From 56f3da782073b8708bc63387c4b41e12181d96ff Mon Sep 17 00:00:00 2001 From: Pierre-Francois Loos Date: Wed, 5 Feb 2020 09:39:44 +0100 Subject: [PATCH] SI --- .gitignore | 2 - BSE-PES.tex | 95 +++++------ Data/BF_GS_VDZ.pdf | Bin 0 -> 64863 bytes Data/BF_GS_VDZ_FC.pdf | Bin 0 -> 63805 bytes Data/BF_GS_VQZ.pdf | Bin 0 -> 42897 bytes Data/BF_GS_VQZ_FC.pdf | Bin 0 -> 65518 bytes Data/BF_GS_VTZ.pdf | Bin 0 -> 65867 bytes Data/BF_GS_VTZ_FC.pdf | Bin 0 -> 66751 bytes Data/CO_GS_VDZ.pdf | Bin 0 -> 57732 bytes Data/CO_GS_VDZ_FC.pdf | Bin 0 -> 57893 bytes Data/CO_GS_VQZ.pdf | Bin 0 -> 37749 bytes Data/CO_GS_VQZ_FC.pdf | Bin 0 -> 60268 bytes Data/CO_GS_VTZ.pdf | Bin 0 -> 59342 bytes Data/CO_GS_VTZ_FC.pdf | Bin 0 -> 60860 bytes Data/F2_GS_VDZ.pdf | Bin 0 -> 63667 bytes Data/F2_GS_VDZ_FC.pdf | Bin 0 -> 64197 bytes Data/F2_GS_VQZ.pdf | Bin 0 -> 58740 bytes Data/F2_GS_VQZ_FC.pdf | Bin 0 -> 47812 bytes Data/F2_GS_VTZ.pdf | Bin 0 -> 64834 bytes Data/F2_GS_VTZ_FC.pdf | Bin 0 -> 63975 bytes Data/H2_GS_VDZ.pdf | Bin 0 -> 65000 bytes Data/H2_GS_VQZ.pdf | Bin 0 -> 57103 bytes Data/H2_GS_VTZ.pdf | Bin 0 -> 62882 bytes Data/HCl_GS_VDZ.pdf | Bin 0 -> 63486 bytes Data/HCl_GS_VDZ_FC.pdf | Bin 0 -> 52096 bytes Data/HCl_GS_VQZ.pdf | Bin 0 -> 40024 bytes Data/HCl_GS_VQZ_FC.pdf | Bin 0 -> 63767 bytes Data/HCl_GS_VTZ.pdf | Bin 0 -> 61226 bytes Data/HCl_GS_VTZ_FC.pdf | Bin 0 -> 64936 bytes Data/LiF_GS_VDZ.pdf | Bin 0 -> 62291 bytes Data/LiF_GS_VDZ_FC.pdf | Bin 0 -> 54765 bytes Data/LiF_GS_VQZ.pdf | Bin 0 -> 54260 bytes Data/LiF_GS_VQZ_FC.pdf | Bin 0 -> 61388 bytes Data/LiF_GS_VTZ.pdf | Bin 0 -> 63427 bytes Data/LiF_GS_VTZ_FC.pdf | Bin 0 -> 61701 bytes Data/LiH_GS_VDZ.pdf | Bin 0 -> 63769 bytes Data/LiH_GS_VDZ_FC.pdf | Bin 0 -> 62826 bytes Data/LiH_GS_VQZ.pdf | Bin 0 -> 54398 bytes Data/LiH_GS_VQZ_FC.pdf | Bin 0 -> 61412 bytes Data/LiH_GS_VTZ.pdf | Bin 0 -> 64284 bytes Data/LiH_GS_VTZ_FC.pdf | Bin 0 -> 63842 bytes Data/N2_GS_VDZ.pdf | Bin 0 -> 54482 bytes Data/N2_GS_VDZ_FC.pdf | Bin 0 -> 56044 bytes Data/N2_GS_VQZ.pdf | Bin 0 -> 50527 bytes Data/N2_GS_VQZ_FC.pdf | Bin 0 -> 55839 bytes Data/N2_GS_VTZ.pdf | Bin 0 -> 55484 bytes Data/N2_GS_VTZ_FC.pdf | Bin 0 -> 55780 bytes SI/BSE-PES-SI.tex | 349 +++++++++++++++++++++++++++++++++++++++++ 48 files changed, 397 insertions(+), 49 deletions(-) create mode 100644 Data/BF_GS_VDZ.pdf create mode 100644 Data/BF_GS_VDZ_FC.pdf create mode 100644 Data/BF_GS_VQZ.pdf create mode 100644 Data/BF_GS_VQZ_FC.pdf create mode 100644 Data/BF_GS_VTZ.pdf create mode 100644 Data/BF_GS_VTZ_FC.pdf create mode 100644 Data/CO_GS_VDZ.pdf create mode 100644 Data/CO_GS_VDZ_FC.pdf create mode 100644 Data/CO_GS_VQZ.pdf create mode 100644 Data/CO_GS_VQZ_FC.pdf create mode 100644 Data/CO_GS_VTZ.pdf create mode 100644 Data/CO_GS_VTZ_FC.pdf create mode 100644 Data/F2_GS_VDZ.pdf create mode 100644 Data/F2_GS_VDZ_FC.pdf create mode 100644 Data/F2_GS_VQZ.pdf create mode 100644 