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%Control: page (0) single %Control: page (0) single
%Control: year (1) truncated %Control: year (1) truncated
%Control: production of eprint (0) enabled %Control: production of eprint (0) enabled
\begin{thebibliography}{87}% \begin{thebibliography}{50}%
\makeatletter \makeatletter
\providecommand \@ifxundefined [1]{% \providecommand \@ifxundefined [1]{%
\@ifx{#1\undefined} \@ifx{#1\undefined}
@ -50,452 +50,6 @@
\providecommand \BibitemShut [1]{\csname bibitem#1\endcsname}% \providecommand \BibitemShut [1]{\csname bibitem#1\endcsname}%
\let\auto@bib@innerbib\@empty \let\auto@bib@innerbib\@empty
%</preamble> %</preamble>
\bibitem [{\citenamefont {Thom}(2010)}]{Thom-PRL-10}%
\BibitemOpen
\bibfield {author} {\bibinfo {author} {\bibfnamefont {A.~J.~W.}\
\bibnamefont {Thom}},\ }\href {\doibase 10.1103/PhysRevLett.105.263004}
{\bibfield {journal} {\bibinfo {journal} {Phys. Rev. Lett.}\ }\textbf
{\bibinfo {volume} {105}},\ \bibinfo {pages} {263004} (\bibinfo {year}
{2010})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Scott}\ and\ \citenamefont
{Thom}(2017)}]{ScoTho-JCP-17}%
\BibitemOpen
\bibfield {author} {\bibinfo {author} {\bibfnamefont {C.~J.~C.}\
\bibnamefont {Scott}}\ and\ \bibinfo {author} {\bibfnamefont {A.~J.~W.}\
\bibnamefont {Thom}},\ }\href {\doibase 10.1063/1.4991795} {\bibfield
{journal} {\bibinfo {journal} {The Journal of Chemical Physics}\ }\textbf
{\bibinfo {volume} {147}},\ \bibinfo {pages} {124105} (\bibinfo {year}
{2017})},\ \Eprint {http://arxiv.org/abs/https://doi.org/10.1063/1.4991795}
{https://doi.org/10.1063/1.4991795} \BibitemShut {NoStop}%
\bibitem [{\citenamefont {Spencer}\ \emph {et~al.}(2018)\citenamefont
{Spencer}, \citenamefont {Neufeld}, \citenamefont {Vigor}, \citenamefont
{Franklin},\ and\ \citenamefont {Thom}}]{SpeNeuVigFraTho-JCP-18}%
\BibitemOpen
\bibfield {author} {\bibinfo {author} {\bibfnamefont {J.~S.}\ \bibnamefont
{Spencer}}, \bibinfo {author} {\bibfnamefont {V.~A.}\ \bibnamefont
{Neufeld}}, \bibinfo {author} {\bibfnamefont {W.~A.}\ \bibnamefont {Vigor}},
\bibinfo {author} {\bibfnamefont {R.~S.~T.}\ \bibnamefont {Franklin}}, \ and\
\bibinfo {author} {\bibfnamefont {A.~J.~W.}\ \bibnamefont {Thom}},\ }\href
{\doibase 10.1063/1.5047420} {\bibfield {journal} {\bibinfo {journal} {The
Journal of Chemical Physics}\ }\textbf {\bibinfo {volume} {149}},\ \bibinfo
{pages} {204103} (\bibinfo {year} {2018})},\ \Eprint
{http://arxiv.org/abs/https://doi.org/10.1063/1.5047420}
{https://doi.org/10.1063/1.5047420} \BibitemShut {NoStop}%
\bibitem [{\citenamefont {Deustua}, \citenamefont {Shen},\ and\ \citenamefont
{Piecuch}(2017)}]{DeuEmiShePie-PRL-17}%
\BibitemOpen
\bibfield {author} {\bibinfo {author} {\bibfnamefont {J.~E.}\ \bibnamefont
{Deustua}}, \bibinfo {author} {\bibfnamefont {J.}~\bibnamefont {Shen}}, \
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{\doibase 10.1103/PhysRevLett.119.223003} {\bibfield {journal} {\bibinfo
{journal} {Phys. Rev. Lett.}\ }\textbf {\bibinfo {volume} {119}},\ \bibinfo
{pages} {223003} (\bibinfo {year} {2017})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Deustua}\ \emph {et~al.}(2018)\citenamefont
{Deustua}, \citenamefont {Magoulas}, \citenamefont {Shen},\ and\
\citenamefont {Piecuch}}]{DeuEmiMagShePie-JCP-18}%
\BibitemOpen
\bibfield {author} {\bibinfo {author} {\bibfnamefont {J.~E.}\ \bibnamefont
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\bibinfo {author} {\bibfnamefont {J.}~\bibnamefont {Shen}}, \ and\ \bibinfo
{author} {\bibfnamefont {P.}~\bibnamefont {Piecuch}},\ }\href {\doibase
10.1063/1.5055769} {\bibfield {journal} {\bibinfo {journal} {The Journal of
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{151101} (\bibinfo {year} {2018})},\ \Eprint
{http://arxiv.org/abs/https://doi.org/10.1063/1.5055769}
{https://doi.org/10.1063/1.5055769} \BibitemShut {NoStop}%
\bibitem [{\citenamefont {Deustua}\ \emph {et~al.}(2019)\citenamefont
{Deustua}, \citenamefont {Yuwono}, \citenamefont {Shen},\ and\ \citenamefont
{Piecuch}}]{DeuEmiYumShePie-JCP-19}%
\BibitemOpen
\bibfield {author} {\bibinfo {author} {\bibfnamefont {J.~E.}\ \bibnamefont
{Deustua}}, \bibinfo {author} {\bibfnamefont {S.~H.}\ \bibnamefont {Yuwono}},
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Chemical Physics}\ }\textbf {\bibinfo {volume} {150}},\ \bibinfo {pages}
{111101} (\bibinfo {year} {2019})},\ \Eprint
{http://arxiv.org/abs/https://doi.org/10.1063/1.5090346}
{https://doi.org/10.1063/1.5090346} \BibitemShut {NoStop}%
\bibitem [{\citenamefont {Qiu}\ \emph {et~al.}(2017)\citenamefont {Qiu},
