loos/seniority
2
0
Fork 0
Code Issues Pull Requests Projects Releases Wiki Activity
6d6222fc5f
seniority/Manuscript/sup.tex
kossoski 6d6222fc5f one fig in, two figs out
2022-03-10 16:02:30 +01:00

637 lines
29 KiB
TeX
Raw Blame History

\documentclass[aip,jcp,preprint,noshowkeys,superscriptaddress]{revtex4-1}
\usepackage{graphicx,dcolumn,bm,xcolor,microtype,multirow,amscd,amsmath,amssymb,amsfonts,physics,wrapfig,txfonts,setspace}
\usepackage{siunitx}[=v2]
\usepackage[version=4]{mhchem}
%\usepackage{natbib}
%\bibliographystyle{achemso}
\maxdeadcycles=200
\newcommand{\ie}{\textit{i.e.}}
\newcommand{\eg}{\textit{e.g.}}
\newcommand{\alert}[1]{\textcolor{black}{#1}}
\usepackage[normalem]{ulem}
\newcommand{\titou}[1]{\textcolor{red}{#1}}
\newcommand{\trashPFL}[1]{\textcolor{red}{\sout{#1}}}
\newcommand{\PFL}[1]{\titou{(\underline{\bf PFL}: #1)}}
\newcommand{\toto}[1]{\textcolor{green}{#1}}
\newcommand{\trashAS}[1]{\textcolor{green}{\sout{#1}}}
\newcommand{\AS}[1]{\toto{(\underline{\bf AS}: #1)}}
\newcommand{\ant}[1]{\textcolor{orange}{#1}}
\newcommand{\SupInf}{\textcolor{blue}{Supporting Information}}
\newcommand{\mc}{\multicolumn}
\newcommand{\fnm}{\footnotemark}
\newcommand{\fnt}{\footnotetext}
\newcommand{\tabc}[1]{\multicolumn{1}{c}{#1}}
\newcommand{\QP}{\textsc{quantum package}}
\newcommand{\EHF}{E_\text{HF}}
\newcommand{\EDOCI}{E_\text{DOCI}}
\newcommand{\EFCI}{E_\text{FCI}}
\renewcommand{\thesection}{S\arabic{section}}
\renewcommand{\thetable}{S\arabic{table}}
\renewcommand{\thefigure}{S\arabic{figure}}
\renewcommand{\theequation}{S\arabic{equation}}
\usepackage[
colorlinks=true,
citecolor=blue,
breaklinks=true
]{hyperref}
\urlstyle{same}
\begin{document}
\newcommand{\LCPQ}{Laboratoire de Chimie et Physique Quantiques (UMR 5626), Universit\'e de Toulouse, CNRS, UPS, France}
\title{Supporting Information for ``Hierarchy Configuration Interaction: Combining Seniority Number and Excitation Degree''}
\author{F\'abris Kossoski}
\email{fkossoski@irsamc.ups-tlse.fr}
\affiliation{\LCPQ}
\author{Yann Damour}
\affiliation{\LCPQ}
\author{Pierre-Fran\c{c}ois Loos}
\email{loos@irsamc.ups-tlse.fr}
\affiliation{\LCPQ}
% Abstract
\begin{abstract}
%Here comes the abstract.
%\bigskip
%\begin{center}
% \boxed{\includegraphics[width=0.4\linewidth]{TOC}}
%\end{center}
%\bigskip
\end{abstract}
% Title
\maketitle
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\section{Equilibrium geometry of ethylene}
%\label{sec:ethylene}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Equilibrium geometry of ethylene, in atomic units:
\begin{singlespace}
\begin{verbatim}
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
\end{verbatim}
\end{singlespace}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\section{\ce{Computational details}}
%\label{sec:comp_details}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Vibrational frequencies and equilibrium geometries were obtained by fitting the computed potential energy curves at the Franck-Condon region with a Morse potential.
