working on the intro
This commit is contained in:
Emmanuel Giner
parent
214c8a8ae2
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db3f0716cf
@ -24,23 +24,42 @@
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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}}
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\@writefile{toc}{\contentsline {section}{\numberline {I}Introduction}{1}{section*.3}}
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\citation{LeiStoWerSav-CPL-97,FroTouJen-JCP-07,FroCimJen-PRA-10,HedKneKieJenRei-JCP-15,HedTouJen-JCP-18,FerGinTou-JCP-18}
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\citation{GinPraFerAssSavTou-JCP-18}
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\citation{GinPraFerAssSavTou-JCP-18}
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\@writefile{toc}{\contentsline {section}{\numberline {II}Theory}{2}{section*.4}}
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\@writefile{toc}{\contentsline {subsection}{\numberline {A}Basic formal equations}{2}{section*.5}}
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\newlabel{sec:basic}{{II\tmspace +\thinmuskip {.1667em}A}{2}{}{section*.5}{}}
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\newlabel{eq:levy}{{1}{2}{}{equation.2.1}{}}
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\newlabel{eq:levy_func}{{2}{2}{}{equation.2.2}{}}
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\@writefile{toc}{\contentsline {subsection}{\numberline {B}Definition of an effective interaction within $\mathcal {B}$}{2}{section*.6}}
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\citation{GinPraFerAssSavTou-JCP-18}
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\citation{GinPraFerAssSavTou-JCP-18}
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\citation{GinPraFerAssSavTou-JCP-18}
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\citation{LooPraSceTouGin-JCPL-19,excited}
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\citation{kato}
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\citation{GinPraFerAssSavTou-JCP-18}
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\citation{GinPraFerAssSavTou-JCP-18}
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\citation{GinPraFerAssSavTou-JCP-18}
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\newlabel{eq:levy}{{1}{3}{}{equation.2.1}{}}
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\newlabel{eq:levy_func}{{2}{3}{}{equation.2.2}{}}
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\newlabel{eq:e0approx}{{5}{3}{}{equation.2.5}{}}
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\@writefile{toc}{\contentsline {subsection}{\numberline {B}Definition of an effective interaction within $\mathcal {B}$}{3}{section*.6}}
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\newlabel{sec:wee}{{II\tmspace +\thinmuskip {.1667em}B}{3}{}{section*.6}{}}
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\newlabel{eq:wbasis}{{6}{3}{}{equation.2.6}{}}
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\newlabel{eq:fbasis}{{8}{3}{}{equation.2.8}{}}
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\@writefile{toc}{\contentsline {subsection}{\numberline {C}Definition of an range-separation parameter varying in real space}{3}{section*.7}}
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\newlabel{sec:mur}{{II\tmspace +\thinmuskip {.1667em}C}{3}{}{section*.7}{}}
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\newlabel{eq:weelr}{{11}{3}{}{equation.2.11}{}}
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\bibdata{srDFT_SCNotes,srDFT_SC}
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\bibcite{Thom-PRL-10}{{1}{2010}{{Thom}}{{}}}
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\bibcite{ScoTho-JCP-17}{{2}{2017}{{Scott\ and\ Thom}}{{}}}
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@ -73,18 +92,6 @@
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\bibcite{SchEva-JCP-16}{{29}{2016}{{Schriber\ and\ Evangelista}}{{}}}
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\bibcite{LiuHofJCTC-16}{{30}{2016}{{Liu\ and\ Hoffmann}}{{}}}
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\bibcite{HolUmrSha-JCP-17}{{31}{2017}{{Holmes, Umrigar,\ and\ Sharma}}{{}}}
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\newlabel{eq:wbasis}{{6}{3}{}{equation.2.6}{}}
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\newlabel{eq:fbasis}{{8}{3}{}{equation.2.8}{}}
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\newlabel{eq:cbs_wbasis}{{10}{3}{}{equation.2.10}{}}
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\@writefile{toc}{\contentsline {subsection}{\numberline {C}Definition of an range-separation parameter varying in real space}{3}{section*.7}}
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\newlabel{sec:mur}{{II\tmspace +\thinmuskip {.1667em}C}{3}{}{section*.7}{}}
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\newlabel{eq:weelr}{{11}{3}{}{equation.2.11}{}}
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\@writefile{toc}{\contentsline {subsection}{\numberline {D}Approximation for $\mathaccentV {bar}916{E}^\mathcal {B}[{n}({\bf r})]$ : link with RSDFT}{3}{section*.8}}
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\@writefile{toc}{\contentsline {subsubsection}{\numberline {1}Generic form of the approximated functionals}{3}{section*.9}}
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\@writefile{toc}{\contentsline {subsubsection}{\numberline {2}Introduction of the effective spin-density}{3}{section*.10}}
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\@writefile{toc}{\contentsline {subsubsection}{\numberline {3}Requirement for $\Psi _{}^{\mathcal {B}}$ for size extensivity}{3}{section*.11}}
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\@writefile{toc}{\contentsline {section}{\numberline {III}Results}{3}{section*.12}}
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\bibcite{ShaHolJeaAlaUmr-JCTC-17}{{32}{2017}{{Sharma\ \emph {et~al.}}}{{Sharma, Holmes, Jeanmairet, Alavi,\ and\ Umrigar}}}
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\bibcite{PerCle-JCP-17}{{34}{2017}{{Per\ and\ Cleland}}{{}}}
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@ -92,29 +99,63 @@
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\bibcite{Zim-JCP-17}{{36}{2017}{{Zimmerman}}{{}}}
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\newlabel{eq:cbs_mu}{{14}{4}{}{equation.2.14}{}}
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\@writefile{toc}{\contentsline {subsection}{\numberline {D}Approximation for $\mathaccentV {bar}916{E}^\mathcal {B}[{n}({\bf r})]$ : link with RSDFT}{4}{section*.8}}
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\@writefile{toc}{\contentsline {subsubsection}{\numberline {1}Generic form of the approximated functionals}{4}{section*.9}}
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\@writefile{toc}{\contentsline {subsubsection}{\numberline {2}Introduction of the effective spin-density}{4}{section*.10}}
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\@writefile{toc}{\contentsline {subsubsection}{\numberline {3}Requirement for $\Psi _{}^{\mathcal {B}}$ for size extensivity}{4}{section*.11}}
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\@writefile{toc}{\contentsline {section}{\numberline {III}Results}{4}{section*.12}}
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\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}{}}
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\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}{}}
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\bibcite{GolWerSto-PCCP-05}{{61}{2005}{{Goll, Werner,\ and\ Stoll}}{{}}}
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\bibcite{TouGerJanSavAng-PRL-09}{{62}{2009}{{Toulouse\ \emph {et~al.}}}{{Toulouse, Gerber, Jansen, Savin,\ and\ \'Angy\'an}}}
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@ -483,9 +483,10 @@
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Chem. Phys.}\ }\textbf {\bibinfo {volume} {146}},\ \bibinfo {pages} {154107}
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{Klopper}(1991)}]{KutKlo-JCP-91}%
|
||||
\BibitemOpen
|
||||
\bibfield {author} {\bibinfo {author} {\bibfnamefont {W.}~\bibnamefont
|
||||
{Kutzelnigg}}\ and\ \bibinfo {author} {\bibfnamefont {W.}~\bibnamefont
|
||||
{Klopper}},\ }\href@noop {} {\bibfield {journal} {\bibinfo {journal} {J.