Data/F2_GS_VQZ_FC.pdf create mode 100644 Data/F2_GS_VTZ.pdf create mode 100644 Data/F2_GS_VTZ_FC.pdf create mode 100644 Data/H2_GS_VDZ.pdf create mode 100644 Data/H2_GS_VQZ.pdf create mode 100644 Data/H2_GS_VTZ.pdf create mode 100644 Data/HCl_GS_VDZ.pdf create mode 100644 Data/HCl_GS_VDZ_FC.pdf create mode 100644 Data/HCl_GS_VQZ.pdf create mode 100644 Data/HCl_GS_VQZ_FC.pdf create mode 100644 Data/HCl_GS_VTZ.pdf create mode 100644 Data/HCl_GS_VTZ_FC.pdf create mode 100644 Data/LiF_GS_VDZ.pdf create mode 100644 Data/LiF_GS_VDZ_FC.pdf create mode 100644 Data/LiF_GS_VQZ.pdf create mode 100644 Data/LiF_GS_VQZ_FC.pdf create mode 100644 Data/LiF_GS_VTZ.pdf create mode 100644 Data/LiF_GS_VTZ_FC.pdf create mode 100644 Data/LiH_GS_VDZ.pdf create mode 100644 Data/LiH_GS_VDZ_FC.pdf create mode 100644 Data/LiH_GS_VQZ.pdf create mode 100644 Data/LiH_GS_VQZ_FC.pdf create mode 100644 Data/LiH_GS_VTZ.pdf create mode 100644 Data/LiH_GS_VTZ_FC.pdf create mode 100644 Data/N2_GS_VDZ.pdf create mode 100644 Data/N2_GS_VDZ_FC.pdf create mode 100644 Data/N2_GS_VQZ.pdf create mode 100644 Data/N2_GS_VQZ_FC.pdf create mode 100644 Data/N2_GS_VTZ.pdf create mode 100644 Data/N2_GS_VTZ_FC.pdf create mode 100644 SI/BSE-PES-SI.tex diff --git a/.gitignore b/.gitignore index 3cb4f5a..e69de29 100644 --- a/.gitignore +++ b/.gitignore @@ -1,2 +0,0 @@ -Data -References diff --git a/BSE-PES.tex b/BSE-PES.tex index c0d3ab5..c9a9ecf 100644 --- a/BSE-PES.tex +++ b/BSE-PES.tex @@ -456,6 +456,54 @@ Because Eq.~\eqref{eq:EcBSE} requires the entire BSE singlet excitation spectrum This step is, by far, the computational bottleneck in our current implementation. However, we are currently pursuing different avenues to lower this cost by computing the two-electron density matrix of Eq.~\eqref{eq:2DM} via a quadrature in frequency space. \cite{Duchemin_2019,Duchemin_2020} +%%% FIG 1 %%% +\begin{figure*} + \includegraphics[width=0.49\linewidth]{H2_GS_VQZ} + \includegraphics[width=0.49\linewidth]{LiH_GS_VQZ} +\caption{ +Ground-state PES of \ce{H2} (left) and \ce{LiH} (right) around their respective equilibrium geometry obtained at various levels of theory with the cc-pVQZ basis set. +%Additional graphs for other basis sets and within the frozen-core approximation can be found in the {\SI}. +\label{fig:PES-H2-LiH} +} +\end{figure*} +%%% %%% %%% + +%%% FIG 2 %%% +\begin{figure*} + \includegraphics[height=0.35\linewidth]{LiF_GS_VQZ} + \includegraphics[height=0.35\linewidth]{HCl_GS_VQZ} +\caption{ +Ground-state PES of \ce{LiF} (left) and \ce{HCl} (right) around their respective equilibrium geometry obtained at various levels of theory with the cc-pVQZ basis set. +%Additional graphs for other basis sets and within the frozen-core approximation can be found in the {\SI}. +\label{fig:PES-LiF-HCl} +} +\end{figure*} +%%% %%% %%% + +%%% FIG 3 %%% +\begin{figure*} + \includegraphics[height=0.26\linewidth]{N2_GS_VQZ} + \includegraphics[height=0.26\linewidth]{CO_GS_VQZ} + \includegraphics[height=0.26\linewidth]{BF_GS_VQZ} +\caption{ +Ground-state PES of the isoelectronic series \ce{N2} (left), \ce{CO} (center), and \ce{BF} (right) around their respective equilibrium geometry obtained at various levels of theory with the cc-pVQZ basis set. +%Additional graphs for other basis sets and within the frozen-core approximation can be found in the {\SI}. +\label{fig:PES-N2-CO-BF} +} +\end{figure*} +%%% %%% %%% + +%%% FIG 4 %%% +\begin{figure} + \includegraphics[width=\linewidth]{F2_GS_VQZ} +\caption{ +Ground-state PES of \ce{F2} around its equilibrium geometry obtained at various levels of theory with the cc-pVQZ basis set. +%Additional graphs for other basis sets and within the frozen-core approximation can be found in the {\SI}. +\label{fig:PES-F2} +} +\end{figure} +%%% %%% %%% + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %\section{Potential energy surfaces} %\label{sec:PES} @@ -547,18 +595,6 @@ Albeit the shallow nature of the \ce{LiH} PES, the scenario is almost identical In this case, RPAx@HF and BSE@{\GOWO}@HF nestle the CCSD and CC3 energy curves, and they are almost perfectly parallel. Here again, the BSE@{\GOWO}@HF equilibrium bond length (obtained with cc-pVQZ) is extremely accurate ($3.017$ bohr) as compared to FCI ($3.019$ bohr). -%%% FIG 1 %%% -\begin{figure*} - \includegraphics[width=0.49\linewidth]{H2_GS_VQZ} - \includegraphics[width=0.49\linewidth]{LiH_GS_VQZ} -\caption{ -Ground-state PES of \ce{H2} (left) and \ce{LiH} (right) around their respective equilibrium geometry obtained at various levels of theory with the cc-pVQZ basis set. -%Additional graphs for other basis sets and within the frozen-core approximation can be found in the {\SI}. -\label{fig:PES-H2-LiH} -} -\end{figure*} -%%% %%% %%% - The cases of \ce{LiF} and \ce{HCl} (see Fig.~\ref{fig:PES-LiF-HCl}) are interesting as they corresponds to strongly polarized bonds towards the halogen atoms which are much more electronegative than the first row elements. For these ionic bonds, the performance of BSE@{\GOWO}@HF are terrific with an almost perfect match to the CC3 curve. %For \ce{LiF}, the two curves starting to deviate a few tenths of bohr after the equilibrium geometry, but they remain tightly bound for much longer in the case of \ce{HCl}. @@ -568,49 +604,14 @@ As observed in Refs.~\onlinecite{vanSetten_2015,Maggio_2017,Loos_2018} and expla Including a broadening via the increasing the value of $\eta$ in the $GW$ self-energy and the screened Coulomb operator soften the problem, but does not remove it completely. Note that these irregularities would be genuine discontinuities in the case of {\evGW}. \cite{Veril_2018} -%%% FIG 2 %%% -\begin{figure*} - \includegraphics[height=0.35\linewidth]{LiF_GS_VQZ} - \includegraphics[height=0.35\linewidth]{HCl_GS_VQZ} -\caption{ -Ground-state PES of \ce{LiF} (left) and \ce{HCl} (right) around their respective equilibrium geometry obtained at various levels of theory with the cc-pVQZ basis set. -%Additional graphs for other basis sets and within the frozen-core approximation can be found in the {\SI}. -\label{fig:PES-LiF-HCl} -} -\end{figure*} -%%% %%% %%% Let us now look at the isoelectronic series \ce{N2}, \ce{CO}, and \ce{BF}, which have a decreasing bond order (from triple bond to single bond). In that case again, the performance of BSE@{\GOWO}@HF are outstanding, as shown in Fig.~\ref{fig:PES-N2-CO-BF}, and systematically outperforms both CC2 and CCSD. -%%% FIG 3 %%% -\begin{figure*} - \includegraphics[height=0.26\linewidth]{N2_GS_VQZ} - \includegraphics[height=0.26\linewidth]{CO_GS_VQZ} - \includegraphics[height=0.26\linewidth]{BF_GS_VQZ} -\caption{ -Ground-state PES of the isoelectronic series \ce{N2} (left), \ce{CO} (center), and \ce{BF} (right) around their respective equilibrium geometry obtained at various levels of theory with the cc-pVQZ basis set. -%Additional graphs for other basis sets and within the frozen-core approximation can be found in the {\SI}. -\label{fig:PES-N2-CO-BF} -} -\end{figure*} -%%% %%% %%% - The \ce{F2} molecule is a notoriously difficult case to treat due to the weakness of its covalent bond (see Fig.~\ref{fig:PES-F2}), hence its relatively long equilibrium bond length ($2.663$ bohr at the CC3/cc-pVQZ level). Similarly to what we have observed for \ce{LiF} and \ce{BF}, there is an irregularities near the minimum of the {\GOWO}-based curves. However, BSE@{\GOWO}@HF is the closest to the CC3 curve -%%% FIG 4 %%% -\begin{figure} - \includegraphics[width=\linewidth]{F2_GS_VQZ} -\caption{ -Ground-state PES of \ce{F2} around its equilibrium geometry obtained at various levels of theory with the cc-pVQZ basis set. -%Additional graphs for other basis sets and within the frozen-core approximation can be found in the {\SI}. -\label{fig:PES-F2} -} -\end{figure} -%%% %%% %%% - %%%%%%%%%%%%%%%%%%%%%%%% %\section{Conclusion} %\label{sec:conclusion} diff --git a/Data/BF_GS_VDZ.pdf b/Data/BF_GS_VDZ.pdf new file mode 100644 index 0000000000000000000000000000000000000000..ee55f0e63185e6cba23c2a4aa5ea361f3777427e GIT binary patch literal 64863 zcmV)sK$yQJP((&8F)lR4?5av(28Y+-a|L}g=dWMv9IJ_>Vma%Ev{3V58fy~~a!Ns}G6kEh6`Bw&(pzW@Xm z0|*2Na3OL4EreMRDUk)DN&u;aUSEE0=Kf_?b+@LAL;S1`&-gq%Jp5vI?D(+kN5j{-j4NtU-sqgN0sdN`?l|I-{1b@^soNYf|}Olc|WgpxHly)_wuRh zv%T;4J>Kh*uk~){^}fx=aBoV!*1PY^`?4;>y(#%x@3HLf&$bWursQkA%Y45-dwc8l 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+\newcommand{\denis}[1]{\textcolor{purple}{#1}} +\newcommand{\xavier}[1]{\textcolor{darkgreen}{#1}} +\newcommand{\trashPFL}[1]{\textcolor{red}{\sout{#1}}} +\newcommand{\trashDJ}[1]{\textcolor{purple}{\sout{#1}}} +\newcommand{\trashXB}[1]{\textcolor{darkgreen}{\sout{#1}}} +\newcommand{\PFL}[1]{\titou{(\underline{\bf PFL}: #1)}} +\renewcommand{\DJ}[1]{\denis{(\underline{\bf