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\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}
2019-10-03 17:02:38 +02:00
\citation { WerKno-JCP-88,KnoWer-CPL-88}
2019-10-03 01:11:25 +02:00
\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}
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\newlabel { FirstPage} { { } { 1} { } { section*.1} { } }
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\@ writefile{ toc} { \contentsline { title} { Mixing density functional theory and wave function theory for strong correlation: the best of both worlds} { 1} { section*.2} }
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\@ writefile{ toc} { \contentsline { abstract} { Abstract} { 1} { section*.1} }
\@ writefile{ toc} { \contentsline { section} { \numberline { I} Introduction} { 1} { section*.3} }
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\citation { Hyl-ZP-29}
\citation { Kut-TCA-85,KutKlo-JCP-91,NogKut-JCP-94}
\citation { HalHelJorKloKocOlsWil-CPL-98}
\citation { IrmHulGru-arxiv-19}
\citation { Ten-TCA-12,TenNog-WIREs-12,HatKloKohTew-CR-12,KonBisVal-CR-12,GruHirOhnTen-JCP-17,MaWer-WIREs-18}
\citation { TewKloNeiHat-PCCP-07}
\citation { TouColSav-PRA-04}
\citation { FraMusLupTou-JCP-15}
\citation { AngGerSavTou-PRA-05,GolWerSto-PCCP-05,TouGerJanSavAng-PRL-09,JanHenScu-JCP-09,TouZhuSavJanAng-JCP-11,MusReiAngTou-JCP-15}
\citation { LeiStoWerSav-CPL-97,FroTouJen-JCP-07,FroCimJen-PRA-10,HedKneKieJenRei-JCP-15,HedTouJen-JCP-18,FerGinTou-JCP-18}
2019-10-03 00:06:28 +02:00
\citation { GinPraFerAssSavTou-JCP-18}
2019-10-07 00:26:02 +02:00
\citation { LooPraSceTouGin-JCPL-19}
\citation { exicted}
\citation { GinPraFerAssSavTou-JCP-18}
\@ writefile{ toc} { \contentsline { section} { \numberline { II} Theory} { 2} { section*.4} }
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\newlabel { sec:theory} { { II} { 2} { } { section*.4} { } }
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\citation { GinPraFerAssSavTou-JCP-18}
\citation { GinPraFerAssSavTou-JCP-18}
\citation { GinPraFerAssSavTou-JCP-18}
2019-10-07 00:26:02 +02:00
\citation { LooPraSceTouGin-JCPL-19,excited}
2019-10-02 20:18:19 +02:00
\citation { kato}
2019-10-03 16:20:30 +02:00
\citation { GinPraFerAssSavTou-JCP-18}
2019-10-03 00:06:28 +02:00
\citation { GinPraFerAssSavTou-JCP-18}
2019-10-07 00:46:47 +02:00
\@ writefile{ toc} { \contentsline { subsection} { \numberline { A} Basic formal equations} { 3} { section*.5} }
\newlabel { sec:basic} { { II\tmspace +\thinmuskip { .1667em} A} { 3} { } { section*.5} { } }
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\newlabel { eq:levy} { { 1} { 3} { } { equation.2.1} { } }
\newlabel { eq:levy_ func} { { 2} { 3} { } { equation.2.2} { } }
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\newlabel { eq:def_ levy_ bas} { { 3} { 3} { } { equation.2.3} { } }
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\newlabel { eq:e0approx} { { 5} { 3} { } { equation.2.5} { } }
\@ writefile{ toc} { \contentsline { subsection} { \numberline { B} Definition of an effective interaction within $ \mathcal { B } $ } { 3} { section*.6} }
\newlabel { sec:wee} { { II\tmspace +\thinmuskip { .1667em} B} { 3} { } { section*.6} { } }
\newlabel { eq:wbasis} { { 6} { 3} { } { equation.2.6} { } }
\newlabel { eq:fbasis} { { 8} { 3} { } { equation.2.8} { } }
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\citation { GinPraFerAssSavTou-JCP-18}
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\citation { GinPraFerAssSavTou-JCP-18}
\citation { TouGorSav-TCA-05}
\citation { LooPraSceTouGin-JCPL-19}
\citation { PerBurErn-PRL-96}
\citation { FerGinTou-JCP-18}
\citation { TouColSav-PRA-04,GoriSav-PRA-06,PazMorGorBac-PRB-06}
\citation { FerGinTou-JCP-18}
\citation { GritMeePer-PRA-18}
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\citation { CarTruGag-JPCA-17}
2019-10-12 07:24:56 +02:00
\newlabel { eq:cbs_ wbasis} { { 10} { 4} { } { equation.2.10} { } }
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\@ writefile{ toc} { \contentsline { subsection} { \numberline { C} Definition of a range-separation parameter varying in real space} { 4} { section*.7} }
\newlabel { sec:mur} { { II\tmspace +\thinmuskip { .1667em} C} { 4} { } { section*.7} { } }