|
||||
Chem. Phys.}\ }\textbf {\bibinfo {volume} {94}},\ \bibinfo {pages} {1985}
|
||||
(\bibinfo {year} {1991})}\BibitemShut {NoStop}%
|
||||
\bibitem [{\citenamefont {Noga}\ and\ \citenamefont
|
||||
{Kutzelnigg}(1994)}]{NogKut-JCP-94}%
|
||||
\BibitemOpen
|
||||
\bibfield {author} {\bibinfo {author} {\bibfnamefont {J.}~\bibnamefont
|
||||
{Noga}}\ and\ \bibinfo {author} {\bibfnamefont {W.}~\bibnamefont
|
||||
{Kutzelnigg}},\ }\href@noop {} {\bibfield {journal} {\bibinfo {journal} {J.
|
||||
Chem. Phys.}\ }\textbf {\bibinfo {volume} {101}},\ \bibinfo {pages} {7738}
|
||||
(\bibinfo {year} {1994})}\BibitemShut {NoStop}%
|
||||
\bibitem [{\citenamefont {Halkier}\ \emph {et~al.}(1998)\citenamefont
|
||||
{Halkier}, \citenamefont {Helgaker}, \citenamefont {J{\o}rgensen},
|
||||
\citenamefont {Klopper}, \citenamefont {Koch}, \citenamefont {Olsen},\ and\
|
||||
\citenamefont {Wilson}}]{HalHelJorKloKocOlsWil-CPL-98}%
|
||||
\BibitemOpen
|
||||
\bibfield {author} {\bibinfo {author} {\bibfnamefont {A.}~\bibnamefont
|
||||
{Halkier}}, \bibinfo {author} {\bibfnamefont {T.}~\bibnamefont {Helgaker}},
|
||||
\bibinfo {author} {\bibfnamefont {P.}~\bibnamefont {J{\o}rgensen}}, \bibinfo
|
||||
{author} {\bibfnamefont {W.}~\bibnamefont {Klopper}}, \bibinfo {author}
|
||||
{\bibfnamefont {H.}~\bibnamefont {Koch}}, \bibinfo {author} {\bibfnamefont
|
||||
{J.}~\bibnamefont {Olsen}}, \ and\ \bibinfo {author} {\bibfnamefont {A.~K.}\
|
||||
\bibnamefont {Wilson}},\ }\href@noop {} {\bibfield {journal} {\bibinfo
|
||||
{journal} {Chem. Phys. Lett.}\ }\textbf {\bibinfo {volume} {286}},\ \bibinfo
|
||||
{pages} {243} (\bibinfo {year} {1998})}\BibitemShut {NoStop}%
|
||||
\bibitem [{\citenamefont {Irmler}, \citenamefont {Hummel},\ and\ \citenamefont
|
||||
{Grüneis}(2019)}]{IrmHulGru-arxiv-19}%
|
||||
\BibitemOpen
|
||||
\bibfield {author} {\bibinfo {author} {\bibfnamefont {A.}~\bibnamefont
|
||||
{Irmler}}, \bibinfo {author} {\bibfnamefont {F.}~\bibnamefont {Hummel}}, \
|
||||
and\ \bibinfo {author} {\bibfnamefont {A.}~\bibnamefont {Grüneis}},\
|
||||
}\href@noop {} {\enquote {\bibinfo {title} {On the duality of ring and ladder
|
||||
diagrams and its importance for many-electron perturbation theories},}\ }
|
||||
(\bibinfo {year} {2019}),\ \Eprint {http://arxiv.org/abs/1903.05458}
|
||||
{arXiv:1903.05458 [cond-mat.mtrl-sci]} \BibitemShut {NoStop}%
|
||||
\bibitem [{\citenamefont {Ten-no}(2012)}]{Ten-TCA-12}%
|
||||
\BibitemOpen
|
||||
\bibfield {author} {\bibinfo {author} {\bibfnamefont {S.}~\bibnamefont
|
||||
{Ten-no}},\ }\href@noop {} {\bibfield {journal} {\bibinfo {journal} {Theor.
|
||||
Chem. Acc.}\ }\textbf {\bibinfo {volume} {131}},\ \bibinfo {pages} {1070}
|
||||
(\bibinfo {year} {2012})}\BibitemShut {NoStop}%
|
||||
\bibitem [{\citenamefont {Ten-no}\ and\ \citenamefont
|
||||
{Noga}(2012)}]{TenNog-WIREs-12}%
|
||||
\BibitemOpen
|
||||
\bibfield {author} {\bibinfo {author} {\bibfnamefont {S.}~\bibnamefont
|
||||
{Ten-no}}\ and\ \bibinfo {author} {\bibfnamefont {J.}~\bibnamefont {Noga}},\
|
||||
}\href@noop {} {\bibfield {journal} {\bibinfo {journal} {WIREs Comput. Mol.
