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73
Manuscript/srDFT_SC.aux
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@ -18,6 +18,7 @@
\providecommand\HyField@AuxAddToCoFields[2]{}
\citation{Thom-PRL-10,ScoTho-JCP-17,SpeNeuVigFraTho-JCP-18,DeuEmiShePie-PRL-17,DeuEmiMagShePie-JCP-18,DeuEmiYumShePie-JCP-19}
\citation{QiuHenZhaScu-JCP-17,QiuHenZhaScu-JCP-18,GomHenScu-JCP-19}
\citation{WerKno-JCP-88,KnoWer-CPL-88}
\citation{BenErn-PhysRev-1969,WhiHac-JCP-1969,HurMalRan-1973,EvaDauMal-ChemPhys-83,Cim-JCP-1985,Cim-JCC-1987,IllRubRic-JCP-88,PovRubIll-TCA-92,BunCarRam-JCP-06,AbrSheDav-CPL-05,MusEngels-JCC-06,BytRue-CP-09,GinSceCaf-CJC-13,CafGinScemRam-JCTC-14,GinSceCaf-JCP-15,CafAplGinScem-arxiv-16,CafAplGinSce-JCP-16,SchEva-JCP-16,LiuHofJCTC-16,HolUmrSha-JCP-17,ShaHolJeaAlaUmr-JCTC-17,HolUmrSha-JCP-17,SchEva-JCTC-17,PerCle-JCP-17,OhtJun-JCP-17,Zim-JCP-17,LiOttHolShaUmr-JCP-2018,ChiHolOttUmrShaZim-JPCA-18,SceBenJacCafLoo-JCP-18,LooSceBloGarCafJac-JCTC-18,GarSceGinCaffLoo-JCP-18,SceGarCafLoo-JCTC-18,GarGinMalSce-JCP-16,LooBogSceCafJac-JCTC-19}
\newlabel{FirstPage}{{}{1}{}{section*.1}{}}
\@writefile{toc}{\contentsline {title}{Mixing density functional theory and wave function theory for strong correlation: the best of both worlds}{1}{section*.2}}
@ -50,27 +51,28 @@
\bibcite{QiuHenZhaScu-JCP-17}{{7}{2017}{{Qiu\ \emph {et~al.}}}{{Qiu, Henderson, Zhao,\ and\ Scuseria}}}
\bibcite{QiuHenZhaScu-JCP-18}{{8}{2018}{{Qiu\ \emph {et~al.}}}{{Qiu, Henderson, Zhao,\ and\ Scuseria}}}
\bibcite{GomHenScu-JCP-19}{{9}{2019}{{Gomez, Henderson,\ and\ Scuseria}}{{}}}
\bibcite{BenErn-PhysRev-1969}{{10}{1969}{{Bender\ and\ Davidson}}{{}}}
\bibcite{WhiHac-JCP-1969}{{11}{1969}{{Whitten\ and\ Hackmeyer}}{{}}}
\bibcite{HurMalRan-1973}{{12}{1973}{{Huron, Malrieu,\ and\ Rancurel}}{{}}}
\bibcite{EvaDauMal-ChemPhys-83}{{13}{1983}{{Evangelisti, Daudey,\ and\ Malrieu}}{{}}}
\bibcite{Cim-JCP-1985}{{14}{1985}{{Cimiraglia}}{{}}}
\bibcite{Cim-JCC-1987}{{15}{1987}{{Cimiraglia\ and\ Persico}}{{}}}
\bibcite{IllRubRic-JCP-88}{{16}{1988}{{Illas, Rubio,\ and\ Ricart}}{{}}}
\bibcite{PovRubIll-TCA-92}{{17}{1992}{{Povill, Rubio,\ and\ Illas}}{{}}}
\bibcite{BunCarRam-JCP-06}{{18}{2006}{{Bunge\ and\ Carb{\'o}-Dorca}}{{}}}
\bibcite{AbrSheDav-CPL-05}{{19}{2005}{{Abrams\ and\ Sherrill}}{{}}}
\bibcite{MusEngels-JCC-06}{{20}{2006}{{Musch\ and\ Engels}}{{}}}
\bibcite{BytRue-CP-09}{{21}{2009}{{Bytautas\ and\ Ruedenberg}}{{}}}
\bibcite{GinSceCaf-CJC-13}{{22}{2013}{{Giner, Scemama,\ and\ Caffarel}}{{}}}
\bibcite{CafGinScemRam-JCTC-14}{{23}{2014}{{Caffarel\ \emph {et~al.}}}{{Caffarel, Giner, Scemama,\ and\ Ram{\'\i }rez-Sol{\'\i }s}}}
\bibcite{GinSceCaf-JCP-15}{{24}{2015}{{Giner, Scemama,\ and\ Caffarel}}{{}}}
