diff --git a/Manuscript/EPAWTFT.aux b/Manuscript/EPAWTFT.aux index 29f9a04..3768c25 100644 --- a/Manuscript/EPAWTFT.aux +++ b/Manuscript/EPAWTFT.aux @@ -81,16 +81,20 @@ \@writefile{toc}{\contentsline {section}{\numberline {III}Historical overview}{4}{section*.10}\protected@file@percent } \@writefile{toc}{\contentsline {subsection}{\numberline {A}Behavior of the M{\o }ller-Plesset series}{4}{section*.11}\protected@file@percent } \@writefile{toc}{\contentsline {subsection}{\numberline {B}Cases of divergence}{4}{section*.12}\protected@file@percent } -\citation{Olsen_2019} \citation{Cremer_1996} +\citation{Olsen_2019} +\citation{Pawlowski_2019a,Pawlowski_2019b,Pawlowski_2019c,Pawlowski_2019d,Pawlowski_2019e} +\citation{Handy_1985,Lepetit_1988,Leininger_2000} +\citation{Pawlowski_2019a,Pawlowski_2019b,Pawlowski_2019c,Pawlowski_2019d,Pawlowski_2019e} +\citation{Handy_1985,Olsen_2000} \citation{Sergeev_2005,Sergeev_2006} \citation{Stillinger_2000} \citation{Baker_1971} +\@writefile{toc}{\contentsline {subsection}{\numberline {C}The singularity structure}{5}{section*.13}\protected@file@percent } +\newlabel{eq:HamiltonianStillinger}{{23}{5}{}{equation.3.23}{}} \citation{Sergeev_2005} \citation{Stillinger_2000} \citation{Olsen_2000} -\@writefile{toc}{\contentsline {subsection}{\numberline {C}The singularity structure}{5}{section*.13}\protected@file@percent } -\newlabel{eq:HamiltonianStillinger}{{23}{5}{}{equation.3.23}{}} \citation{Goodson_2004} \citation{Olsen_2000} \citation{Heiss_1988,Heiss_2002,Cejnar_2005,Cejnar_2007,Cejnar_2009,Borisov_2015,Sindelka_2017} @@ -146,6 +150,8 @@ \bibcite{Gill_1994}{{42}{1994}{{Gill}}{{}}} \bibcite{Gill_1986}{{43}{1986}{{Gill\ and\ Radom}}{{}}} \bibcite{Gill_1988}{{44}{1988}{{Gill\ \emph {et~al.}}}{{Gill, Pople, Radom,\ and\ Nobes}}} +\@writefile{toc}{\contentsline {section}{\numberline {}Acknowledgments}{7}{section*.16}\protected@file@percent } +\@writefile{toc}{\contentsline {section}{\numberline {}References}{7}{section*.17}\protected@file@percent } \bibcite{Handy_1985}{{45}{1985}{{Handy\ \emph {et~al.}}}{{Handy, Knowles,\ and\ Somasundram}}} \bibcite{Lepetit_1988}{{46}{1988}{{Lepetit\ \emph {et~al.}}}{{Lepetit, P{\'e}lissier,\ and\ Malrieu}}} \bibcite{Leininger_2000}{{47}{2000}{{Leininger\ \emph {et~al.}}}{{Leininger, Allen, Schaefer,\ and\ Sherrill}}} @@ -153,30 +159,33 @@ \bibcite{Nesbet_1955}{{49}{1955}{{Nesbet\ and\ Hartree}}{{}}} \bibcite{Epstein_1926}{{50}{1926}{{Epstein}}{{}}} \bibcite{Seidl_2018}{{51}{2018}{{Seidl\ \emph {et~al.