|
||||
Sci.}\ }\textbf {\bibinfo {volume} {2}},\ \bibinfo {pages} {114} (\bibinfo
|
||||
{year} {2012})}\BibitemShut {NoStop}%
|
||||
\bibitem [{\citenamefont {Hattig}\ \emph {et~al.}(2012)\citenamefont {Hattig},
|
||||
\citenamefont {Klopper}, \citenamefont {Kohn},\ and\ \citenamefont
|
||||
{Tew}}]{HatKloKohTew-CR-12}%
|
||||
\BibitemOpen
|
||||
\bibfield {author} {\bibinfo {author} {\bibfnamefont {C.}~\bibnamefont
|
||||
{Hattig}}, \bibinfo {author} {\bibfnamefont {W.}~\bibnamefont {Klopper}},
|
||||
\bibinfo {author} {\bibfnamefont {A.}~\bibnamefont {Kohn}}, \ and\ \bibinfo
|
||||
{author} {\bibfnamefont {D.~P.}\ \bibnamefont {Tew}},\ }\href@noop {}
|
||||
{\bibfield {journal} {\bibinfo {journal} {Chem. Rev.}\ }\textbf {\bibinfo
|
||||
{volume} {112}},\ \bibinfo {pages} {4} (\bibinfo {year} {2012})}\BibitemShut
|
||||
{NoStop}%
|
||||
\bibitem [{\citenamefont {Kong}, \citenamefont {Bischo},\ and\ \citenamefont
|
||||
{Valeev}(2012)}]{KonBisVal-CR-12}%
|
||||
\BibitemOpen
|
||||
\bibfield {author} {\bibinfo {author} {\bibfnamefont {L.}~\bibnamefont
|
||||
{Kong}}, \bibinfo {author} {\bibfnamefont {F.~A.}\ \bibnamefont {Bischo}}, \
|
||||
and\ \bibinfo {author} {\bibfnamefont {E.~F.}\ \bibnamefont {Valeev}},\
|
||||
}\href@noop {} {\bibfield {journal} {\bibinfo {journal} {Chem. Rev.}\
|
||||
}\textbf {\bibinfo {volume} {112}},\ \bibinfo {pages} {75} (\bibinfo {year}
|
||||
{2012})}\BibitemShut {NoStop}%
|
||||
\bibitem [{\citenamefont {Gr\"uneis}\ \emph {et~al.}(2017)\citenamefont
|
||||
{Gr\"uneis}, \citenamefont {Hirata}, \citenamefont {Ohnishi},\ and\
|
||||
\citenamefont {Ten-no}}]{GruHirOhnTen-JCP-17}%
|
||||
\BibitemOpen
|
||||
\bibfield {author} {\bibinfo {author} {\bibfnamefont {A.}~\bibnamefont
|
||||
{Gr\"uneis}}, \bibinfo {author} {\bibfnamefont {S.}~\bibnamefont {Hirata}},
|
||||
\bibinfo {author} {\bibfnamefont {Y.-Y.}\ \bibnamefont {Ohnishi}}, \ and\
|
||||
\bibinfo {author} {\bibfnamefont {S.}~\bibnamefont {Ten-no}},\ }\href
|
||||
{\doibase 10.1063/1.4976974} {\bibfield {journal} {\bibinfo {journal} {J.
|
||||
Chem. Phys.}\ }\textbf {\bibinfo {volume} {146}},\ \bibinfo {pages} {080901}
|
||||
(\bibinfo {year} {2017})}\BibitemShut {NoStop}%
|
||||
\bibitem [{\citenamefont {Ma}\ and\ \citenamefont
|
||||
{Werner}(2018)}]{MaWer-WIREs-18}%
|
||||
\BibitemOpen
|
||||
\bibfield {author} {\bibinfo {author} {\bibfnamefont {Q.}~\bibnamefont
|
||||
{Ma}}\ and\ \bibinfo {author} {\bibfnamefont {H.-J.}\ \bibnamefont
|
||||
{Werner}},\ }\href@noop {} {\bibfield {journal} {\bibinfo {journal} {WIREs
|
||||
Comput. Mol. Sci.}\ }\textbf {\bibinfo {volume} {8}},\ \bibinfo {pages}
|
||||
{e1371} (\bibinfo {year} {2018})}\BibitemShut {NoStop}%
|
||||
\bibitem [{\citenamefont {Tew}\ \emph {et~al.}(2007)\citenamefont {Tew},
|
||||
\citenamefont {Klopper}, \citenamefont {Neiss},\ and\ \citenamefont
|
||||
{Hattig}}]{TewKloNeiHat-PCCP-07}%
|
||||
\BibitemOpen
|
||||
\bibfield {author} {\bibinfo {author} {\bibfnamefont {D.~P.}\ \bibnamefont
|
||||
{Tew}}, \bibinfo {author} {\bibfnamefont {W.}~\bibnamefont {Klopper}},
|
||||
\bibinfo {author} {\bibfnamefont {C.}~\bibnamefont {Neiss}}, \ and\ \bibinfo
|
||||
{author} {\bibfnamefont {C.}~\bibnamefont {Hattig}},\ }\href@noop {}
|
||||
{\bibfield {journal} {\bibinfo {journal} {Phys. Chem. Chem. Phys.}\
|
||||
}\textbf {\bibinfo {volume} {9}},\ \bibinfo {pages} {1921} (\bibinfo {year}
|
||||
{2007})}\BibitemShut {NoStop}%
|
||||
\bibitem [{\citenamefont {Toulouse}, \citenamefont {Colonna},\ and\
|
||||
\citenamefont {Savin}(2004)}]{TouColSav-PRA-04}%
|
||||
\BibitemOpen
|
||||
\bibfield {author} {\bibinfo {author} {\bibfnamefont {J.}~\bibnamefont
|
||||
{Toulouse}}, \bibinfo {author} {\bibfnamefont {F.}~\bibnamefont {Colonna}}, \
|
||||
and\ \bibinfo {author} {\bibfnamefont {A.}~\bibnamefont {Savin}},\
|
||||
}\href@noop {} {\bibfield {journal} {\bibinfo {journal} {Phys. Rev. A}\
|
||||
}\textbf {\bibinfo {volume} {70}},\ \bibinfo {pages} {062505} (\bibinfo
|
