Merge branch 'master' of https://git.irsamc.ups-tlse.fr/loos/seniority

H8_cc-pvdz/pes_CISDTQ.dat

@@ -58,7 +58,7 @@
 6.1           -3.94150395
 6.2           -3.94193508
 6.3           -3.94234878
-6.4           -3.93442801
+6.4           -3.94275670
 6.5           -3.94315183
 6.6           -3.94353415
 6.7           -3.94390984

Manuscript/sup.tex

@@ -23,20 +23,9 @@
 \newcommand{\tabc}[1]{\multicolumn{1}{c}{#1}}
 \newcommand{\QP}{\textsc{quantum package}}
 
-\newcommand{\hI}{\Hat{1}}
-\newcommand{\hT}{\Hat{T}}
-\newcommand{\hH}{\Hat{H}}
-\newcommand{\bH}{\Bar{H}}
-\newcommand{\ERI}[2]{v_{#1}^{#2}}
-
 \newcommand{\EHF}{E_\text{HF}}
 \newcommand{\EDOCI}{E_\text{DOCI}}
 \newcommand{\EFCI}{E_\text{FCI}}
-\newcommand{\ECC}{E_\text{CC}}
-\newcommand{\EVCC}{E_\text{VCC}}
-\newcommand{\EpCCD}{E_\text{pCCD}}
-
-\newcommand{\si}{\sigma}
 
 \renewcommand{\thesection}{S\arabic{section}}
 \renewcommand{\thetable}{S\arabic{table}}
@@ -89,45 +78,55 @@
 %x
 %\newpage
 
-%Start.
-
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 %\section{oo-CI}
 %\label{sec:oo-CI}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 \begin{figure}[h!]
-\includegraphics[width=\linewidth]{plot_stat_opt}
-        \caption{Non-parallelity errors as function of the number of determinants, for the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and our proposed hCI (green),
+\includegraphics[width=0.8\linewidth]{plot_stat_opt}
+        \caption{Non-parallelity errors as function of the number of determinants, for the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
 	with orbitals optimized at each CI level.
         }
         \label{fig:plot_stat_opt}
 \end{figure}
 
 \begin{figure}[h!]
-\includegraphics[width=\linewidth]{plot_distance_opt}
-        \caption{Distance errors as function of the number of determinants, for the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and our proposed hCI (green),
+\includegraphics[width=0.8\linewidth]{plot_distance_opt}
+        \caption{Distance errors as function of the number of determinants, for the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
         with orbitals optimized at each CI level.
         }
         \label{fig:plot_distance_opt}
 \end{figure}
 
 \begin{figure}[h!]
-        \includegraphics[width=\linewidth]{xe_opt}
-        \caption{Equilibrium geometries as function of the number of determinants, for the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and our proposed hCI (green),
+        \includegraphics[width=0.8\linewidth]{xe_opt}
+        \caption{Equilibrium geometries as function of the number of determinants, for the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
 	with orbitals optimized at each CI level.
         }
         \label{fig:xe_opt}
 \end{figure}
 
 \begin{figure}[h!]
-\includegraphics[width=\linewidth]{freq_opt}
-        \caption{Vibrational frequencies (or force constants) as function of the number of determinants, for the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and our proposed hCI (green),
+\includegraphics[width=0.8\linewidth]{freq_opt}
+        \caption{Vibrational frequencies (or force constants) as function of the number of determinants, for the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
 	with orbitals optimized at each CI level.
         }
         \label{fig:freq_opt}
 \end{figure}
 
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%\section{oo-CIS
+%\label{sec:oo-CIS}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{figure}[h!]
+\includegraphics[width=0.8\linewidth]{plot_pes}
+	\caption{Potential energy curves for dissociation of six molecular systems (see main text for details), according to RHF (gray), oo-CIS (red), and FCI (black) calculations.
+        }
+        \label{fig:plot_pes}
+\end{figure}
+
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 %\section{\ce{HF}, different basis sets}
 %\label{sec:HF_basis}
@@ -136,7 +135,7 @@
 \begin{figure}[h!]
 \includegraphics[width=\linewidth]{plot_pes_HF}
 	\caption{Potential energy curves (top) and energy differences with respect to FCI (bottom), for dissociation of \ce{HF},
-	according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and our proposed hybrid hCI (green),
+	according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
 	with Hartree-Fock orbitals, 
 	and for the cc-pVDZ (left), cc-pVTZ (center), and cc-pVQZ (right) basis sets.
         }
@@ -145,9 +144,9 @@
 
