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@ -1,5 +1,5 @@
\documentclass[aip,jcp,preprint,noshowkeys,superscriptaddress]{revtex4-1} \documentclass[aip,jcp,preprint,noshowkeys,superscriptaddress]{revtex4-1}
\usepackage{graphicx,dcolumn,bm,xcolor,microtype,multirow,amscd,amsmath,amssymb,amsfonts,physics,wrapfig,txfonts} \usepackage{graphicx,dcolumn,bm,xcolor,microtype,multirow,amscd,amsmath,amssymb,amsfonts,physics,wrapfig,txfonts,setspace}
\usepackage{siunitx}[=v2] \usepackage{siunitx}[=v2]
\usepackage[version=4]{mhchem} \usepackage[version=4]{mhchem}
%\usepackage{natbib} %\usepackage{natbib}
@ -46,7 +46,7 @@
\newcommand{\LCPQ}{Laboratoire de Chimie et Physique Quantiques (UMR 5626), Universit\'e de Toulouse, CNRS, UPS, France} \newcommand{\LCPQ}{Laboratoire de Chimie et Physique Quantiques (UMR 5626), Universit\'e de Toulouse, CNRS, UPS, France}
\title{Supporting Information of ``Hierarchy Configuration Interaction: Combining Seniority Number and Excitation Degree''} \title{Supporting Information for ``Hierarchy Configuration Interaction: Combining Seniority Number and Excitation Degree''}
\author{F\'abris Kossoski} \author{F\'abris Kossoski}
\email{fkossoski@irsamc.ups-tlse.fr} \email{fkossoski@irsamc.ups-tlse.fr}
@ -75,16 +75,17 @@
%\label{sec:ethylene} %\label{sec:ethylene}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Equilibrium geometry of ethylene, in atomic units. Equilibrium geometry of ethylene, in atomic units:
\begin{singlespace}
\begin{tabular}{ r r r r } \begin{verbatim}
C & 0.00000000 & 1.26026583 & 0.00000000 \\ C 0.00000000 1.26026583 0.00000000
C & 0.00000000 & -1.26026583 & 0.00000000 \\ C 0.00000000 -1.26026583 0.00000000
H & 0.00000000 & 2.32345976 & 1.74287672 \\ H 0.00000000 2.32345976 1.74287672
H & 0.00000000 & -2.32345976 & 1.74287672 \\ H 0.00000000 -2.32345976 1.74287672
H & 0.00000000 & 2.32345976 & -1.74287672 \\ H 0.00000000 2.32345976 -1.74287672
H & 0.00000000 & -2.32345976 & -1.74287672 \\ H 0.00000000 -2.32345976 -1.74287672
\end{tabular} \end{verbatim}
\end{singlespace}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\section{\ce{Computational details}} %\section{\ce{Computational details}}
@ -197,7 +198,7 @@ The following intervals have been considered for the fitting:
\caption{Potential energy curves for \ce{HF}, \caption{Potential energy curves for \ce{HF},
according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green), 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 $h$), (dashed lines for half-integer $h$),
with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right), with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.} and with the cc-pVDZ basis set.}
\label{fig:HF_pes} \label{fig:HF_pes}
\end{figure} \end{figure}
@ -207,7 +208,7 @@ The following intervals have been considered for the fitting:
\caption{Energy differences between the potential energy curves of Fig.~\ref{fig:HF_pes} and FCI results for \ce{HF}, \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), 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 $h$), (dashed lines for half-integer $h$),
with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right), with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.} and with the cc-pVDZ basis set.}
\label{fig:HF_pes_error} \label{fig:HF_pes_error}
\end{figure} \end{figure}
@ -217,7 +218,7 @@ The following intervals have been considered for the fitting:
\caption{Non-parallelity error for \ce{HF}, corresponding to the potential energy curves of Fig.~\ref{fig:HF_pes}, \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, 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), 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), with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.} and with the cc-pVDZ basis set.}
\label{fig:HF_npe} \label{fig:HF_npe}
\end{figure} \end{figure}
@ -227,7 +228,7 @@ The following intervals have been considered for the fitting:
\caption{Distance error for \ce{HF}, corresponding to the potential energy curves of Fig.~\ref{fig:HF_pes}, \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, 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), 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), with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.} and with the cc-pVDZ basis set.}
\label{fig:HF_distance} \label{fig:HF_distance}
\end{figure} \end{figure}
@ -237,7 +238,7 @@ The following intervals have been considered for the fitting:
\caption{Vibrational frequency of \ce{HF}, \caption{Vibrational frequency of \ce{HF},
as function of the number of determinants, 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), 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), with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.} and with the cc-pVDZ basis set.}
\label{fig:HF_freq} \label{fig:HF_freq}
\end{figure} \end{figure}
@ -247,7 +248,7 @@ The following intervals have been considered for the fitting:
\caption{Equilibrium bond length of \ce{HF}, \caption{Equilibrium bond length of \ce{HF},
as function of the number of determinants, 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), 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), with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.} and with the cc-pVDZ basis set.}
