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Pierre-Francois Loos 2021-07-30 11:36:20 +02:00
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Manuscript/Ec.tex
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@ -359,7 +359,7 @@ More details can be found in Ref.~\onlinecite{Nocedal_1999}.
%%% TABLE I %%% %%% TABLE I %%%
\begin{squeezetable} \begin{squeezetable}
\begin{table*} \begin{table*}
\caption{Total energy $E$ (in \SI{}{\hartree}) and correlation energy $\Delta E$ (in \SI{}{\milli\hartree}) for the frozen-core ground state of five-membered rings in the cc-pVDZ basis set. \caption{Total energy $E$ (in \si{\hartree}) and correlation energy $\Delta E$ (in \si{\milli\hartree}) for the frozen-core ground state of five-membered rings in the cc-pVDZ basis set.
For the CIPSI estimates of the FCI correlation energy, the fitting error associated with the weighted five-point linear fit is reported in parenthesis. For the CIPSI estimates of the FCI correlation energy, the fitting error associated with the weighted five-point linear fit is reported in parenthesis.
\label{tab:Tab5-VDZ}} \label{tab:Tab5-VDZ}}
\begin{ruledtabular} \begin{ruledtabular}
@ -398,7 +398,7 @@ More details can be found in Ref.~\onlinecite{Nocedal_1999}.
%%% TABLE II %%% %%% TABLE II %%%
\begin{squeezetable} \begin{squeezetable}
\begin{table*} \begin{table*}
\caption{Total energy $E$ (in \SI{}{\hartree}) and correlation energy $\Delta E$ (in \SI{}{\milli\hartree}) for the frozen-core ground state of six-membered rings in the cc-pVDZ basis set. \caption{Total energy $E$ (in \si{\hartree}) and correlation energy $\Delta E$ (in \si{\milli\hartree}) for the frozen-core ground state of six-membered rings in the cc-pVDZ basis set.
For the CIPSI estimates of the FCI correlation energy, the fitting error associated with the weighted five-point linear fit is reported in parenthesis. For the CIPSI estimates of the FCI correlation energy, the fitting error associated with the weighted five-point linear fit is reported in parenthesis.
\label{tab:Tab6-VDZ}} \label{tab:Tab6-VDZ}}
\begin{ruledtabular} \begin{ruledtabular}
@ -437,7 +437,7 @@ More details can be found in Ref.~\onlinecite{Nocedal_1999}.
\begin{squeezetable} \begin{squeezetable}
\begin{table} \begin{table}
\caption{ \caption{
Extrapolated correlation energies $\Delta \Eextrap$ (in \SI{}{\milli\hartree}) for the twelve cyclic molecules represented in Fig.~\ref{fig:mol} and their associated fitting errors (in \SI{}{\milli\hartree}) obtained via weighted linear fits with a varying number of points. Extrapolated correlation energies $\Delta \Eextrap$ (in \si{\milli\hartree}) for the twelve cyclic molecules represented in Fig.~\ref{fig:mol} and their associated fitting errors (in \si{\milli\hartree}) obtained via weighted linear fits with a varying number of points.
Two sets of orbitals are considered: natural orbitals and optimized orbitals. Two sets of orbitals are considered: natural orbitals and optimized orbitals.
The weights are taken as the inverse square of the perturbative corrections. The weights are taken as the inverse square of the perturbative corrections.
For a $m$-point fit, the $m$ largest variational wave functions are used. For a $m$-point fit, the $m$ largest variational wave functions are used.
@ -552,7 +552,7 @@ More details can be found in Ref.~\onlinecite{Nocedal_1999}.
\includegraphics[width=0.32\textwidth]{Pyrimidine_MPCC} \includegraphics[width=0.32\textwidth]{Pyrimidine_MPCC}
\includegraphics[width=0.32\textwidth]{Tetrazine_MPCC} \includegraphics[width=0.32\textwidth]{Tetrazine_MPCC}
\includegraphics[width=0.32\textwidth]{Triazine_MPCC} \includegraphics[width=0.32\textwidth]{Triazine_MPCC}
\caption{Convergence of the correlation energy (in \SI{}{\milli\hartree}) as a function of the computational cost for the twelve cyclic molecules represented in Fig.~\ref{fig:mol}. \caption{Convergence of the correlation energy (in \si{\milli\hartree}) as a function of the computational cost 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). 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. The FCI estimate of the correlation energy is represented as a black line.
\label{fig:MPCC}} \label{fig:MPCC}}
@ -563,7 +563,7 @@ More details can be found in Ref.~\onlinecite{Nocedal_1999}.
\begin{squeezetable} \begin{squeezetable}
\begin{table} \begin{table}
\caption{ \caption{
Mean absolute error (MAE), mean signed error (MSE), and minimum (Min) and maximum (Max) absolute errors (in \SI{}{\milli\hartree}) with respect to the FCI correlation energy for various methods. Mean absolute error (MAE), mean signed error (MSE), and minimum (Min) and maximum (Max) absolute errors (in \si{\milli\hartree}) with respect to the FCI correlation energy for various methods.
The formal computational scaling of each method is also reported. The formal computational scaling of each method is also reported.
\label{tab:stats}} \label{tab:stats}}
\begin{ruledtabular} \begin{ruledtabular}
@ -623,7 +623,7 @@ Each Irene's AMD node is a dual-socket AMD Rome (EPYC) CPU at 2.60 GHz with 256G
These nodes are connected via Infiniband HDR100. These nodes are connected via Infiniband HDR100.
In total, the present calculations have required around 3~million core hours. In total, the present calculations have required around 3~million core hours.
All the data (geometries, energies, etc) and supplementary material associated with the present manuscript are openly available in Zenodo at \href{http://doi.org/XX.XXXX/zenodo.XXXXXXX}{http://doi.org/XX.XXXX/zenodo.XXXXXXX}. All the data (geometries, energies, etc) and supplementary material associated with the present manuscript are openly available in Zenodo at \url{http://doi.org/XX.XXXX/zenodo.XXXXXXX}.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Results and discussion} \section{Results and discussion}
@ -723,7 +723,7 @@ This project has received funding from the European Research Council (ERC) under
%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%
\section*{Data availability statement} \section*{Data availability statement}
%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%
The data that support the findings of this study are openly available in Zenodo at \href{http://doi.org/XX.XXXX/zenodo.XXXXXXX}{http://doi.org/XX.XXXX/zenodo.XXXXXXX}. The data that support the findings of this study are openly available in Zenodo at \url{http://doi.org/XX.XXXX/zenodo.XXXXXXX}.
%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%
\bibliography{Ec} \bibliography{Ec}