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\begin{document}

\newcommand{\LCPQ}{Laboratoire de Chimie et Physique Quantiques (UMR 5626), Universit\'e de Toulouse, CNRS, UPS, France}

\title{Supporting Information for ``Hierarchy Configuration Interaction: Combining Seniority Number and Excitation Degree''}

\author{F\'abris Kossoski}
\email{fkossoski@irsamc.ups-tlse.fr}
\affiliation{\LCPQ}
\author{Yann Damour}
\affiliation{\LCPQ}
\author{Pierre-Fran\c{c}ois Loos}
\email{loos@irsamc.ups-tlse.fr}
\affiliation{\LCPQ}

% Abstract
\begin{abstract}
%Here comes the abstract.
%\bigskip
%\begin{center}
%        \boxed{\includegraphics[width=0.4\linewidth]{TOC}}
%\end{center}
%\bigskip
\end{abstract}

% Title
\maketitle

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\section{Equilibrium geometry of ethylene}
%\label{sec:ethylene}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Equilibrium geometry of ethylene, in atomic units:
\begin{singlespace}
\begin{verbatim}
	C  0.00000000       1.26026583        0.00000000 
	C  0.00000000      -1.26026583        0.00000000 
	H  0.00000000       2.32345976        1.74287672 
	H  0.00000000      -2.32345976        1.74287672 
	H  0.00000000       2.32345976       -1.74287672 
	H  0.00000000      -2.32345976       -1.74287672 
\end{verbatim}
\end{singlespace}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\section{\ce{Computational details}}
%\label{sec:comp_details}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Vibrational frequencies and equilibrium geometries were obtained by fitting the computed potential energy curves at the Franck-Condon region with a Morse potential.
The following intervals have been considered for the fitting:
\SI{0.8}{\angstrom} to \SI{1.3}{\angstrom} (\ce{HF}),
\SI{1.25}{\angstrom} to \SI{1.65}{\angstrom} (\ce{F2}),
\SI{2.2}{\bohr} to \SI{2.9}{\bohr} (ethylene),
\SI{0.95}{\angstrom} to \SI{1.3}{\angstrom} (\ce{N2}),
\SI{1.45}{\bohr} to \SI{1.95}{\bohr} (\ce{H4}),
\SI{1.6}{\bohr} to \SI{2.05}{\bohr} (\ce{H8}).

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\section{\ce{HF}, different basis sets}
%\label{sec:HF_basis}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\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 hierarchy-based CI (green),
	with Hartree-Fock orbitals, 
	for the cc-pVDZ (left), cc-pVTZ (center), and cc-pVQZ (right) basis sets.
        }
        \label{fig:plot_pes_HF}
\end{figure}

\begin{figure}[h!]
\includegraphics[width=0.8\linewidth]{plot_stat_HF}
	\caption{Non-parallelity error (left) and distance error (right) of \ce{HF},
	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,
	for the cc-pVDZ (top), cc-pVTZ (center), and cc-pVQZ (bottom) basis sets.}
        \label{fig:plot_stat_HF}
\end{figure}

\begin{figure}[h!]
\includegraphics[width=0.8\linewidth]{freq_HF}
        \caption{Vibrational frequencies (left) and equilibrium geometries (right) of \ce{HF},
        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,
        and according to the exact FCI result (black horizontal line),
        for the cc-pVDZ (top), cc-pVTZ (center), and cc-pVQZ (bottom) basis sets.}
        \label{fig:freq_HF}
\end{figure}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\section{Distance error}
%\label{sec:distance}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{figure}[h!]
\includegraphics[width=0.8\linewidth]{plot_distance}
        \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 Hartree-Fock orbitals.
        }
        \label{fig:plot_distance}
\end{figure}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\section{oo-CI}
%\label{sec:oo-CI}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{figure}[h!]
\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=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=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,
	and according to the exact FCI result (black horizontal line).
        }
        \label{fig:xe_opt}
\end{figure}

\begin{figure}[h!]
\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,
	and according to the exact FCI result (black horizontal line).
        }
        \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).
        }
        \label{fig:plot_pes}
\end{figure}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\section{\ce{HF}}
%\label{sec:HF}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{figure}[h!]
\includegraphics[width=\linewidth]{HF_pes}
	\caption{Potential energy curves for \ce{HF},
        according to RHF, FCI, and 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 CI level (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 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 CI level (right),
	and with the cc-pVDZ basis set.}
        \label{fig:HF_pes_error}
\end{figure}

\begin{figure}[h!]
\includegraphics[width=\linewidth]{HF_npe}
	\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 CI level (right),
	and with the cc-pVDZ basis set.}
        \label{fig:HF_npe}
\end{figure}