\label{fig:HF_xe} \label{fig:HF_xe}
\end{figure} \end{figure}
@ -262,7 +263,7 @@ The following intervals have been considered for the fitting:
\caption{Potential energy curves for \ce{F2}, \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), 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 $h$), (dashed lines for half-integer $h$),
with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right), with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.} and with the cc-pVDZ basis set.}
\label{fig:F2_pes} \label{fig:F2_pes}
\end{figure} \end{figure}
@ -272,7 +273,7 @@ The following intervals have been considered for the fitting:
\caption{Energy differences between the potential energy curves of Fig.~\ref{fig:F2_pes} and FCI results for \ce{F2}, \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), 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 $h$), (dashed lines for half-integer $h$),
with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right), with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.} and with the cc-pVDZ basis set.}
\label{fig:F2_pes_error} \label{fig:F2_pes_error}
\end{figure} \end{figure}
@ -282,7 +283,7 @@ The following intervals have been considered for the fitting:
\caption{Non-parallelity error for \ce{F2}, corresponding to the potential energy curves of Fig.~\ref{fig:F2_pes}, \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, 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), 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), with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.} and with the cc-pVDZ basis set.}
\label{fig:F2_npe} \label{fig:F2_npe}
\end{figure} \end{figure}
@ -292,7 +293,7 @@ The following intervals have been considered for the fitting:
\caption{Distance error for \ce{F2}, corresponding to the potential energy curves of Fig.~\ref{fig:F2_pes}, \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, 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), 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), with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.} and with the cc-pVDZ basis set.}
\label{fig:F2_distance} \label{fig:F2_distance}
\end{figure} \end{figure}
@ -302,7 +303,7 @@ The following intervals have been considered for the fitting:
\caption{Vibrational frequency of \ce{F2}, \caption{Vibrational frequency of \ce{F2},
as function of the number of determinants, 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), 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), with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.} and with the cc-pVDZ basis set.}
\label{fig:F2_freq} \label{fig:F2_freq}
\end{figure} \end{figure}
@ -312,7 +313,7 @@ The following intervals have been considered for the fitting:
\caption{Equilibrium bond length of \ce{F2}, \caption{Equilibrium bond length of \ce{F2},
as function of the number of determinants, 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), 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), with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.} and with the cc-pVDZ basis set.}
\label{fig:F2_xe} \label{fig:F2_xe}
\end{figure} \end{figure}
@ -327,7 +328,7 @@ The following intervals have been considered for the fitting:
\caption{Potential energy curves for \ce{ethylene}, \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), 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 $h$), (dashed lines for half-integer $h$),
with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right), with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.} and with the cc-pVDZ basis set.}
\label{fig:ethylene_pes} \label{fig:ethylene_pes}
\end{figure} \end{figure}
@ -337,7 +338,7 @@ The following intervals have been considered for the fitting:
\caption{Energy differences between the potential energy curves of Fig.~\ref{fig:ethylene_pes} and FCI results for \ce{ethylene}, \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), 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 $h$), (dashed lines for half-integer $h$),
with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right), with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.} and with the cc-pVDZ basis set.}
\label{fig:ethylene_pes_error} \label{fig:ethylene_pes_error}
\end{figure} \end{figure}
@ -347,7 +348,7 @@ The following intervals have been considered for the fitting:
\caption{Non-parallelity error for \ce{ethylene}, corresponding to the potential energy curves of Fig.~\ref{fig:ethylene_pes}, \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, 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), 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), with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.} and with the cc-pVDZ basis set.}
\label{fig:ethylene_npe} \label{fig:ethylene_npe}
\end{figure} \end{figure}
@ -357,7 +358,7 @@ The following intervals have been considered for the fitting:
\caption{Distance error for \ce{ethylene}, corresponding to the potential energy curves of Fig.~\ref{fig:ethylene_pes}, \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, 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), 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), with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.} and with the cc-pVDZ basis set.}
