diff --git a/H8_cc-pvdz/pes_CISDTQ.dat b/H8_cc-pvdz/pes_CISDTQ.dat index 81d787a..e09b963 100644 --- a/H8_cc-pvdz/pes_CISDTQ.dat +++ b/H8_cc-pvdz/pes_CISDTQ.dat @@ -58,7 +58,7 @@ 6.1 -3.94150395 6.2 -3.94193508 6.3 -3.94234878 -6.4 -3.93442801 +6.4 -3.94275670 6.5 -3.94315183 6.6 -3.94353415 6.7 -3.94390984 diff --git a/Manuscript/F2_distance.pdf b/Manuscript/F2_distance.pdf new file mode 100644 index 0000000..cf3f3ba Binary files /dev/null and b/Manuscript/F2_distance.pdf differ diff --git a/Manuscript/F2_freq.pdf b/Manuscript/F2_freq.pdf new file mode 100644 index 0000000..3ccf2fe Binary files /dev/null and b/Manuscript/F2_freq.pdf differ diff --git a/Manuscript/F2_npe.pdf b/Manuscript/F2_npe.pdf new file mode 100644 index 0000000..ae918b4 Binary files /dev/null and b/Manuscript/F2_npe.pdf differ diff --git a/Manuscript/F2_pes.pdf b/Manuscript/F2_pes.pdf new file mode 100644 index 0000000..67dc141 Binary files /dev/null and b/Manuscript/F2_pes.pdf differ diff --git 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\newcommand{\QP}{\textsc{quantum package}} -\newcommand{\hI}{\Hat{1}} -\newcommand{\hT}{\Hat{T}} -\newcommand{\hH}{\Hat{H}} -\newcommand{\bH}{\Bar{H}} -\newcommand{\ERI}[2]{v_{#1}^{#2}} - \newcommand{\EHF}{E_\text{HF}} \newcommand{\EDOCI}{E_\text{DOCI}} \newcommand{\EFCI}{E_\text{FCI}} -\newcommand{\ECC}{E_\text{CC}} -\newcommand{\EVCC}{E_\text{VCC}} -\newcommand{\EpCCD}{E_\text{pCCD}} - -\newcommand{\si}{\sigma} \renewcommand{\thesection}{S\arabic{section}} \renewcommand{\thetable}{S\arabic{table}} @@ -89,45 +78,55 @@ %x %\newpage -%Start. - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %\section{oo-CI} %\label{sec:oo-CI} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{figure}[h!] -\includegraphics[width=\linewidth]{plot_stat_opt} - \caption{Non-parallelity errors as function of the number of determinants, for the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and our proposed hCI (green), +\includegraphics[width=0.8\linewidth]{plot_stat_opt} + \caption{Non-parallelity errors as function of the number of determinants, for the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green), with orbitals optimized at each CI level. } \label{fig:plot_stat_opt} \end{figure} \begin{figure}[h!] -\includegraphics[width=\linewidth]{plot_distance_opt} - \caption{Distance errors as function of the number of determinants, for the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and our proposed hCI (green), +\includegraphics[width=0.8\linewidth]{plot_distance_opt} + \caption{Distance errors as function of the number of determinants, for the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green), with orbitals optimized at each CI level. } \label{fig:plot_distance_opt} \end{figure} \begin{figure}[h!] - \includegraphics[width=\linewidth]{xe_opt} - \caption{Equilibrium geometries as function of the number of determinants, for the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and our proposed hCI (green), + \includegraphics[width=0.8\linewidth]{xe_opt} + \caption{Equilibrium geometries as function of the number of determinants, for the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green), with orbitals optimized at each CI level. } \label{fig:xe_opt} \end{figure} \begin{figure}[h!] -\includegraphics[width=\linewidth]{freq_opt} - \caption{Vibrational frequencies (or force constants) as function of the number of determinants, for the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and our proposed hCI (green), +\includegraphics[width=0.8\linewidth]{freq_opt} + \caption{Vibrational frequencies (or force constants) as function of the number of determinants, for the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green), with orbitals optimized at each CI level. } \label{fig:freq_opt} \end{figure} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%\section{oo-CIS +%\label{sec:oo-CIS} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{figure}[h!] +\includegraphics[width=0.8\linewidth]{plot_pes} + \caption{Potential energy curves for dissociation of six molecular systems (see main text for details), according to RHF (gray), oo-CIS (red), and FCI (black) calculations. + } + \label{fig:plot_pes} +\end{figure} + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %\section{\ce{HF}, different basis sets} %\label{sec:HF_basis} @@ -136,7 +135,7 @@ \begin{figure}[h!] \includegraphics[width=\linewidth]{plot_pes_HF} \caption{Potential energy curves (top) and energy differences with respect to FCI (bottom), for dissociation of \ce{HF}, - according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and our proposed hybrid hCI (green), + according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green), with Hartree-Fock orbitals, and for the cc-pVDZ (left), cc-pVTZ (center), and cc-pVQZ (right) basis sets. } @@ -145,9 +144,9 @@ \begin{figure}[h!] \includegraphics[width=\linewidth]{freq_HF} - \caption{Nonparallelity error (left), vibrational frequencies (center), and equilibrium geometries (right) for \ce{HF}, + \caption{Non-parallelity error (left), vibrational frequencies (center), and equilibrium geometries (right) of \ce{HF}, as function of the number of determinants, - for the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and our proposed hybrid hCI (green), + according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green), with Hartree-Fock orbitals, and for the cc-pVDZ (left), cc-pVTZ (center), and cc-pVQZ (right) basis sets.} \label{fig:freq_HF} @@ -161,48 +160,60 @@ \begin{figure}[h!] \includegraphics[width=\linewidth]{HF_pes} \caption{Potential energy curves for \ce{HF}, - computed with different CI methods and the cc-pVDZ basis set, - with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right).} + according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green), + (dashed lines for half-integer $h$), + with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right), + and with the cc-pVDZ basis set.} \label{fig:HF_pes} \end{figure} \begin{figure}[h!] \includegraphics[width=\linewidth]{HF_pes_error} - \caption{Energy difference to the FCI results for \ce{HF}, - computed with different CI methods and the cc-pVDZ basis set, - with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right).} + \caption{Energy differences between the potential energy curves of Fig.~\ref{fig:HF_pes} and FCI results for \ce{HF}, + according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green), + (dashed lines for half-integer $h$), + with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right), + and with the cc-pVDZ basis set.} \label{fig:HF_pes_error} \end{figure} \begin{figure}[h!] \includegraphics[width=\linewidth]{HF_npe} - \caption{Nonparallelity error for \ce{HF}, - as function of the computational scaling of excitation-based CI (red) and CIo (green) methods, - with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right), for the cc-pVDZ basis set.} + \caption{Non-parallelity error for \ce{HF}, corresponding to the potential energy curves of Fig.~\ref{fig:HF_pes}, + as function of the number of determinants, + according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green), + with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right), + and with the cc-pVDZ basis set.} \label{fig:HF_npe} \end{figure} \begin{figure}[h!] \includegraphics[width=\linewidth]{HF_distance} - \caption{Nonparallelity error for \ce{HF}, - as function of the computational scaling of excitation-based CI (red) and CIo (green) methods, - with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right), for the cc-pVDZ basis set.} + \caption{Distance error for \ce{HF}, corresponding to the potential energy curves of Fig.~\ref{fig:HF_pes}, + as function of the number of determinants, + according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green), + with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right), + and with the cc-pVDZ basis set.} \label{fig:HF_distance} \end{figure} \begin{figure}[h!] \includegraphics[width=\linewidth]{HF_freq} \caption{Vibrational frequency of \ce{HF}, - as function of the computational scaling of excitation-based CI (red) and CIo (green) methods, - with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right), for the cc-pVDZ basis set.} + as function of the number of determinants, + according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green), + with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right), + and with the cc-pVDZ basis set.} \label{fig:HF_freq} \end{figure} \begin{figure}[h!] \includegraphics[width=\linewidth]{HF_xe} \caption{Equilibrium bond length of \ce{HF}, - as function of the computational scaling of excitation-based CI (red) and CIo (green) methods, - with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right), for the cc-pVDZ basis set.} + as function of the number of determinants, + according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green), + with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right), + and with the cc-pVDZ basis set.} \label{fig:HF_xe} \end{figure} @@ -213,33 +224,61 @@ \begin{figure}[h!] \includegraphics[width=\linewidth]{F2_pes} - \caption{Potential energy curves for \ce{F2}, - computed with different CI methods and the cc-pVDZ basis set, - with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right).