 \begin{figure}[h!]
 \includegraphics[width=\linewidth]{freq_HF}
-	\caption{Nonparallelity error (left), vibrational frequencies (center), and equilibrium geometries (right) for \ce{HF},
+	\caption{Non-parallelity error (left), vibrational frequencies (center), and equilibrium geometries (right) of \ce{HF},
 	as function of the number of determinants,
-	for the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and our proposed hybrid hCI (green),
+	according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
         with Hartree-Fock orbitals,
 	and for the cc-pVDZ (left), cc-pVTZ (center), and cc-pVQZ (right) basis sets.}
         \label{fig:freq_HF}
@@ -161,48 +160,60 @@
 \begin{figure}[h!]
 \includegraphics[width=\linewidth]{HF_pes}
 	\caption{Potential energy curves for \ce{HF},
-	computed with different CI methods and the cc-pVDZ basis set, 
-	with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right).}
+        according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
+	(dashed lines for half-integer $h$),
+	with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right),
+	and with the cc-pVDZ basis set.}
         \label{fig:HF_pes}
 \end{figure}
 
 \begin{figure}[h!]
 \includegraphics[width=\linewidth]{HF_pes_error}
-	\caption{Energy difference to the FCI results for \ce{HF},
-	computed with different CI methods and the cc-pVDZ basis set, 
-	with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right).}
+	\caption{Energy differences between the potential energy curves of Fig.~\ref{fig:HF_pes} and FCI results for \ce{HF},
+        according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
+	(dashed lines for half-integer $h$),
+	with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right),
+	and with the cc-pVDZ basis set.}
         \label{fig:HF_pes_error}
 \end{figure}
 
 \begin{figure}[h!]
 \includegraphics[width=\linewidth]{HF_npe}
-	\caption{Nonparallelity error for \ce{HF},
-	as function of the computational scaling of excitation-based CI (red) and CIo (green) methods,
-	with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right), for the cc-pVDZ basis set.}
+	\caption{Non-parallelity error for \ce{HF}, corresponding to the potential energy curves of Fig.~\ref{fig:HF_pes},
+	as function of the number of determinants,
+        according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
+	with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right),
+	and with the cc-pVDZ basis set.}
         \label{fig:HF_npe}
 \end{figure}
 
 \begin{figure}[h!]
 \includegraphics[width=\linewidth]{HF_distance}
-        \caption{Nonparallelity error for \ce{HF},
-        as function of the computational scaling of excitation-based CI (red) and CIo (green) methods,
-        with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right), for the cc-pVDZ basis set.}
+	\caption{Distance error for \ce{HF}, corresponding to the potential energy curves of Fig.~\ref{fig:HF_pes},
+	as function of the number of determinants,
+        according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
+	with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right),
+	and with the cc-pVDZ basis set.}
         \label{fig:HF_distance}
 \end{figure}
 
 \begin{figure}[h!]
 \includegraphics[width=\linewidth]{HF_freq}
         \caption{Vibrational frequency of \ce{HF},
-        as function of the computational scaling of excitation-based CI (red) and CIo (green) methods,
-        with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right), for the cc-pVDZ basis set.}
+	as function of the number of determinants,
+        according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
+	with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right),
+	and with the cc-pVDZ basis set.}
         \label{fig:HF_freq}
 \end{figure}
 
 \begin{figure}[h!]
 \includegraphics[width=\linewidth]{HF_xe}
 	\caption{Equilibrium bond length of \ce{HF},
-	as function of the computational scaling of excitation-based CI (red) and CIo (green) methods,
-	with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right), for the cc-pVDZ basis set.}
+	as function of the number of determinants,
+        according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
+	with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right),
+	and with the cc-pVDZ basis set.}
         \label{fig:HF_xe}
 \end{figure}
 