\newlabel { eq:weelr} { { 11} { 4} { } { equation.2.11} { } }
\newlabel { eq:def_ mur} { { 12} { 4} { } { equation.2.12} { } }
\newlabel { eq:cbs_ mu} { { 14} { 4} { } { equation.2.14} { } }
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\@ writefile{ toc} { \contentsline { subsection} { \numberline { D} Generic form and properties of the approximations for $ \mathaccentV { bar } 916 { E } ^ \mathcal { B } [ { n } ( { \bf r } ) ] $ } { 4} { section*.8} }
\@ writefile{ toc} { \contentsline { subsubsection} { \numberline { 1} Generic form of the approximated functionals} { 4} { section*.9} }
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\newlabel { eq:def_ ecmdpbebasis} { { 15} { 4} { } { equation.2.15} { } }
\newlabel { eq:def_ ecmdpbe} { { 16} { 4} { } { equation.2.16} { } }
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\newlabel { eq:def_ beta} { { 17} { 4} { } { equation.2.17} { } }
\newlabel { eq:lim_ mularge} { { 19} { 4} { } { equation.2.19} { } }
\newlabel { eq:lim_ n2} { { 20} { 4} { } { equation.2.20} { } }
\newlabel { eq:lim_ muinf} { { 21} { 4} { } { equation.2.21} { } }
\@ writefile{ toc} { \contentsline { subsubsection} { \numberline { 2} Properties of approximated functionals} { 4} { section*.10} }
\newlabel { eq:lim_ ebasis} { { 22} { 4} { } { equation.2.22} { } }
\citation { GarBulHenScu-PCCP-15}
2019-10-13 17:22:30 +02:00
\citation { LooPraSceTouGin-JCPL-19}
\citation { GorSav-PRA-06}
\@ writefile{ toc} { \contentsline { subsection} { \numberline { E} Requirements for the approximated functionals in the strong correlation } { 5} { section*.11} }
\@ writefile{ toc} { \contentsline { subsubsection} { \numberline { 1} Requirements: separability of the energies and $ S _ z $ invariance} { 5} { section*.12} }
\@ writefile{ toc} { \contentsline { subsubsection} { \numberline { 2} Condition for the functional $ \mathaccentV { bar } 916 { E } _ { \text { PBE } } ^ \mathcal { B } [ { n } , \xi ,s,n ^ { ( 2 ) } , \mu _ { \Psi ^ { \mathcal { B } } } ] $ to obtain $ S _ z $ invariance} { 5} { section*.13} }
\newlabel { eq:def_ effspin} { { 23} { 5} { } { equation.2.23} { } }
\@ writefile{ toc} { \contentsline { subsection} { \numberline { F} Requirement on $ \Psi ^ { \mathcal { B } } $ for the extensivity} { 5} { section*.14} }
\@ writefile{ toc} { \contentsline { subsection} { \numberline { G} Approximations for the strong correlation regime} { 5} { section*.15} }
\@ writefile{ toc} { \contentsline { subsubsection} { \numberline { 1} Definition of the different types of functionals} { 5} { section*.16} }
\newlabel { eq:def_ pbeueg} { { 24} { 5} { } { equation.2.24} { } }
\newlabel { eq:def_ n2ueg} { { 25} { 5} { } { equation.2.25} { } }
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\bibdata { srDFT_ SCNotes,srDFT_ SC}
\bibcite { Thom-PRL-10} { { 1} { 2010} { { Thom} } { { } } }
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\bibcite { ScoTho-JCP-17} { { 2} { 2017} { { Scott\ and\ Thom} } { { } } }
\bibcite { SpeNeuVigFraTho-JCP-18} { { 3} { 2018} { { Spencer\ \emph { et~al.} } } { { Spencer, Neufeld, Vigor, Franklin,\ and\ Thom} } }
\bibcite { DeuEmiShePie-PRL-17} { { 4} { 2017} { { Deustua, Shen,\ and\ Piecuch} } { { } } }
\bibcite { DeuEmiMagShePie-JCP-18} { { 5} { 2018} { { Deustua\ \emph { et~al.} } } { { Deustua, Magoulas, Shen,\ and\ Piecuch} } }
\bibcite { DeuEmiYumShePie-JCP-19} { { 6} { 2019} { { Deustua\ \emph { et~al.} } } { { Deustua, Yuwono, Shen,\ and\ Piecuch} } }
\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} } }
2019-10-03 16:20:30 +02:00
\bibcite { GomHenScu-JCP-19} { { 9} { 2019} { { Gomez, Henderson,\ and\ Scuseria} } { { } } }
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\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} } }
2019-10-11 18:15:50 +02:00
\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} } }
2019-10-03 17:02:38 +02:00
\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} } { { } } }
\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} } }
2019-10-13 17:22:30 +02:00
\@ writefile{ lot} { \contentsline { table} { \numberline { I} { \ignorespaces Total energies (in Hartree) for HF and $ E $ in aug-cc-pvdz for the He atom, F$ _ 2 $ (with F-F=1.411 angstroms) and the super non interacting system He--F$ _ 2 $ . } } { 6} { table.1} }