} + \caption{Potential energy curves for \ce{F2}, + according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green), + (dashed lines for half-integer $h$), + with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right), + and with the cc-pVDZ basis set.} \label{fig:F2_pes} \end{figure} \begin{figure}[h!] \includegraphics[width=\linewidth]{F2_pes_error} - \caption{Energy difference to the FCI results for \ce{F2}, - computed with different CI methods and the cc-pVDZ basis set, - with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right).} + \caption{Energy differences between the potential energy curves of Fig.~\ref{fig:F2_pes} and FCI results for \ce{F2}, + according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green), + (dashed lines for half-integer $h$), + with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right), + and with the cc-pVDZ basis set.} \label{fig:F2_pes_error} \end{figure} \begin{figure}[h!] \includegraphics[width=\linewidth]{F2_npe} - \caption{Nonparallelity error for \ce{F2}, - as function of the computational scaling of excitation-based CI (red) and CIo (green) methods, - with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right), for the cc-pVDZ basis set.} + \caption{Non-parallelity error for \ce{F2}, corresponding to the potential energy curves of Fig.~\ref{fig:F2_pes}, + as function of the number of determinants, + according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green), + with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right), + and with the cc-pVDZ basis set.} \label{fig:F2_npe} \end{figure} +\begin{figure}[h!] +\includegraphics[width=\linewidth]{F2_distance} + \caption{Distance error for \ce{F2}, corresponding to the potential energy curves of Fig.~\ref{fig:F2_pes}, + as function of the number of determinants, + according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green), + with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right), + and with the cc-pVDZ basis set.} + \label{fig:F2_distance} +\end{figure} + +\begin{figure}[h!] +\includegraphics[width=\linewidth]{F2_freq} + \caption{Vibrational frequency of \ce{F2}, + as function of the number of determinants, + according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green), + with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right), + and with the cc-pVDZ basis set.} + \label{fig:F2_freq} +\end{figure} + \begin{figure}[h!] \includegraphics[width=\linewidth]{F2_xe} - \caption{Equilibrium bond length of \ce{F2}, - as function of the computational scaling of excitation-based CI (red) and CIo (green) methods, - with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right), for the cc-pVDZ basis set.} + \caption{Equilibrium bond length of \ce{F2}, + as function of the number of determinants, + according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green), + with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right), + and with the cc-pVDZ basis set.} \label{fig:F2_xe} \end{figure} @@ -250,33 +289,61 @@ \begin{figure}[h!] \includegraphics[width=\linewidth]{ethylene_pes} - \caption{Potential energy curves for ethylene, as function of the C$=$C distance, - computed with different CI methods and the cc-pVDZ basis set, - with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right).} + \caption{Potential energy curves for \ce{ethylene}, + according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green), + (dashed lines for half-integer $h$), + with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right), + and with the cc-pVDZ basis set.} \label{fig:ethylene_pes} \end{figure} \begin{figure}[h!] \includegraphics[width=\linewidth]{ethylene_pes_error} - \caption{Energy difference to the FCI results for ethylene, as function of the C$=$C distance, - computed with different CI methods and the cc-pVDZ basis set, - with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right).} + \caption{Energy differences between the potential energy curves of Fig.~\ref{fig:ethylene_pes} and FCI results for \ce{ethylene}, + according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green), + (dashed lines for half-integer $h$), + with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right), + and with the cc-pVDZ basis set.} \label{fig:ethylene_pes_error} \end{figure} \begin{figure}[h!] \includegraphics[width=\linewidth]{ethylene_npe} - \caption{Nonparallelity error for ethylene, - as function of the computational scaling of excitation-based CI (red) and CIo (green) methods, - with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right), for the cc-pVDZ basis set.