\citenamefont {Henderson}, \citenamefont {Zhao},\ and\ \citenamefont
{Scuseria}}]{QiuHenZhaScu-JCP-17}%
\BibitemOpen
\bibfield {author} {\bibinfo {author} {\bibfnamefont {Y.}~\bibnamefont
{Qiu}}, \bibinfo {author} {\bibfnamefont {T.~M.}\ \bibnamefont {Henderson}},
\bibinfo {author} {\bibfnamefont {J.}~\bibnamefont {Zhao}}, \ and\ \bibinfo
{author} {\bibfnamefont {G.~E.}\ \bibnamefont {Scuseria}},\ }\href {\doibase
10.1063/1.4991020} {\bibfield {journal} {\bibinfo {journal} {The Journal of
Chemical Physics}\ }\textbf {\bibinfo {volume} {147}},\ \bibinfo {pages}
{064111} (\bibinfo {year} {2017})},\ \Eprint
{http://arxiv.org/abs/https://doi.org/10.1063/1.4991020}
{https://doi.org/10.1063/1.4991020} \BibitemShut {NoStop}%
\bibitem [{\citenamefont {Qiu}\ \emph {et~al.}(2018)\citenamefont {Qiu},
\citenamefont {Henderson}, \citenamefont {Zhao},\ and\ \citenamefont
{Scuseria}}]{QiuHenZhaScu-JCP-18}%
\BibitemOpen
\bibfield {author} {\bibinfo {author} {\bibfnamefont {Y.}~\bibnamefont
{Qiu}}, \bibinfo {author} {\bibfnamefont {T.~M.}\ \bibnamefont {Henderson}},
\bibinfo {author} {\bibfnamefont {J.}~\bibnamefont {Zhao}}, \ and\ \bibinfo
{author} {\bibfnamefont {G.~E.}\ \bibnamefont {Scuseria}},\ }\href {\doibase
10.1063/1.5053605} {\bibfield {journal} {\bibinfo {journal} {The Journal of
Chemical Physics}\ }\textbf {\bibinfo {volume} {149}},\ \bibinfo {pages}
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{http://arxiv.org/abs/https://doi.org/10.1063/1.5053605}
{https://doi.org/10.1063/1.5053605} \BibitemShut {NoStop}%
\bibitem [{\citenamefont {Gomez}, \citenamefont {Henderson},\ and\
\citenamefont {Scuseria}(2019)}]{GomHenScu-JCP-19}%
\BibitemOpen
\bibfield {author} {\bibinfo {author} {\bibfnamefont {J.~A.}\ \bibnamefont
{Gomez}}, \bibinfo {author} {\bibfnamefont {T.~M.}\ \bibnamefont
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{\bibinfo {journal} {The Journal of Chemical Physics}\ }\textbf {\bibinfo
{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
\bibfield {author} {\bibinfo {author} {\bibfnamefont {C.~F.}\ \bibnamefont
{Bender}}\ and\ \bibinfo {author} {\bibfnamefont {E.~R.}\ \bibnamefont
{Davidson}},\ }\href {\doibase 10.1103/physrev.183.23} {\bibfield {journal}
{\bibinfo {journal} {Phys. Rev.}\ }\textbf {\bibinfo {volume} {183}},\
\bibinfo {pages} {23} (\bibinfo {year} {1969})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Whitten}\ and\ \citenamefont
{Hackmeyer}(1969)}]{WhiHac-JCP-1969}%
\BibitemOpen
\bibfield {author} {\bibinfo {author} {\bibfnamefont {J.~L.}\ \bibnamefont
{Whitten}}\ and\ \bibinfo {author} {\bibfnamefont {M.}~\bibnamefont
{Hackmeyer}},\ }\href {\doibase 10.1063/1.1671985} {\bibfield {journal}
{\bibinfo {journal} {J. Chem. Phys.}\ }\textbf {\bibinfo {volume} {51}},\
\bibinfo {pages} {5584} (\bibinfo {year} {1969})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Huron}, \citenamefont {Malrieu},\ and\ \citenamefont
{Rancurel}(1973)}]{HurMalRan-1973}%
\BibitemOpen
\bibfield {author} {\bibinfo {author} {\bibfnamefont {B.}~\bibnamefont
{Huron}}, \bibinfo {author} {\bibfnamefont {J.~P.}\ \bibnamefont {Malrieu}},
\ and\ \bibinfo {author} {\bibfnamefont {P.}~\bibnamefont {Rancurel}},\
}\href {\doibase 10.1063/1.1679199} {\bibfield {journal} {\bibinfo
{journal} {J. Chem. Phys.}\ }\textbf {\bibinfo {volume} {58}},\ \bibinfo
{pages} {5745} (\bibinfo {year} {1973})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Evangelisti}, \citenamefont {Daudey},\ and\
\citenamefont {Malrieu}(1983)}]{EvaDauMal-ChemPhys-83}%
\BibitemOpen
\bibfield {author} {\bibinfo {author} {\bibfnamefont {S.}~\bibnamefont
{Evangelisti}}, \bibinfo {author} {\bibfnamefont {J.-P.}\ \bibnamefont
{Daudey}}, \ and\ \bibinfo {author} {\bibfnamefont {J.-P.}\ \bibnamefont
{Malrieu}},\ }\href {\doibase 10.1016/0301-0104(83)85011-3} {\bibfield
{journal} {\bibinfo {journal} {Chemical Physics}\ }\textbf {\bibinfo
{volume} {75}},\ \bibinfo {pages} {91} (\bibinfo {year} {1983})}\BibitemShut
{NoStop}%
\bibitem [{\citenamefont {Cimiraglia}(1985)}]{Cim-JCP-1985}%
\BibitemOpen
\bibfield {author} {\bibinfo {author} {\bibfnamefont {R.}~\bibnamefont
{Cimiraglia}},\ }\href {\doibase 10.1063/1.449362} {\bibfield {journal}
{\bibinfo {journal} {J. Chem. Phys.}\ }\textbf {\bibinfo {volume} {83}},\
\bibinfo {pages} {1746} (\bibinfo {year} {1985})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Cimiraglia}\ and\ \citenamefont
{Persico}(1987)}]{Cim-JCC-1987}%
\BibitemOpen
\bibfield {author} {\bibinfo {author} {\bibfnamefont {R.}~\bibnamefont
{Cimiraglia}}\ and\ \bibinfo {author} {\bibfnamefont {M.}~\bibnamefont
{Persico}},\ }\href@noop {} {\bibfield {journal} {\bibinfo {journal} {J.