DJ}: #1)}} +\newcommand{\XB}[1]{\xavier{(\underline{\bf XB}: #1)}} + +\newcommand{\mc}{\multicolumn} +\newcommand{\fnm}{\footnotemark} +\newcommand{\fnt}{\footnotetext} +\newcommand{\tabc}[1]{\multicolumn{1}{c}{#1}} +\newcommand{\SI}{\textcolor{blue}{supporting information}} +\newcommand{\QP}{\textsc{quantum package}} +\newcommand{\T}[1]{#1^{\intercal}} + +% coordinates +\newcommand{\br}[1]{\mathbf{r}_{#1}} +\newcommand{\dbr}[1]{d\br{#1}} + +% methods +\newcommand{\evGW}{ev$GW$} +\newcommand{\qsGW}{qs$GW$} +\newcommand{\GOWO}{$G_0W_0$} +\newcommand{\Hxc}{\text{Hxc}} +\newcommand{\xc}{\text{xc}} +\newcommand{\Ha}{\text{H}} +\newcommand{\co}{\text{x}} + +% +\newcommand{\Norb}{N} +\newcommand{\Nocc}{O} +\newcommand{\Nvir}{V} +\newcommand{\IS}{\lambda} + +% operators +\newcommand{\hH}{\Hat{H}} + +% energies +\newcommand{\Enuc}{E^\text{nuc}} +\newcommand{\Ec}{E_\text{c}} +\newcommand{\EHF}{E^\text{HF}} +\newcommand{\EBSE}{E^\text{BSE}} +\newcommand{\EcRPA}{E_\text{c}^\text{RPA}} +\newcommand{\EcRPAx}{E_\text{c}^\text{RPAx}} +\newcommand{\EcBSE}{E_\text{c}^\text{BSE}} +\newcommand{\IP}{\text{IP}} +\newcommand{\EA}{\text{EA}} + +% orbital energies +\newcommand{\e}[1]{\epsilon_{#1}} +\newcommand{\eHF}[1]{\epsilon^\text{HF}_{#1}} +\newcommand{\eKS}[1]{\epsilon^\text{KS}_{#1}} +\newcommand{\eQP}[1]{\epsilon^\text{QP}_{#1}} +\newcommand{\eGOWO}[1]{\epsilon^\text{\GOWO}_{#1}} +\newcommand{\eGW}[1]{\epsilon^{GW}_{#1}} +\newcommand{\eevGW}[1]{\epsilon^\text{\evGW}_{#1}} +\newcommand{\eGnWn}[2]{\epsilon^\text{\GnWn{#2}}_{#1}} +\newcommand{\Om}[2]{\Omega_{#1}^{#2}} + +% Matrix elements +\newcommand{\A}[2]{A_{#1}^{#2}} +\newcommand{\tA}[2]{\Tilde{A}_{#1}^{#2}} +\newcommand{\B}[2]{B_{#1}^{#2}} +\renewcommand{\S}[1]{S_{#1}} +\newcommand{\ABSE}[2]{A_{#1}^{#2,\text{BSE}}} +\newcommand{\BBSE}[2]{B_{#1}^{#2,\text{BSE}}} +\newcommand{\ARPA}[2]{A_{#1}^{#2,\text{RPA}}} +\newcommand{\BRPA}[2]{B_{#1}^{#2,\text{RPA}}} +\newcommand{\ARPAx}[2]{A_{#1}^{#2,\text{RPAx}}} +\newcommand{\BRPAx}[2]{B_{#1}^{#2,\text{RPAx}}} +\newcommand{\G}[1]{G_{#1}} +\newcommand{\LBSE}[1]{L_{#1}} +\newcommand{\XiBSE}[1]{\Xi_{#1}} +\newcommand{\Po}[1]{P_{#1}} +\newcommand{\W}[2]{W_{#1}^{#2}} +\newcommand{\Wc}[1]{W^\text{c}_{#1}} +\newcommand{\vc}[1]{v_{#1}} +\newcommand{\Sig}[1]{\Sigma_{#1}} +\newcommand{\SigGW}[1]{\Sigma^{GW}_{#1}} +\newcommand{\Z}[1]{Z_{#1}} +\newcommand{\MO}[1]{\phi_{#1}} +\newcommand{\ERI}[2]{(#1|#2)} +\newcommand{\sERI}[2]{[#1|#2]} + +%% bold in Table +\newcommand{\bb}[1]{\textbf{#1}} +\newcommand{\rb}[1]{\textbf{\textcolor{red}{#1}}} +\newcommand{\gb}[1]{\textbf{\textcolor{darkgreen}{#1}}} + +% excitation energies +\newcommand{\OmRPA}[2]{\Omega_{#1}^{#2,\text{RPA}}} +\newcommand{\OmRPAx}[2]{\Omega_{#1}^{#2,\text{RPAx}}} +\newcommand{\OmBSE}[2]{\Omega_{#1}^{#2,\text{BSE}}} + +\newcommand{\spinup}{\downarrow} +\newcommand{\spindw}{\uparrow} +\newcommand{\singlet}{\uparrow\downarrow} +\newcommand{\triplet}{\uparrow\uparrow} + +% Matrices +\newcommand{\bO}{\mathbf{0}} +\newcommand{\bI}{\mathbf{1}} +\newcommand{\bvc}{\mathbf{v}} +\newcommand{\bSig}{\mathbf{\Sigma}} +\newcommand{\bSigX}{\mathbf{\Sigma}^\text{x}} +\newcommand{\bSigC}{\mathbf{\Sigma}^\text{c}} +\newcommand{\bSigGW}{\mathbf{\Sigma}^{GW}} +\newcommand{\be}{\mathbf{\epsilon}} +\newcommand{\beGW}{\mathbf{\epsilon}^{GW}} +\newcommand{\beGnWn}[1]{\mathbf{\epsilon}^\text{\GnWn{#1}}} +\newcommand{\bde}{\mathbf{\Delta\epsilon}} +\newcommand{\bdeHF}{\mathbf{\Delta\epsilon}^\text{HF}} +\newcommand{\bdeGW}{\mathbf{\Delta\epsilon}^{GW}} +\newcommand{\bOm}[1]{\mathbf{\Omega}^{#1}} +\newcommand{\bA}[1]{\mathbf{A}^{#1}} +\newcommand{\btA}[1]{\Tilde{\mathbf{A}}^{#1}} +\newcommand{\bB}[1]{\mathbf{B}^{#1}} +\newcommand{\bX}[1]{\mathbf{X}^{#1}} +\newcommand{\bY}[1]{\mathbf{Y}^{#1}} +\newcommand{\bZ}[1]{\mathbf{Z}^{#1}} +\newcommand{\bK}{\mathbf{K}} +\newcommand{\bP}[1]{\mathbf{P}^{#1}} + +% units +\newcommand{\IneV}[1]{#1 eV} +\newcommand{\InAU}[1]{#1 a.u.} +\newcommand{\InAA}[1]{#1 \AA} +\newcommand{\kcal}{kcal/mol} + +\newcommand{\NEEL}{Univ. Grenoble Alpes, CNRS, Institut NEEL, F-38042 Grenoble, France} +\newcommand{\CEISAM}{Laboratoire CEISAM - UMR CNRS 6230, Universit\'e de Nantes, 2 Rue de la Houssini\`ere, BP 92208, 44322 Nantes Cedex 3, France} +\newcommand{\LCPQ}{Laboratoire de Chimie et Physique Quantiques (UMR 5626), Universit\'e de Toulouse, CNRS, UPS, France} +\newcommand{\CEA}{ Univ. Grenoble Alpes, CEA, IRIG-MEM-L Sim, 38054 Grenoble, France } + +\begin{document} + +\title{Supporting Information for ``Ground-State Potential Energy Surfaces Within the Bethe-Salpeter Formalism: Pros and Cons''} + +\author{Xavier \surname{Blase}} +\email{xavier.blase@neel.cnrs.fr } +\affiliation{\NEEL} +\author{Ivan \surname{Duchemin}} +\email{ivan.duchemin@cea.fr} +\affiliation{\CEA} +\author{Anthony \surname{Scemama}} +\email{scemama@irsamc.ups-tlse.fr} +\affiliation{\LCPQ} +\author{Denis \surname{Jacquemin}} +\email{denis.jacquemin@univ-nantes.fr} +\affiliation{\CEISAM} +\author{Pierre-Fran\c{c}ois \surname{Loos}} +\email{loos@irsamc.ups-tlse.fr} +\affiliation{\LCPQ} + +\begin{abstract} +\end{abstract} + +\maketitle + +%%% FIG 1 %%% +\begin{figure*} + % H2 + \includegraphics[width=0.49\linewidth]{../Data/H2_GS_VDZ} + \includegraphics[width=0.49\linewidth]{../Data/H2_GS_VTZ} +\caption{ +Ground-state potential energy surfaces of \ce{H2} around its respective equilibrium geometry obtained at various levels of theory and basis sets. +\label{fig:PES-H2} +} +\end{figure*} +%%% %%% %%% + +%%% FIG 2 %%% +\begin{figure*} + % LiH + \includegraphics[width=0.49\linewidth]{../Data/LiH_GS_VDZ} + \includegraphics[width=0.49\linewidth]{../Data/LiH_GS_VDZ_FC} + \includegraphics[width=0.49\linewidth]{../Data/LiH_GS_VTZ} + \includegraphics[width=0.49\linewidth]{../Data/LiH_GS_VTZ_FC} + \includegraphics[width=0.49\linewidth]{../Data/LiH_GS_VQZ_FC} +\caption{ +Ground-state potential energy surfaces of \ce{LiH} around its respective equilibrium geometry obtained at various levels of theory and basis sets. +\label{fig:PES-LiH} +} +\end{figure*} +%%% %%% %%% + +%%% FIG 3 %%% +\begin{figure*} + % LiF + \includegraphics[width=0.49\linewidth]{../Data/LiF_GS_VDZ} + \includegraphics[width=0.49\linewidth]{../Data/LiF_GS_VDZ_FC} + \includegraphics[width=0.49\linewidth]{../Data/LiF_GS_VTZ} + \includegraphics[width=0.49\linewidth]{../Data/LiF_GS_VTZ_FC} + \includegraphics[width=0.49\linewidth]{../Data/LiF_GS_VQZ_FC} +\caption{ +Ground-state potential energy surfaces of \ce{LiF} around its respective equilibrium geometry obtained at various levels of theory and basis sets. +\label{fig:PES-LiF} +} +\end{figure*} +%%% %%% %%% + +%%% FIG 5 %%% +\begin{figure*} + % HCl + \includegraphics[width=0.49\linewidth]{../Data/HCl_GS_VDZ} + \includegraphics[width=0.49\linewidth]{../Data/HCl_GS_VDZ_FC} + \includegraphics[width=0.49\linewidth]{../Data/HCl_GS_VTZ} + \includegraphics[width=0.49\linewidth]{../Data/HCl_GS_VTZ_FC} + \includegraphics[width=0.49\linewidth]{../Data/HCl_GS_VQZ_FC} +\caption{ +Ground-state potential energy surfaces of \ce{HCl} around its respective equilibrium geometry obtained at various levels of theory and basis sets. +\label{fig:PES-HCl} +} +\end{figure*} +%%% %%% %%% + +%%% FIG 6 %%% +\begin{figure*} + % N2 + \includegraphics[width=0.49\linewidth]{../Data/N2_GS_VDZ} + \includegraphics[width=0.49\linewidth]{../Data/N2_GS_VDZ_FC} + \includegraphics[width=0.49\linewidth]{../Data/N2_GS_VTZ} + \includegraphics[width=0.49\linewidth]{../Data/N2_GS_VTZ_FC} + \includegraphics[width=0.49\linewidth]{../Data/N2_GS_VQZ_FC} +\caption{ +Ground-state potential energy surfaces of \ce{N2} around its respective equilibrium geometry obtained at various levels of theory and basis sets. +\label{fig:PES-N2} +} +\end{figure*} +%%% %%% %%% + +%%% FIG 6 %%% +\begin{figure*} + % CO + \includegraphics[width=0.49\linewidth]{../Data/CO_GS_VDZ} + \includegraphics[width=0.49\linewidth]{../Data/CO_GS_VDZ_FC} + \includegraphics[width=0.49\linewidth]{../Data/CO_GS_VTZ} + \includegraphics[width=0.49\linewidth]{../Data/CO_GS_VTZ_FC} + \includegraphics[width=0.49\linewidth]{../Data/CO_GS_VQZ_FC} +\caption{ +Ground-state potential energy surfaces of \ce{CO} around its respective equilibrium geometry obtained at various levels of theory and basis sets. +\label{fig:PES-CO} +} +\end{figure*} +%%% %%% %%% + +%%% FIG 6 %%% +\begin{figure*} + % N2 + \includegraphics[width=0.49\linewidth]{../Data/BF_GS_VDZ} + \includegraphics[width=0.49\linewidth]{../Data/BF_GS_VDZ_FC} + \includegraphics[width=0.49\linewidth]{../Data/BF_GS_VTZ} + \includegraphics[width=0.49\linewidth]{../Data/BF_GS_VTZ_FC} + \includegraphics[width=0.49\linewidth]{../Data/BF_GS_VQZ_FC} +\caption{ +Ground-state potential energy surfaces of \ce{BF} around