} + \caption{Non-parallelity error for \ce{ethylene}, corresponding to the potential energy curves of Fig.~\ref{fig:ethylene_pes}, + as function of the number of determinants, + according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green), + with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right), + and with the cc-pVDZ basis set.} \label{fig:ethylene_npe} \end{figure} +\begin{figure}[h!] +\includegraphics[width=\linewidth]{ethylene_distance} + \caption{Distance error for \ce{ethylene}, corresponding to the potential energy curves of Fig.~\ref{fig:ethylene_pes}, + as function of the number of determinants, + according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green), + with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right), + and with the cc-pVDZ basis set.} + \label{fig:ethylene_distance} +\end{figure} + +\begin{figure}[h!] +\includegraphics[width=\linewidth]{ethylene_freq} + \caption{Vibrational frequency of \ce{ethylene}, + as function of the number of determinants, + according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green), + with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right), + and with the cc-pVDZ basis set.} + \label{fig:ethylene_freq} +\end{figure} + \begin{figure}[h!] \includegraphics[width=\linewidth]{ethylene_xe} - \caption{C$=$C equilibrium bond length of ethylene, - as function of the computational scaling of excitation-based CI (red) and CIo (green) methods, - with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right), for the cc-pVDZ basis set.} + \caption{Equilibrium bond length of \ce{ethylene}, + as function of the number of determinants, + according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green), + with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right), + and with the cc-pVDZ basis set.} \label{fig:ethylene_xe} \end{figure} @@ -287,36 +354,63 @@ \begin{figure}[h!] \includegraphics[width=\linewidth]{N2_pes} - \caption{Potential energy curves for \ce{N2}, - computed with different CI methods and the cc-pVDZ basis set, - with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right).} + \caption{Potential energy curves for \ce{N2}, + according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green), + (dashed lines for half-integer $h$), + with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right), + and with the cc-pVDZ basis set.} \label{fig:N2_pes} \end{figure} \begin{figure}[h!] \includegraphics[width=\linewidth]{N2_pes_error} - \caption{Energy difference to the FCI results for \ce{N2}, - computed with different CI methods and the cc-pVDZ basis set, - with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right).} + \caption{Energy differences between the potential energy curves of Fig.~\ref{fig:N2_pes} and FCI results for \ce{N2}, + according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green), + (dashed lines for half-integer $h$), + with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right), + and with the cc-pVDZ basis set.} \label{fig:N2_pes_error} \end{figure} \begin{figure}[h!] \includegraphics[width=\linewidth]{N2_npe} - \caption{Nonparallelity error for \ce{N2}, - as function of the computational scaling of excitation-based CI (red) and CIo (green) methods, - with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right), for the cc-pVDZ basis set.} + \caption{Non-parallelity error for \ce{N2}, corresponding to the potential energy curves of Fig.~\ref{fig:N2_pes}, + as function of the number of determinants, + according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green), + with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right), + and with the cc-pVDZ basis set.} \label{fig:N2_npe} \end{figure} \begin{figure}[h!] -\includegraphics[width=\linewidth]{N2_xe} - \caption{Equilibrium bond length of \ce{N2}, - as function of the computational scaling of excitation-based CI (red) and CIo (green) methods, - with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right), for the cc-pVDZ basis set.} - \label{fig:N2_xe} +\includegraphics[width=\linewidth]{N2_distance} + \caption{Distance error for \ce{N2}, corresponding to the potential energy curves of Fig.~\ref{fig:N2_pes}, + as function of the number of determinants, + according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green), + with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right), + and with the cc-pVDZ basis set.} + \label{fig:N2_distance} \end{figure} +\begin{figure}[h!] +\includegraphics[width=\linewidth]{N2_freq} + \caption{Vibrational frequency of \ce{N2}, + as function of the number of determinants, + according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green), + with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right), + and with the cc-pVDZ basis set.