Comput. Chem.}\ }\textbf {\bibinfo {volume} {8}},\ \bibinfo {pages} {39}
(\bibinfo {year} {1987})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Illas}, \citenamefont {Rubio},\ and\ \citenamefont
{Ricart}(1988)}]{IllRubRic-JCP-88}%
\BibitemOpen
\bibfield {author} {\bibinfo {author} {\bibfnamefont {F.}~\bibnamefont
{Illas}}, \bibinfo {author} {\bibfnamefont {J.}~\bibnamefont {Rubio}}, \ and\
\bibinfo {author} {\bibfnamefont {J.~M.}\ \bibnamefont {Ricart}},\ }\href
{\doibase 10.1063/1.455405} {\bibfield {journal} {\bibinfo {journal} {J.
Chem. Phys.}\ }\textbf {\bibinfo {volume} {89}},\ \bibinfo {pages} {6376}
(\bibinfo {year} {1988})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Povill}, \citenamefont {Rubio},\ and\ \citenamefont
{Illas}(1992)}]{PovRubIll-TCA-92}%
\BibitemOpen
\bibfield {author} {\bibinfo {author} {\bibfnamefont {A.}~\bibnamefont
{Povill}}, \bibinfo {author} {\bibfnamefont {J.}~\bibnamefont {Rubio}}, \
and\ \bibinfo {author} {\bibfnamefont {F.}~\bibnamefont {Illas}},\ }\href
{\doibase 10.1007/BF01113255} {\bibfield {journal} {\bibinfo {journal}
{Theor. Chem. Acc.}\ }\textbf {\bibinfo {volume} {82}},\ \bibinfo {pages}
{229} (\bibinfo {year} {1992})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Bunge}\ and\ \citenamefont
{Carb{\'o}-Dorca}(2006)}]{BunCarRam-JCP-06}%
\BibitemOpen
\bibfield {author} {\bibinfo {author} {\bibfnamefont {C.~F.}\ \bibnamefont
{Bunge}}\ and\ \bibinfo {author} {\bibfnamefont {R.}~\bibnamefont
{Carb{\'o}-Dorca}},\ }\href {\doibase 10.1063/1.2207621} {\bibfield
{journal} {\bibinfo {journal} {J. Chem. Phys.}\ }\textbf {\bibinfo {volume}
{125}},\ \bibinfo {pages} {014108} (\bibinfo {year} {2006})}\BibitemShut
{NoStop}%
\bibitem [{\citenamefont {Abrams}\ and\ \citenamefont
{Sherrill}(2005)}]{AbrSheDav-CPL-05}%
\BibitemOpen
\bibfield {author} {\bibinfo {author} {\bibfnamefont {M.~L.}\ \bibnamefont
{Abrams}}\ and\ \bibinfo {author} {\bibfnamefont {C.~D.}\ \bibnamefont
{Sherrill}},\ }\href {\doibase 10.1016/j.cplett.2005.06.107} {\bibfield
{journal} {\bibinfo {journal} {Chem. Phys. Lett.}\ }\textbf {\bibinfo
{volume} {412}},\ \bibinfo {pages} {121} (\bibinfo {year}
{2005})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Musch}\ and\ \citenamefont
{Engels}(2006)}]{MusEngels-JCC-06}%
\BibitemOpen
\bibfield {author} {\bibinfo {author} {\bibfnamefont {P.}~\bibnamefont
{Musch}}\ and\ \bibinfo {author} {\bibfnamefont {B.}~\bibnamefont {Engels}},\
}\href@noop {} {\bibfield {journal} {\bibinfo {journal} {{Journal of
Computational Chemistry}}\ } (\bibinfo {year} {{2006}})}\BibitemShut
{NoStop}%
\bibitem [{\citenamefont {Bytautas}\ and\ \citenamefont
{Ruedenberg}(2009)}]{BytRue-CP-09}%
\BibitemOpen
\bibfield {author} {\bibinfo {author} {\bibfnamefont {L.}~\bibnamefont
{Bytautas}}\ and\ \bibinfo {author} {\bibfnamefont {K.}~\bibnamefont
{Ruedenberg}},\ }\href {\doibase 10.1016/j.chemphys.2008.11.021} {\bibfield
{journal} {\bibinfo {journal} {Chemical Physics}\ }\textbf {\bibinfo
{volume} {356}},\ \bibinfo {pages} {64} (\bibinfo {year} {2009})}\BibitemShut
{NoStop}%
\bibitem [{\citenamefont {Giner}, \citenamefont {Scemama},\ and\ \citenamefont
{Caffarel}(2013)}]{GinSceCaf-CJC-13}%
\BibitemOpen
\bibfield {author} {\bibinfo {author} {\bibfnamefont {E.}~\bibnamefont
{Giner}}, \bibinfo {author} {\bibfnamefont {A.}~\bibnamefont {Scemama}}, \
and\ \bibinfo {author} {\bibfnamefont {M.}~\bibnamefont {Caffarel}},\ }\href
{\doibase 10.1139/cjc-2013-0017} {\bibfield {journal} {\bibinfo {journal}
{Can. J. Chem.}\ }\textbf {\bibinfo {volume} {91}},\ \bibinfo {pages} {879}
(\bibinfo {year} {2013})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Caffarel}\ \emph {et~al.}(2014)\citenamefont
{Caffarel}, \citenamefont {Giner}, \citenamefont {Scemama},\ and\
\citenamefont {Ram{\'\i}rez-Sol{\'\i}s}}]{CafGinScemRam-JCTC-14}%
\BibitemOpen
\bibfield {author} {\bibinfo {author} {\bibfnamefont {M.}~\bibnamefont
{Caffarel}}, \bibinfo {author} {\bibfnamefont {E.}~\bibnamefont {Giner}},
\bibinfo {author} {\bibfnamefont {A.}~\bibnamefont {Scemama}}, \ and\
\bibinfo {author} {\bibfnamefont {A.}~\bibnamefont
{Ram{\'\i}rez-Sol{\'\i}s}},\ }\href {\doibase 10.1021/ct5004252} {\bibfield
{journal} {\bibinfo {journal} {J. Chem. Theory Comput.}\ }\textbf {\bibinfo
{volume} {10}},\ \bibinfo {pages} {5286} (\bibinfo {year}
{2014})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Giner}, \citenamefont {Scemama},\ and\ \citenamefont
{Caffarel}(2015)}]{GinSceCaf-JCP-15}%
\BibitemOpen
\bibfield {author} {\bibinfo {author} {\bibfnamefont {E.}~\bibnamefont
{Giner}}, \bibinfo {author} {\bibfnamefont {A.}~\bibnamefont {Scemama}}, \
and\ \bibinfo {author} {\bibfnamefont {M.}~\bibnamefont {Caffarel}},\ }\href
{\doibase 10.1063/1.4905528} {\bibfield {journal} {\bibinfo {journal} {J.
