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