@@ -213,33 +224,61 @@
 
 \begin{figure}[h!]
 \includegraphics[width=\linewidth]{F2_pes}
-	\caption{Potential energy curves for \ce{F2},
-	computed with different CI methods and the cc-pVDZ basis set, 
-	with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right).}
+        \caption{Potential energy curves for \ce{F2},
+        according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
+        (dashed lines for half-integer $h$),
+        with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right),
+        and with the cc-pVDZ basis set.}
         \label{fig:F2_pes}
 \end{figure}
 
 \begin{figure}[h!]
 \includegraphics[width=\linewidth]{F2_pes_error}
-	\caption{Energy difference to the FCI results for \ce{F2},
-	computed with different CI methods and the cc-pVDZ basis set, 
-	with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right).}
+        \caption{Energy differences between the potential energy curves of Fig.~\ref{fig:F2_pes} and FCI results for \ce{F2},
+        according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
+        (dashed lines for half-integer $h$),
+        with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right),
+        and with the cc-pVDZ basis set.}
         \label{fig:F2_pes_error}
 \end{figure}
 
 \begin{figure}[h!]
 \includegraphics[width=\linewidth]{F2_npe}
-	\caption{Nonparallelity error for \ce{F2},
-	as function of the computational scaling of excitation-based CI (red) and CIo (green) methods,
-	with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right), for the cc-pVDZ basis set.}
+        \caption{Non-parallelity error for \ce{F2}, corresponding to the potential energy curves of Fig.~\ref{fig:F2_pes},
+        as function of the number of determinants,
+        according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
+        with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right),
+        and with the cc-pVDZ basis set.}
         \label{fig:F2_npe}
 \end{figure}
 
+\begin{figure}[h!]
+\includegraphics[width=\linewidth]{F2_distance}
+        \caption{Distance error for \ce{F2}, corresponding to the potential energy curves of Fig.~\ref{fig:F2_pes},
+        as function of the number of determinants,
+        according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
+        with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right),
+        and with the cc-pVDZ basis set.}
+        \label{fig:F2_distance}
+\end{figure}
+
+\begin{figure}[h!]
+\includegraphics[width=\linewidth]{F2_freq}
+        \caption{Vibrational frequency of \ce{F2},
+        as function of the number of determinants,
+        according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
+        with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right),
+        and with the cc-pVDZ basis set.}
+        \label{fig:F2_freq}
+\end{figure}
+
 \begin{figure}[h!]
 \includegraphics[width=\linewidth]{F2_xe}
-	\caption{Equilibrium bond length of \ce{F2},
-	as function of the computational scaling of excitation-based CI (red) and CIo (green) methods,
-	with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right), for the cc-pVDZ basis set.}
+        \caption{Equilibrium bond length of \ce{F2},
+        as function of the number of determinants,
+        according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
+        with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right),
+        and with the cc-pVDZ basis set.}
         \label{fig:F2_xe}
 \end{figure}
 
@@ -250,33 +289,61 @@
 
 \begin{figure}[h!]
 \includegraphics[width=\linewidth]{ethylene_pes}
-	\caption{Potential energy curves for ethylene, as function of the C$=$C distance,
-	computed with different CI methods and the cc-pVDZ basis set, 
-	with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right).}
+        \caption{Potential energy curves for \ce{ethylene},
+        according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
+        (dashed lines for half-integer $h$),
+        with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right),
+        and with the cc-pVDZ basis set.}
         \label{fig:ethylene_pes}
 \end{figure}
 
 \begin{figure}[h!]
 \includegraphics[width=\linewidth]{ethylene_pes_error}
-	\caption{Energy difference to the FCI results for ethylene, as function of the C$=$C distance,
-	computed with different CI methods and the cc-pVDZ basis set, 
-	with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right).}
+        \caption{Energy differences between the potential energy curves of Fig.~\ref{fig:ethylene_pes} and FCI results for \ce{ethylene},
+        according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
+        (dashed lines for half-integer $h$),
+        with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right),
+        and with the cc-pVDZ basis set.}
         \label{fig:ethylene_pes_error}
 \end{figure}
 
 \begin{figure}[h!]
 \includegraphics[width=\linewidth]{ethylene_npe}
-	\caption{Nonparallelity error for ethylene,
-	as function of the computational scaling of excitation-based CI (red) and CIo (green) methods,
-	with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right), for the cc-pVDZ basis set.}
+        \caption{Non-parallelity error for \ce{ethylene}, corresponding to the potential energy curves of Fig.~\ref{fig:ethylene_pes},
+        as function of the number of determinants,
+        according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
+        with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right),
+        and with the cc-pVDZ basis set.}
         \label{fig:ethylene_npe}
 \end{figure}
 