Chem. Phys.}\ }\textbf {\bibinfo {volume} {142}},\ \bibinfo {pages} {044115}
(\bibinfo {year} {2015})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Caffarel}\ \emph
{et~al.}(2016{\natexlab{a}})\citenamefont {Caffarel}, \citenamefont
{Applencourt}, \citenamefont {Giner},\ and\ \citenamefont
{Scemama}}]{CafAplGinScem-arxiv-16}%
\BibitemOpen
\bibfield {author} {\bibinfo {author} {\bibfnamefont {M.}~\bibnamefont
{Caffarel}}, \bibinfo {author} {\bibfnamefont {T.}~\bibnamefont
{Applencourt}}, \bibinfo {author} {\bibfnamefont {E.}~\bibnamefont {Giner}},
\ and\ \bibinfo {author} {\bibfnamefont {A.}~\bibnamefont {Scemama}},\ }\href
{\doibase 10.1021/bk-2016-1234.ch002} {\ (\bibinfo {year}
{2016}{\natexlab{a}}),\ 10.1021/bk-2016-1234.ch002},\ \Eprint
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{NoStop}%
\bibitem [{\citenamefont {Caffarel}\ \emph
{et~al.}(2016{\natexlab{b}})\citenamefont {Caffarel}, \citenamefont
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{Scemama}}]{CafAplGinSce-JCP-16}%
\BibitemOpen
\bibfield {author} {\bibinfo {author} {\bibfnamefont {M.}~\bibnamefont
{Caffarel}}, \bibinfo {author} {\bibfnamefont {T.}~\bibnamefont
{Applencourt}}, \bibinfo {author} {\bibfnamefont {E.}~\bibnamefont {Giner}},
\ and\ \bibinfo {author} {\bibfnamefont {A.}~\bibnamefont {Scemama}},\ }\href
{\doibase 10.1063/1.4947093} {\bibfield {journal} {\bibinfo {journal} {J.
Chem. Phys.}\ }\textbf {\bibinfo {volume} {144}},\ \bibinfo {pages} {151103}
(\bibinfo {year} {2016}{\natexlab{b}})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Schriber}\ and\ \citenamefont
{Evangelista}(2016)}]{SchEva-JCP-16}%
\BibitemOpen
\bibfield {author} {\bibinfo {author} {\bibfnamefont {J.~B.}\ \bibnamefont
{Schriber}}\ and\ \bibinfo {author} {\bibfnamefont {F.~A.}\ \bibnamefont
{Evangelista}},\ }\href {\doibase 10.1063/1.4948308} {\bibfield {journal}
{\bibinfo {journal} {J. Chem. Phys.}\ }\textbf {\bibinfo {volume} {144}},\
\bibinfo {pages} {161106} (\bibinfo {year} {2016})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Liu}\ and\ \citenamefont
{Hoffmann}(2016)}]{LiuHofJCTC-16}%
\BibitemOpen
\bibfield {author} {\bibinfo {author} {\bibfnamefont {W.}~\bibnamefont
{Liu}}\ and\ \bibinfo {author} {\bibfnamefont {M.~R.}\ \bibnamefont
{Hoffmann}},\ }\href {\doibase 10.1021/acs.jctc.5b01099} {\bibfield
{journal} {\bibinfo {journal} {J. Chem. Theory Comput.}\ }\textbf {\bibinfo
{volume} {12}},\ \bibinfo {pages} {1169} (\bibinfo {year}
{2016})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Holmes}, \citenamefont {Umrigar},\ and\ \citenamefont
{Sharma}(2017)}]{HolUmrSha-JCP-17}%
\BibitemOpen
\bibfield {author} {\bibinfo {author} {\bibfnamefont {A.~A.}\ \bibnamefont
{Holmes}}, \bibinfo {author} {\bibfnamefont {C.~J.}\ \bibnamefont {Umrigar}},
\ and\ \bibinfo {author} {\bibfnamefont {S.}~\bibnamefont {Sharma}},\ }\href
{\doibase 10.1063/1.4998614} {\bibfield {journal} {\bibinfo {journal} {J.
Chem. Phys.}\ }\textbf {\bibinfo {volume} {147}},\ \bibinfo {pages} {164111}
(\bibinfo {year} {2017})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Sharma}\ \emph {et~al.}(2017)\citenamefont {Sharma},
\citenamefont {Holmes}, \citenamefont {Jeanmairet}, \citenamefont {Alavi},\
and\ \citenamefont {Umrigar}}]{ShaHolJeaAlaUmr-JCTC-17}%
\BibitemOpen
\bibfield {author} {\bibinfo {author} {\bibfnamefont {S.}~\bibnamefont
{Sharma}}, \bibinfo {author} {\bibfnamefont {A.~A.}\ \bibnamefont {Holmes}},
\bibinfo {author} {\bibfnamefont {G.}~\bibnamefont {Jeanmairet}}, \bibinfo
{author} {\bibfnamefont {A.}~\bibnamefont {Alavi}}, \ and\ \bibinfo {author}
{\bibfnamefont {C.~J.}\ \bibnamefont {Umrigar}},\ }\href {\doibase
10.1021/acs.jctc.6b01028} {\bibfield {journal} {\bibinfo {journal} {J.
