srDFT_SC/Manuscript/srDFT_SC.aux
2019-10-07 00:46:47 +02:00

166 lines
14 KiB
TeX

\relax
\providecommand\hyper@newdestlabel[2]{}
\providecommand\HyperFirstAtBeginDocument{\AtBeginDocument}
\HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined
\global\let\oldcontentsline\contentsline
\gdef\contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}}
\global\let\oldnewlabel\newlabel
\gdef\newlabel#1#2{\newlabelxx{#1}#2}
\gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}}
\AtEndDocument{\ifx\hyper@anchor\@undefined
\let\contentsline\oldcontentsline
\let\newlabel\oldnewlabel
\fi}
\fi}
\global\let\hyper@last\relax
\gdef\HyperFirstAtBeginDocument#1{#1}
\providecommand\HyField@AuxAddToFields[1]{}
\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}}
\@writefile{toc}{\contentsline {abstract}{Abstract}{1}{section*.1}}
\@writefile{toc}{\contentsline {section}{\numberline {I}Introduction}{1}{section*.3}}
\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}
\citation{GinPraFerAssSavTou-JCP-18}
\citation{LooPraSceTouGin-JCPL-19}
\citation{exicted}
\citation{GinPraFerAssSavTou-JCP-18}
\@writefile{toc}{\contentsline {section}{\numberline {II}Theory}{2}{section*.4}}
\newlabel{sec:theory}{{II}{2}{}{section*.4}{}}
\citation{GinPraFerAssSavTou-JCP-18}
\citation{GinPraFerAssSavTou-JCP-18}
\citation{GinPraFerAssSavTou-JCP-18}
\citation{LooPraSceTouGin-JCPL-19,excited}
\citation{kato}
\citation{GinPraFerAssSavTou-JCP-18}
\citation{GinPraFerAssSavTou-JCP-18}
\@writefile{toc}{\contentsline {subsection}{\numberline {A}Basic formal equations}{3}{section*.5}}
\newlabel{sec:basic}{{II\tmspace +\thinmuskip {.1667em}A}{3}{}{section*.5}{}}
\newlabel{eq:levy}{{1}{3}{}{equation.2.1}{}}
\newlabel{eq:levy_func}{{2}{3}{}{equation.2.2}{}}
\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}{}}
\newlabel{eq:cbs_wbasis}{{10}{3}{}{equation.2.10}{}}
\citation{GinPraFerAssSavTou-JCP-18}
\bibdata{srDFT_SCNotes,srDFT_SC}
\bibcite{Thom-PRL-10}{{1}{2010}{{Thom}}{{}}}
\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}}}
\bibcite{GomHenScu-JCP-19}{{9}{2019}{{Gomez, Henderson,\ and\ Scuseria}}{{}}}
\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}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {C}Definition of an 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:cbs_mu}{{14}{4}{}{equation.2.14}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {D}Approximation for $\mathaccentV {bar}916{E}^\mathcal {B}[{n}({\bf r})]$ : link with RSDFT}{4}{section*.8}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {1}Generic form of the approximated functionals}{4}{section*.9}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {2}Introduction of the effective spin-density}{4}{section*.10}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {3}Requirement for $\Psi _{}^{\mathcal {B}}$ for size extensivity}{4}{section*.11}}
\@writefile{toc}{\contentsline {section}{\numberline {III}Results}{4}{section*.12}}
\newlabel{sec:results}{{III}{4}{}{section*.12}{}}
\@writefile{toc}{\contentsline {section}{\numberline {IV}Conclusion}{4}{section*.13}}
\newlabel{sec:conclusion}{{IV}{4}{}{section*.13}{}}
\@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. }}{4}{figure.1}}
\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}{}}
\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}}}
\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{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}}}
\@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. }}{5}{figure.2}}
\newlabel{fig:N2_avtz}{{2}{5}{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. }}{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}{}}