The following intervals have been considered for the fitting:
\SI{0.8}{\angstrom} to \SI{1.3}{\angstrom} (\ce{HF}),
\SI{1.25}{\angstrom} to \SI{1.65}{\angstrom} (\ce{F2}),
\SI{2.2}{\bohr} to \SI{2.9}{\bohr} (ethylene),
\SI{0.95}{\angstrom} to \SI{1.3}{\angstrom} (\ce{N2}),
\SI{1.45}{\bohr} to \SI{1.95}{\bohr} (\ce{H4}),
\SI{1.6}{\bohr} to \SI{2.05}{\bohr} (\ce{H8}).
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\section{\ce{HF}, different basis sets}
%\label{sec:HF_basis}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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 hierarchy-based CI (green),
with Hartree-Fock orbitals,
for the cc-pVDZ (left), cc-pVTZ (center), and cc-pVQZ (right) basis sets.
}
\label{fig:plot_pes_HF}
\end{figure}
\begin{figure}[h!]
\includegraphics[width=0.8\linewidth]{plot_stat_HF}
\caption{Non-parallelity error (left) and distance error (right) of \ce{HF},
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,
for the cc-pVDZ (top), cc-pVTZ (center), and cc-pVQZ (bottom) basis sets.}
\label{fig:plot_stat_HF}
\end{figure}
\begin{figure}[h!]
\includegraphics[width=0.8\linewidth]{freq_HF}
\caption{Vibrational frequencies (left) and equilibrium geometries (right) of \ce{HF},
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,
and according to the exact FCI result (black horizontal line),
for the cc-pVDZ (top), cc-pVTZ (center), and cc-pVQZ (bottom) basis sets.}
\label{fig:freq_HF}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\section{HF-CI}
%\label{sec:HF-CI}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[h!]
\includegraphics[width=0.8\linewidth]{plot_stat}
\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 hybrid hCI (green),
with Hartree-Fock orbitals.
}
\label{fig:plot_stat}
\end{figure}
\begin{figure}[h!]
\includegraphics[width=0.8\linewidth]{plot_distance}
\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 Hartree-Fock orbitals.
}
\label{fig:plot_distance}
\end{figure}
\begin{figure}[h!]
\includegraphics[width=0.8\linewidth]{xe}
\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 hybrid hCI (green),
with Hartree-Fock orbitals,
and according to the exact FCI result (black horizontal line).
}
\label{fig:xe}
\end{figure}
\begin{figure}[h!]
\includegraphics[width=0.8\linewidth]{freq}
\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 hybrid hCI (green),
with Hartree-Fock orbitals,
and according to the exact FCI result (black horizontal line).
}
\label{fig:freq}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\section{oo-CI}
%\label{sec:oo-CI}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[h!]
\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=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=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,
and according to the exact FCI result (black horizontal line).
}
\label{fig:xe_opt}
\end{figure}
\begin{figure}[h!]
\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,
and according to the exact FCI result (black horizontal line).
}
\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).
}
\label{fig:plot_pes}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\section{\ce{HF}}
%\label{sec:HF}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[h!]
\includegraphics[width=\linewidth]{HF_pes}
\caption{Potential energy curves for \ce{HF},
according to RHF, FCI, and the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
(dashed lines for half-integer $h$),
with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.}
\label{fig:HF_pes}
\end{figure}
\begin{figure}[h!]
\includegraphics[width=\linewidth]{HF_pes_error}
\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 CI level (right),
and with the cc-pVDZ basis set.}
\label{fig:HF_pes_error}
\end{figure}
\begin{figure}[h!]
\includegraphics[width=\linewidth]{HF_npe}
\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 CI level (right),
and with the cc-pVDZ basis set.}
\label{fig:HF_npe}
\end{figure}
\begin{figure}[h!]
\includegraphics[width=\linewidth]{HF_distance}
\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 CI level (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 number of determinants,
according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and according to the exact FCI result (black horizontal line),
for the cc-pVDZ basis set.}
\label{fig:HF_freq}
\end{figure}
\begin{figure}[h!]
