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\begin { document}
\newcommand { \LCPQ } { Laboratoire de Chimie et Physique Quantiques (UMR 5626), Universit\' e de Toulouse, CNRS, UPS, France}
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\title { Supporting Information of ``Hierarchy Configuration Interaction: Combining Seniority Number and Excitation Degree''}
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\author { F\' abris Kossoski}
\email { fkossoski@irsamc.ups-tlse.fr}
\affiliation { \LCPQ }
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\author { Yann Damour}
\affiliation { \LCPQ }
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\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{\ce{Computational details}}
%\label{sec:comp_details}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Vibrational frequencies and equilibrium geometries were obtained by fitting the computed potential energy curves limited to 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} ).
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\section{Equilibrium geometry of ethylene}
%\label{sec:ethylene}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Equilibrium geometry of ethylene, in atomic units.
\begin { tabular} { r r r r }
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 { tabular}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%\section{oo-CI}
%\label{sec:oo-CI}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin { figure} [h!]
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\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),
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with orbitals optimized at each CI level.
}
\label { fig:plot_ stat_ opt}
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\end { figure}
\begin { figure} [h!]
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\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),
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with orbitals optimized at each CI level.
}
\label { fig:plot_ distance_ opt}
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\end { figure}
\begin { figure} [h!]
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\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),
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with orbitals optimized at each CI level.
}
\label { fig:xe_ opt}
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\end { figure}
\begin { figure} [h!]
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\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),
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with orbitals optimized at each CI level.
}
\label { fig:freq_ opt}
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\end { figure}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\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}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%\section{\ce{HF}, different basis sets}
%\label{sec:HF_basis}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin { figure} [h!]
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\includegraphics [width=\linewidth] { plot_ pes_ HF}
\caption { Potential energy curves (top) and energy differences with respect to FCI (bottom), for dissociation of \ce { HF} ,
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according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
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with Hartree-Fock orbitals,
and for the cc-pVDZ (left), cc-pVTZ (center), and cc-pVQZ (right) basis sets.
}
\label { fig:plot_ pes_ HF}
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\end { figure}
\begin { figure} [h!]
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\includegraphics [width=\linewidth] { freq_ HF}
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\caption { Non-parallelity error (left), vibrational frequencies (center), and equilibrium geometries (right) of \ce { HF} ,
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as function of the number of determinants,
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according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
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with Hartree-Fock orbitals,
and for the cc-pVDZ (left), cc-pVTZ (center), and cc-pVQZ (right) basis sets.}
\label { fig:freq_ HF}
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\end { figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%\section{\ce{HF}}
%\label{sec:HF}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin { figure} [h!]
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\includegraphics [width=\linewidth] { HF_ pes}
\caption { Potential energy curves for \ce { HF} ,
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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.}
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\label { fig:HF_ pes}
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\end { figure}
\begin { figure} [h!]
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\includegraphics [width=\linewidth] { HF_ pes_ error}
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\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.}
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\label { fig:HF_ pes_ error}
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\end { figure}
\begin { figure} [h!]
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\includegraphics [width=\linewidth] { HF_ npe}
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\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.}
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\label { fig:HF_ npe}
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\end { figure}
\begin { figure} [h!]
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\includegraphics [width=\linewidth] { HF_ distance}
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\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.}
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\label { fig:HF_ distance}
\end { figure}
\begin { figure} [h!]
\includegraphics [width=\linewidth] { HF_ freq}
\caption { Vibrational frequency of \ce { HF} ,
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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.}
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\label { fig:HF_ freq}
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\end { figure}
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\begin { figure} [h!]
\includegraphics [width=\linewidth] { HF_ xe}
\caption { Equilibrium bond length of \ce { HF} ,
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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.}
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\label { fig:HF_ xe}
\end { figure}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%\section{\ce{F2}}
%\label{sec:F2}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin { figure} [h!]
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\includegraphics [width=\linewidth] { F2_ pes}
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\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.}
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\label { fig:F2_ pes}
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\end { figure}
\begin { figure} [h!]
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\includegraphics [width=\linewidth] { F2_ pes_ error}
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\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.}
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\label { fig:F2_ pes_ error}
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\end { figure}
\begin { figure} [h!]
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\includegraphics [width=\linewidth] { F2_ npe}
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\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.}
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\label { fig:F2_ npe}
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\end { figure}
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\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}
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\begin { figure} [h!]
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\includegraphics [width=\linewidth] { F2_ xe}
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\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.}
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\label { fig:F2_ xe}
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\end { figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\section{\ce{Ethylene}}
%\label{sec:ethylene}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin { figure} [h!]
\includegraphics [width=\linewidth] { ethylene_ pes}
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\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.}
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\label { fig:ethylene_ pes}
\end { figure}
\begin { figure} [h!]
\includegraphics [width=\linewidth] { ethylene_ pes_ error}
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\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.}
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\label { fig:ethylene_ pes_ error}
\end { figure}
\begin { figure} [h!]
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\includegraphics [width=\linewidth] { ethylene_ npe}
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\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.}
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\label { fig:ethylene_ npe}
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\end { figure}
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\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}
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\begin { figure} [h!]
\includegraphics [width=\linewidth] { ethylene_ xe}
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\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.}
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\label { fig:ethylene_ xe}
\end { figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%\section{\ce{N2}}
%\label{sec:N2}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin { figure} [h!]
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\includegraphics [width=\linewidth] { N2_ pes}
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\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.}
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\label { fig:N2_ pes}
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\end { figure}
\begin { figure} [h!]
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\includegraphics [width=\linewidth] { N2_ pes_ error}
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\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.}
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\label { fig:N2_ pes_ error}
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\end { figure}
\begin { figure} [h!]
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\includegraphics [width=\linewidth] { N2_ npe}
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\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.}
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\label { fig:N2_ npe}
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\end { figure}
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\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 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}
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\begin { figure} [h!]
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\includegraphics [width=\linewidth] { N2_ xe}
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\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.}
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\label { fig:N2_ xe}
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\end { figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%\section{\ce{H4}}
%\label{sec:H4}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin { figure} [h!]
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\includegraphics [width=\linewidth] { H4_ pes}
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\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.}
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\label { fig:H4_ pes}
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\end { figure}
\begin { figure} [h!]
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\includegraphics [width=\linewidth] { H4_ pes_ error}
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\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.}
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\label { fig:H4_ pes_ error}
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\end { figure}
\begin { figure} [h!]
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\includegraphics [width=\linewidth] { H4_ npe}
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\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.}
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\label { fig:H4_ npe}
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\end { figure}
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\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 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}
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\begin { figure} [h!]
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\includegraphics [width=\linewidth] { H4_ xe}
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\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.}
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\label { fig:H4_ xe}
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\end { figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%\section{\ce{H8}}
%\label{sec:H8}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin { figure} [h!]
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\includegraphics [width=\linewidth] { H8_ pes}
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\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.}
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\label { fig:H8_ pes}
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\end { figure}
\begin { figure} [h!]
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\includegraphics [width=\linewidth] { H8_ pes_ error}
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\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.}
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\label { fig:H8_ pes_ error}
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\end { figure}
\begin { figure} [h!]
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\includegraphics [width=\linewidth] { H8_ npe}
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\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.}
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\label { fig:H8_ npe}
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\end { figure}
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\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 level of CI (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 level of CI (right),
and with the cc-pVDZ basis set.}
\label { fig:H8_ force}
\end { figure}
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\begin { figure} [h!]
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\includegraphics [width=\linewidth] { H8_ xe}
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\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.}
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\label { fig:H8_ xe}
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\end { figure}
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%\bibliography{seniority}
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\end { document}