}}}{{Seidl, Giarrusso, Vuckovic, Fabiano,\ and\ Gori-Giorgi}}} -\@writefile{toc}{\contentsline {section}{\numberline {}Acknowledgments}{7}{section*.16}\protected@file@percent } -\@writefile{toc}{\contentsline {section}{\numberline {}References}{7}{section*.17}\protected@file@percent } \bibcite{Cremer_1996}{{52}{1996}{{Cremer\ and\ He}}{{}}} \bibcite{Christiansen_1996}{{53}{1996}{{Christiansen\ \emph {et~al.}}}{{Christiansen, Olsen, J{\o }rgensen, Koch,\ and\ Malmqvist}}} -\bibcite{Sergeev_2005}{{54}{2005}{{Sergeev\ \emph {et~al.}}}{{Sergeev, Goodson, Wheeler,\ and\ Allen}}} -\bibcite{Sergeev_2006}{{55}{2006}{{Sergeev\ and\ Goodson}}{{}}} -\bibcite{Stillinger_2000}{{56}{2000}{{Stillinger}}{{}}} -\bibcite{Baker_1971}{{57}{1971}{{{Baker}}}{{}}} -\bibcite{Goodson_2004}{{58}{2004}{{Goodson\ and\ Sergeev}}{{}}} -\bibcite{Heiss_2002}{{59}{2002}{{Heiss\ and\ M{\"u}ller}}{{}}} -\bibcite{Cejnar_2005}{{60}{2005}{{Cejnar\ \emph {et~al.}}}{{Cejnar, Heinze,\ and\ Dobe{\v s}}}} -\bibcite{Cejnar_2007}{{61}{2007}{{Cejnar\ \emph {et~al.}}}{{Cejnar, Heinze,\ and\ Macek}}} -\bibcite{Cejnar_2009}{{62}{2009}{{Cejnar\ and\ Jolie}}{{}}} -\bibcite{Borisov_2015}{{63}{2015}{{Borisov\ \emph {et~al.}}}{{Borisov, Ru{\v z}i{\v c}ka,\ and\ Znojil}}} -\bibcite{Sindelka_2017}{{64}{2017}{{{\v S}indelka\ \emph {et~al.}}}{{{\v S}indelka, Santos,\ and\ Moiseyev}}} -\bibcite{Sachdev_2011}{{65}{2011}{{Sachdev}}{{}}} -\bibcite{Cejnar_2015}{{66}{2015}{{Cejnar\ \emph {et~al.}}}{{Cejnar, Str{\'a}nsk{\'y},\ and\ Kloc}}} -\bibcite{Cejnar_2016}{{67}{2016}{{Cejnar\ and\ Str{\'a}nsk{\'y}}}{{}}} -\bibcite{Caprio_2008}{{68}{2008}{{Caprio\ \emph {et~al.}}}{{Caprio, Cejnar,\ and\ Iachello}}} -\bibcite{Macek_2019}{{69}{2019}{{Macek\ \emph {et~al.}}}{{Macek, Str{\'a}nsk{\'y}, Leviatan,\ and\ Cejnar}}} -\bibcite{Stransky_2018}{{70}{2018}{{Str{\'a}nsk{\'y}\ \emph {et~al.}}}{{Str{\'a}nsk{\'y}, Dvo{\v r}{\'a}k,\ and\ Cejnar}}} -\bibcite{Lipkin_1965}{{71}{1965}{{Lipkin\ \emph {et~al.}}}{{Lipkin, Meshkov,\ and\ Glick}}} +\bibcite{Pawlowski_2019a}{{54}{2019{}}{{Paw{\l }owski\ \emph {et~al.}}}{{Paw{\l }owski, Olsen,\ and\ J{\o }rgensen}}} +\bibcite{Pawlowski_2019b}{{55}{2019{}}{{Paw{\l }owski\ \emph {et~al.}}}{{Paw{\l }owski, Olsen,\ and\ J{\o }rgensen}}} +\bibcite{Pawlowski_2019c}{{56}{2019}{{Baudin\ \emph {et~al.}}}{{Baudin, Paw{\l }owski, Bykov, Liakh, Kristensen, Olsen,\ and\ J{\o }rgensen}}} +\bibcite{Pawlowski_2019d}{{57}{2019{}}{{Paw{\l }owski\ \emph {et~al.