611 lines
28 KiB
TeX
611 lines
28 KiB
TeX
\documentclass[aip,jcp,preprint,noshowkeys,superscriptaddress]{revtex4-1}
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]{hyperref}
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\begin{document}
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\newcommand{\LCPQ}{Laboratoire de Chimie et Physique Quantiques (UMR 5626), Universit\'e de Toulouse, CNRS, UPS, France}
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\title{Supporting Information for ``Hierarchy Configuration Interaction: Combining Seniority Number and Excitation Degree''}
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\author{F\'abris Kossoski}
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\email{fkossoski@irsamc.ups-tlse.fr}
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\affiliation{\LCPQ}
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\author{Yann Damour}
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\affiliation{\LCPQ}
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\author{Pierre-Fran\c{c}ois Loos}
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\email{loos@irsamc.ups-tlse.fr}
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\affiliation{\LCPQ}
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% Abstract
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\begin{abstract}
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%Here comes the abstract.
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%\bigskip
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%\begin{center}
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% \boxed{\includegraphics[width=0.4\linewidth]{TOC}}
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%\end{center}
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%\bigskip
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\end{abstract}
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% Title
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\maketitle
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%\section{Equilibrium geometry of ethylene}
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%\label{sec:ethylene}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Equilibrium geometry of ethylene, in atomic units:
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\begin{singlespace}
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\begin{verbatim}
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C 0.00000000 1.26026583 0.00000000
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C 0.00000000 -1.26026583 0.00000000
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H 0.00000000 2.32345976 1.74287672
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H 0.00000000 -2.32345976 1.74287672
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H 0.00000000 2.32345976 -1.74287672
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H 0.00000000 -2.32345976 -1.74287672
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\end{verbatim}
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\end{singlespace}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%\section{\ce{Computational details}}
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%\label{sec:comp_details}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Vibrational frequencies and equilibrium geometries were obtained by fitting the computed potential energy curves at the Franck-Condon region with a Morse potential.
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The following intervals have been considered for the fitting:
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\SI{0.8}{\angstrom} to \SI{1.3}{\angstrom} (\ce{HF}),
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\SI{1.25}{\angstrom} to \SI{1.65}{\angstrom} (\ce{F2}),
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\SI{2.2}{\bohr} to \SI{2.9}{\bohr} (ethylene),
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\SI{0.95}{\angstrom} to \SI{1.3}{\angstrom} (\ce{N2}),
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\SI{1.45}{\bohr} to \SI{1.95}{\bohr} (\ce{H4}),
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\SI{1.6}{\bohr} to \SI{2.05}{\bohr} (\ce{H8}).
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%\section{\ce{HF}, different basis sets}
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%\label{sec:HF_basis}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{figure}[h!]
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\includegraphics[width=\linewidth]{plot_pes_HF}
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\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,
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for the cc-pVDZ (left), cc-pVTZ (center), and cc-pVQZ (right) basis sets.
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}
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\label{fig:plot_pes_HF}
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\end{figure}
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\begin{figure}[h!]
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\includegraphics[width=0.8\linewidth]{plot_stat_HF}
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\caption{Non-parallelity error (left) and distance error (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,
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for the cc-pVDZ (top), cc-pVTZ (center), and cc-pVQZ (bottom) basis sets.}
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\label{fig:plot_stat_HF}
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\end{figure}
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\begin{figure}[h!]
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\includegraphics[width=0.8\linewidth]{freq_HF}
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\caption{Vibrational frequencies (left) 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,
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and according to the exact FCI result (black horizontal line),
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for the cc-pVDZ (top), cc-pVTZ (center), and cc-pVQZ (bottom) basis sets.}
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\label{fig:freq_HF}
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\end{figure}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%\section{Distance error}
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%\label{sec:distance}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{figure}[h!]
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\includegraphics[width=0.8\linewidth]{plot_distance}
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\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 Hartree-Fock orbitals.
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}
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\label{fig:plot_distance}
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\end{figure}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%\section{oo-CI}
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%\label{sec:oo-CI}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{figure}[h!]
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\includegraphics[width=0.8\linewidth]{plot_stat_opt}
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\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.
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}
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\label{fig:plot_stat_opt}
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\end{figure}
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\begin{figure}[h!]
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\includegraphics[width=0.8\linewidth]{plot_distance_opt}
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\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.
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}
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\label{fig:plot_distance_opt}
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\end{figure}
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\begin{figure}[h!]
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\includegraphics[width=0.8\linewidth]{xe_opt}
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\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,
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and according to the exact FCI result (black horizontal line).
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}
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\label{fig:xe_opt}
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\end{figure}
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\begin{figure}[h!]
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\includegraphics[width=0.8\linewidth]{freq_opt}
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\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,
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and according to the exact FCI result (black horizontal line).
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}
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\label{fig:freq_opt}
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\end{figure}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%\section{oo-CIS
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%\label{sec:oo-CIS}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{figure}[h!]
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\includegraphics[width=0.8\linewidth]{plot_pes}
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\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).