\bibcite{CafAplGinScem-arxiv-16}{{25}{2016{}}{{Caffarel\ \emph {et~al.}}}{{Caffarel, Applencourt, Giner,\ and\ Scemama}}}
\bibcite{CafAplGinSce-JCP-16}{{26}{2016{}}{{Caffarel\ \emph {et~al.}}}{{Caffarel, Applencourt, Giner,\ and\ Scemama}}}
\bibcite{SchEva-JCP-16}{{27}{2016}{{Schriber\ and\ Evangelista}}{{}}}
\bibcite{LiuHofJCTC-16}{{28}{2016}{{Liu\ and\ Hoffmann}}{{}}}
\bibcite{HolUmrSha-JCP-17}{{29}{2017}{{Holmes, Umrigar,\ and\ Sharma}}{{}}}
\bibcite{ShaHolJeaAlaUmr-JCTC-17}{{30}{2017}{{Sharma\ \emph {et~al.}}}{{Sharma, Holmes, Jeanmairet, Alavi,\ and\ Umrigar}}}
\bibcite{WerKno-JCP-88}{{10}{1988}{{Werner\ and\ Knowles}}{{}}}
\bibcite{KnoWer-CPL-88}{{11}{1988}{{Knowles\ and\ Werner}}{{}}}
\bibcite{BenErn-PhysRev-1969}{{12}{1969}{{Bender\ and\ Davidson}}{{}}}
\bibcite{WhiHac-JCP-1969}{{13}{1969}{{Whitten\ and\ Hackmeyer}}{{}}}
\bibcite{HurMalRan-1973}{{14}{1973}{{Huron, Malrieu,\ and\ Rancurel}}{{}}}
\bibcite{EvaDauMal-ChemPhys-83}{{15}{1983}{{Evangelisti, Daudey,\ and\ Malrieu}}{{}}}
\bibcite{Cim-JCP-1985}{{16}{1985}{{Cimiraglia}}{{}}}
\bibcite{Cim-JCC-1987}{{17}{1987}{{Cimiraglia\ and\ Persico}}{{}}}
\bibcite{IllRubRic-JCP-88}{{18}{1988}{{Illas, Rubio,\ and\ Ricart}}{{}}}
\bibcite{PovRubIll-TCA-92}{{19}{1992}{{Povill, Rubio,\ and\ Illas}}{{}}}
\bibcite{BunCarRam-JCP-06}{{20}{2006}{{Bunge\ and\ Carb{\'o}-Dorca}}{{}}}
\bibcite{AbrSheDav-CPL-05}{{21}{2005}{{Abrams\ and\ Sherrill}}{{}}}
\bibcite{MusEngels-JCC-06}{{22}{2006}{{Musch\ and\ Engels}}{{}}}
\bibcite{BytRue-CP-09}{{23}{2009}{{Bytautas\ and\ Ruedenberg}}{{}}}
\bibcite{GinSceCaf-CJC-13}{{24}{2013}{{Giner, Scemama,\ and\ Caffarel}}{{}}}
\bibcite{CafGinScemRam-JCTC-14}{{25}{2014}{{Caffarel\ \emph {et~al.}}}{{Caffarel, Giner, Scemama,\ and\ Ram{\'\i }rez-Sol{\'\i }s}}}
\bibcite{GinSceCaf-JCP-15}{{26}{2015}{{Giner, Scemama,\ and\ Caffarel}}{{}}}
\bibcite{CafAplGinScem-arxiv-16}{{27}{2016{}}{{Caffarel\ \emph {et~al.}}}{{Caffarel, Applencourt, Giner,\ and\ Scemama}}}
\bibcite{CafAplGinSce-JCP-16}{{28}{2016{}}{{Caffarel\ \emph {et~al.}}}{{Caffarel, Applencourt, Giner,\ and\ Scemama}}}
\bibcite{SchEva-JCP-16}{{29}{2016}{{Schriber\ and\ Evangelista}}{{}}}
\bibcite{LiuHofJCTC-16}{{30}{2016}{{Liu\ and\ Hoffmann}}{{}}}
\bibcite{HolUmrSha-JCP-17}{{31}{2017}{{Holmes, Umrigar,\ and\ Sharma}}{{}}}
\newlabel{eq:wbasis}{{6}{3}{}{equation.2.6}{}}
\newlabel{eq:fbasis}{{8}{3}{}{equation.2.8}{}}
\newlabel{eq:cbs_wbasis}{{10}{3}{}{equation.2.10}{}}
@ -83,19 +85,20 @@
\@writefile{toc}{\contentsline {subsubsection}{\numberline {2}Introduction of the effective spin-density}{3}{section*.10}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {3}Requirement for $\Psi _{}^{\mathcal {B}}$ for size extensivity}{3}{section*.11}}
\@writefile{toc}{\contentsline {section}{\numberline {III}Results}{3}{section*.12}}