Chem. Theory Comput.}\ }\textbf {\bibinfo {volume} {13}},\ \bibinfo {pages}
{1595} (\bibinfo {year} {2017})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Schriber}\ and\ \citenamefont
{Evangelista}(2017)}]{SchEva-JCTC-17}%
\BibitemOpen
\bibfield {author} {\bibinfo {author} {\bibfnamefont {J.~B.}\ \bibnamefont
{Schriber}}\ and\ \bibinfo {author} {\bibfnamefont {F.~A.}\ \bibnamefont
{Evangelista}},\ }\href {\doibase 10.1021/acs.jctc.7b00725} {\bibfield
{journal} {\bibinfo {journal} {J. Chem. Theory Comput.}\ } (\bibinfo {year}
{2017}),\ 10.1021/acs.jctc.7b00725}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Per}\ and\ \citenamefont
{Cleland}(2017)}]{PerCle-JCP-17}%
\BibitemOpen
\bibfield {author} {\bibinfo {author} {\bibfnamefont {M.~C.}\ \bibnamefont
{Per}}\ and\ \bibinfo {author} {\bibfnamefont {D.~M.}\ \bibnamefont
{Cleland}},\ }\href {\doibase 10.1063/1.4981527} {\bibfield {journal}
{\bibinfo {journal} {J. Chem. Phys.}\ }\textbf {\bibinfo {volume} {146}},\
\bibinfo {pages} {164101} (\bibinfo {year} {2017})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Ohtsuka}\ and\ \citenamefont
{ya~Hasegawa}(2017)}]{OhtJun-JCP-17}%
\BibitemOpen
\bibfield {author} {\bibinfo {author} {\bibfnamefont {Y.}~\bibnamefont
{Ohtsuka}}\ and\ \bibinfo {author} {\bibfnamefont {J.}~\bibnamefont
{ya~Hasegawa}},\ }\href {\doibase 10.1063/1.4993214} {\bibfield {journal}
{\bibinfo {journal} {J. Chem. Phys.}\ }\textbf {\bibinfo {volume} {147}},\
\bibinfo {pages} {034102} (\bibinfo {year} {2017})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Zimmerman}(2017)}]{Zim-JCP-17}%
\BibitemOpen
\bibfield {author} {\bibinfo {author} {\bibfnamefont {P.~M.}\ \bibnamefont
{Zimmerman}},\ }\href {\doibase 10.1063/1.4977727} {\bibfield {journal}
{\bibinfo {journal} {J. Chem. Phys.}\ }\textbf {\bibinfo {volume} {146}},\
\bibinfo {pages} {104102} (\bibinfo {year} {2017})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Li}\ \emph {et~al.}(2018)\citenamefont {Li},
\citenamefont {Otten}, \citenamefont {Holmes}, \citenamefont {Sharma},\ and\
\citenamefont {Umrigar}}]{LiOttHolShaUmr-JCP-2018}%
\BibitemOpen
\bibfield {author} {\bibinfo {author} {\bibfnamefont {J.}~\bibnamefont
{Li}}, \bibinfo {author} {\bibfnamefont {M.}~\bibnamefont {Otten}}, \bibinfo
{author} {\bibfnamefont {A.~A.}\ \bibnamefont {Holmes}}, \bibinfo {author}
{\bibfnamefont {S.}~\bibnamefont {Sharma}}, \ and\ \bibinfo {author}
{\bibfnamefont {C.~J.}\ \bibnamefont {Umrigar}},\ }\href {\doibase
10.1063/1.5055390} {\bibfield {journal} {\bibinfo {journal} {J. Chem.
Phys.}\ }\textbf {\bibinfo {volume} {149}},\ \bibinfo {pages} {214110}
(\bibinfo {year} {2018})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Chien}\ \emph {et~al.}(2018)\citenamefont {Chien},
\citenamefont {Holmes}, \citenamefont {Otten}, \citenamefont {Umrigar},
\citenamefont {Sharma},\ and\ \citenamefont
{Zimmerman}}]{ChiHolOttUmrShaZim-JPCA-18}%
\BibitemOpen
\bibfield {author} {\bibinfo {author} {\bibfnamefont {A.~D.}\ \bibnamefont
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\bibinfo {author} {\bibfnamefont {M.}~\bibnamefont {Otten}}, \bibinfo
{author} {\bibfnamefont {C.~J.}\ \bibnamefont {Umrigar}}, \bibinfo {author}
{\bibfnamefont {S.}~\bibnamefont {Sharma}}, \ and\ \bibinfo {author}
{\bibfnamefont {P.~M.}\ \bibnamefont {Zimmerman}},\ }\href {\doibase
10.1021/acs.jpca.8b01554} {\bibfield {journal} {\bibinfo {journal} {J.