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}
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\label{fig:plot_pes}
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\end{figure}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%\section{\ce{HF}}
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%\label{sec:HF}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{figure}[h!]
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\includegraphics[width=\linewidth]{HF_pes}
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\caption{Potential energy curves for \ce{HF},
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according to RHF, FCI, and the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
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(dashed lines for half-integer $h$),
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with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
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and with the cc-pVDZ basis set.}
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\label{fig:HF_pes}
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\end{figure}
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\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},
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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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(dashed lines for half-integer $h$),
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with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
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and with the cc-pVDZ basis set.}
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\label{fig:HF_pes_error}
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\end{figure}
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\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},
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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 (left) and orbitals optimized at a given CI level (right),
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and with the cc-pVDZ basis set.}
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\label{fig:HF_npe}
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\end{figure}
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\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},
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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 (left) and orbitals optimized at a given CI level (right),
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and with the cc-pVDZ basis set.}
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\label{fig:HF_distance}
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\end{figure}
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\begin{figure}[h!]
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\includegraphics[width=\linewidth]{HF_freq}
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\caption{Vibrational frequency 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 (left) and orbitals optimized at a given CI level (right),
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and according to the exact FCI result (black horizontal line),
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for 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!]
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\includegraphics[width=\linewidth]{HF_xe}
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\caption{Equilibrium bond length 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 (left) and orbitals optimized at a given CI level (right),
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and according to the exact FCI result (black horizontal line),
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for the cc-pVDZ basis set.}
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\label{fig:HF_xe}
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\end{figure}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%\section{\ce{F2}}
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%\label{sec:F2}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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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},
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according to RHF, FCI, and the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
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(dashed lines for half-integer $h$),
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with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
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and with the cc-pVDZ basis set.}
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\label{fig:F2_pes}
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\end{figure}
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\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},
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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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(dashed lines for half-integer $h$),
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with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
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and with the cc-pVDZ basis set.}
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\label{fig:F2_pes_error}
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\end{figure}
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\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},
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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 (left) and orbitals optimized at a given CI level (right),
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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!]
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\includegraphics[width=\linewidth]{F2_distance}
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\caption{Distance error for \ce{F2}, corresponding to the potential energy curves of Fig.~\ref{fig:F2_pes},
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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 (left) and orbitals optimized at a given CI level (right),
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and with the cc-pVDZ basis set.}
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\label{fig:F2_distance}
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\end{figure}
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\begin{figure}[h!]
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\includegraphics[width=\linewidth]{F2_freq}
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\caption{Vibrational frequency of \ce{F2},
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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 (left) and orbitals optimized at a given CI level (right),
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and according to the exact FCI result (black horizontal line),
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for the cc-pVDZ basis set.}
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\label{fig:F2_freq}
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\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},
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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 (left) and orbitals optimized at a given CI level (right),
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and according to the exact FCI result (black horizontal line),
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for the cc-pVDZ basis set.}
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\label{fig:F2_xe}
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\end{figure}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%\section{\ce{Ethylene}}
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%\label{sec:ethylene}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{figure}[h!]
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\includegraphics[width=\linewidth]{ethylene_pes}
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\caption{Potential energy curves for \ce{ethylene},
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according to RHF, FCI, and the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
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(dashed lines for half-integer $h$),
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with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
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and with the cc-pVDZ basis set.}
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\label{fig:ethylene_pes}
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\end{figure}
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\begin{figure}[h!]
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\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},
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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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(dashed lines for half-integer $h$),
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with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
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and with the cc-pVDZ basis set.}
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\label{fig:ethylene_pes_error}
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\end{figure}
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\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},
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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 (left) and orbitals optimized at a given CI level (right),
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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!]
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\includegraphics[width=\linewidth]{ethylene_distance}
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\caption{Distance error for \ce{ethylene}, corresponding to the potential energy curves of Fig.~\ref{fig:ethylene_pes},
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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 (left) and orbitals optimized at a given CI level (right),
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and with the cc-pVDZ basis set.}
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\label{fig:ethylene_distance}
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\end{figure}
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\begin{figure}[h!]
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\includegraphics[width=\linewidth]{ethylene_freq}
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\caption{Vibrational frequency of \ce{ethylene},
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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 (left) and orbitals optimized at a given CI level (right),
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and according to the exact FCI result (black horizontal line),
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for the cc-pVDZ basis set.}
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\label{fig:ethylene_freq}
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\end{figure}
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\begin{figure}[h!]
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\includegraphics[width=\linewidth]{ethylene_xe}
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\caption{Equilibrium bond length of \ce{ethylene},
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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 (left) and orbitals optimized at a given CI level (right),
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and according to the exact FCI result (black horizontal line),
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for the cc-pVDZ basis set.}
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\label{fig:ethylene_xe}
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\end{figure}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%\section{\ce{N2}}
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%\label{sec:N2}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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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},
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according to RHF, FCI, and the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
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(dashed lines for half-integer $h$),
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with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
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and with the cc-pVDZ basis set.}
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|
\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}
|
|
|
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
%\bibliography{seniority}
|
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
|
\end{document}
|