\bibcite{SchEva-JCTC-17}{{31}{2017}{{Schriber\ and\ Evangelista}}{{}}}
\bibcite{PerCle-JCP-17}{{32}{2017}{{Per\ and\ Cleland}}{{}}}
\bibcite{OhtJun-JCP-17}{{33}{2017}{{Ohtsuka\ and\ ya~Hasegawa}}{{}}}
\bibcite{Zim-JCP-17}{{34}{2017}{{Zimmerman}}{{}}}
\bibcite{LiOttHolShaUmr-JCP-2018}{{35}{2018}{{Li\ \emph {et~al.}}}{{Li, Otten, Holmes, Sharma,\ and\ Umrigar}}}
\bibcite{ChiHolOttUmrShaZim-JPCA-18}{{36}{2018}{{Chien\ \emph {et~al.}}}{{Chien, Holmes, Otten, Umrigar, Sharma,\ and\ Zimmerman}}}
\bibcite{SceBenJacCafLoo-JCP-18}{{37}{2018{}}{{Scemama\ \emph {et~al.}}}{{Scemama, Benali, Jacquemin, Caffarel,\ and\ Loos}}}
\bibcite{LooSceBloGarCafJac-JCTC-18}{{38}{2018}{{Loos\ \emph {et~al.}}}{{Loos, Scemama, Blondel, Garniron, Caffarel,\ and\ Jacquemin}}}
\bibcite{GarSceGinCaffLoo-JCP-18}{{39}{2018}{{Garniron\ \emph {et~al.}}}{{Garniron, Scemama, Giner, Caffarel,\ and\ Loos}}}
\bibcite{SceGarCafLoo-JCTC-18}{{40}{2018{}}{{Scemama\ \emph {et~al.}}}{{Scemama, Garniron, Caffarel,\ and\ Loos}}}
\bibcite{GarGinMalSce-JCP-16}{{41}{2017}{{Garniron\ \emph {et~al.}}}{{Garniron, Giner, Malrieu,\ and\ Scemama}}}
\bibcite{LooBogSceCafJac-JCTC-19}{{42}{2019}{{Loos\ \emph {et~al.}}}{{Loos, Boggio-Pasqua, Scemama, Caffarel,\ and\ Jacquemin}}}
\bibcite{GinPraFerAssSavTou-JCP-18}{{43}{2018}{{Giner\ \emph {et~al.}}}{{Giner, Pradines, Fert\'e, Assaraf, Savin,\ and\ Toulouse}}}
\bibcite{ShaHolJeaAlaUmr-JCTC-17}{{32}{2017}{{Sharma\ \emph {et~al.}}}{{Sharma, Holmes, Jeanmairet, Alavi,\ and\ Umrigar}}}
\bibcite{SchEva-JCTC-17}{{33}{2017}{{Schriber\ and\ Evangelista}}{{}}}
\bibcite{PerCle-JCP-17}{{34}{2017}{{Per\ and\ Cleland}}{{}}}
\bibcite{OhtJun-JCP-17}{{35}{2017}{{Ohtsuka\ and\ ya~Hasegawa}}{{}}}
\bibcite{Zim-JCP-17}{{36}{2017}{{Zimmerman}}{{}}}
\bibcite{LiOttHolShaUmr-JCP-2018}{{37}{2018}{{Li\ \emph {et~al.}}}{{Li, Otten, Holmes, Sharma,\ and\ Umrigar}}}
\bibcite{ChiHolOttUmrShaZim-JPCA-18}{{38}{2018}{{Chien\ \emph {et~al.}}}{{Chien, Holmes, Otten, Umrigar, Sharma,\ and\ Zimmerman}}}
\bibcite{SceBenJacCafLoo-JCP-18}{{39}{2018{}}{{Scemama\ \emph {et~al.}}}{{Scemama, Benali, Jacquemin, Caffarel,\ and\ Loos}}}
\bibcite{LooSceBloGarCafJac-JCTC-18}{{40}{2018}{{Loos\ \emph {et~al.}}}{{Loos, Scemama, Blondel, Garniron, Caffarel,\ and\ Jacquemin}}}
\bibcite{GarSceGinCaffLoo-JCP-18}{{41}{2018}{{Garniron\ \emph {et~al.}}}{{Garniron, Scemama, Giner, Caffarel,\ and\ Loos}}}
\bibcite{SceGarCafLoo-JCTC-18}{{42}{2018{}}{{Scemama\ \emph {et~al.}}}{{Scemama, Garniron, Caffarel,\ and\ Loos}}}
\bibcite{GarGinMalSce-JCP-16}{{43}{2017}{{Garniron\ \emph {et~al.}}}{{Garniron, Giner, Malrieu,\ and\ Scemama}}}
\bibcite{LooBogSceCafJac-JCTC-19}{{44}{2019}{{Loos\ \emph {et~al.}}}{{Loos, Boggio-Pasqua, Scemama, Caffarel,\ and\ Jacquemin}}}