Phys. Chem. A}\ }\textbf {\bibinfo {volume} {122}},\ \bibinfo {pages} {2714}
(\bibinfo {year} {2018})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Scemama}\ \emph
{et~al.}(2018{\natexlab{a}})\citenamefont {Scemama}, \citenamefont {Benali},
\citenamefont {Jacquemin}, \citenamefont {Caffarel},\ and\ \citenamefont
{Loos}}]{SceBenJacCafLoo-JCP-18}%
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\bibinfo {author} {\bibfnamefont {D.}~\bibnamefont {Jacquemin}}, \bibinfo
{author} {\bibfnamefont {M.}~\bibnamefont {Caffarel}}, \ and\ \bibinfo
{author} {\bibfnamefont {P.-F.}\ \bibnamefont {Loos}},\ }\href {\doibase
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Phys.}\ }\textbf {\bibinfo {volume} {149}},\ \bibinfo {pages} {034108}
(\bibinfo {year} {2018}{\natexlab{a}})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Loos}\ \emph {et~al.}(2018)\citenamefont {Loos},
\citenamefont {Scemama}, \citenamefont {Blondel}, \citenamefont {Garniron},
\citenamefont {Caffarel},\ and\ \citenamefont
{Jacquemin}}]{LooSceBloGarCafJac-JCTC-18}%
\BibitemOpen
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\bibinfo {author} {\bibfnamefont {A.}~\bibnamefont {Blondel}}, \bibinfo
{author} {\bibfnamefont {Y.}~\bibnamefont {Garniron}}, \bibinfo {author}
{\bibfnamefont {M.}~\bibnamefont {Caffarel}}, \ and\ \bibinfo {author}
{\bibfnamefont {D.}~\bibnamefont {Jacquemin}},\ }\href {\doibase
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\bibitem [{\citenamefont {Garniron}\ \emph {et~al.}(2018)\citenamefont
{Garniron}, \citenamefont {Scemama}, \citenamefont {Giner}, \citenamefont
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Phys.}\ }\textbf {\bibinfo {volume} {149}},\ \bibinfo {pages} {064103}
(\bibinfo {year} {2018})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Scemama}\ \emph
{et~al.}(2018{\natexlab{b}})\citenamefont {Scemama}, \citenamefont
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{NoStop}%
\bibitem [{\citenamefont {Garniron}\ \emph {et~al.}(2017)\citenamefont
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{author} {\bibfnamefont {D.}~\bibnamefont {Jacquemin}},\ }\href {\doibase
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\bibitem [{\citenamefont {Hylleraas}(1929)}]{Hyl-ZP-29}% \bibitem [{\citenamefont {Hylleraas}(1929)}]{Hyl-ZP-29}%
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\bibfield {author} {\bibinfo {author} {\bibfnamefont {E.~A.}\ \bibnamefont \bibfield {author} {\bibinfo {author} {\bibfnamefont {E.~A.}\ \bibnamefont
@ -612,6 +166,29 @@
{\bibfield {journal} {\bibinfo {journal} {Phys. Chem. Chem. Phys.}\ {\bibfield {journal} {\bibinfo {journal} {Phys. Chem. Chem. Phys.}\
}\textbf {\bibinfo {volume} {9}},\ \bibinfo {pages} {1921} (\bibinfo {year} }\textbf {\bibinfo {volume} {9}},\ \bibinfo {pages} {1921} (\bibinfo {year}
{2007})}\BibitemShut {NoStop}% {2007})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Shiozaki}\ and\ \citenamefont
{Werner}(2010)}]{ShiWer-JCP-10}%
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{Shiozaki}}\ and\ \bibinfo {author} {\bibfnamefont {H.-J.}\ \bibnamefont
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{\bibinfo {journal} {The Journal of Chemical Physics}\ }\textbf {\bibinfo
{volume} {133}},\ \bibinfo {pages} {141103} (\bibinfo {year} {2010})},\
\Eprint {http://arxiv.org/abs/https://doi.org/10.1063/1.3489000}
{https://doi.org/10.1063/1.3489000} \BibitemShut {NoStop}%
\bibitem [{\citenamefont {Guo}\ \emph {et~al.}(2017)\citenamefont {Guo},
\citenamefont {Sivalingam}, \citenamefont {Valeev},\ and\ \citenamefont
{Neese}}]{GuoSivValNee-JCP-17}%
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\bibfield {author} {\bibinfo {author} {\bibfnamefont {Y.}~\bibnamefont
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\bibinfo {author} {\bibfnamefont {E.~F.}\ \bibnamefont {Valeev}}, \ and\
\bibinfo {author} {\bibfnamefont {F.}~\bibnamefont {Neese}},\ }\href
{\doibase 10.1063/1.4996560} {\bibfield {journal} {\bibinfo {journal} {The
Journal of Chemical Physics}\ }\textbf {\bibinfo {volume} {147}},\ \bibinfo
{pages} {064110} (\bibinfo {year} {2017})},\ \Eprint
{http://arxiv.org/abs/https://doi.org/10.1063/1.4996560}
{https://doi.org/10.1063/1.4996560} \BibitemShut {NoStop}%
\bibitem [{\citenamefont {Toulouse}, \citenamefont {Colonna},\ and\ \bibitem [{\citenamefont {Toulouse}, \citenamefont {Colonna},\ and\
\citenamefont {Savin}(2004)}]{TouColSav-PRA-04}% \citenamefont {Savin}(2004)}]{TouColSav-PRA-04}%
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@ -774,7 +351,7 @@
{149}},\ \bibinfo {pages} {194301} (\bibinfo {year} {2018})}\BibitemShut {149}},\ \bibinfo {pages} {194301} (\bibinfo {year} {2018})}\BibitemShut
{NoStop}% {NoStop}%
\bibitem [{\citenamefont {Loos}\ \emph \bibitem [{\citenamefont {Loos}\ \emph
{et~al.}(2019{\natexlab{b}})\citenamefont {Loos}, \citenamefont {Pradines}, {et~al.}(2019{\natexlab{a}})\citenamefont {Loos}, \citenamefont {Pradines},
\citenamefont {Scemama}, \citenamefont {Toulouse},\ and\ \citenamefont \citenamefont {Scemama}, \citenamefont {Toulouse},\ and\ \citenamefont
{Giner}}]{LooPraSceTouGin-JCPL-19}% {Giner}}]{LooPraSceTouGin-JCPL-19}%
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@ -785,7 +362,7 @@
{author} {\bibfnamefont {E.}~\bibnamefont {Giner}},\ }\href {\doibase {author} {\bibfnamefont {E.}~\bibnamefont {Giner}},\ }\href {\doibase
10.1021/acs.jpclett.9b01176} {\bibfield {journal} {\bibinfo {journal} {The 10.1021/acs.jpclett.9b01176} {\bibfield {journal} {\bibinfo {journal} {The
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{http://arxiv.org/abs/https://doi.org/10.1021/acs.jpclett.9b01176} {http://arxiv.org/abs/https://doi.org/10.1021/acs.jpclett.9b01176}
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@ -876,6 +453,68 @@
{\bibinfo {journal} {Phys. Rev. A}\ }\textbf {\bibinfo {volume} {73}},\ {\bibinfo {journal} {Phys. Rev. A}\ }\textbf {\bibinfo {volume} {73}},\
\bibinfo {pages} {032506} (\bibinfo {year} {2006}{\natexlab{b}})}\BibitemShut \bibinfo {pages} {032506} (\bibinfo {year} {2006}{\natexlab{b}})}\BibitemShut
{NoStop}% {NoStop}%
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\citenamefont {Benali}, \citenamefont {Fert{\'e}}, \citenamefont {Paquier}, \citenamefont {Benali}, \citenamefont {Fert{\'e}}, \citenamefont {Paquier},

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@ -12709,3 +12709,136 @@ eprint = {https://doi.org/10.1063/1.5122976}