\bibcite{IrmHulGru-arxiv-19}{{50}{2019}{{Irmler, Hummel,\ and\ Grüneis}}{{}}}
\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}}}
\bibcite{KonBisVal-CR-12}{{54}{2012}{{Kong, Bischo,\ and\ Valeev}}{{}}}
\bibcite{GruHirOhnTen-JCP-17}{{55}{2017}{{Gr\"uneis\ \emph {et~al.}}}{{Gr\"uneis, Hirata, Ohnishi,\ and\ Ten-no}}}
\bibcite{MaWer-WIREs-18}{{56}{2018}{{Ma\ and\ Werner}}{{}}}
\bibcite{TewKloNeiHat-PCCP-07}{{57}{2007}{{Tew\ \emph {et~al.}}}{{Tew, Klopper, Neiss,\ and\ Hattig}}}
\bibcite{TouColSav-PRA-04}{{58}{2004}{{Toulouse, Colonna,\ and\ Savin}}{{}}}
\bibcite{FraMusLupTou-JCP-15}{{59}{2015}{{Franck\ \emph {et~al.}}}{{Franck, Mussard, Luppi,\ and\ Toulouse}}}
\bibcite{AngGerSavTou-PRA-05}{{60}{2005}{{\'Angy\'an\ \emph {et~al.}}}{{\'Angy\'an, Gerber, Savin,\ and\ Toulouse}}}
\@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}}
\newlabel{fig:F2_avtz}{{4}{6}{F$_2$, aug-cc-pvtz: Comparison between the near FCI and corrected near FCI energies and the estimated exact one}{figure.4}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {5}{\ignorespaces H$_{10}$, cc-pvdz: Comparison between the near FCI and corrected near FCI energies and the estimated exact one. }}{6}{figure.5}}
\newlabel{fig:H10_vdz}{{5}{6}{H$_{10}$, cc-pvdz: Comparison between the near FCI and corrected near FCI energies and the estimated exact one}{figure.5}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {6}{\ignorespaces H$_{10}$, cc-pvtz: Comparison between the near FCI and corrected near FCI energies and the estimated exact one. }}{6}{figure.6}}
\newlabel{fig:H10_vtz}{{6}{6}{H$_{10}$, cc-pvtz: Comparison between the near FCI and corrected near FCI energies and the estimated exact one}{figure.6}{}}
\bibcite{GolWerSto-PCCP-05}{{61}{2005}{{Goll, Werner,\ and\ Stoll}}{{}}}
\bibcite{TouGerJanSavAng-PRL-09}{{62}{2009}{{Toulouse\ \emph {et~al.}}}{{Toulouse, Gerber, Jansen, Savin,\ and\ \'Angy\'an}}}
\bibcite{JanHenScu-JCP-09}{{63}{2009}{{Janesko, Henderson,\ and\ Scuseria}}{{}}}
\bibcite{TouZhuSavJanAng-JCP-11}{{64}{2011}{{Toulouse\ \emph {et~al.}}}{{Toulouse, Zhu, Savin, Jansen,\ and\ \'Angy\'an}}}
\bibcite{MusReiAngTou-JCP-15}{{65}{2015}{{Mussard\ \emph {et~al.}}}{{Mussard, Reinhardt, \'Angy\'an,\ and\ Toulouse}}}
\bibcite{LeiStoWerSav-CPL-97}{{66}{1997}{{Leininger\ \emph {et~al.}}}{{Leininger, Stoll, Werner,\ and\ Savin}}}
\bibcite{FroTouJen-JCP-07}{{67}{2007}{{Fromager, Toulouse,\ and\ Jensen}}{{}}}
\bibcite{FroCimJen-PRA-10}{{68}{2010}{{Fromager, Cimiraglia,\ and\ Jensen}}{{}}}
\bibcite{HedKneKieJenRei-JCP-15}{{69}{2015}{{Hedeg{\r a}rd\ \emph {et~al.}}}{{Hedeg{\r a}rd, Knecht, Kielberg, Jensen,\ and\ Reiher}}}
\bibcite{HedTouJen-JCP-18}{{70}{2018}{{Hedeg{\r a}rd, Toulouse,\ and\ Jensen}}{{}}}
\bibcite{FerGinTou-JCP-18}{{71}{2019}{{Fert{\'e}, Giner,\ and\ Toulouse}}{{}}}
\bibcite{GinPraFerAssSavTou-JCP-18}{{72}{2018}{{Giner\ \emph {et~al.}}}{{Giner, Pradines, Fert\'e, Assaraf, Savin,\ and\ Toulouse}}}
\bibcite{LooPraSceTouGin-JCPL-19}{{73}{2019{}}{{Loos\ \emph {et~al.}}}{{Loos, Pradines, Scemama, Toulouse,\ and\ Giner}}}
\bibstyle{aipnum4-1}
\citation{REVTEX41Control}
\citation{aip41Control}
\@writefile{lof}{\contentsline {figure}{\numberline {7}{\ignorespaces H$_{10}$, cc-pvqz: Comparison between the near FCI and corrected near FCI energies and the estimated exact one. }}{7}{figure.7}}
\newlabel{fig:H10_vqz}{{7}{7}{H$_{10}$, cc-pvqz: Comparison between the near FCI and corrected near FCI energies and the estimated exact one}{figure.7}{}}
\newlabel{LastBibItem}{{73}{7}{}{section*.13}{}}
\newlabel{LastPage}{{}{7}{}{}{}}