||||
{year} {2004})}\BibitemShut {NoStop}%
|
||||
\bibitem [{\citenamefont {Franck}\ \emph {et~al.}(2015)\citenamefont {Franck},
|
||||
\citenamefont {Mussard}, \citenamefont {Luppi},\ and\ \citenamefont
|
||||
{Toulouse}}]{FraMusLupTou-JCP-15}%
|
||||
\BibitemOpen
|
||||
\bibfield {author} {\bibinfo {author} {\bibfnamefont {O.}~\bibnamefont
|
||||
{Franck}}, \bibinfo {author} {\bibfnamefont {B.}~\bibnamefont {Mussard}},
|
||||
\bibinfo {author} {\bibfnamefont {E.}~\bibnamefont {Luppi}}, \ and\ \bibinfo
|
||||
{author} {\bibfnamefont {J.}~\bibnamefont {Toulouse}},\ }\href@noop {}
|
||||
{\bibfield {journal} {\bibinfo {journal} {J. Chem. Phys.}\ }\textbf
|
||||
{\bibinfo {volume} {142}},\ \bibinfo {pages} {074107} (\bibinfo {year}
|
||||
{2015})}\BibitemShut {NoStop}%
|
||||
\bibitem [{\citenamefont {\'Angy\'an}\ \emph {et~al.}(2005)\citenamefont
|
||||
{\'Angy\'an}, \citenamefont {Gerber}, \citenamefont {Savin},\ and\
|
||||
\citenamefont {Toulouse}}]{AngGerSavTou-PRA-05}%
|
||||
\BibitemOpen
|
||||
\bibfield {author} {\bibinfo {author} {\bibfnamefont {J.~G.}\ \bibnamefont
|
||||
{\'Angy\'an}}, \bibinfo {author} {\bibfnamefont {I.~C.}\ \bibnamefont
|
||||
{Gerber}}, \bibinfo {author} {\bibfnamefont {A.}~\bibnamefont {Savin}}, \
|
||||
and\ \bibinfo {author} {\bibfnamefont {J.}~\bibnamefont {Toulouse}},\
|
||||
}\href@noop {} {\bibfield {journal} {\bibinfo {journal} {Phys. Rev. A}\
|
||||
}\textbf {\bibinfo {volume} {72}},\ \bibinfo {pages} {012510} (\bibinfo
|
||||
{year} {2005})}\BibitemShut {NoStop}%
|
||||
\bibitem [{\citenamefont {Goll}, \citenamefont {Werner},\ and\ \citenamefont
|
||||
{Stoll}(2005)}]{GolWerSto-PCCP-05}%
|
||||
\BibitemOpen
|
||||
\bibfield {author} {\bibinfo {author} {\bibfnamefont {E.}~\bibnamefont
|
||||
{Goll}}, \bibinfo {author} {\bibfnamefont {H.-J.}\ \bibnamefont {Werner}}, \
|
||||
and\ \bibinfo {author} {\bibfnamefont {H.}~\bibnamefont {Stoll}},\
|
||||
}\href@noop {} {\bibfield {journal} {\bibinfo {journal} {Phys. Chem. Chem.
|
||||
Phys.}\ }\textbf {\bibinfo {volume} {7}},\ \bibinfo {pages} {3917} (\bibinfo
|
||||
{year} {2005})}\BibitemShut {NoStop}%
|
||||
\bibitem [{\citenamefont {Toulouse}\ \emph {et~al.}(2009)\citenamefont
|
||||
{Toulouse}, \citenamefont {Gerber}, \citenamefont {Jansen}, \citenamefont
|
||||
{Savin},\ and\ \citenamefont {\'Angy\'an}}]{TouGerJanSavAng-PRL-09}%
|
||||
\BibitemOpen
|
||||
\bibfield {author} {\bibinfo {author} {\bibfnamefont {J.}~\bibnamefont
|
||||
{Toulouse}}, \bibinfo {author} {\bibfnamefont {I.~C.}\ \bibnamefont
|
||||
{Gerber}}, \bibinfo {author} {\bibfnamefont {G.}~\bibnamefont {Jansen}},
|
||||
\bibinfo {author} {\bibfnamefont {A.}~\bibnamefont {Savin}}, \ and\ \bibinfo
|
||||
{author} {\bibfnamefont {J.~G.}\ \bibnamefont {\'Angy\'an}},\ }\href@noop {}
|
||||
{\bibfield {journal} {\bibinfo {journal} {Phys. Rev. Lett.}\ }\textbf
|
||||
{\bibinfo {volume} {102}},\ \bibinfo {pages} {096404} (\bibinfo {year}
|
||||
{2009})}\BibitemShut {NoStop}%
|
||||
\bibitem [{\citenamefont {Janesko}, \citenamefont {Henderson},\ and\
|
||||
\citenamefont {Scuseria}(2009)}]{JanHenScu-JCP-09}%
|
||||
\BibitemOpen
|
||||
\bibfield {author} {\bibinfo {author} {\bibfnamefont {B.~G.}\ \bibnamefont
|
||||
{Janesko}}, \bibinfo {author} {\bibfnamefont {T.~M.}\ \bibnamefont
|
||||
{Henderson}}, \ and\ \bibinfo {author} {\bibfnamefont {G.~E.}\ \bibnamefont
|
||||
{Scuseria}},\ }\href@noop {} {\bibfield {journal} {\bibinfo {journal} {J.
|
||||
Chem. Phys.}\ }\textbf {\bibinfo {volume} {130}},\ \bibinfo {pages} {081105}
|
||||
(\bibinfo {year} {2009})}\BibitemShut {NoStop}%
|
||||
\bibitem [{\citenamefont {Toulouse}\ \emph {et~al.}(2011)\citenamefont
|
||||
{Toulouse}, \citenamefont {Zhu}, \citenamefont {Savin}, \citenamefont
|
||||
{Jansen},\ and\ \citenamefont {\'Angy\'an}}]{TouZhuSavJanAng-JCP-11}%
|
||||
\BibitemOpen
|
||||
\bibfield {author} {\bibinfo {author} {\bibfnamefont {J.}~\bibnamefont
|
||||
{Toulouse}}, \bibinfo {author} {\bibfnamefont {W.}~\bibnamefont {Zhu}},