\newlabel { conv_ He_ table} { { I} { 6} { Total energies (in Hartree) for HF and $ E $ in aug-cc-pvdz for the He atom, F$ _ 2 $ (with F-F=1.411 angstroms) and the super non interacting system He--F$ _ 2 $ } { table.1} { } }
\@ writefile{ toc} { \contentsline { subsubsection} { \numberline { 2} Introduction of the effective spin-density} { 6} { section*.17} }
\@ writefile{ toc} { \contentsline { subsubsection} { \numberline { 3} Requirement for $ \Psi _ { } ^ { \mathcal { B } } $ for size extensivity} { 6} { section*.18} }
\@ writefile{ toc} { \contentsline { section} { \numberline { III} Results} { 6} { section*.19} }
\newlabel { sec:results} { { III} { 6} { } { section*.19} { } }
\@ writefile{ toc} { \contentsline { section} { \numberline { IV} Conclusion} { 6} { section*.20} }
\newlabel { sec:conclusion} { { IV} { 6} { } { section*.20} { } }
\@ writefile{ lof} { \contentsline { figure} { \numberline { 1} { \ignorespaces N$ _ 2 $ , aug-cc-pvdz: Comparison between the near FCI and corrected near FCI energies and the estimated exact one. } } { 6} { figure.1} }
\newlabel { fig:N2_ avdz} { { 1} { 6} { N$ _ 2 $ , aug-cc-pvdz: Comparison between the near FCI and corrected near FCI energies and the estimated exact one} { figure.1} { } }
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\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} } }
2019-10-07 00:26:02 +02:00
\bibcite { LooBogSceCafJac-JCTC-19} { { 44} { 2019{ } } { { Loos\ \emph { et~al.} } } { { Loos, Boggio-Pasqua, Scemama, Caffarel,\ and\ Jacquemin} } }
\bibcite { Hyl-ZP-29} { { 45} { 1929} { { Hylleraas} } { { } } }
\bibcite { Kut-TCA-85} { { 46} { 1985} { { Kutzelnigg} } { { } } }
\bibcite { KutKlo-JCP-91} { { 47} { 1991} { { Kutzelnigg\ and\ Klopper} } { { } } }
\bibcite { NogKut-JCP-94} { { 48} { 1994} { { Noga\ and\ Kutzelnigg} } { { } } }
\bibcite { HalHelJorKloKocOlsWil-CPL-98} { { 49} { 1998} { { Halkier\ \emph { et~al.} } } { { Halkier, Helgaker, J{ \o } rgensen, Klopper, Koch, Olsen,\ and\ Wilson} } }
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\bibcite { Ten-TCA-12} { { 51} { 2012} { { Ten-no} } { { } } }
\bibcite { TenNog-WIREs-12} { { 52} { 2012} { { Ten-no\ and\ Noga} } { { } } }
\bibcite { HatKloKohTew-CR-12} { { 53} { 2012} { { Hattig\ \emph { et~al.} } } { { Hattig, Klopper, Kohn,\ and\ Tew} } }
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\bibcite { GruHirOhnTen-JCP-17} { { 55} { 2017} { { Gr\" uneis\ \emph { et~al.} } } { { Gr\" uneis, Hirata, Ohnishi,\ and\ Ten-no} } }
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2019-10-13 17:22:30 +02:00
\@ 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. } } { 7} { figure.2} }
\newlabel { fig:N2_ avtz} { { 2} { 7} { N$ _ 2 $ , aug-cc-pvtz: Comparison between the near FCI and corrected near FCI energies and the estimated exact one} { figure.2} { } }
\@ 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. } } { 7} { figure.3} }
\newlabel { fig:F2_ avdz} { { 3} { 7} { F$ _ 2 $ , aug-cc-pvdz: Comparison between the near FCI and corrected near FCI energies and the estimated exact one} { figure.3} { } }
2019-10-07 00:26:02 +02:00
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\bibcite { LeiStoWerSav-CPL-97} { { 66} { 1997} { { Leininger\ \emph { et~al.} } } { { Leininger, Stoll, Werner,\ and\ Savin} } }
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\bibcite { FroCimJen-PRA-10} { { 68} { 2010} { { Fromager, Cimiraglia,\ and\ Jensen} } { { } } }
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\@ 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. } } { 8} { figure.4} }
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\bibcite { HedTouJen-JCP-18} { { 70} { 2018} { { Hedeg{ \r a} rd, Toulouse,\ and\ Jensen} } { { } } }
\bibcite { FerGinTou-JCP-18} { { 71} { 2019} { { Fert{ \' e} , Giner,\ and\ Toulouse} } { { } } }
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\bibcite { LooPraSceTouGin-JCPL-19} { { 73} { 2019{ } } { { Loos\ \emph { et~al.} } } { { Loos, Pradines, Scemama, Toulouse,\ and\ Giner} } }
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\bibcite { GoriSav-PRA-06} { { 76} { 2006{ } } { { Gori-Giorgi\ and\ Savin} } { { } } }
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