+\begin{figure}[h!]
+\includegraphics[width=\linewidth]{ethylene_distance}
+        \caption{Distance error for \ce{ethylene}, corresponding to the potential energy curves of Fig.~\ref{fig:ethylene_pes},
+        as function of the number of determinants,
+        according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
+        with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right),
+        and with the cc-pVDZ basis set.}
+        \label{fig:ethylene_distance}
+\end{figure}
+
+\begin{figure}[h!]
+\includegraphics[width=\linewidth]{ethylene_freq}
+        \caption{Vibrational frequency of \ce{ethylene},
+        as function of the number of determinants,
+        according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
+        with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right),
+        and with the cc-pVDZ basis set.}
+        \label{fig:ethylene_freq}
+\end{figure}
+
 \begin{figure}[h!]
 \includegraphics[width=\linewidth]{ethylene_xe}
-	\caption{C$=$C equilibrium bond length of ethylene,
-	as function of the computational scaling of excitation-based CI (red) and CIo (green) methods,
-	with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right), for the cc-pVDZ basis set.}
+        \caption{Equilibrium bond length of \ce{ethylene},
+        as function of the number of determinants,
+        according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
+        with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right),
+        and with the cc-pVDZ basis set.}
         \label{fig:ethylene_xe}
 \end{figure}
 
@@ -287,36 +354,63 @@
 
 \begin{figure}[h!]
 \includegraphics[width=\linewidth]{N2_pes}
-	\caption{Potential energy curves for \ce{N2},
-	computed with different CI methods and the cc-pVDZ basis set, 
-	with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right).}
+        \caption{Potential energy curves for \ce{N2},
+        according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
+        (dashed lines for half-integer $h$),
+        with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right),
+        and with the cc-pVDZ basis set.}
         \label{fig:N2_pes}
 \end{figure}
 
 \begin{figure}[h!]
 \includegraphics[width=\linewidth]{N2_pes_error}
-	\caption{Energy difference to the FCI results for \ce{N2},
-	computed with different CI methods and the cc-pVDZ basis set, 
-	with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right).}
+        \caption{Energy differences between the potential energy curves of Fig.~\ref{fig:N2_pes} and FCI results for \ce{N2},
+        according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
+        (dashed lines for half-integer $h$),
+        with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right),
+        and with the cc-pVDZ basis set.}
         \label{fig:N2_pes_error}
 \end{figure}
 
 \begin{figure}[h!]
 \includegraphics[width=\linewidth]{N2_npe}
-	\caption{Nonparallelity error for \ce{N2},
-	as function of the computational scaling of excitation-based CI (red) and CIo (green) methods,
-	with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right), for the cc-pVDZ basis set.}
+        \caption{Non-parallelity error for \ce{N2}, corresponding to the potential energy curves of Fig.~\ref{fig:N2_pes},
+        as function of the number of determinants,
+        according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
+        with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right),
+        and with the cc-pVDZ basis set.}
         \label{fig:N2_npe}
 \end{figure}
 
 \begin{figure}[h!]
-\includegraphics[width=\linewidth]{N2_xe}
-	\caption{Equilibrium bond length of \ce{N2},
-	as function of the computational scaling of excitation-based CI (red) and CIo (green) methods,
-	with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right), for the cc-pVDZ basis set.}
-        \label{fig:N2_xe}
+\includegraphics[width=\linewidth]{N2_distance}
+        \caption{Distance error for \ce{N2}, corresponding to the potential energy curves of Fig.~\ref{fig:N2_pes},
+        as function of the number of determinants,
+        according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
+        with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right),
+        and with the cc-pVDZ basis set.}
+        \label{fig:N2_distance}
 \end{figure}
 
