403 lines
15 KiB
TeX
403 lines
15 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{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{\ce{Computational details}}
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%\label{sec:comp_details}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%\vspace{20cm}
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%x
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%\newpage
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%x
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%\newpage
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%Start.
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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=\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 our proposed hCI (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=\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 our proposed hCI (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=\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 our proposed hCI (green),
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with orbitals optimized at each CI level.
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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=\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 our proposed hCI (green),
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with orbitals optimized at each CI level.
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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{\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 our proposed hybrid hCI (green),
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with Hartree-Fock orbitals,
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and 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=\linewidth]{freq_HF}
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\caption{Nonparallelity error (left), vibrational frequencies (center), and equilibrium geometries (right) for \ce{HF},
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as function of the number of determinants,
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for the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and our proposed hybrid hCI (green),
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with Hartree-Fock orbitals,
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and for the cc-pVDZ (left), cc-pVTZ (center), and cc-pVQZ (right) 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{\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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computed with different CI methods and the cc-pVDZ basis set,
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with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right).}
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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 difference to the FCI results for \ce{HF},
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computed with different CI methods and the cc-pVDZ basis set,
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with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right).}
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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{Nonparallelity error for \ce{HF},
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as function of the computational scaling of excitation-based CI (red) and CIo (green) methods,
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with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right), for 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{Nonparallelity error for \ce{HF},
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as function of the computational scaling of excitation-based CI (red) and CIo (green) methods,
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with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right), for 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 computational scaling of excitation-based CI (red) and CIo (green) methods,
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with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right), 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 computational scaling of excitation-based CI (red) and CIo (green) methods,
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with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right), 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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computed with different CI methods and the cc-pVDZ basis set,
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with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right).}
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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 difference to the FCI results for \ce{F2},
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computed with different CI methods and the cc-pVDZ basis set,
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with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right).}
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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{Nonparallelity error for \ce{F2},
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as function of the computational scaling of excitation-based CI (red) and CIo (green) methods,
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with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right), for 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_xe}
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\caption{Equilibrium bond length of \ce{F2},
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as function of the computational scaling of excitation-based CI (red) and CIo (green) methods,
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with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right), 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 ethylene, as function of the C$=$C distance,
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computed with different CI methods and the cc-pVDZ basis set,
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with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right).}
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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 difference to the FCI results for ethylene, as function of the C$=$C distance,
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computed with different CI methods and the cc-pVDZ basis set,
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with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right).}
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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{Nonparallelity error for ethylene,
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as function of the computational scaling of excitation-based CI (red) and CIo (green) methods,
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with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right), for 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_xe}
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\caption{C$=$C equilibrium bond length of ethylene,
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as function of the computational scaling of excitation-based CI (red) and CIo (green) methods,
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with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right), 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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computed with different CI methods and the cc-pVDZ basis set,
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with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right).}
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\label{fig:N2_pes}
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\end{figure}
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\begin{figure}[h!]
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\includegraphics[width=\linewidth]{N2_pes_error}
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\caption{Energy difference to the FCI results for \ce{N2},
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computed with different CI methods and the cc-pVDZ basis set,
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with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right).}
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\label{fig:N2_pes_error}
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\end{figure}
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\begin{figure}[h!]
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\includegraphics[width=\linewidth]{N2_npe}
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\caption{Nonparallelity error for \ce{N2},
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as function of the computational scaling of excitation-based CI (red) and CIo (green) methods,
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with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right), for 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!]
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\includegraphics[width=\linewidth]{N2_xe}
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\caption{Equilibrium bond length of \ce{N2},
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as function of the computational scaling of excitation-based CI (red) and CIo (green) methods,
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with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right), for the cc-pVDZ basis set.}
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\label{fig:N2_xe}
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\end{figure}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%\section{\ce{H4}}
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%\label{sec:H4}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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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 linear \ce{H4}, as function of the symmetric stretching coordinate,
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computed with different CI methods and the cc-pVDZ basis set,
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with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right).}
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\label{fig:H4_pes}
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\end{figure}
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\begin{figure}[h!]
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\includegraphics[width=\linewidth]{H4_pes_error}
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\caption{Energy difference to the FCI results for linear \ce{H4}, as function of the symmetric stretching coordinate,
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computed with different CI methods and the cc-pVDZ basis set,
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with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right).}
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\label{fig:H4_pes_error}
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\end{figure}
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\begin{figure}[h!]
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\includegraphics[width=\linewidth]{H4_npe}
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\caption{Nonparallelity error for linear \ce{H4},
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as function of the computational scaling of excitation-based CI (red) and CIo (green) methods,
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with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right), for 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!]
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\includegraphics[width=\linewidth]{H4_xe}
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\caption{Equilibrium bond length of linear \ce{H4},
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as function of the computational scaling of excitation-based CI (red) and CIo (green) methods,
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with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right), for the cc-pVDZ basis set.}
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\label{fig:H4_xe}
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\end{figure}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%\section{\ce{H8}}
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%\label{sec:H8}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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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 linear \ce{H8}, as function of the symmetric stretching coordinate,
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computed with different CI methods and the cc-pVDZ basis set,
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with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right).}
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\label{fig:H8_pes}
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\end{figure}
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\begin{figure}[h!]
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\includegraphics[width=\linewidth]{H8_pes_error}
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\caption{Energy difference to the FCI results for linear \ce{H8}, as function of the symmetric stretching coordinate,
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computed with different CI methods and the cc-pVDZ basis set,
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with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right).}
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\label{fig:H8_pes_error}
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\end{figure}
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\begin{figure}[h!]
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\includegraphics[width=\linewidth]{H8_npe}
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\caption{Nonparallelity error for linear \ce{H8},
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as function of the computational scaling of excitation-based CI (red) and CIo (green) methods,
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with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right), for 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!]
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\includegraphics[width=\linewidth]{H8_xe}
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\caption{Equilibrium bond length of linear \ce{H8},
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as function of the computational scaling of excitation-based CI (red) and CIo (green) methods,
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with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right), for the cc-pVDZ basis set.}
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\label{fig:H8_xe}
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\end{figure}
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%End.
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%\bibliography{seniority}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\end{document}
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