Modified conclusions
This commit is contained in:
Hugh Burton
parent
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\begin{thebibliography}{159}%
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\begin{thebibliography}{174}%
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\makeatletter
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\providecommand \@ifxundefined [1]{%
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\@ifx{#1\undefined}
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@ -1364,6 +1364,147 @@
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{journal} {\bibinfo {journal} {Theor. Chem. Acc.}\ }\textbf {\bibinfo
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{volume} {137}},\ \bibinfo {pages} {149} (\bibinfo {year}
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{2018})}\BibitemShut {NoStop}%
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\bibitem [{\citenamefont {Thom}\ and\ \citenamefont {Alavi}(2007)}]{Thom_2007}%
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\BibitemOpen
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\bibfield {author} {\bibinfo {author} {\bibfnamefont {A.~J.~W.}\
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\bibnamefont {Thom}}\ and\ \bibinfo {author} {\bibfnamefont {A.}~\bibnamefont
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{Alavi}},\ }\href {\doibase 10.1103/PhysRevLett.99.143001} {\bibfield
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{journal} {\bibinfo {journal} {Phys. Rev. Lett.}\ }\textbf {\bibinfo
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{volume} {99}},\ \bibinfo {pages} {143001} (\bibinfo {year}
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{2007})}\BibitemShut {NoStop}%
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\bibitem [{\citenamefont {Neuhauser}\ \emph {et~al.}(2012)\citenamefont
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{Neuhauser}, \citenamefont {Rabani},\ and\ \citenamefont
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{Baer}}]{Neuhauser_2012}%
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\BibitemOpen
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{Neuhauser}}, \bibinfo {author} {\bibfnamefont {E.}~\bibnamefont {Rabani}}, \
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and\ \bibinfo {author} {\bibfnamefont {R.}~\bibnamefont {Baer}},\ }\href
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{\doibase 10.1021/ct.300946j} {\bibfield {journal} {\bibinfo {journal} {J.
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Chem. Theory Comput.}\ }\textbf {\bibinfo {volume} {9}},\ \bibinfo {pages}
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{24} (\bibinfo {year} {2012})}\BibitemShut {NoStop}%
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\bibitem [{\citenamefont {Willow}\ \emph {et~al.}(2012)\citenamefont {Willow},
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\citenamefont {Kim},\ and\ \citenamefont {Hirata}}]{Willow_2012}%
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\BibitemOpen
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\bibfield {author} {\bibinfo {author} {\bibfnamefont {S.~Y.}\ \bibnamefont
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{Willow}}, \bibinfo {author} {\bibfnamefont {K.~S.}\ \bibnamefont {Kim}}, \
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and\ \bibinfo {author} {\bibfnamefont {S.}~\bibnamefont {Hirata}},\ }\href
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{\doibase 10.1063/1.4768697} {\bibfield {journal} {\bibinfo {journal} {J.
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Chem. Phys.}\ }\textbf {\bibinfo {volume} {137}},\ \bibinfo {pages} {204122}
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(\bibinfo {year} {2012})}\BibitemShut {NoStop}%
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\bibitem [{\citenamefont {Takeshita}\ \emph {et~al.}(2017)\citenamefont
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{Takeshita}, \citenamefont {{de Jong}}, \citenamefont {Neuhauser},
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\citenamefont {Baer},\ and\ \citenamefont {Rabani}}]{Takeshita_2017}%
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\BibitemOpen
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\bibfield {author} {\bibinfo {author} {\bibfnamefont {T.~Y.}\ \bibnamefont
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{Takeshita}}, \bibinfo {author} {\bibfnamefont {W.~A.}\ \bibnamefont {{de
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Jong}}}, \bibinfo {author} {\bibfnamefont {D.}~\bibnamefont {Neuhauser}},
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\bibinfo {author} {\bibfnamefont {R.}~\bibnamefont {Baer}}, \ and\ \bibinfo
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{author} {\bibfnamefont {E.}~\bibnamefont {Rabani}},\ }\href {\doibase
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10.1021/acs.jctc.7b00343} {\bibfield {journal} {\bibinfo {journal} {J.