|
||||
\bibinfo {author} {\bibfnamefont {A.}~\bibnamefont {Savin}}, \bibinfo
|
||||
{author} {\bibfnamefont {G.}~\bibnamefont {Jansen}}, \ and\ \bibinfo {author}
|
||||
{\bibfnamefont {J.~G.}\ \bibnamefont {\'Angy\'an}},\ }\href@noop {}
|
||||
{\bibfield {journal} {\bibinfo {journal} {J. Chem. Phys.}\ }\textbf
|
||||
{\bibinfo {volume} {135}},\ \bibinfo {pages} {084119} (\bibinfo {year}
|
||||
{2011})}\BibitemShut {NoStop}%
|
||||
\bibitem [{\citenamefont {Mussard}\ \emph {et~al.}(2015)\citenamefont
|
||||
{Mussard}, \citenamefont {Reinhardt}, \citenamefont {\'Angy\'an},\ and\
|
||||
\citenamefont {Toulouse}}]{MusReiAngTou-JCP-15}%
|
||||
\BibitemOpen
|
||||
\bibfield {author} {\bibinfo {author} {\bibfnamefont {B.}~\bibnamefont
|
||||
{Mussard}}, \bibinfo {author} {\bibfnamefont {P.}~\bibnamefont {Reinhardt}},
|
||||
\bibinfo {author} {\bibfnamefont {J.~G.}\ \bibnamefont {\'Angy\'an}}, \ and\
|
||||
\bibinfo {author} {\bibfnamefont {J.}~\bibnamefont {Toulouse}},\ }\href@noop
|
||||
{} {\bibfield {journal} {\bibinfo {journal} {J. Chem. Phys.}\ }\textbf
|
||||
{\bibinfo {volume} {142}},\ \bibinfo {pages} {154123} (\bibinfo {year}
|
||||
{2015})},\ \bibinfo {note} {erratum: J. Chem. Phys. {\bf 142}, 219901
|
||||
(2015)}\BibitemShut {NoStop}%
|
||||
\bibitem [{\citenamefont {Leininger}\ \emph {et~al.}(1997)\citenamefont
|
||||
{Leininger}, \citenamefont {Stoll}, \citenamefont {Werner},\ and\
|
||||
\citenamefont {Savin}}]{LeiStoWerSav-CPL-97}%
|
||||
\BibitemOpen
|
||||
\bibfield {author} {\bibinfo {author} {\bibfnamefont {T.}~\bibnamefont
|
||||
{Leininger}}, \bibinfo {author} {\bibfnamefont {H.}~\bibnamefont {Stoll}},
|
||||
\bibinfo {author} {\bibfnamefont {H.-J.}\ \bibnamefont {Werner}}, \ and\
|
||||
\bibinfo {author} {\bibfnamefont {A.}~\bibnamefont {Savin}},\ }\href@noop {}
|
||||
{\bibfield {journal} {\bibinfo {journal} {Chem. Phys. Lett.}\ }\textbf
|
||||
{\bibinfo {volume} {{275}}},\ \bibinfo {pages} {151} (\bibinfo {year}
|
||||
{1997})}\BibitemShut {NoStop}%
|
||||
\bibitem [{\citenamefont {Fromager}, \citenamefont {Toulouse},\ and\
|
||||
\citenamefont {Jensen}(2007)}]{FroTouJen-JCP-07}%
|
||||
\BibitemOpen
|
||||
\bibfield {author} {\bibinfo {author} {\bibfnamefont {E.}~\bibnamefont
|
||||
{Fromager}}, \bibinfo {author} {\bibfnamefont {J.}~\bibnamefont {Toulouse}},
|
||||
\ and\ \bibinfo {author} {\bibfnamefont {H.~J.~A.}\ \bibnamefont {Jensen}},\
|
||||
}\href@noop {} {\bibfield {journal} {\bibinfo {journal} {J. Chem. Phys.}\
|
||||
}\textbf {\bibinfo {volume} {126}},\ \bibinfo {pages} {074111} (\bibinfo
|
||||
{year} {2007})}\BibitemShut {NoStop}%
|
||||
\bibitem [{\citenamefont {Fromager}, \citenamefont {Cimiraglia},\ and\
|
||||
\citenamefont {Jensen}(2010)}]{FroCimJen-PRA-10}%
|
||||
\BibitemOpen
|
||||
\bibfield {author} {\bibinfo {author} {\bibfnamefont {E.}~\bibnamefont
|
||||
{Fromager}}, \bibinfo {author} {\bibfnamefont {R.}~\bibnamefont
|
||||
{Cimiraglia}}, \ and\ \bibinfo {author} {\bibfnamefont {H.~J.~A.}\
|
||||
\bibnamefont {Jensen}},\ }\href@noop {} {\bibfield {journal} {\bibinfo
|
||||
{journal} {Phys. Rev. A}\ }\textbf {\bibinfo {volume} {81}},\ \bibinfo
|
||||
{pages} {024502} (\bibinfo {year} {2010})}\BibitemShut {NoStop}%
|
||||
\bibitem [{\citenamefont {Hedeg{\aa}rd}\ \emph {et~al.}(2015)\citenamefont
|
||||
{Hedeg{\aa}rd}, \citenamefont {Knecht}, \citenamefont {Kielberg},
|
||||
\citenamefont {Jensen},\ and\ \citenamefont
|
||||
{Reiher}}]{HedKneKieJenRei-JCP-15}%
|
||||
\BibitemOpen
|
||||
\bibfield {author} {\bibinfo {author} {\bibfnamefont {E.~D.}\ \bibnamefont
|
||||
{Hedeg{\aa}rd}}, \bibinfo {author} {\bibfnamefont {S.}~\bibnamefont
|
||||
{Knecht}}, \bibinfo {author} {\bibfnamefont {J.~S.}\ \bibnamefont
|
||||
{Kielberg}}, \bibinfo {author} {\bibfnamefont {H.~J.~A.}\ \bibnamefont
|
||||
{Jensen}}, \ and\ \bibinfo {author} {\bibfnamefont {M.}~\bibnamefont
|
||||
{Reiher}},\ }\href@noop {} {\bibfield {journal} {\bibinfo {journal} {J.