\bibcite{GinPraFerAssSavTou-JCP-18}{{45}{2018}{{Giner\ \emph {et~al.}}}{{Giner, Pradines, Fert\'e, Assaraf, Savin,\ and\ Toulouse}}}
\bibstyle{aipnum4-1}
\citation{REVTEX41Control}
\citation{aip41Control}
@ -103,7 +106,7 @@
\newlabel{fig:N2_avdz}{{1}{4}{N$_2$, aug-cc-pvdz: Comparison between the near FCI and corrected near FCI energies and the estimated exact one}{figure.1}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces N$_2$, aug-cc-pvtz: Comparison between the near FCI and corrected near FCI energies and the estimated exact one. }}{4}{figure.2}}
\newlabel{fig:N2_avtz}{{2}{4}{N$_2$, aug-cc-pvtz: Comparison between the near FCI and corrected near FCI energies and the estimated exact one}{figure.2}{}}
\newlabel{LastBibItem}{{43}{4}{}{figure.7}{}}
\newlabel{LastBibItem}{{45}{4}{}{figure.7}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces F$_2$, aug-cc-pvdz: Comparison between the near FCI and corrected near FCI energies and the estimated exact one. }}{5}{figure.3}}
\newlabel{fig:F2_avdz}{{3}{5}{F$_2$, aug-cc-pvdz: Comparison between the near FCI and corrected near FCI energies and the estimated exact one}{figure.3}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces F$_2$, aug-cc-pvtz: Comparison between the near FCI and corrected near FCI energies and the estimated exact one. }}{6}{figure.4}}

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Manuscript/srDFT_SC.bbl
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%Control: page (0) single
%Control: year (1) truncated
%Control: production of eprint (0) enabled
\begin{thebibliography}{43}%
\begin{thebibliography}{45}%
\makeatletter
\providecommand \@ifxundefined [1]{%
\@ifx{#1\undefined}
@ -153,6 +153,22 @@
{volume} {150}},\ \bibinfo {pages} {144108} (\bibinfo {year} {2019})},\
\Eprint {http://arxiv.org/abs/https://doi.org/10.1063/1.5085314}
{https://doi.org/10.1063/1.5085314} \BibitemShut {NoStop}%
\bibitem [{\citenamefont {Werner}\ and\ \citenamefont
{Knowles}(1988)}]{WerKno-JCP-88}%
\BibitemOpen
\bibfield {author} {\bibinfo {author} {\bibfnamefont {H.-J.}\ \bibnamefont
{Werner}}\ and\ \bibinfo {author} {\bibfnamefont {P.~J.}\ \bibnamefont
{Knowles}},\ }\href@noop {} {\bibfield {journal} {\bibinfo {journal} {J.
Chem. Phys.}\ }\textbf {\bibinfo {volume} {{89}}},\ \bibinfo {pages} {5003}
(\bibinfo {year} {1988})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Knowles}\ and\ \citenamefont
{Werner}(1988)}]{KnoWer-CPL-88}%
\BibitemOpen
\bibfield {author} {\bibinfo {author} {\bibfnamefont {P.~J.}\ \bibnamefont
{Knowles}}\ and\ \bibinfo {author} {\bibfnamefont {H.-J.}\ \bibnamefont
{Werner}},\ }\href@noop {} {\bibfield {journal} {\bibinfo {journal} {Chem.