} + \label{fig:N2_freq} +\end{figure} + +\begin{figure}[h!] +\includegraphics[width=\linewidth]{N2_xe} + \caption{Equilibrium bond length of \ce{N2}, + as function of the number of determinants, + according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green), + with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right), + and with the cc-pVDZ basis set.} + \label{fig:N2_xe} +\end{figure} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %\section{\ce{H4}} @@ -325,36 +419,63 @@ \begin{figure}[h!] \includegraphics[width=\linewidth]{H4_pes} - \caption{Potential energy curves for linear \ce{H4}, as function of the symmetric stretching coordinate, - computed with different CI methods and the cc-pVDZ basis set, - with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right).} + \caption{Potential energy curves for \ce{H4}, + according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green), + (dashed lines for half-integer $h$), + with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right), + and with the cc-pVDZ basis set.} \label{fig:H4_pes} \end{figure} \begin{figure}[h!] \includegraphics[width=\linewidth]{H4_pes_error} - \caption{Energy difference to the FCI results for linear \ce{H4}, as function of the symmetric stretching coordinate, - computed with different CI methods and the cc-pVDZ basis set, - with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right).} + \caption{Energy differences between the potential energy curves of Fig.~\ref{fig:H4_pes} and FCI results for \ce{H4}, + according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green), + (dashed lines for half-integer $h$), + with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right), + and with the cc-pVDZ basis set.} \label{fig:H4_pes_error} \end{figure} \begin{figure}[h!] \includegraphics[width=\linewidth]{H4_npe} - \caption{Nonparallelity error for linear \ce{H4}, - as function of the computational scaling of excitation-based CI (red) and CIo (green) methods, - with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right), for the cc-pVDZ basis set.} + \caption{Non-parallelity error for \ce{H4}, corresponding to the potential energy curves of Fig.~\ref{fig:H4_pes}, + as function of the number of determinants, + according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green), + with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right), + and with the cc-pVDZ basis set.} \label{fig:H4_npe} \end{figure} \begin{figure}[h!] -\includegraphics[width=\linewidth]{H4_xe} - \caption{Equilibrium bond length of linear \ce{H4}, - as function of the computational scaling of excitation-based CI (red) and CIo (green) methods, - with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right), for the cc-pVDZ basis set.} - \label{fig:H4_xe} +\includegraphics[width=\linewidth]{H4_distance} + \caption{Distance error for \ce{H4}, corresponding to the potential energy curves of Fig.~\ref{fig:H4_pes}, + as function of the number of determinants, + according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green), + with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right), + and with the cc-pVDZ basis set.} + \label{fig:H4_distance} \end{figure} +\begin{figure}[h!] +\includegraphics[width=\linewidth]{H4_force} + \caption{Force constants for symmetric dissociation of \ce{H4}, + as function of the number of determinants, + according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green), + with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right), + and with the cc-pVDZ basis set.} + \label{fig:H4_force} +\end{figure} + +\begin{figure}[h!] +\includegraphics[width=\linewidth]{H4_xe} + \caption{Equilibrium bond length of \ce{H4}, + as function of the number of determinants, + according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green), + with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right), + and with the cc-pVDZ basis set.} + \label{fig:H4_xe} +\end{figure} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %\section{\ce{H8}} @@ -363,37 +484,63 @@ \begin{figure}[h!] \includegraphics[width=\linewidth]{H8_pes} - \caption{Potential energy curves for linear \ce{H8}, as function of the symmetric stretching coordinate, - computed with different CI methods and the cc-pVDZ basis set, - with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right).} + \caption{Potential energy curves for \ce{H8}, + according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green), + (dashed lines for half-integer $h$), + with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right), + and with the cc-pVDZ basis set.