url = {https://link.aps.org/doi/10.1103/PhysRevX.7.031059} url = {https://link.aps.org/doi/10.1103/PhysRevX.7.031059}
} }
@article{ShiWer-JCP-10,
author = {Shiozaki,Toru and Werner,Hans-Joachim },
title = {Communication: Second-order multireference perturbation theory with explicit correlation: CASPT2-F12},
journal = {The Journal of Chemical Physics},
volume = {133},
number = {14},
pages = {141103},
year = {2010},
doi = {10.1063/1.3489000},
URL = {https://doi.org/10.1063/1.348900},
eprint = {https://doi.org/10.1063/1.3489000}
}
@article{GuoSivValNee-JCP-17,
author = {Guo,Yang and Sivalingam,Kantharuban and Valeev,Edward F. and Neese,Frank },
title = {Explicitly correlated N-electron valence state perturbation theory (NEVPT2-F12)},
journal = {The Journal of Chemical Physics},
volume = {147},
number = {6},
pages = {064110},
year = {2017},
doi = {10.1063/1.4996560},
URL = {https://doi.org/10.1063/1.4996560},
eprint = {https://doi.org/10.1063/1.4996560}
}
@article{TorVal-JCP-09,
author = {Torheyden,Martin and Valeev,Edward F. },
title = {Universal perturbative explicitly correlated basis set incompleteness correction},
journal = {The Journal of Chemical Physics},
volume = {131},
number = {17},
pages = {171103},
year = {2009},
doi = {10.1063/1.3254836},
URL = {https://doi.org/10.1063/1.3254836},
eprint = {https://doi.org/10.1063/1.3254836}
}
@article{Ten-CPL-07,
title = "A simple F12 geminal correction in multi-reference perturbation theory",
journal = "Chemical Physics Letters",
volume = "447",
number = "1",
pages = "175 - 179",
year = "2007",
issn = "0009-2614",
doi = "https://doi.org/10.1016/j.cplett.2007.09.006",
url = "http://www.sciencedirect.com/science/article/pii/S0009261407012286",
author = "Seiichiro Ten-no",
abstract = "We propose a simple F12 geminal correction in multi-reference perturbation theory. An explicitly correlated term is introduced in the external excitations of the first order wave function in an internally contracted manner. By the use of the s- and p-wave cusp conditions, the F12 correction is expressed as the expectation value of a two-body effective operator, which reduces to the MP2-F12/A∗(SP) energy in the single reference limit. The performance of the F12 multi-reference perturbation method is demonstrated for C, CH2, O2, and SiC3."
}
@article{KedDemPitTenNog-CPL-11,
title = "Multireference F12 coupled cluster theory: The Brillouin-Wigner approach with single and double excitations",
journal = "Chemical Physics Letters",
volume = "511",
number = "4",
pages = "418 - 423",
year = "2011",
issn = "0009-2614",
doi = "https://doi.org/10.1016/j.cplett.2011.06.023",
url = "http://www.sciencedirect.com/science/article/pii/S0009261411007160",
author = "Stanislav Kedžuch and Ondřej Demel and Jiří Pittner and Seiichiro Ten-no and Jozef Noga",
abstract = "This Letter reports development and implementation of the explicitly correlated multireference Brillouin Wigner (MR BW-CC) coupled cluster method with Slater type geminals. The performance of the new approach is tested on the H4 model system and the dissociation curve of the fluorine molecule. Like in single reference methods, results show a dramatically improved convergence of total energies towards complete basis set limit as compared to a conventional MR BW-CC approach. In comparison with previously reported calculations with a linear correlation factor, there is a better performance for calculations in smaller basis sets."
}
@article{TorKniWer-JCP-11,
author = {Shiozaki,Toru and Knizia,Gerald and Werner,Hans-Joachim },
title = {Explicitly correlated multireference configuration interaction: MRCI-F12},
journal = {The Journal of Chemical Physics},
volume = {134},
number = {3},
pages = {034113},
year = {2011},
doi = {10.1063/1.3528720},
URL = {https://doi.org/10.1063/1.3528720},
eprint = {https://doi.org/10.1063/1.3528720}
}
@Article{DemStanMatTenPitNog-PCCP-12,
author ="Demel, Ondřej and Kedžuch, Stanislav and Švaňa, Matej and Ten-no, Seiichiro and Pittner, Jiří and Noga, Jozef",
title ="An explicitly correlated Mukherjee{'}s state specific coupled cluster method: development and pilot applications",
journal ="Phys. Chem. Chem. Phys.",
year ="2012",
volume ="14",
issue ="14",
pages ="4753-4762",
publisher ="The Royal Society of Chemistry",
doi ="10.1039/C2CP23198K",
url ="http://dx.doi.org/10.1039/C2CP23198K",
abstract ="This paper reports development of the explicitly correlated variant of Mukherjee{'}s state specific multireference coupled cluster method (MkCC-F12). The current implementation is restricted to conventional single and double excitations and to pseudo-double excitations related to the Slater Type Geminal (STG) correlation factor using the SP ansatz. The performance of the MkCCSD-F12 was tested on calculations of singlet methylene{,} dissociation curve of the fluorine molecule{,} and the BeH2 insertion pathway. As expected{,} the results of the newly developed method reconfirm the significantly faster convergence with respect to the basis set limit compared to the traditional expansion in Slater determinants. Results prove that treating the correlation factor separately for each reference is appropriate."}
@article{HauMaoMukKlo-CPL-12,
title = "A universal explicit electron correlation correction applied to Mukherjee’s multi-reference perturbation theory",
journal = "Chemical Physics Letters",
volume = "531",
pages = "247 - 251",
year = "2012",
issn = "0009-2614",
doi = "https://doi.org/10.1016/j.cplett.2012.02.020",
url = "http://www.sciencedirect.com/science/article/pii/S0009261412002072",
author = "Robin Haunschild and Shuneng Mao and Debashis Mukherjee and Wim Klopper",
abstract = "We present a universally applicable explicit electron correlation (F12) correction and apply it to Mukherjee’s multi-reference perturbation theory (Mk-MRPT2). Two different F12 corrections are proposed: one is a universal F12 correction which is added to the conventional orbital correction, which is referred to as Mk-MRPT2+F12. In the second type of F12 correction the individual F12 contributions are added to each matrix element of the effective Hamiltonian. Subsequent diagonalization yields the Mk-MRPT2-F12 correction. Thereby, we achieve for both F12 corrections the accuracy of a quadruple-ζ basis set calculation when a triple-ζ basis set is employed and the F12 correction is added. Both F12 corrections reduce to MP2-F12/1A (fixed) in the single-reference limit."