\begin{figure}[h!]
\includegraphics[width=\linewidth]{HF_distance}
	\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 CI level (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 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 CI level (right),
	and according to the exact FCI result (black horizontal line),
	for 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 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 CI level (right),
	and according to the exact FCI result (black horizontal line),
	for the cc-pVDZ basis set.}
        \label{fig:HF_xe}
\end{figure}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\section{\ce{F2}}
%\label{sec:F2}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{figure}[h!]
\includegraphics[width=\linewidth]{F2_pes}
        \caption{Potential energy curves for \ce{F2},
        according to RHF, FCI, and 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 CI level (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 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 CI level (right),
        and with the cc-pVDZ basis set.}
        \label{fig:F2_pes_error}
\end{figure}

\begin{figure}[h!]
\includegraphics[width=\linewidth]{F2_npe}
        \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 CI level (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 CI level (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 CI level (right),
	and according to the exact FCI result (black horizontal line),
	for 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 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 CI level (right),
	and according to the exact FCI result (black horizontal line),
	for the cc-pVDZ basis set.}
        \label{fig:F2_xe}
\end{figure}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\section{\ce{Ethylene}}
%\label{sec:ethylene}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{figure}[h!]
\includegraphics[width=\linewidth]{ethylene_pes}
        \caption{Potential energy curves for \ce{ethylene},
        according to RHF, FCI, and 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 CI level (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 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 CI level (right),
        and with the cc-pVDZ basis set.}
        \label{fig:ethylene_pes_error}
\end{figure}

\begin{figure}[h!]
\includegraphics[width=\linewidth]{ethylene_npe}
        \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 CI level (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 CI level (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 CI level (right),
	and according to the exact FCI result (black horizontal line),
	for the cc-pVDZ basis set.}
        \label{fig:ethylene_freq}
\end{figure}

\begin{figure}[h!]
\includegraphics[width=\linewidth]{ethylene_xe}
        \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 CI level (right),
	and according to the exact FCI result (black horizontal line),
	for the cc-pVDZ basis set.}
        \label{fig:ethylene_xe}
\end{figure}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\section{\ce{N2}}
%\label{sec:N2}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{figure}[h!]
\includegraphics[width=\linewidth]{N2_pes}
        \caption{Potential energy curves for \ce{N2},
        according to RHF, FCI, and 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 CI level (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 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 CI level (right),
        and with the cc-pVDZ basis set.}
        \label{fig:N2_pes_error}
\end{figure}

\begin{figure}[h!]
\includegraphics[width=\linewidth]{N2_npe}
        \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 CI level (right),
        and with the cc-pVDZ basis set.}
        \label{fig:N2_npe}
\end{figure}

\begin{figure}[h!]
\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 CI level (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 CI level (right),
	and according to the exact FCI result (black horizontal line),
	for 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 CI level (right),
	and according to the exact FCI result (black horizontal line),
	for the cc-pVDZ basis set.}
        \label{fig:N2_xe}
\end{figure}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\section{\ce{H4}}
%\label{sec:H4}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{figure}[h!]
\includegraphics[width=\linewidth]{H4_pes}
        \caption{Potential energy curves for \ce{H4},
        according to RHF, FCI, and 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 CI level (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 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 CI level (right),
        and with the cc-pVDZ basis set.}
        \label{fig:H4_pes_error}
\end{figure}

\begin{figure}[h!]
\includegraphics[width=\linewidth]{H4_npe}
        \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 CI level (right),
        and with the cc-pVDZ basis set.}
        \label{fig:H4_npe}
\end{figure}

\begin{figure}[h!]
\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 CI level (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 CI level (right),
	and according to the exact FCI result (black horizontal line),
	for 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 CI level (right),
	and according to the exact FCI result (black horizontal line),
	for the cc-pVDZ basis set.}
        \label{fig:H4_xe}
\end{figure}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\section{\ce{H8}}
%\label{sec:H8}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{figure}[h!]
\includegraphics[width=\linewidth]{H8_pes}
        \caption{Potential energy curves for \ce{H8},
        according to RHF, FCI, and 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 CI level (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 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 CI level (right),
        and with the cc-pVDZ basis set.}
        \label{fig:H8_pes_error}
\end{figure}

\begin{figure}[h!]
\includegraphics[width=\linewidth]{H8_npe}
        \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 CI level (right),
        and with the cc-pVDZ basis set.}
        \label{fig:H8_npe}
\end{figure}

\begin{figure}[h!]
\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 CI level (right),
        and with the cc-pVDZ basis set.}
        \label{fig:H8_distance}
\end{figure}

\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 CI level (right),
	and according to the exact FCI result (black horizontal line),
	for 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 CI level (right),
	and according to the exact FCI result (black horizontal line),
	for the cc-pVDZ basis set.}
        \label{fig:H8_xe}
\end{figure}

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\end{document}