\label{fig:ethylene_distance} \label{fig:ethylene_distance}
\end{figure} \end{figure}
@ -367,7 +368,7 @@ The following intervals have been considered for the fitting:
\caption{Vibrational frequency of \ce{ethylene}, \caption{Vibrational frequency of \ce{ethylene},
as function of the number of determinants, 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), 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), with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.} and with the cc-pVDZ basis set.}
\label{fig:ethylene_freq} \label{fig:ethylene_freq}
\end{figure} \end{figure}
@ -377,7 +378,7 @@ The following intervals have been considered for the fitting:
\caption{Equilibrium bond length of \ce{ethylene}, \caption{Equilibrium bond length of \ce{ethylene},
as function of the number of determinants, 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), 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), with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.} and with the cc-pVDZ basis set.}
\label{fig:ethylene_xe} \label{fig:ethylene_xe}
\end{figure} \end{figure}
@ -392,7 +393,7 @@ The following intervals have been considered for the fitting:
\caption{Potential energy curves for \ce{N2}, \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), 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 $h$), (dashed lines for half-integer $h$),
with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right), with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.} and with the cc-pVDZ basis set.}
\label{fig:N2_pes} \label{fig:N2_pes}
\end{figure} \end{figure}
@ -402,7 +403,7 @@ The following intervals have been considered for the fitting:
\caption{Energy differences between the potential energy curves of Fig.~\ref{fig:N2_pes} and FCI results for \ce{N2}, \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), 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 $h$), (dashed lines for half-integer $h$),
with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right), with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.} and with the cc-pVDZ basis set.}
\label{fig:N2_pes_error} \label{fig:N2_pes_error}
\end{figure} \end{figure}
@ -412,7 +413,7 @@ The following intervals have been considered for the fitting:
\caption{Non-parallelity error for \ce{N2}, corresponding to the potential energy curves of Fig.~\ref{fig:N2_pes}, \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, 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), 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), with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.} and with the cc-pVDZ basis set.}
\label{fig:N2_npe} \label{fig:N2_npe}
\end{figure} \end{figure}
@ -422,7 +423,7 @@ The following intervals have been considered for the fitting:
\caption{Distance error for \ce{N2}, corresponding to the potential energy curves of Fig.~\ref{fig:N2_pes}, \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, 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), 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), with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.} and with the cc-pVDZ basis set.}
\label{fig:N2_distance} \label{fig:N2_distance}
\end{figure} \end{figure}
@ -432,7 +433,7 @@ The following intervals have been considered for the fitting:
\caption{Vibrational frequency of \ce{N2}, \caption{Vibrational frequency of \ce{N2},
as function of the number of determinants, 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), 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), with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.} and with the cc-pVDZ basis set.}
\label{fig:N2_freq} \label{fig:N2_freq}
\end{figure} \end{figure}
@ -442,7 +443,7 @@ The following intervals have been considered for the fitting:
\caption{Equilibrium bond length of \ce{N2}, \caption{Equilibrium bond length of \ce{N2},
as function of the number of determinants, 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), 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), with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.} and with the cc-pVDZ basis set.}
\label{fig:N2_xe} \label{fig:N2_xe}
\end{figure} \end{figure}
@ -457,7 +458,7 @@ The following intervals have been considered for the fitting:
\caption{Potential energy curves for \ce{H4}, \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), 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 $h$), (dashed lines for half-integer $h$),
with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right), with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.} and with the cc-pVDZ basis set.}
\label{fig:H4_pes} \label{fig:H4_pes}
\end{figure} \end{figure}
@ -467,7 +468,7 @@ The following intervals have been considered for the fitting:
\caption{Energy differences between the potential energy curves of Fig.~\ref{fig:H4_pes} and FCI results for \ce{H4}, \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), 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 $h$), (dashed lines for half-integer $h$),
with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right), with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.} and with the cc-pVDZ basis set.}