\includegraphics[width=\linewidth]{HF_xe}
\caption{Equilibrium bond length of \ce{HF},
as function of the number of determinants,
according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and according to the exact FCI result (black horizontal line),
for the cc-pVDZ basis set.}
\label{fig:HF_xe}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\section{\ce{F2}}
%\label{sec:F2}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[h!]
\includegraphics[width=\linewidth]{F2_pes}
\caption{Potential energy curves for \ce{F2},
according to RHF, FCI, and the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
(dashed lines for half-integer $h$),
with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.}
\label{fig:F2_pes}
\end{figure}
\begin{figure}[h!]
\includegraphics[width=\linewidth]{F2_pes_error}
\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 CI level (right),
and with the cc-pVDZ basis set.}
\label{fig:F2_pes_error}
\end{figure}
\begin{figure}[h!]
\includegraphics[width=\linewidth]{F2_npe}
\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 CI level (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 CI level (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 CI level (right),
and according to the exact FCI result (black horizontal line),
for 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 number of determinants,
according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and according to the exact FCI result (black horizontal line),
for the cc-pVDZ basis set.}
\label{fig:F2_xe}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\section{\ce{Ethylene}}
%\label{sec:ethylene}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[h!]
\includegraphics[width=\linewidth]{ethylene_pes}
\caption{Potential energy curves for \ce{ethylene},
according to RHF, FCI, and the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
(dashed lines for half-integer $h$),
with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.}
\label{fig:ethylene_pes}
\end{figure}
\begin{figure}[h!]
\includegraphics[width=\linewidth]{ethylene_pes_error}
\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 CI level (right),
and with the cc-pVDZ basis set.}
\label{fig:ethylene_pes_error}
\end{figure}
\begin{figure}[h!]
\includegraphics[width=\linewidth]{ethylene_npe}
\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 CI level (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 CI level (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 CI level (right),
and according to the exact FCI result (black horizontal line),
for the cc-pVDZ basis set.}
\label{fig:ethylene_freq}
\end{figure}
\begin{figure}[h!]
\includegraphics[width=\linewidth]{ethylene_xe}
\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 CI level (right),
and according to the exact FCI result (black horizontal line),
for the cc-pVDZ basis set.}
\label{fig:ethylene_xe}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\section{\ce{N2}}
%\label{sec:N2}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[h!]
\includegraphics[width=\linewidth]{N2_pes}
\caption{Potential energy curves for \ce{N2},
according to RHF, FCI, and the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
(dashed lines for half-integer $h$),
with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.}
\label{fig:N2_pes}
\end{figure}
\begin{figure}[h!]
\includegraphics[width=\linewidth]{N2_pes_error}
\caption{Energy differences between the potential energy curves of Fig.~\ref{fig:N2_pes} and FCI results for \ce{N2},
according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
(dashed lines for half-integer $h$),
with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.}
\label{fig:N2_pes_error}
\end{figure}
\begin{figure}[h!]
\includegraphics[width=\linewidth]{N2_npe}
\caption{Non-parallelity error for \ce{N2}, corresponding to the potential energy curves of Fig.~\ref{fig:N2_pes},
as function of the number of determinants,
according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.}
\label{fig:N2_npe}
\end{figure}
\begin{figure}[h!]
\includegraphics[width=\linewidth]{N2_distance}
\caption{Distance error for \ce{N2}, corresponding to the potential energy curves of Fig.~\ref{fig:N2_pes},
as function of the number of determinants,
according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.}
\label{fig:N2_distance}
\end{figure}
\begin{figure}[h!]
\includegraphics[width=\linewidth]{N2_freq}
\caption{Vibrational frequency of \ce{N2},
as function of the number of determinants,
according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and according to the exact FCI result (black horizontal line),
for the cc-pVDZ basis set.}
\label{fig:N2_freq}
\end{figure}
\begin{figure}[h!]
\includegraphics[width=\linewidth]{N2_xe}
\caption{Equilibrium bond length of \ce{N2},
as function of the number of determinants,
according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and according to the exact FCI result (black horizontal line),
for the cc-pVDZ basis set.}
\label{fig:N2_xe}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\section{\ce{H4}}
%\label{sec:H4}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[h!]