+\begin{figure}[h!]
+\includegraphics[width=\linewidth]{N2_freq}
+        \caption{Vibrational frequency of \ce{N2},
+        as function of the number of determinants,
+        according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
+        with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right),
+        and with the cc-pVDZ basis set.}
+        \label{fig:N2_freq}
+\end{figure}
+
+\begin{figure}[h!]
+\includegraphics[width=\linewidth]{N2_xe}
+        \caption{Equilibrium bond length of \ce{N2},
+        as function of the number of determinants,
+        according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
+        with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right),
+        and with the cc-pVDZ basis set.}
+        \label{fig:N2_xe}
+\end{figure}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 %\section{\ce{H4}}
@@ -325,36 +419,63 @@
 
 \begin{figure}[h!]
 \includegraphics[width=\linewidth]{H4_pes}
-	\caption{Potential energy curves for linear \ce{H4}, as function of the symmetric stretching coordinate,
-	computed with different CI methods and the cc-pVDZ basis set, 
-	with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right).}
+        \caption{Potential energy curves for \ce{H4},
+        according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
+        (dashed lines for half-integer $h$),
+        with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right),
+        and with the cc-pVDZ basis set.}
         \label{fig:H4_pes}
 \end{figure}
 
 \begin{figure}[h!]
 \includegraphics[width=\linewidth]{H4_pes_error}
-	\caption{Energy difference to the FCI results for linear \ce{H4}, as function of the symmetric stretching coordinate,
-	computed with different CI methods and the cc-pVDZ basis set, 
-	with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right).}
+        \caption{Energy differences between the potential energy curves of Fig.~\ref{fig:H4_pes} and FCI results for \ce{H4},
+        according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
+        (dashed lines for half-integer $h$),
+        with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right),
+        and with the cc-pVDZ basis set.}
         \label{fig:H4_pes_error}
 \end{figure}
 
 \begin{figure}[h!]
 \includegraphics[width=\linewidth]{H4_npe}
-	\caption{Nonparallelity error for linear \ce{H4},
-	as function of the computational scaling of excitation-based CI (red) and CIo (green) methods,
-	with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right), for the cc-pVDZ basis set.}
+        \caption{Non-parallelity error for \ce{H4}, corresponding to the potential energy curves of Fig.~\ref{fig:H4_pes},
+        as function of the number of determinants,
+        according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
+        with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right),
+        and with the cc-pVDZ basis set.}
         \label{fig:H4_npe}
 \end{figure}
 
 \begin{figure}[h!]
-\includegraphics[width=\linewidth]{H4_xe}
-	\caption{Equilibrium bond length of linear \ce{H4},
-	as function of the computational scaling of excitation-based CI (red) and CIo (green) methods,
-	with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right), for the cc-pVDZ basis set.}
-        \label{fig:H4_xe}
+\includegraphics[width=\linewidth]{H4_distance}
+        \caption{Distance error for \ce{H4}, corresponding to the potential energy curves of Fig.~\ref{fig:H4_pes},
+        as function of the number of determinants,
+        according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
+        with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right),
+        and with the cc-pVDZ basis set.}
+        \label{fig:H4_distance}
 \end{figure}
 
+\begin{figure}[h!]
+\includegraphics[width=\linewidth]{H4_force}
+        \caption{Force constants for symmetric dissociation of \ce{H4},
+        as function of the number of determinants,
+        according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
+        with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right),
+        and with the cc-pVDZ basis set.}
+        \label{fig:H4_force}
+\end{figure}
+
+\begin{figure}[h!]
+\includegraphics[width=\linewidth]{H4_xe}
+        \caption{Equilibrium bond length of \ce{H4},
+        as function of the number of determinants,
+        according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
+        with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right),
+        and with the cc-pVDZ basis set.}
+        \label{fig:H4_xe}
+\end{figure}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 %\section{\ce{H8}}
@@ -363,37 +484,63 @@
 
 \begin{figure}[h!]
 \includegraphics[width=\linewidth]{H8_pes}
-	\caption{Potential energy curves for linear \ce{H8}, as function of the symmetric stretching coordinate,
-	computed with different CI methods and the cc-pVDZ basis set, 
-	with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right).}
+        \caption{Potential energy curves for \ce{H8},
+        according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
+        (dashed lines for half-integer $h$),
+        with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right),
+        and with the cc-pVDZ basis set.}
         \label{fig:H8_pes}
 \end{figure}
 