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Chem. Theory Comput.}\ }\textbf {\bibinfo {volume} {13}},\ \bibinfo {pages}
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{4605} (\bibinfo {year} {2017})}\BibitemShut {NoStop}%
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\bibitem [{\citenamefont {Li}(2019)}]{Li_2019}%
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\BibitemOpen
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\bibfield {author} {\bibinfo {author} {\bibfnamefont {Z.}~\bibnamefont
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{Li}},\ }\href {\doibase 10.1063/1.5128719} {\bibfield {journal} {\bibinfo
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{journal} {J. Chem. Phys.}\ }\textbf {\bibinfo {volume} {151}},\ \bibinfo
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{pages} {244114} (\bibinfo {year} {2019})}\BibitemShut {NoStop}%
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\bibitem [{\citenamefont {G.~Rauhut}\ and\ \citenamefont
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{Werner}(1998)}]{Rauhut_1998}%
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\BibitemOpen
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\bibfield {author} {\bibinfo {author} {\bibfnamefont {P.~P.}\ \bibnamefont
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{G.~Rauhut}}\ and\ \bibinfo {author} {\bibfnamefont {H.-J.}\ \bibnamefont
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{Werner}},\ }\href {\doibase
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10.1002/(SICI)1096-987X(199808)19:11<1241::AID-JCC4>3.0.CO;2-K} {\bibfield
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{journal} {\bibinfo {journal} {J. Comp. Chem.}\ }\textbf {\bibinfo {volume}
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{19}},\ \bibinfo {pages} {1241} (\bibinfo {year} {1998})}\BibitemShut
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{NoStop}%
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\bibitem [{\citenamefont {Sch{\"u}tz}\ \emph {et~al.}(1999)\citenamefont
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{Sch{\"u}tz}, \citenamefont {Hetzer},\ and\ \citenamefont
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{Werner}}]{Schutz_1999}%
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\BibitemOpen
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\bibfield {author} {\bibinfo {author} {\bibfnamefont {M.}~\bibnamefont
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{Sch{\"u}tz}}, \bibinfo {author} {\bibfnamefont {G.}~\bibnamefont {Hetzer}},
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\ and\ \bibinfo {author} {\bibfnamefont {H.-J.}\ \bibnamefont {Werner}},\
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}\href {\doibase 10.1063/1.479957} {\bibfield {journal} {\bibinfo {journal}
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{J. Chem. Phys.}\ }\textbf {\bibinfo {volume} {111}},\ \bibinfo {pages}
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{5691} (\bibinfo {year} {1999})}\BibitemShut {NoStop}%
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\bibitem [{\citenamefont {Bozkaya}(2011)}]{Bozkaya_2011}%
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\BibitemOpen
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\bibfield {author} {\bibinfo {author} {\bibfnamefont {U.}~\bibnamefont
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{Bozkaya}},\ }\href {\doibase 10.1063/1.3665134} {\bibfield {journal}
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{\bibinfo {journal} {J. Chem. Phys.}\ }\textbf {\bibinfo {volume} {135}},\
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\bibinfo {pages} {224103} (\bibinfo {year} {2011})}\BibitemShut {NoStop}%
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\bibitem [{\citenamefont {Neese}\ \emph {et~al.}(2009)\citenamefont {Neese},
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\citenamefont {Schwabe}, \citenamefont {Kossmann}, \citenamefont {Schirmer},\
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and\ \citenamefont {Grimme}}]{Neese_2009}%
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\BibitemOpen
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\bibfield {author} {\bibinfo {author} {\bibfnamefont {F.}~\bibnamefont
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{Neese}}, \bibinfo {author} {\bibfnamefont {T.}~\bibnamefont {Schwabe}},
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\bibinfo {author} {\bibfnamefont {S.}~\bibnamefont {Kossmann}}, \bibinfo
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{author} {\bibfnamefont {B.}~\bibnamefont {Schirmer}}, \ and\ \bibinfo
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{author} {\bibfnamefont {S.}~\bibnamefont {Grimme}},\ }\href {\doibase
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10.1021/ct9003299} {\bibfield {journal} {\bibinfo {journal} {J. Chem. Teory
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Comput.}\ }\textbf {\bibinfo {volume} {5}},\ \bibinfo {pages} {3060}
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(\bibinfo {year} {2009})}\BibitemShut {NoStop}%
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\bibitem [{\citenamefont {Lee}\ and\ \citenamefont
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{Head-Gordon}(2018)}]{Lee_2018}%
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\BibitemOpen
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\bibfield {author} {\bibinfo {author} {\bibfnamefont {J.}~\bibnamefont
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{Lee}}\ and\ \bibinfo {author} {\bibfnamefont {M.}~\bibnamefont
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{Head-Gordon}},\ }\href {\doibase 10.1021/acs.jctc.8b00731} {\bibfield
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{journal} {\bibinfo {journal} {J. Chem. Theory Comput.}\ ,\ \bibinfo {pages}
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{5203}} (\bibinfo {year} {2018})}\BibitemShut {NoStop}%
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\bibitem [{\citenamefont {Bertels}\ \emph {et~al.}(2019)\citenamefont
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{Bertels}, \citenamefont {Lee},\ and\ \citenamefont
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{Head-Gordon}}]{Bertels_2019}%
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\BibitemOpen
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\bibfield {author} {\bibinfo {author} {\bibfnamefont {L.~W.}\ \bibnamefont