its respective equilibrium geometry obtained at various levels of theory and basis sets. +\label{fig:PES-BF} +} +\end{figure*} +%%% %%% %%% + +%%% FIG 6 %%% +\begin{figure*} + % N2 + \includegraphics[width=0.49\linewidth]{../Data/F2_GS_VDZ} + \includegraphics[width=0.49\linewidth]{../Data/F2_GS_VTZ} + \includegraphics[width=0.49\linewidth]{../Data/F2_GS_VDZ_FC} + \includegraphics[width=0.49\linewidth]{../Data/F2_GS_VTZ_FC} + \includegraphics[width=0.49\linewidth]{../Data/F2_GS_VQZ_FC} +\caption{ +Ground-state potential energy surfaces of \ce{F2} around its respective equilibrium geometry obtained at various levels of theory and basis sets. +\label{fig:PES-F2} +} +\end{figure*} +%%% %%% %%% + + +%%% %%% %%% +%%% TABLE I %%% +%\begin{table*} +%\caption{ +%Equilibrium distances (in bohr) of the ground state of diatomic molecules obtained at various levels of theory and basis sets. +%All these values have been obtained within the frozen-core approximation. +%The reference CC3 and corresponding BSE@{\GOWO}@HF data are highlighted in bold black and bold red for visual convenience, respectively. +%The values in parenthesis have been obtained by fitting a Morse potential to the PES. +%} +%\label{tab:Req-FC} +% +% \begin{ruledtabular} +% \begin{tabular}{llcccccccc} +% & & \mc{8}{c}{Molecules} \\ +% \cline{3-10} +% Method & Basis & \ce{H2} & \ce{LiH} & \ce{LiF} & \ce{HCl} & \ce{N2} & \ce{CO} & \ce{BF} & \ce{F2} \\ +% \hline +% CC3 & cc-pVDZ & 1.438 & 3.052 & 3.014 & 2.115 & 2.167 & 2.447 & 2.741 & 2.438 \\ +% & cc-pVTZ & 1.403 & 3.036 & 2.985 & 2.087 & 2.150 & 2.405 & 2.672 & 2.414 \\ +% & cc-pVQZ & 1.402 & 3.037 & 2.985 & 2.080 & 2.142 & 2.398 & 2.667 & 2.413 \\ +% CCSD & cc-pVDZ & 1.438 & 3.044 & 3.006 & 2.101 & 2.149 & 2.435 & 2.695 & 2.433 \\ +% & cc-pVTZ & 1.403 & 3.012 & 2.954 & 2.064 & 2.126 & 2.382 & 2.629 & 2.409 \\ +% & cc-pVQZ & 1.402 & 3.020 & 2.953 & 2.059 & 2.118 & 2.380 & 2.621 & 2.398 \\ +% CC2 & cc-pVDZ & 1.426 & & & & & & & \\ +% & cc-pVTZ & 1.393 & & & & & & & \\ +% & cc-pVQZ & 1.391 & & & & & & & \\ +% MP2 & cc-pVDZ & 1.426 & 3.049 & 3.012 & 2.134 & 2.167 & 2.433 & 2.681 & 2.429 \\ +% & cc-pVTZ & 1.393 & 3.026 & 2.990 & 2.104 & 2.151 & 2.395 & 2.640 & 2.407 \\ +% & cc-pVQZ & 1.391 & 3.026 & 2.990 & 2.098 & 2.144 & 2.389 & 2.638 & 2.405 \\ +% BSE@{\GOWO}@HF & cc-pVDZ & 1.437 & & & & & & & \\ +% & cc-pVTZ & 1.404 & & & & & & & \\ +% & cc-pVQZ & 1.399 & & & & & & & \\ +% RPA@{\GOWO}@HF & cc-pVDZ & 1.426 & & & & & & & \\ +% & cc-pVTZ & 1.388 & & & & & & & \\ +% & cc-pVQZ & 1.382 & & & & & & & \\ +% RPAx@HF & cc-pVDZ & 1.428 & & & & & & & \\ +% & cc-pVTZ & 1.395 & & & & & & & \\ +% & cc-pVQZ & 1.394 & & & & & & & \\ +% RPA@HF & cc-pVDZ & 1.431 & & & & & & & \\ +% & cc-pVTZ & 1.388 & & & & & & & \\ +% & cc-pVQZ & 1.386 & & & & & & & \\ +% \end{tabular} +% \end{ruledtabular} +%\end{table*} + + +\bibliography{../BSE-PES,../BSE-PES-control} + +\end{document}