\includegraphics[width=\linewidth]{H4_pes}
\caption{Potential energy curves for \ce{H4},
according to RHF, FCI, and the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
(dashed lines for half-integer $h$),
with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.}
\label{fig:H4_pes}
\end{figure}
\begin{figure}[h!]
\includegraphics[width=\linewidth]{H4_pes_error}
\caption{Energy differences between the potential energy curves of Fig.~\ref{fig:H4_pes} and FCI results for \ce{H4},
according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
(dashed lines for half-integer $h$),
with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.}
\label{fig:H4_pes_error}
\end{figure}
\begin{figure}[h!]
\includegraphics[width=\linewidth]{H4_npe}
\caption{Non-parallelity error for \ce{H4}, corresponding to the potential energy curves of Fig.~\ref{fig:H4_pes},
as function of the number of determinants,
according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.}
\label{fig:H4_npe}
\end{figure}
\begin{figure}[h!]
\includegraphics[width=\linewidth]{H4_distance}
\caption{Distance error for \ce{H4}, corresponding to the potential energy curves of Fig.~\ref{fig:H4_pes},
as function of the number of determinants,
according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.}
\label{fig:H4_distance}
\end{figure}
\begin{figure}[h!]
\includegraphics[width=\linewidth]{H4_force}
\caption{Force constants for symmetric dissociation of \ce{H4},
as function of the number of determinants,
according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and according to the exact FCI result (black horizontal line),
for the cc-pVDZ basis set.}
\label{fig:H4_force}
\end{figure}
\begin{figure}[h!]
\includegraphics[width=\linewidth]{H4_xe}
\caption{Equilibrium bond length of \ce{H4},
as function of the number of determinants,
according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and according to the exact FCI result (black horizontal line),
for the cc-pVDZ basis set.}
\label{fig:H4_xe}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\section{\ce{H8}}
%\label{sec:H8}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[h!]
\includegraphics[width=\linewidth]{H8_pes}
\caption{Potential energy curves for \ce{H8},
according to RHF, FCI, and the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
(dashed lines for half-integer $h$),
with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.}
\label{fig:H8_pes}
\end{figure}
\begin{figure}[h!]
\includegraphics[width=\linewidth]{H8_pes_error}
\caption{Energy differences between the potential energy curves of Fig.~\ref{fig:H8_pes} and FCI results for \ce{H8},
according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
(dashed lines for half-integer $h$),
with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.}
\label{fig:H8_pes_error}
\end{figure}
\begin{figure}[h!]
\includegraphics[width=\linewidth]{H8_npe}
\caption{Non-parallelity error for \ce{H8}, corresponding to the potential energy curves of Fig.~\ref{fig:H8_pes},
as function of the number of determinants,
according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.}
\label{fig:H8_npe}
\end{figure}
\begin{figure}[h!]
\includegraphics[width=\linewidth]{H8_distance}
\caption{Distance error for \ce{H8}, corresponding to the potential energy curves of Fig.~\ref{fig:H8_pes},
as function of the number of determinants,
according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and with the cc-pVDZ basis set.}
\label{fig:H8_distance}
\end{figure}
\begin{figure}[h!]
\includegraphics[width=\linewidth]{H8_force}
\caption{Force constants for symmetric dissociation of \ce{H8},
as function of the number of determinants,
according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and according to the exact FCI result (black horizontal line),
for the cc-pVDZ basis set.}
\label{fig:H8_force}
\end{figure}
\begin{figure}[h!]
\includegraphics[width=\linewidth]{H8_xe}
\caption{Equilibrium bond length of \ce{H8},
as function of the number of determinants,
according to the three classes of CI methods: seniority-based CI (blue), excitation-based CI (red), and hierarchy-based CI (green),
with Hartree-Fock orbitals (left) and orbitals optimized at a given CI level (right),
and according to the exact FCI result (black horizontal line),
for the cc-pVDZ basis set.}
\label{fig:H8_xe}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\bibliography{seniority}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\end{document}
Reference in New Issue View Git Blame Copy Permalink