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{Bertels}}, \bibinfo {author} {\bibfnamefont {J.}~\bibnamefont {Lee}}, \ and\
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\bibinfo {author} {\bibfnamefont {M.}~\bibnamefont {Head-Gordon}},\ }\href
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{\doibase 10.1021/acs.jpclett.9b01641} {\bibfield {journal} {\bibinfo
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{journal} {J. Phys. Chem. Lett.}\ }\textbf {\bibinfo {volume} {10}},\
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\bibinfo {pages} {4170} (\bibinfo {year} {2019})}\BibitemShut {NoStop}%
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\bibitem [{\citenamefont {Rettig}\ \emph {et~al.}(2020)\citenamefont {Rettig},
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\citenamefont {Hait}, \citenamefont {Bertels},\ and\ \citenamefont
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{Head-Gordon}}]{Rettig_2020}%
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\BibitemOpen
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\bibfield {author} {\bibinfo {author} {\bibfnamefont {A.}~\bibnamefont
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{Rettig}}, \bibinfo {author} {\bibfnamefont {D.}~\bibnamefont {Hait}},
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\bibinfo {author} {\bibfnamefont {L.~W.}\ \bibnamefont {Bertels}}, \ and\
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\bibinfo {author} {\bibfnamefont {M.}~\bibnamefont {Head-Gordon}},\ }\href
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{\doibase 10.1021/acs.jctc.0c00986} {\bibfield {journal} {\bibinfo
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{journal} {J. Chem. Teory Comput.}\ } (\bibinfo {year} {2020}),\
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10.1021/acs.jctc.0c00986}\BibitemShut {NoStop}%
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\bibitem [{\citenamefont {Gilbert}\ \emph {et~al.}(2008)\citenamefont
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{Gilbert}, \citenamefont {Besley},\ and\ \citenamefont
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{Gill}}]{Gilbert_2008}%
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\BibitemOpen
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\bibfield {author} {\bibinfo {author} {\bibfnamefont {A.~T.~B.}\
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\bibnamefont {Gilbert}}, \bibinfo {author} {\bibfnamefont {N.~A.}\
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\bibnamefont {Besley}}, \ and\ \bibinfo {author} {\bibfnamefont {P.~M.~W.}\
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\bibnamefont {Gill}},\ }\href {\doibase 10.1021/jp801738f} {\bibfield
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{journal} {\bibinfo {journal} {J. Phys. Chem. A}\ }\textbf {\bibinfo
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{volume} {112}},\ \bibinfo {pages} {13164} (\bibinfo {year}
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{2008})}\BibitemShut {NoStop}%
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\bibitem [{\citenamefont {Lee}\ \emph {et~al.}(2019)\citenamefont {Lee},
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\citenamefont {Small},\ and\ \citenamefont {Head-Gordon}}]{Lee_2019}%
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\BibitemOpen
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\bibfield {author} {\bibinfo {author} {\bibfnamefont {J.}~\bibnamefont
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{Lee}}, \bibinfo {author} {\bibfnamefont {D.~W.}\ \bibnamefont {Small}}, \
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and\ \bibinfo {author} {\bibfnamefont {M.}~\bibnamefont {Head-Gordon}},\
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}\href {\doibase 10.1063/1.5128795} {\bibfield {journal} {\bibinfo
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{journal} {J. Chem. Phys.}\ }\textbf {\bibinfo {volume} {151}},\ \bibinfo
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{pages} {214103} (\bibinfo {year} {2019})}\BibitemShut {NoStop}%
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\bibitem [{\citenamefont {Carter-Fenk}\ and\ \citenamefont
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{Herbert}(2020)}]{CarterFenk_2020}%
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\BibitemOpen
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\bibfield {author} {\bibinfo {author} {\bibfnamefont {K.}~\bibnamefont
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{Carter-Fenk}}\ and\ \bibinfo {author} {\bibfnamefont {J.~M.}\ \bibnamefont
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{Herbert}},\ }\href {\doibase 10.1021/acs.jctc.0c00502} {\bibfield {journal}
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{\bibinfo {journal} {J. Chem. Teory Comput.}\ }\textbf {\bibinfo {volume}
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{16}},\ \bibinfo {pages} {5067} (\bibinfo {year} {2020})}\BibitemShut
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{NoStop}%
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\bibitem [{\citenamefont {Cohen}\ and\ \citenamefont
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{Mori-S\'anchez}(2016)}]{Cohen_2016}%
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\BibitemOpen
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@ -5,8 +5,105 @@
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%% Saved with string encoding Unicode (UTF-8)
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%
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@article{Rauhut_1998,
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author ={G. Rauhut, P. Pulay and Hans-Joachim Werner},
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journal={J. Comp. Chem.},
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year ={1998},
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volume ={19},
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pages ={1241},
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title ={Integral transformation with low‐order scaling for large local second‐order {M\oller--Plesset} calculations},
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doi ={10.1002/(SICI)1096-987X(199808)19:11<1241::AID-JCC4>3.0.CO;2-K},
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}
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@article{Schutz_1999,
