\documentclass[aip,jcp,reprint,noshowkeys]{revtex4-1} \usepackage{graphicx,dcolumn,bm,xcolor,microtype,multirow,amscd,amsmath,amssymb,amsfonts,physics,mhchem,longtable} \usepackage{mathpazo,libertine} \usepackage[normalem]{ulem} \newcommand{\alert}[1]{\textcolor{red}{#1}} \definecolor{darkgreen}{RGB}{0, 180, 0} \newcommand{\beurk}[1]{\textcolor{darkgreen}{#1}} \newcommand{\trash}[1]{\textcolor{red}{\sout{#1}}} \usepackage{xspace} \usepackage{hyperref} \hypersetup{ colorlinks=true, linkcolor=blue, filecolor=blue, urlcolor=blue, citecolor=blue } \newcommand{\cdash}{\multicolumn{1}{c}{---}} \newcommand{\mc}{\multicolumn} \newcommand{\fnm}{\footnotemark} \newcommand{\fnt}{\footnotetext} \newcommand{\tabc}[1]{\multicolumn{1}{c}{#1}} \newcommand{\mr}{\multirow} \newcommand{\SI}{\textcolor{blue}{supporting information}} % second quantized operators \newcommand{\psix}[1]{\hat{\Psi}\left({\bf X}_{#1}\right)} \newcommand{\psixc}[1]{\hat{\Psi}^{\dagger}\left({\bf X}_{#1}\right)} \newcommand{\ai}[1]{\hat{a}_{#1}} \newcommand{\aic}[1]{\hat{a}^{\dagger}_{#1}} \newcommand{\vijkl}[0]{V_{ij}^{kl}} \newcommand{\phix}[2]{\phi_{#1}(\bfr{#2})} \newcommand{\phixprim}[2]{\phi_{#1}(\bfr{#2}')} %operators \newcommand{\elemm}[3]{{\ensuremath{\bra{#1}{#2}\ket{#3}}\xspace}} \newcommand{\ovrlp}[2]{{\ensuremath{\langle #1|#2\rangle}\xspace}} %\newcommand{\ket}[1]{{\ensuremath{|#1\rangle}\xspace}} %\newcommand{\bra}[1]{{\ensuremath{\langle #1|}\xspace}} % % energies \newcommand{\Ec}{E_\text{c}} \newcommand{\EPT}{E_\text{PT2}} \newcommand{\EsCI}{E_\text{sCI}} \newcommand{\EDMC}{E_\text{DMC}} \newcommand{\EexFCI}{E_\text{exFCI}} \newcommand{\EexFCIbasis}{E_\text{exFCI}^{\Bas}} \newcommand{\EexFCIinfty}{E_\text{exFCI}^{\infty}} \newcommand{\EexDMC}{E_\text{exDMC}} \newcommand{\Ead}{\Delta E_\text{ad}} \newcommand{\efci}[0]{E_{\text{FCI}}^{\Bas}} \newcommand{\emodel}[0]{E_{\model}^{\Bas}} \newcommand{\emodelcomplete}[0]{E_{\model}^{\infty}} \newcommand{\efcicomplete}[0]{E_{\text{FCI}}^{\infty}} \newcommand{\ecccomplete}[0]{E_{\text{CCSD(T)}}^{\infty}} \newcommand{\ecc}[0]{E_{\text{CCSD(T)}}^{\Bas}} \newcommand{\efuncbasisfci}[0]{\bar{E}^\Bas[\denfci]} \newcommand{\efuncbasis}[0]{\bar{E}^\Bas[\den]} \newcommand{\efuncden}[1]{\bar{E}^\Bas[#1]} \newcommand{\ecompmodel}[0]{\bar{E}^\Bas[\denmodel]} \newcommand{\ecmubis}[0]{\bar{E}_{\text{c,md}}^{\text{sr}}[\denr;\,\mu]} \newcommand{\ecmubisldapbe}[0]{\bar{E}_{\text{c,md}\,\text{PBE}}^{\text{sr}}[\denr;\,\mu]} \newcommand{\ecmuapprox}[0]{\bar{E}_{\text{c,md-}\mathcal{X}}^{\text{sr}}[\den;\,\mu]} \newcommand{\ecmuapproxmur}[0]{\bar{E}_{\text{c,md-}\mathcal{X}}^{\text{sr}}[\den;\,\mur]} \newcommand{\ecmuapproxmurfci}[0]{\bar{E}_{\text{c,md-}\mathcal{X}}^{\text{sr}}[\denfci;\,\mur]} \newcommand{\ecmuapproxmurmodel}[0]{\bar{E}_{\text{c,md-}\mathcal{X}}^{\text{sr}}[\denmodel;\,\mur]} \newcommand{\ecompmodellda}[0]{\bar{E}_{\text{LDA}}^{\Bas,\wf{}{\Bas}}[\denmodel]} \newcommand{\ecompmodelldaval}[0]{\bar{E}_{\text{LDA, val}}^{\Bas,\wf{}{\Bas}}[\den]} \newcommand{\ecompmodelpbe}[0]{\bar{E}_{\text{PBE}}^{\Bas,\wf{}{\Bas}}[\den]} \newcommand{\ecompmodelpbeval}[0]{\bar{E}_{\text{PBE, val}}^{\Bas,\wf{}{\Bas}}[\den]} \newcommand{\emulda}[0]{\bar{\varepsilon}^{\text{sr},\text{unif}}_{\text{c,md}}\left(\denr;\mu({\bf r};\wf{}{\Bas})\right)} \newcommand{\emuldamodel}[0]{\bar{\varepsilon}^{\text{sr},\text{unif}}_{\text{c,md}}\left(\denmodelr;\mu({\bf r};\wf{}{\Bas})\right)} \newcommand{\emuldaval}[0]{\bar{\varepsilon}^{\text{sr},\text{unif}}_{\text{c,md}}\left(\denval ({\bf r});\murval;\wf{}{\Bas})\right)} % numbers \newcommand{\rnum}[0]{{\rm I\!R}} \newcommand{\bfr}[1]{{\bf x}_{#1}} \newcommand{\bfrb}[1]{{\bf r}_{#1}} \newcommand{\dr}[1]{\text{d}\bfr{#1}} \newcommand{\rr}[2]{\bfr{#1}, \bfr{#2}} \newcommand{\rrrr}[4]{\bfr{#1}, \bfr{#2},\bfr{#3},\bfr{#4} } % effective interaction \newcommand{\twodm}[4]{\elemm{\Psi}{\psixc{#4}\psixc{#3} \psix{#2}\psix{#1}}{\Psi}} \newcommand{\murpsi}[0]{\mu({\bf r};\wf{}{\Bas})} \newcommand{\mur}[0]{\mu({\bf r})} \newcommand{\murr}[1]{\mu({\bf r}_{#1})} \newcommand{\murval}[0]{\mu_{\text{val}}({\bf r})} \newcommand{\murpsival}[0]{\mu_{\text{val}}({\bf r};\wf{}{\Bas})} \newcommand{\murrval}[1]{\mu_{\text{val}}({\bf r}_{#1})} \newcommand{\weeopmu}[0]{\hat{W}_{\text{ee}}^{\text{lr},\mu}} \newcommand{\wbasis}[0]{W_{\wf{}{\Bas}}(\bfr{1},\bfr{2})} \newcommand{\wbasisval}[0]{W_{\wf{}{\Bas}}^{\text{val}}(\bfr{1},\bfr{2})} \newcommand{\fbasis}[0]{f_{\wf{}{\Bas}}(\bfr{1},\bfr{2})} \newcommand{\fbasisval}[0]{f_{\wf{}{\Bas}}^{\text{val}}(\bfr{1},\bfr{2})} \newcommand{\ontop}[2]{ n^{(2)}_{#1}({\bf #2}_1)} \newcommand{\twodmrpsi}[0]{ n^{(2)}_{\wf{}{\Bas}}(\rrrr{1}{2}{2}{1})} \newcommand{\twodmrdiagpsi}[0]{ n^{(2)}_{\wf{}{\Bas}}(\rr{1}{2})} \newcommand{\twodmrdiagpsival}[0]{ n^{(2)}_{\wf{}{\Bas},\,\text{val}}(\rr{1}{2})} \newcommand{\gammamnpq}[1]{\Gamma_{mn}^{pq}[#1]} \newcommand{\gammamnkl}[0]{\Gamma_{mn}^{kl}} \newcommand{\gammaklmn}[1]{\Gamma_{kl}^{mn}[#1]} \newcommand{\wbasiscoal}[1]{W_{\wf{}{\Bas}}({\bf r}_{#1})} \newcommand{\ontoppsi}[1]{ n^{(2)}_{\wf{}{\Bas}}(\bfr{#1},\barr{#1},\barr{#1},\bfr{#1})} \newcommand{\wbasiscoalval}[1]{W_{\wf{}{\Bas}}^{\text{val}}({\bf r}_{#1})} \newcommand{\ontoppsival}[1]{ n^{(2)}_{\wf{}{\Bas}}^{\text{val}}(\bfr{#1},\barr{#1},\barr{#1},\bfr{#1})} \newcommand{\ex}[4]{$^{#1}#2_{#3}^{#4}$} \newcommand{\ra}{\rightarrow} \newcommand{\De}{D_\text{e}} % MODEL \newcommand{\model}[0]{\mathcal{Y}} % densities \newcommand{\denmodel}[0]{\den_{\model}^\Bas} \newcommand{\denmodelr}[0]{\den_{\model}^\Bas ({\bf r})} \newcommand{\denfci}[0]{\den_{\psifci}} \newcommand{\denhf}[0]{\den_{\text{HF}}^\Bas} \newcommand{\denrfci}[0]{\denr_{\psifci}} \newcommand{\dencipsir}[0]{{n}_{\text{CIPSI}}^\Bas({\bf r})} \newcommand{\dencipsi}[0]{{n}_{\text{CIPSI}}^\Bas} \newcommand{\den}[0]{{n}} \newcommand{\denval}[0]{{n}^{\text{val}}} \newcommand{\denr}[0]{{n}({\bf r})} \newcommand{\onedmval}[0]{\rho_{ij,\sigma}^{\text{val}}} % wave functions \newcommand{\psifci}[0]{\Psi^{\Bas}_{\text{FCI}}} \newcommand{\psimu}[0]{\Psi^{\mu}} % operators \newcommand{\weeopbasis}[0]{\hat{W}_{\text{ee}}^\Bas} \newcommand{\kinop}[0]{\hat{T}} \newcommand{\weeopbasisval}[0]{\hat{W}_{\text{ee}}^{\Basval}} \newcommand{\weeop}[0]{\hat{W}_{\text{ee}}} % units \newcommand{\IneV}[1]{#1 eV} \newcommand{\InAU}[1]{#1 a.u.} \newcommand{\InAA}[1]{#1 \AA} % methods \newcommand{\UEG}{\text{UEG}} \newcommand{\LDA}{\text{LDA}} \newcommand{\PBE}{\text{PBE}} \newcommand{\FCI}{\text{FCI}} \newcommand{\CCSDT}{\text{CCSD(T)}} \newcommand{\lr}{\text{lr}} \newcommand{\sr}{\text{sr}} \newcommand{\Nel}{N} \newcommand{\n}[2]{n_{#1}^{#2}} \newcommand{\E}[2]{E_{#1}^{#2}} \newcommand{\bE}[2]{\Bar{E}_{#1}^{#2}} \newcommand{\bEc}[1]{\Bar{E}_\text{c}^{#1}} \newcommand{\e}[2]{\varepsilon_{#1}^{#2}} \newcommand{\be}[2]{\Bar{\varepsilon}_{#1}^{#2}} \newcommand{\bec}[1]{\Bar{e}^{#1}} \newcommand{\wf}[2]{\Psi_{#1}^{#2}} \newcommand{\W}[2]{W_{#1}^{#2}} \newcommand{\w}[2]{w_{#1}^{#2}} \newcommand{\hn}[2]{\Hat{n}_{#1}^{#2}} \newcommand{\rsmu}[2]{\mu_{#1}^{#2}} \newcommand{\SO}[2]{\phi_{#1}(\bx{#2})} \newcommand{\modX}{\text{X}} \newcommand{\modY}{\text{Y}} % basis