|
||||
Chem. Phys.}\ }\textbf {\bibinfo {volume} {142}},\ \bibinfo {pages} {224108}
|
||||
(\bibinfo {year} {2015})}\BibitemShut {NoStop}%
|
||||
\bibitem [{\citenamefont {Hedeg{\aa}rd}, \citenamefont {Toulouse},\ and\
|
||||
\citenamefont {Jensen}(2018)}]{HedTouJen-JCP-18}%
|
||||
\BibitemOpen
|
||||
\bibfield {author} {\bibinfo {author} {\bibfnamefont {E.~D.}\ \bibnamefont
|
||||
{Hedeg{\aa}rd}}, \bibinfo {author} {\bibfnamefont {J.}~\bibnamefont
|
||||
{Toulouse}}, \ and\ \bibinfo {author} {\bibfnamefont {H.~J.~A.}\ \bibnamefont
|
||||
{Jensen}},\ }\href {\doibase 10.1063/1.5013306} {\bibfield {journal}
|
||||
{\bibinfo {journal} {J. Chem. Phys.}\ }\textbf {\bibinfo {volume} {148}},\
|
||||
\bibinfo {pages} {214103} (\bibinfo {year} {2018})}\BibitemShut {NoStop}%
|
||||
\bibitem [{\citenamefont {Fert{\'e}}, \citenamefont {Giner},\ and\
|
||||
\citenamefont {Toulouse}(2019)}]{FerGinTou-JCP-18}%
|
||||
\BibitemOpen
|
||||
\bibfield {author} {\bibinfo {author} {\bibfnamefont {A.}~\bibnamefont
|
||||
{Fert{\'e}}}, \bibinfo {author} {\bibfnamefont {E.}~\bibnamefont {Giner}}, \
|
||||
and\ \bibinfo {author} {\bibfnamefont {J.}~\bibnamefont {Toulouse}},\ }\href
|
||||
{\doibase 10.1063/1.5082638} {\bibfield {journal} {\bibinfo {journal} {The
|
||||
Journal of Chemical Physics}\ }\textbf {\bibinfo {volume} {150}},\ \bibinfo
|
||||
{pages} {084103} (\bibinfo {year} {2019})},\ \Eprint
|
||||
{http://arxiv.org/abs/https://doi.org/10.1063/1.5082638}
|
||||
{https://doi.org/10.1063/1.5082638} \BibitemShut {NoStop}%
|
||||
\bibitem [{\citenamefont {Giner}\ \emph {et~al.}(2018)\citenamefont {Giner},
|
||||
\citenamefont {Pradines}, \citenamefont {Fert\'e}, \citenamefont {Assaraf},
|
||||
\citenamefont {Savin},\ and\ \citenamefont
|
||||
@ -509,4 +773,20 @@
|
||||
{journal} {\bibinfo {journal} {J. Chem. Phys.}\ }\textbf {\bibinfo {volume}
|
||||
{149}},\ \bibinfo {pages} {194301} (\bibinfo {year} {2018})}\BibitemShut
|
||||
{NoStop}%
|
||||
\bibitem [{\citenamefont {Loos}\ \emph
|
||||
{et~al.}(2019{\natexlab{b}})\citenamefont {Loos}, \citenamefont {Pradines},
|
||||
\citenamefont {Scemama}, \citenamefont {Toulouse},\ and\ \citenamefont
|
||||
{Giner}}]{LooPraSceTouGin-JCPL-19}%
|
||||
\BibitemOpen
|
||||
\bibfield {author} {\bibinfo {author} {\bibfnamefont {P.-F.}\ \bibnamefont
|
||||
{Loos}}, \bibinfo {author} {\bibfnamefont {B.}~\bibnamefont {Pradines}},
|
||||
\bibinfo {author} {\bibfnamefont {A.}~\bibnamefont {Scemama}}, \bibinfo
|
||||
{author} {\bibfnamefont {J.}~\bibnamefont {Toulouse}}, \ and\ \bibinfo
|
||||
{author} {\bibfnamefont {E.}~\bibnamefont {Giner}},\ }\href {\doibase
|
||||
10.1021/acs.jpclett.9b01176} {\bibfield {journal} {\bibinfo {journal} {The
|
||||
Journal of Physical Chemistry Letters}\ }\textbf {\bibinfo {volume} {10}},\
|
||||
\bibinfo {pages} {2931} (\bibinfo {year} {2019}{\natexlab{b}})},\ \bibinfo
|
||||
{note} {pMID: 31090432},\ \Eprint
|
||||
{http://arxiv.org/abs/https://doi.org/10.1021/acs.jpclett.9b01176}
|
||||
{https://doi.org/10.1021/acs.jpclett.9b01176} \BibitemShut {NoStop}%
|
||||
\end{thebibliography}%
|
||||
|
||||
@ -207,14 +207,6 @@
|
||||
Volume = {94},
|
||||
Year = {1991}}
|
||||
|
||||
@article{KutKlo-JCP-91,
|
||||
Author = {W. Kutzelnigg and W. Klopper},
|
||||
Date-Added = {2019-04-03 21:35:04 +0200},
|
||||
Date-Modified = {2019-04-03 21:35:52 +0200},
|
||||
Journal = {J. Chem. Phys.},
|
||||
Pages = {1985},
|
||||
Volume = {94},
|
||||
Year = {1991}}
|
||||
|
||||
@article{Kut-TCA-85,
|
||||
Author = {W. Kutzelnigg},
|
||||
@ -12602,3 +12594,67 @@ URL = {https://doi.org/10.1063/1.5085314},
|
||||
eprint = {https://doi.org/10.1063/1.5085314}
|
||||
}
|
||||
|
||||
@article{Hyl-ZP-29,
|
||||
Author = {E. A. Hylleraas},
|
||||
Date-Added = {2019-04-07 14:28:17 +0200},
|
||||
Date-Modified = {2019-04-07 14:29:49 +0200},
|
||||
Journal = {Z. Phys.},
|
||||
Pages = {347},
|
||||
Title = {Neue Berechnung der Energie des Heliums im Grundzustande, sowie des tiefsten Terms von Ortho-Helium},
|
||||
Volume = {54},
|
||||
Year = {1929}}
|
||||
|
||||
@article{KutKlo-JCP-91,
|
||||
Author = {W. Kutzelnigg and W. Klopper},
|
||||
Date-Added = {2019-04-03 21:35:04 +0200},
|
||||
Date-Modified = {2019-04-07 14:31:15 +0200},
|
||||
Journal = {J. Chem. Phys.},
|
||||
Pages = {1985},
|
||||
Title = {Wave functions with terms linear in the interelectronic coordinates to take care of the correlation cusp. I. General theory},
|
||||
Volume = {94},
|
||||
Year = {1991}}
|
||||
|
||||
@misc{IrmHulGru-arxiv-19,
|
||||
title={On the duality of ring and ladder diagrams and its importance for many-electron perturbation theories},
|
||||
author={Andreas Irmler and Felix Hummel and Andreas Grüneis},
|
||||
year={2019},
|
||||
eprint={1903.05458},
|
||||
archivePrefix={arXiv},
|
||||
primaryClass={cond-mat.mtrl-sci}
|
||||
}
|
||||
@article{GruHirOhnTen-JCP-17,
|
||||
Author = {A. Gr\"uneis and S. Hirata and Y.-Y. Ohnishi and S. Ten-no},
|
||||
Date-Added = {2019-05-08 10:24:45 +0200},
|
||||
Date-Modified = {2019-05-08 10:27:42 +0200},
|
||||
Doi = {10.1063/1.4976974},
|
||||
Journal = {J. Chem. Phys.},
|
||||
Pages = {080901},
|
||||
Title = {Perspective: Explicitly correlated electronic structure theory for complex systems},
|
||||
Volume = {146},
|
||||
Year = {2017}}
|
||||
|
||||
@article{MaWer-WIREs-18,
|
||||
Author = {Q. Ma and H.-J. Werner},
|
||||
Date-Added = {2019-05-08 10:32:33 +0200},
|
||||
Date-Modified = {2019-05-08 10:33:31 +0200},
|
||||
Journal = {WIREs Comput. Mol. Sci.},
|
||||
Keywords = {10.1002/wcms.1371},
|
||||
Pages = {e1371},
|
||||
Title = {Explicitly correlated local coupled‐cluster methods using pair natural orbitals},
|
||||
Volume = {8},
|
||||
Year = {2018}}
|
||||
|
||||
@article{LooPraSceTouGin-JCPL-19,
|
||||
author = {Loos, Pierre-François and Pradines, Barthélémy and Scemama, Anthony and Toulouse, Julien and Giner, Emmanuel},
|
||||
title = {A Density-Based Basis-Set Correction for Wave Function Theory},
|
||||
journal = {The Journal of Physical Chemistry Letters},
|
||||
volume = {10},
|
||||
number = {11},
|
||||
pages = {2931-2937},
|
||||
year = {2019},
|
||||
doi = {10.1021/acs.jpclett.9b01176},
|
||||
note ={PMID: 31090432},
|
||||
URL = {https://doi.org/10.1021/acs.jpclett.9b01176},
|
||||
eprint = {https://doi.org/10.1021/acs.jpclett.9b01176}
|
||||
}
|
||||
|
||||
|
||||
@ -11,7 +11,7 @@ Reallocated singl_function (elt_size=4) to 100 items from 50.