Phys. Lett.}\ }\textbf {\bibinfo {volume} {{514}}},\ \bibinfo {pages} {145}
(\bibinfo {year} {1988})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Bender}\ and\ \citenamefont
{Davidson}(1969)}]{BenErn-PhysRev-1969}%
\BibitemOpen

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@ -27,45 +27,45 @@ Control: page (0) single
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Manuscript/srDFT_SC.tex
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@ -266,7 +266,7 @@ which consists in increasing the rank of the excitation operators used to genera
Despite its appealing elegant simplicity, the computational cost of the CC methods increase drastically with the rank of the excitation
operators, even if promising alternative approaches have been proposed using stochastic techniques\cite{Thom-PRL-10,ScoTho-JCP-17,SpeNeuVigFraTho-JCP-18,DeuEmiShePie-PRL-17,DeuEmiMagShePie-JCP-18,DeuEmiYumShePie-JCP-19} or symmetry-broken approaches\cite{QiuHenZhaScu-JCP-17,QiuHenZhaScu-JCP-18,GomHenScu-JCP-19}.
In the MR approaches, the zeroth order wave function consists in a linear combination of Slater determinants which are supposed to concentrate most of strong interactions and near degeneracies inherent in the structure of the Hamiltonian for a strongly correlated system. The usual approach to build such a zeroth-order wave function is to perform a complete active space self consistent field (CASSCF) whose variational property prevent any divergence, and which can provide extensive energies. Of course, the choice of the active space is rather a subtle art and the CASSCF results might strongly depend on the level of chemical/physical knowledge of the user.
On top of this zeroth-order wave function, weak correlation is introduced by the addition of other configurations through either configuration interaction (MRCI) or perturbation theory (MRPT) and even coupled cluster (MRCC), which have their strengths and weaknesses,
On top of this zeroth-order wave function, weak correlation is introduced by the addition of other configurations through either configuration interaction\cite{WerKno-JCP-88,KnoWer-CPL-88} (MRCI) or perturbation theory (MRPT) and even coupled cluster (MRCC), which have their strengths and weaknesses,
The advantage of MRCI approaches rely essentially in their simple linear parametrisation for the wave function together with the variational property of their energies, whose inherent drawback is the lack of size extensivity of their energies unless reaching the FCI limit. On the other hand, MRPT and MRCC can provide extensive energies but to the price of rather complicated formalisms, and these approaches might be subject to divergences and/or convergence problems due to the non linearity of the parametrisation for MRCC or a too poor choice of the zeroth-order Hamiltonian.
A natural alternative is to combine MRCI and MRPT, which falls in the category of selected CI (SCI) which goes back to the late 60's and who has received a revival of interest and applications during the last decade \cite{BenErn-PhysRev-1969,WhiHac-JCP-1969,HurMalRan-1973,EvaDauMal-ChemPhys-83,Cim-JCP-1985,Cim-JCC-1987,IllRubRic-JCP-88,PovRubIll-TCA-92,BunCarRam-JCP-06,AbrSheDav-CPL-05,MusEngels-JCC-06,BytRue-CP-09,GinSceCaf-CJC-13,CafGinScemRam-JCTC-14,GinSceCaf-JCP-15,CafAplGinScem-arxiv-16,CafAplGinSce-JCP-16,SchEva-JCP-16,LiuHofJCTC-16,HolUmrSha-JCP-17,ShaHolJeaAlaUmr-JCTC-17,HolUmrSha-JCP-17,SchEva-JCTC-17,PerCle-JCP-17,OhtJun-JCP-17,Zim-JCP-17,LiOttHolShaUmr-JCP-2018,ChiHolOttUmrShaZim-JPCA-18,SceBenJacCafLoo-JCP-18,LooSceBloGarCafJac-JCTC-18,GarSceGinCaffLoo-JCP-18,SceGarCafLoo-JCTC-18,GarGinMalSce-JCP-16,LooBogSceCafJac-JCTC-19}, and among which the CI perturbatively selected iteratively (CIPSI) can be considered as a pioneer. The main idea of the CIPSI and other related SCI algorithms is to iteratively select the most important Slater determinants thanks to perturbation theory in order to build a MRCI zeroth-order wave function which automatically concentrate the strongly interacting part of the wave function. On top of this MRCI zeroth-order wave function, a rather simple MRPT approach is used to recover the missing weak correlation and the process is iterated until reaching a given stopping criterion. It is important to notice that in the SCI algorithms, neither the SCI or the MRPT are size extensive \text{per se}, but the extensivity property is almost recovered by approaching the FCI limit.
When the SCI are affordable, their clear advantage are they provide near FCI wave functions and energies, whatever the level of knowledge of the user on the specific physical/chemical problem considered. The drawback of SCI is certainly their \textit{intrinsic} exponential scaling due to their linear parametrisation. Nevertheless, such an exponential scaling is lowered by the smart selection of the zeroth-order wave function together with the MRPT calculation.