} \label{fig:H8_pes} \end{figure} \begin{figure}[h!] \includegraphics[width=\linewidth]{H8_pes_error} - \caption{Energy difference to the FCI results for linear \ce{H8}, as function of the symmetric stretching coordinate, - computed with different CI methods and the cc-pVDZ basis set, - with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right).} + \caption{Energy differences between the potential energy curves of Fig.~\ref{fig:H8_pes} and FCI results for \ce{H8}, + according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green), + (dashed lines for half-integer $h$), + with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right), + and with the cc-pVDZ basis set.} \label{fig:H8_pes_error} \end{figure} \begin{figure}[h!] \includegraphics[width=\linewidth]{H8_npe} - \caption{Nonparallelity error for linear \ce{H8}, - as function of the computational scaling of excitation-based CI (red) and CIo (green) methods, - with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right), for the cc-pVDZ basis set.} + \caption{Non-parallelity error for \ce{H8}, corresponding to the potential energy curves of Fig.~\ref{fig:H8_pes}, + as function of the number of determinants, + according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green), + with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right), + and with the cc-pVDZ basis set.} \label{fig:H8_npe} \end{figure} \begin{figure}[h!] -\includegraphics[width=\linewidth]{H8_xe} - \caption{Equilibrium bond length of linear \ce{H8}, - as function of the computational scaling of excitation-based CI (red) and CIo (green) methods, - with Hartree-Fock orbitals (left) and orbitals optimized for a given CI method (right), for the cc-pVDZ basis set.} - \label{fig:H8_xe} +\includegraphics[width=\linewidth]{H8_distance} + \caption{Distance error for \ce{H8}, corresponding to the potential energy curves of Fig.~\ref{fig:H8_pes}, + as function of the number of determinants, + according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green), + with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right), + and with the cc-pVDZ basis set.} + \label{fig:H8_distance} \end{figure} -%End. +\begin{figure}[h!] +\includegraphics[width=\linewidth]{H8_force} + \caption{Force constants for symmetric dissociation of \ce{H8}, + as function of the number of determinants, + according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green), + with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right), + and with the cc-pVDZ basis set.} + \label{fig:H8_force} +\end{figure} + +\begin{figure}[h!] +\includegraphics[width=\linewidth]{H8_xe} + \caption{Equilibrium bond length of \ce{H8}, + as function of the number of determinants, + according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green), + with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right), + and with the cc-pVDZ basis set.} + \label{fig:H8_xe} +\end{figure} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %\bibliography{seniority} diff --git a/Manuscript/xe.pdf b/Manuscript/xe.pdf index 5dc9428..9cf0919 100644 Binary files a/Manuscript/xe.pdf and b/Manuscript/xe.pdf differ diff --git a/plot_all/xe.gnu b/plot_all/xe.gnu index b6258f0..269d820 100644 --- a/plot_all/xe.gnu +++ b/plot_all/xe.gnu @@ -51,8 +51,8 @@ set label 11 'HF' at screen 0.34,0.94 tc ls 2 font 'Helvet set label 12 'F_2' at screen 0.79,0.94 tc ls 2 font 'Helvetica,26' set label 13 'ethylene' at screen 0.34,0.63 tc ls 2 font 'Helvetica,26' set label 14 'N_2' at screen 0.79,0.63 tc ls 2 font 'Helvetica,26' -set label 15 'H_4' at screen 0.34,0.315 tc ls 2 font 'Helvetica,26' -set label 16 'H_8' at screen 0.79,0.315 tc ls 2 font 'Helvetica,26' +set label 15 'H_4' at screen 0.34,0.310 tc ls 2 font 'Helvetica,26' +set label 16 'H_8' at screen 0.79,0.310 tc ls 2 font 'Helvetica,26' set format y "%.1f" diff --git a/plot_all/xe_opt.gnu b/plot_all/xe_opt.gnu index 4d3ae19..e07cf53 100644 --- a/plot_all/xe_opt.gnu +++ b/plot_all/xe_opt.gnu @@ -51,8 +51,8 @@ set label 11 'HF' at screen 0.34,0.94 tc ls 2 font 'Helvet set label 12 'F_2' at screen 0.79,0.94 tc ls 2 font 'Helvetica,26' set label 13 'ethylene' at screen 0.34,0.63 tc ls 2 font 'Helvetica,26' set label 14 'N_2' at screen 0.79,0.63 tc ls 2 font 'Helvetica,26' -set label 15 'H_4' at screen 0.34,0.315 tc ls 2 font 'Helvetica,26' -set label 16 'H_8' at screen 0.79,0.315 tc ls 2 font 'Helvetica,26' +set label 15 'H_4' at screen 0.34,0.310 tc ls 2 font 'Helvetica,26' +set label 16 'H_8' at screen 0.79,0.310 tc ls 2 font 'Helvetica,26' set format y "%.1f"