|
||||
Reallocated wiz_functions (elt_size=4) to 6000 items from 3000.
|
||||
Database file #1: srDFT_SCNotes.bib
|
||||
Database file #2: srDFT_SC.bib
|
||||
Warning--I didn't find a database entry for "G2"
|
||||
Warning--I didn't find a database entry for "exicted"
|
||||
Warning--I didn't find a database entry for "excited"
|
||||
Warning--I didn't find a database entry for "kato"
|
||||
control{REVTEX41Control}, control.key{N/A}, control.author{N/A}, control.editor{N/A}, control.title{N/A}, control.pages{N/A}, control.year{N/A}, control.eprint{N/A},
|
||||
@ -27,45 +27,45 @@ Control: page (0) single
|
||||
Control: year (1) truncated
|
||||
Control: production of eprint (0) enabled
|
||||
Warning--missing journal in CafAplGinScem-arxiv-16
|
||||
You've used 47 entries,
|
||||
You've used 75 entries,
|
||||
5918 wiz_defined-function locations,
|
||||
1984 strings with 25640 characters,
|
||||
and the built_in function-call counts, 47889 in all, are:
|
||||
= -- 3057
|
||||
> -- 1547
|
||||
< -- 301
|
||||
+ -- 482
|
||||
- -- 399
|
||||
* -- 7387
|
||||
:= -- 4925
|
||||
add.period$ -- 45
|
||||
call.type$ -- 47
|
||||
change.case$ -- 180
|
||||
chr.to.int$ -- 45
|
||||
cite$ -- 48
|
||||
duplicate$ -- 4273
|
||||
empty$ -- 3372
|
||||
format.name$ -- 798
|
||||
if$ -- 9458
|
||||
int.to.chr$ -- 3
|
||||
int.to.str$ -- 54
|
||||
missing$ -- 571
|
||||
newline$ -- 187
|
||||
num.names$ -- 135
|
||||
pop$ -- 1824
|
||||
2149 strings with 30040 characters,
|
||||
and the built_in function-call counts, 77568 in all, are:
|
||||
= -- 4961
|
||||
> -- 2536
|
||||
< -- 476
|
||||
+ -- 789
|
||||
- -- 647
|
||||
* -- 11979
|
||||
:= -- 7981
|
||||
add.period$ -- 74
|
||||
call.type$ -- 75
|
||||
change.case$ -- 295
|
||||
chr.to.int$ -- 72
|
||||
cite$ -- 76
|
||||
duplicate$ -- 6909
|
||||
empty$ -- 5499
|
||||
format.name$ -- 1307
|
||||
if$ -- 15373
|
||||
int.to.chr$ -- 4
|
||||
int.to.str$ -- 82
|
||||
missing$ -- 913
|
||||
newline$ -- 271
|
||||
num.names$ -- 219
|
||||
pop$ -- 2950
|
||||
preamble$ -- 1
|
||||
purify$ -- 225
|
||||
purify$ -- 365
|
||||
quote$ -- 0
|
||||
skip$ -- 1707
|
||||
skip$ -- 2736
|
||||
stack$ -- 0
|
||||
substring$ -- 1245
|
||||
swap$ -- 4169
|
||||
text.length$ -- 144
|
||||
substring$ -- 2018
|
||||
swap$ -- 6723
|
||||
text.length$ -- 237
|
||||
text.prefix$ -- 0
|
||||
top$ -- 10
|
||||
type$ -- 651
|
||||
type$ -- 1052
|
||||
warning$ -- 2
|
||||
while$ -- 179
|
||||
while$ -- 290
|
||||
width$ -- 0
|
||||
write$ -- 418
|
||||
write$ -- 646
|
||||
(There were 5 warnings)
|
||||
|
||||
@ -254,7 +254,7 @@ ii) the quantitative description of the systems must take into account weak corr
|
||||
other electronic configurations with typically much smaller weights in the wave function.
|
||||
Fulfilling these two objectives is a rather complicated task, specially if one adds the requirement of size-extensivity and additivity of the computed energy in the case of non interacting fragments, which is a very desirable property for any approximated method.
|
||||
|
||||
To tackle this complicated problem, many methods have been proposed and an exhaustive review of the zoology of methods for strong correlation goes beyond the scope and purpose of this article.
|
||||
%To tackle this complicated problem, many methods have been proposed and an exhaustive review of the zoology of methods for strong correlation goes beyond the scope and purpose of this article.
|
||||
|
||||
To tackle this problem, many WFT methods have emerged which can be categorized in two branches: the single-reference (SR)
|
||||
and multi-reference (MR) methods.
|
||||
@ -271,13 +271,19 @@ The advantage of MRCI approaches rely essentially in their simple linear paramet
|
||||
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.