\label{fig:H4_pes_error} \label{fig:H4_pes_error}
\end{figure} \end{figure}
@ -477,7 +478,7 @@ The following intervals have been considered for the fitting:
\caption{Non-parallelity error for \ce{H4}, corresponding to the potential energy curves of Fig.~\ref{fig:H4_pes}, \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, 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), 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), with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.} and with the cc-pVDZ basis set.}
\label{fig:H4_npe} \label{fig:H4_npe}
\end{figure} \end{figure}
@ -487,7 +488,7 @@ The following intervals have been considered for the fitting:
\caption{Distance error for \ce{H4}, corresponding to the potential energy curves of Fig.~\ref{fig:H4_pes}, \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, 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), 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), with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.} and with the cc-pVDZ basis set.}
\label{fig:H4_distance} \label{fig:H4_distance}
\end{figure} \end{figure}
@ -497,7 +498,7 @@ The following intervals have been considered for the fitting:
\caption{Force constants for symmetric dissociation of \ce{H4}, \caption{Force constants for symmetric dissociation of \ce{H4},
as function of the number of determinants, 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), 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), with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.} and with the cc-pVDZ basis set.}
\label{fig:H4_force} \label{fig:H4_force}
\end{figure} \end{figure}
@ -507,7 +508,7 @@ The following intervals have been considered for the fitting:
\caption{Equilibrium bond length of \ce{H4}, \caption{Equilibrium bond length of \ce{H4},
as function of the number of determinants, 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), 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), with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.} and with the cc-pVDZ basis set.}
\label{fig:H4_xe} \label{fig:H4_xe}
\end{figure} \end{figure}
@ -522,7 +523,7 @@ The following intervals have been considered for the fitting:
\caption{Potential energy curves for \ce{H8}, \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), 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 $h$), (dashed lines for half-integer $h$),
with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right), with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.} and with the cc-pVDZ basis set.}
\label{fig:H8_pes} \label{fig:H8_pes}
\end{figure} \end{figure}
@ -532,7 +533,7 @@ The following intervals have been considered for the fitting:
\caption{Energy differences between the potential energy curves of Fig.~\ref{fig:H8_pes} and FCI results for \ce{H8}, \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), 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 $h$), (dashed lines for half-integer $h$),
with Hartree-Fock orbitals (left) and orbitals optimized at a given level of CI (right), with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.} and with the cc-pVDZ basis set.}
\label{fig:H8_pes_error} \label{fig:H8_pes_error}
\end{figure} \end{figure}
@ -542,7 +543,7 @@ The following intervals have been considered for the fitting:
\caption{Non-parallelity error for \ce{H8}, corresponding to the potential energy curves of Fig.~\ref{fig:H8_pes}, \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, 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), 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), with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.} and with the cc-pVDZ basis set.}
\label{fig:H8_npe} \label{fig:H8_npe}
\end{figure} \end{figure}
@ -552,7 +553,7 @@ The following intervals have been considered for the fitting:
\caption{Distance error for \ce{H8}, corresponding to the potential energy curves of Fig.~\ref{fig:H8_pes}, \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, 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), 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), with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.} and with the cc-pVDZ basis set.}
\label{fig:H8_distance} \label{fig:H8_distance}
\end{figure} \end{figure}
@ -562,7 +563,7 @@ The following intervals have been considered for the fitting:
\caption{Force constants for symmetric dissociation of \ce{H8}, \caption{Force constants for symmetric dissociation of \ce{H8},
as function of the number of determinants, 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), 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), with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.} and with the cc-pVDZ basis set.}
\label{fig:H8_force} \label{fig:H8_force}
\end{figure} \end{figure}
@ -572,7 +573,7 @@ The following intervals have been considered for the fitting:
\caption{Equilibrium bond length of \ce{H8}, \caption{Equilibrium bond length of \ce{H8},
as function of the number of determinants, 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), 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), with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.} and with the cc-pVDZ basis set.}
\label{fig:H8_xe} \label{fig:H8_xe}
\end{figure} \end{figure}