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