|
||||
|
||||
Besides the difficulties of accurately describing the electronic structure within a given basis set, a crucial component of the limitations of applicability of WFT concerns the slow convergence of the energies and properties with respect to the quality of the basis set. As initially shown by the seminal work of Hylleraas\cite{Hyl-ZP-29} and further developed by Kutzelnigg \textit{et. al.}\cite{Kut-TCA-85,KutKlo-JCP-91, NogKut-JCP-94}, the main convergence problem originates from the divergence of the coulomb interaction at the electron coalescence point, which induces a discontinuity in the first-derivative of the wave function (the so-called electron-electron cusp). Describing such a discontinuity with an incomplete basis set is impossible and as a consequence, the convergence of the computed energies and properties can be strongly affected. To attenuate this problem, extrapolation techniques has been developed, either based on the Hylleraas's expansion of the coulomb operator\cite{HalHelJorKloKocOlsWil-CPL-98}, or more recently based on perturbative arguments\cite{IrmHulGru-arxiv-19}. A more rigorous approach to tackle the basis set convergence problem has been proposed by the so-called R12 and F12 methods\cite{Ten-TCA-12,TenNog-WIREs-12,HatKloKohTew-CR-12, KonBisVal-CR-12, GruHirOhnTen-JCP-17, MaWer-WIREs-18} which introduce a function explicitly depending on the interelectronic coordinates ensuring the correct cusp condition in the wave function, and the resulting correlation energies converge much faster than the usual WFT. For instance, using the explicitly correlated version of coupled cluster with single, double and perturbative triple substitution (CCSD(T)) in a triple-$\zeta$ quality basis set is equivalent to a quintuple-$\zeta$ quality of the usual CCSD(T) method\cite{TewKloNeiHat-PCCP-07}, although inherent computational overhead are introduced by the auxiliary basis sets needed to resolve the rather complex three- and four-electron integrals involved in the F12 theory.
|
||||
|
||||
An alternative point of view is to leave the short-range correlation effects to DFT and to use WFT to deal only with the long-range and/or strong-correlation effects. A rigorous approach to do so is the range-separated DFT (RSDFT) formalism (see Ref.~\onlinecite{TouColSav-PRA-04} and references therein) which rely on a splitting of the coulomb interaction in terms of the interelectronic distance thanks to a range-separation parameter $\mu$. The advantage of such approach is at least two-folds: i) the DFT part deals only with the short-range part of the coulomb interaction, and therefore the usual semi-local approximations to the unknown exchange-correlation functional are more suited to that correlation regime, ii) the WFT part deals with a smooth non divergent interaction, which removes the cusp condition and therefore the basis set convergence is much faster\cite{FraMusLupTou-JCP-15}.
|
||||
Therefore, a number of approximate RS-DFT schemes have been developed within single-reference \cite{AngGerSavTou-PRA-05, GolWerSto-PCCP-05, TouGerJanSavAng-PRL-09,JanHenScu-JCP-09, TouZhuSavJanAng-JCP-11, MusReiAngTou-JCP-15} or multi-reference \cite{LeiStoWerSav-CPL-97, FroTouJen-JCP-07, FroCimJen-PRA-10, HedKneKieJenRei-JCP-15, HedTouJen-JCP-18, FerGinTou-JCP-18} WFT approaches. Nevertheless, there are still some open issues in RSDFT, such as the dependence of the quality of the results on the value of the range separation $\mu$ which can be seen as an empirical parameter, together with the remaining self-interaction errors.
|
||||
|
||||
Following this path, a very recent solution to the basis set convergence problem has been proposed by some of the preset authors\cite{GinPraFerAssSavTou-JCP-18} where they proposed to use RSDFT to take into account only the correlation effects outside a given basis set. The key idea in such a work is to realize that as a wave function developed in an incomplete basis set is cusp-less, it could also come from a Hamiltonian with a non divergent electron-electron interaction. Therefore, the authors proposed a mapping with RSDFT through the introduction of an effective non-divergent interaction representing the usual coulomb interaction projected in an incomplete basis set. First applications to weakly correlated molecular systems have been successfully carried recently\cite{LooPraSceTouGin-JCPL-19} together with the first attempt to generalize this approach to excited states\cite{exicted}.
|
||||
The goal of the present work is to push the development of this new theory toward the direction of strongly correlated systems.
|
||||
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\section{Theory}
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
The theoretical framework of the basis set correction have been derived in details in \cite{GinPraFerAssSavTou-JCP-18}, so we recall briefly the main equations involved for the present study.
|
||||
The theoretical framework of the basis set correction has been derived in details in \cite{GinPraFerAssSavTou-JCP-18}, so we recall briefly the main equations involved for the present study.
|
||||
First in section \ref{sec:basic} we recall the basic mathematical framework of the present theory by introducing the density functional complementary to a basis set $\Bas$. Then in section \ref{sec:wee} we introduce an effective non divergent interaction in a basis set $\Bas$, which leads us to the definition of an effective range separation parameter varying in space in section \ref{sec:mur}. Thanks to the range separation parameter, we make a mapping with a specific class of RSDFT functionals and propose practical approximations for the unknown density functional complementary to a basis set $\Bas$, for which new approximations for the strong correlation regime are given in section \ref{sec:functional}.
|
||||
\subsection{Basic formal equations}
|
||||
\label{sec:basic}
|
||||
@ -313,7 +319,7 @@ Assuming that the FCI density $\denFCI$ in $\Bas$ is a good approximation of the
|
||||
\label{eq:e0approx}
|
||||
E_0 = \efci + \efuncbasisFCI
|
||||
\end{equation}
|
||||
where $\efci$ is the ground state FCI energy within $\Bas$. As it was originally shown in \cite{GinPraFerAssSavTou-JCP-18} and further emphasized in \cite{G2,excited}, the main role of $\efuncbasisFCI$ is to correct for the basis set incompleteness errors, a large part of which originates from the lack of cusp in any wave function developed in an incomplete basis set.
|
||||
where $\efci$ is the ground state FCI energy within $\Bas$. As it was originally shown in \cite{GinPraFerAssSavTou-JCP-18} and further emphasized in \cite{LooPraSceTouGin-JCPL-19,excited}, the main role of $\efuncbasisFCI$ is to correct for the basis set incompleteness errors, a large part of which originates from the lack of cusp in any wave function developed in an incomplete basis set.
|
||||
The whole purpose of this paper is to determine approximations for $\efuncbasisFCI$ which are suited for treating strong correlation regimes. The two requirement for such conditions are that i) it can be defined for multi-reference wave functions, ii) it must provide size extensive energies, iii) it is invariant of the $S_z$ component of a given spin multiplicity.
|
||||
|
||||
\subsection{Definition of an effective interaction within $\Bas$}
|
||||
|
||||
Loading…
Reference in New Issue
Block a user