
-	\includegraphics[width=0.24\textwidth]{Benzene_EvsPT2}
-	\includegraphics[width=0.24\textwidth]{Pyrazine_EvsPT2}
-	\includegraphics[width=0.24\textwidth]{Pyridazine_EvsPT2}
+	\includegraphics[width=0.24\textwidth]{fig3e}
+	\includegraphics[width=0.24\textwidth]{fig3f}
+	\includegraphics[width=0.24\textwidth]{fig3g}
+	\includegraphics[width=0.24\textwidth]{fig3h}
 	\\
-	\includegraphics[width=0.24\textwidth]{Pyridine_EvsPT2}
-	\includegraphics[width=0.24\textwidth]{Pyrimidine_EvsPT2}
-	\includegraphics[width=0.24\textwidth]{Tetrazine_EvsPT2}
-	\includegraphics[width=0.24\textwidth]{Triazine_EvsPT2}
+	\includegraphics[width=0.24\textwidth]{fig3i}
+	\includegraphics[width=0.24\textwidth]{fig3j}
+	\includegraphics[width=0.24\textwidth]{fig3k}
+	\includegraphics[width=0.24\textwidth]{fig3l}
 	\caption{$\Delta \Evar$ as a function of $\EPT$ computed in the cc-pVDZ basis for the twelve cyclic molecules represented in Fig.~\ref{fig:mol}.
 	Two sets of orbitals are considered: natural orbitals (NOs, in red) and optimized orbitals (OOs, in blue).
 	The five-point weighted linear fit using the five largest variational wave functions for each set is depicted as a dashed black line.
@@ -537,7 +537,7 @@ More details can be found in Ref.~\onlinecite{Nocedal_1999}.
 
 %%% FIG 4 %%%
 \begin{figure}
-	\includegraphics[width=\linewidth]{Benzene_EvsNdetLO}
+	\includegraphics[width=\linewidth]{fig4}
 	\caption{$\Delta \Evar$ (solid) and $\Delta \Evar + \EPT$ (dashed) computed in the cc-pVDZ basis as functions of the number of determinants $\Ndet$ in the variational space for the benzene molecule.
 	Three sets of orbitals are considered: natural orbitals (NOs, in red), localized orbitals (LOs, in green), and optimized orbitals (OOs, in blue).
 	The FCI estimate of the correlation energy is represented as a thick black line.
@@ -547,20 +547,20 @@ More details can be found in Ref.~\onlinecite{Nocedal_1999}.
 
 %%% FIG 5 %%%
 \begin{figure*}
-	\includegraphics[width=0.24\textwidth]{Cyclopentadiene_MPCC}
-	\includegraphics[width=0.24\textwidth]{Furan_MPCC}
-	\includegraphics[width=0.24\textwidth]{Imidazole_MPCC}
-	\includegraphics[width=0.24\textwidth]{Pyrrole_MPCC}
+	\includegraphics[width=0.24\textwidth]{fig5a}
+	\includegraphics[width=0.24\textwidth]{fig5b}
+	\includegraphics[width=0.24\textwidth]{fig5c}
+	\includegraphics[width=0.24\textwidth]{fig5d}
 	\\
-	\includegraphics[width=0.24\textwidth]{Thiophene_MPCC}
-	\includegraphics[width=0.24\textwidth]{Benzene_MPCC}
-	\includegraphics[width=0.24\textwidth]{Pyrazine_MPCC}
-	\includegraphics[width=0.24\textwidth]{Pyridazine_MPCC}
+	\includegraphics[width=0.24\textwidth]{fig5e}
+	\includegraphics[width=0.24\textwidth]{fig5f}
+	\includegraphics[width=0.24\textwidth]{fig5g}
+	\includegraphics[width=0.24\textwidth]{fig5h}
 	\\
-	\includegraphics[width=0.24\textwidth]{Pyridine_MPCC}
-	\includegraphics[width=0.24\textwidth]{Pyrimidine_MPCC}
-	\includegraphics[width=0.24\textwidth]{Tetrazine_MPCC}
-	\includegraphics[width=0.24\textwidth]{Triazine_MPCC}
+	\includegraphics[width=0.24\textwidth]{fig5i}
+	\includegraphics[width=0.24\textwidth]{fig5j}
+	\includegraphics[width=0.24\textwidth]{fig5k}
+	\includegraphics[width=0.24\textwidth]{fig5l}
 	\caption{Convergence of the correlation energy (in \si{\milli\hartree}) computed in the cc-pVDZ basis as a function of the formal computational scaling for the twelve cyclic molecules represented in Fig.~\ref{fig:mol}.
 	Three series of methods are considered: i) MP2, MP3, MP4, and MP5 (blue), ii) CC2, CC3, and CC4 (green), and iii) CCSD, CCSDT, CCSDTQ (red).
 	The FCI estimate of the correlation energy is represented as a black line.
@@ -725,6 +725,11 @@ As perspectives, we are currently investigating the performance of the present a
 We hope to report on this in the near future.
 The compression of the variational space brought by optimized orbitals could be also beneficial in the context of quantum Monte Carlo methods to generate compact, yet accurate multi-determinant trial wave functions. \cite{Dash_2018,Dash_2019,Scemama_2020,Dash_2021}
 
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\section*{Supplementary Material}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+Included in the supplementary material are the raw data for each figure, geometries, basis set files, orbitals obtained at various levels of theory, input and output files for each calculation, as well as a standalone \textsc{mathematica} notebook gathering modules for generating figures and statistics.
+
 %%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{acknowledgements}
 This work was performed using HPC resources from GENCI-TGCC (2021-gen1738), from the CCIPL computational center installed in Nantes, and from CALMIP (Toulouse) under allocation 2021-18005, and was also supported by the European Centre of Excellence in Exascale Computing TREX --- Targeting Real Chemical Accuracy at the Exascale. This project has received funding from the European Union's Horizon 2020 --- Research and Innovation program --- under grant agreement no.~952165.