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author ={M. Sch{\"u}tz and G. Hetzer and Hans-Joachim Werner},
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journal={J. Chem. Phys.},
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year ={1999},
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volume ={111},
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pages ={5691},
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title ={Low-order scaling local electron correlation methods. I. Linear scaling local MP2},
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doi ={10.1063/1.479957}
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}
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@article{Takeshita_2017,
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author ={T. Y. Takeshita and W. A. {de Jong} and D. Neuhauser and R. Baer and E. Rabani},
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journal={J. Chem. Theory Comput.},
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year ={2017},
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volume ={13},
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pages ={4605},
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title ={Stochastic Formulation of the Resolution of Identity: Application to Second Order {M\oller--Plesset} Perturbation Theory},
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doi ={10.1021/acs.jctc.7b00343},
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}
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@article{Li_2019,
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author ={Zhendong Li},
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journal={J. Chem. Phys.},
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year ={2019},
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volume ={151},
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pages ={244114},
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title ={Stochastic many-body perturbation theory for electron correlation energies},
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doi ={10.1063/1.5128719},
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}
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@article{Thom_2007,
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author ={A. J. W. Thom and A. Alavi},
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journal={Phys. Rev. Lett.},
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year ={2007},
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pages ={143001},
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volume ={99},
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title ={Stochastic Perturbation Theory: A Low-Scaling Approach to Correlated Electronic Energies},
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doi ={10.1103/PhysRevLett.99.143001},
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}
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@article{Willow_2012,
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author ={S. Y. Willow and K. S. Kim and S. Hirata},
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journal={J. Chem. Phys.},
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year ={2012},
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volume ={137},
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pages ={204122},
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title ={Stochastic evaluation of second-order many-body perturbation energies},
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doi ={10.1063/1.4768697},
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}
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@article{Neuhauser_2012,
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author ={D. Neuhauser and E. Rabani and R. Baer},
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journal={J. Chem. Theory Comput.},
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year ={2012},
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pages ={24},
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volume ={9},
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title ={Expeditious Stochastic Approach for MP2 Energies in Large Electronic Systems},
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doi ={10.1021/ct.300946j},
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}
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@article{Lee_2018,
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author ={J. Lee and M. Head-Gordon},
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journal={J. Chem. Theory Comput.},
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year ={2018},
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pages ={5203},
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title ={Regularized Orbital-Optimized Second-Order Møller–Plesset Perturbation Theory: A Reliable Fifth-Order-Scaling Electron Correlation Model with Orbital Energy Dependent Regularizers},
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doi ={10.1021/acs.jctc.8b00731},
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}
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@article{Bertels_2019,
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author ={L. W. Bertels and J. Lee and M. Head-Gordon},
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journal={J. Phys. Chem. Lett.},
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year ={2019},
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volume ={10},
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pages ={4170},
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title ={Third-Order {M\oller–Plesset} Perturbation Theory Made Useful? Choice of Orbitals and Scaling Greatly Improves Accuracy for Thermochemistry, Kinetics, and Intermolecular Interactions},
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doi ={10.1021/acs.jpclett.9b01641},
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}
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@article{CarterFenk_2020,
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author ={K. Carter-Fenk and J. M. Herbert},
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journal={J. Chem. Teory Comput.},
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year ={2020},