 \begin{figure}[h!]
 \includegraphics[width=\linewidth]{H8_pes_error}
-	\caption{Energy difference to the FCI results for linear \ce{H8}, as function of the symmetric stretching coordinate,
-	computed with different CI methods and the cc-pVDZ basis set, 
-	with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right).}
+        \caption{Energy differences between the potential energy curves of Fig.~\ref{fig:H8_pes} and FCI results for \ce{H8},
+        according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
+        (dashed lines for half-integer $h$),
+        with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right),
+        and with the cc-pVDZ basis set.}
         \label{fig:H8_pes_error}
 \end{figure}
 
 \begin{figure}[h!]
 \includegraphics[width=\linewidth]{H8_npe}
-	\caption{Nonparallelity error for linear \ce{H8},
-	as function of the computational scaling of excitation-based CI (red) and CIo (green) methods,
-	with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right), for the cc-pVDZ basis set.}
+        \caption{Non-parallelity error for \ce{H8}, corresponding to the potential energy curves of Fig.~\ref{fig:H8_pes},
+        as function of the number of determinants,
+        according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
+        with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right),
+        and with the cc-pVDZ basis set.}
         \label{fig:H8_npe}
 \end{figure}
 
 \begin{figure}[h!]
-\includegraphics[width=\linewidth]{H8_xe}
-	\caption{Equilibrium bond length of linear \ce{H8},
-	as function of the computational scaling of excitation-based CI (red) and CIo (green) methods,
-	with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right), for the cc-pVDZ basis set.}
-        \label{fig:H8_xe}
+\includegraphics[width=\linewidth]{H8_distance}
+        \caption{Distance error for \ce{H8}, corresponding to the potential energy curves of Fig.~\ref{fig:H8_pes},
+        as function of the number of determinants,
+        according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
+        with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right),
+        and with the cc-pVDZ basis set.}
+        \label{fig:H8_distance}
 \end{figure}
 
-%End.
+\begin{figure}[h!]
+\includegraphics[width=\linewidth]{H8_force}
+        \caption{Force constants for symmetric dissociation of \ce{H8},
+        as function of the number of determinants,
+        according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
+        with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right),
+        and with the cc-pVDZ basis set.}
+        \label{fig:H8_force}
+\end{figure}
+
+\begin{figure}[h!]
+\includegraphics[width=\linewidth]{H8_xe}
+        \caption{Equilibrium bond length of \ce{H8},
+        as function of the number of determinants,
+        according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
+        with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right),
+        and with the cc-pVDZ basis set.}
+        \label{fig:H8_xe}
+\end{figure}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 %\bibliography{seniority}

plot_all/xe.gnu

@@ -51,8 +51,8 @@ set label 11 'HF'          at screen 0.34,0.94              tc ls 2 font 'Helvet
 set label 12 'F_2'         at screen 0.79,0.94              tc ls 2 font 'Helvetica,26'
 set label 13 'ethylene'    at screen 0.34,0.63              tc ls 2 font 'Helvetica,26'
 set label 14 'N_2'         at screen 0.79,0.63              tc ls 2 font 'Helvetica,26'
-set label 15 'H_4'         at screen 0.34,0.315             tc ls 2 font 'Helvetica,26'
-set label 16 'H_8'         at screen 0.79,0.315             tc ls 2 font 'Helvetica,26'
+set label 15 'H_4'         at screen 0.34,0.310             tc ls 2 font 'Helvetica,26'
+set label 16 'H_8'         at screen 0.79,0.310             tc ls 2 font 'Helvetica,26'
 
 set format y "%.1f"
 

plot_all/xe_opt.gnu

@@ -51,8 +51,8 @@ set label 11 'HF'          at screen 0.34,0.94              tc ls 2 font 'Helvet
 set label 12 'F_2'         at screen 0.79,0.94              tc ls 2 font 'Helvetica,26'
 set label 13 'ethylene'    at screen 0.34,0.63              tc ls 2 font 'Helvetica,26'
 set label 14 'N_2'         at screen 0.79,0.63              tc ls 2 font 'Helvetica,26'
-set label 15 'H_4'         at screen 0.34,0.315             tc ls 2 font 'Helvetica,26'
-set label 16 'H_8'         at screen 0.79,0.315             tc ls 2 font 'Helvetica,26'
+set label 15 'H_4'         at screen 0.34,0.310             tc ls 2 font 'Helvetica,26'
+set label 16 'H_8'         at screen 0.79,0.310             tc ls 2 font 'Helvetica,26'
 
 set format y "%.1f"