sets \newcommand{\Bas}{\mathcal{B}} \newcommand{\Basval}{\mathcal{B}_\text{val}} \newcommand{\Val}{\mathcal{V}} \newcommand{\Cor}{\mathcal{C}} % operators \newcommand{\hT}{\Hat{T}} \newcommand{\hWee}[1]{\Hat{W}_\text{ee}^{#1}} \newcommand{\f}[2]{f_{#1}^{#2}} \newcommand{\Gam}[2]{\Gamma_{#1}^{#2}} % coordinates \newcommand{\br}[1]{\mathbf{r}_{#1}} \newcommand{\bx}[1]{\mathbf{x}_{#1}} \newcommand{\dbr}[1]{d\br{#1}} \newcommand{\dbx}[1]{d\bx{#1}} \newcommand{\LCPQ}{Laboratoire de Chimie et Physique Quantiques (UMR 5626), Universit\'e de Toulouse, CNRS, UPS, France} \newcommand{\LCT}{Laboratoire de Chimie Th\'eorique, Universit\'e Pierre et Marie Curie, Sorbonne Universit\'e, CNRS, Paris, France} \begin{document} \title{A Density-Based Basis Set Correction For strong correlation: I), ground state potential energy curve} \begin{abstract} bla bla bla youpi tralala \end{abstract} \maketitle %%%%%%%%%%%%%%%%%%%%%%%% \section{Introduction} %%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%% \section{Theory} %%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%% \section{Results} %%%%%%%%%%%%%%%%%%%%%%%% \begin{figure*} \includegraphics[width=\linewidth]{N2_dz_PBE_on_top_den_vs_exact.eps} \includegraphics[width=\linewidth]{N2_tz_PBE_on_top_den_vs_exact.eps} % \includegraphics[width=\linewidth]{fig2c} \caption{ N$_2$: Comparison between the near FCI and corrected near FCI energies and the estimated exact one in the aug-cc-pvdz and aug-cc-pvtz basis sets. \label{fig:N2_compared}} \end{figure*} \begin{figure*} \includegraphics[width=\linewidth]{N2_dz_PBE_on_top_den_vs_exact_truncated.eps} \includegraphics[width=\linewidth]{N2_tz_PBE_on_top_den_vs_exact_truncated.eps} % \includegraphics[width=\linewidth]{fig2c} \caption{ N$_2$: Comparison between the CASSCF and CASSCF corrected near FCI energies and the estimated exact one in the aug-cc-pvdz and aug-cc-pvtz basis sets. \label{fig:N2_compared}} \end{figure*} \begin{figure*} \includegraphics[width=\linewidth]{F2_dz_PBE_on_top_den_vs_exact.eps} \includegraphics[width=\linewidth]{F2_tz_PBE_on_top_den_vs_exact.eps} % \includegraphics[width=\linewidth]{fig2c} \caption{ F$_2$: Comparison between the near FCI and corrected near FCI energies and the estimated exact one in the aug-cc-pvdz and aug-cc-pvtz basis sets. \label{fig:N2_compared}} \end{figure*} \bibliography{srDFT_SC} \end{document}