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volume ={16},
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pages ={5067},
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title ={State-Targeted Energy Projection: A Simple and Robust Approach to Orbital Relaxation of Non-Aufbau Self-Consistent Field Solutions},
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doi ={10.1021/acs.jctc.0c00502},
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}
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@article{Rettig_2020,
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author ={A. Rettig and D. Hait and L. W. Bertels and M. Head-Gordon},
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journal={J. Chem. Teory Comput.},
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year ={2020},
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title ={Third-Order {M\oller--Plesset} Theory Made More Useful? The Role of Density Functional Theory Orbitals},
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doi ={10.1021/acs.jctc.0c00986},
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}
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@article{Neese_2009,
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author ={F. Neese and T. Schwabe and S. Kossmann and B. Schirmer and S. Grimme},
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journal={J. Chem. Teory Comput.},
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@ -1871,8 +1871,9 @@ worth highlighting.
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In Cremer and He's original classification, ``class A'' systems exhibit monotonic convergence and generally
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correspond to weakly correlated electron pairs, while ``class B'' systems show erratic convergence after initial
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oscillations and generally contain spatially dense electron clusters.\cite{Cremer_1996}
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Further insights were provided by Olsen and coworkers\cite{Christiansen_1996,Olsen_1996,Olsen_2000,Olsen_2019}
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who employed a two-state model to understand the various convergence behaviours of Hermitian and non-Hermitian perturbation series.
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Further insights were provided by Olsen and coworkers
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who employed a two-state model to understand the various convergence behaviours of Hermitian and non-Hermitian
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perturbation series.\cite{Christiansen_1996,Olsen_1996,Olsen_2000,Olsen_2019}
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The careful analysis from Sergeev and Goodson later refined these classes depending on the position of the
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singularity closest to the origin, giving $\alpha$ singularities which have large imaginary component,
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and $\beta$ singularities which have a very small imaginary component.%
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@ -1893,7 +1894,8 @@ systematically improvable series can dramatically improve the accuracy and appli
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\hugh{However, the application of these approaches requires the evaluation of higher-order MP coefficents
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(\eg, MP3, MP4, MP5, etc) that are generally expensive to compute in practice.
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There is therefore a strong demand for computationally efficient approaches to evaluate general terms in the MP
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series, and the development of stochastic, resolution-of-the-identity, or linear-scaling approximations
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series, and the development of stochastic,\cite{Thom_2007,Neuhauser_2012,Willow_2012,Takeshita_2017,Li_2019}
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or linear-scaling approximations\cite{Rauhut_1998,Schutz_1999}
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may prove fruitful avenues in this direction.
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}
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@ -1902,14 +1904,14 @@ may prove fruitful avenues in this direction.
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The present review has only considered the convergence of the MP series using the RHF or UHF
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reference orbitals.
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However, numerous recent studies have shown that the use of orbitals optimised in the presence of the MP2
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correction or using Kohn--Sham density-functional theory (DFT) orbitals
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can significantly improve the accuracy of the MP3 correction,
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correction\cite{Bozkaya_2011,Neese_2009,Lee_2018} or Kohn--Sham density-functional theory (DFT) orbitals
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can significantly improve the accuracy of the MP3 correction,\cite{Bertels_2019,Rettig_2020}
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particularly in the presence of symmetry-breaking.
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Beyond intuitive heuristics, it is not clear why these alternative orbitals provide such accurate results,
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and a detailed investigation of their MP energy function in the complex plane is therefore bound to provide
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fascinating insights.
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Furthermore, the convergence properties of the excited-state MP series using orbital-optimised higher energy
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HF solutions remains entirely unexplored.
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HF solutions\cite{Gilbert_2008} remains entirely unexplored.\cite{Lee_2019,CarterFenk_2020}
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}
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% HUBBARD
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