}
@article{KonVal-JCP-11,
author = {Kong,Liguo and Valeev,Edward F. },
title = {SF-[2]R12: A spin-adapted explicitly correlated method applicable to arbitrary electronic states},
journal = {The Journal of Chemical Physics},
volume = {135},
number = {21},
pages = {214105},
year = {2011},
doi = {10.1063/1.3664729},
URL = {https://doi.org/10.1063/1.3664729},
eprint = {https://doi.org/10.1063/1.3664729}
}
@article{BooCleAlaTew-JCP-12,
author = {Booth,George H. and Cleland,Deidre and Alavi,Ali and Tew,David P. },
title = {An explicitly correlated approach to basis set incompleteness in full configuration interaction quantum Monte Carlo},
journal = {The Journal of Chemical Physics},
volume = {137},
number = {16},
pages = {164112},
year = {2012},
doi = {10.1063/1.4762445},
URL = {https://doi.org/10.1063/1.4762445},
eprint = {https://doi.org/10.1063/1.4762445}
}

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@ -295,7 +295,9 @@ Transition metals containing systems, low-spin open shell systems, covalent bond
have all in common that they cannot be even qualitatively described by a single electronic configuration. have all in common that they cannot be even qualitatively described by a single electronic configuration.
It is now clear that the usual approximations in KS-DFT fails in giving an accurate description of these situations and WFT has become It is now clear that the usual approximations in KS-DFT fails in giving an accurate description of these situations and WFT has become
the standard for the treatment of strongly correlated systems. the standard for the treatment of strongly correlated systems.
From the theoretical point of view, the complexity of the strong correlation problem is, at least, two-fold:
In practice WFT uses a finite one-particle basis set (here after as $\basis$) to project the Schroedinger equation whose exact solution becomes clear: the full configuration interaction (FCI) which consists in a linear algebra problem whose dimension scales exponentially with the system size.
Because of the exponential growth of the FCI, many approximations have appeared and in that regard the complexity of the strong correlation problem is, at least, two-fold:
i) the qualitative description of the wave function is determined by a primary set of electronic configurations (whose size can scale exponentially in many cases) among which near degeneracies and/or strong interactions appear in the Hamiltonian matrix, i) the qualitative description of the wave function is determined by a primary set of electronic configurations (whose size can scale exponentially in many cases) among which near degeneracies and/or strong interactions appear in the Hamiltonian matrix,
ii) the quantitative description of the systems must take into account weak correlation effects which requires to take into account many ii) the quantitative description of the systems must take into account weak correlation effects which requires to take into account many
other electronic configurations with typically much smaller weights in the wave function. other electronic configurations with typically much smaller weights in the wave function.
@ -303,23 +305,23 @@ Fulfilling these two objectives is a rather complicated task for a given approxi
%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) %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. %and multi-reference (MR) methods.
The SR methods rely on a single electronic configuration as a zeroth-order wave function, typically Hartree-Fock (HF). %The SR methods rely on a single electronic configuration as a zeroth-order wave function, typically Hartree-Fock (HF).
Then the electron correlation is introduced by increasing the rank of multiple hole-particle excitations, %Then the electron correlation is introduced by increasing the rank of multiple hole-particle excitations,
preferably treated in a coupled-cluster (CC) fashion for the sake of compactness of the wave function and extensivity of the computed energies. %preferably treated in a coupled-cluster (CC) fashion for the sake of compactness of the wave function and extensivity of the computed energies.
The advantage of these approaches rely on the rather straightforward way to improve the level of accuracy, %The advantage of these approaches rely on the rather straightforward way to improve the level of accuracy,
which consists in increasing the rank of the excitation operators used to generate the CC wave function. %which consists in increasing the rank of the excitation operators used to generate the CC wave function.
Despite its appealing elegant simplicity, the computational cost of the CC methods increase drastically with the rank of the excitation %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}. %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. %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\cite{WerKno-JCP-88,KnoWer-CPL-88} (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. %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}. %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}.
Among the SCI algorithms, 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 convergence criterion. It is important to notice that in the SCI algorithms, neither the SCI or the MRPT are size extensive \textit{per se}, but the extensivity property is almost recovered by approaching the FCI limit. %Among the SCI algorithms, 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 convergence criterion. It is important to notice that in the SCI algorithms, neither the SCI or the MRPT are size extensive \textit{per se}, but the extensivity property is almost recovered by approaching the FCI limit.
When the SCI are affordable, their clear advantage are that 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. %When the SCI are affordable, their clear advantage are that 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. 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. In addition to the computational cost, a possible drawback of F12 theory is its rather complex formalism which requires a quite involved mathematical development to adapt to a new theory. In the context of strong correlation, several multi-reference methods have been extended to explicitly correlation (see for instance Ref. \cite{Ten-CPL-07,TorVal-JCP-09,ShiWer-JCP-10,KedDemPitTenNog-CPL-11,TorKniWer-JCP-11,DemStanMatTenPitNog-PCCP-12,HauMaoMukKlo-CPL-12,GuoSivValNee-JCP-17}), including so-called universal approaches potentially applicable to any electronic structure approaches\cite{TorVal-JCP-09,KonVal-JCP-11,HauMaoMukKlo-CPL-12,BooCleAlaTew-JCP-12}.
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) as the WFT part deals with a smooth non divergent interaction, the exact wave function has no cusp removed and therefore the basis set convergence is much faster\cite{FraMusLupTou-JCP-15}. 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) as the WFT part deals with a smooth non divergent interaction, the exact wave function has no cusp removed 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, and the remaining self-interaction errors. 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, and the remaining self-interaction errors.