}}}{{Paw{\l }owski, Olsen,\ and\ J{\o }rgensen}}} +\bibcite{Pawlowski_2019e}{{58}{2019{}}{{Paw{\l }owski\ \emph {et~al.}}}{{Paw{\l }owski, Olsen,\ and\ J{\o }rgensen}}} +\bibcite{Sergeev_2005}{{59}{2005}{{Sergeev\ \emph {et~al.}}}{{Sergeev, Goodson, Wheeler,\ and\ Allen}}} +\bibcite{Sergeev_2006}{{60}{2006}{{Sergeev\ and\ Goodson}}{{}}} +\bibcite{Stillinger_2000}{{61}{2000}{{Stillinger}}{{}}} +\bibcite{Baker_1971}{{62}{1971}{{{Baker}}}{{}}} +\bibcite{Goodson_2004}{{63}{2004}{{Goodson\ and\ Sergeev}}{{}}} +\bibcite{Heiss_2002}{{64}{2002}{{Heiss\ and\ M{\"u}ller}}{{}}} +\bibcite{Cejnar_2005}{{65}{2005}{{Cejnar\ \emph {et~al.}}}{{Cejnar, Heinze,\ and\ Dobe{\v s}}}} +\bibcite{Cejnar_2007}{{66}{2007}{{Cejnar\ \emph {et~al.}}}{{Cejnar, Heinze,\ and\ Macek}}} +\bibcite{Cejnar_2009}{{67}{2009}{{Cejnar\ and\ Jolie}}{{}}} +\bibcite{Borisov_2015}{{68}{2015}{{Borisov\ \emph {et~al.}}}{{Borisov, Ru{\v z}i{\v c}ka,\ and\ Znojil}}} +\bibcite{Sindelka_2017}{{69}{2017}{{{\v S}indelka\ \emph {et~al.}}}{{{\v S}indelka, Santos,\ and\ Moiseyev}}} +\bibcite{Sachdev_2011}{{70}{2011}{{Sachdev}}{{}}} +\bibcite{Cejnar_2015}{{71}{2015}{{Cejnar\ \emph {et~al.}}}{{Cejnar, Str{\'a}nsk{\'y},\ and\ Kloc}}} +\bibcite{Cejnar_2016}{{72}{2016}{{Cejnar\ and\ Str{\'a}nsk{\'y}}}{{}}} +\bibcite{Caprio_2008}{{73}{2008}{{Caprio\ \emph {et~al.}}}{{Caprio, Cejnar,\ and\ Iachello}}} +\bibcite{Macek_2019}{{74}{2019}{{Macek\ \emph {et~al.}}}{{Macek, Str{\'a}nsk{\'y}, Leviatan,\ and\ Cejnar}}} +\bibcite{Stransky_2018}{{75}{2018}{{Str{\'a}nsk{\'y}\ \emph {et~al.}}}{{Str{\'a}nsk{\'y}, Dvo{\v r}{\'a}k,\ and\ Cejnar}}} +\bibcite{Lipkin_1965}{{76}{1965}{{Lipkin\ \emph {et~al.}}}{{Lipkin, Meshkov,\ and\ Glick}}} \bibstyle{apsrev4-1} \citation{REVTEX41Control} \citation{apsrev41Control} -\newlabel{LastBibItem}{{71}{8}{}{section*.17}{}} +\newlabel{LastBibItem}{{76}{8}{}{section*.17}{}} \newlabel{LastPage}{{}{8}{}{}{}} diff --git a/Manuscript/EPAWTFT.bbl b/Manuscript/EPAWTFT.bbl index 9adf5bc..f8b3bc7 100644 --- a/Manuscript/EPAWTFT.bbl +++ b/Manuscript/EPAWTFT.bbl @@ -6,7 +6,7 @@ %Control: page (0) single %Control: year (1) truncated %Control: production of eprint (0) enabled -\begin{thebibliography}{71}% +\begin{thebibliography}{76}% \makeatletter \providecommand \@ifxundefined [1]{% \@ifx{#1\undefined} @@ -587,6 +587,65 @@ 10.1016/0009-2614(96)00974-8} {\bibfield {journal} {\bibinfo {journal} {Chem. Phys. Lett.}\ }\textbf {\bibinfo {volume} {261}},\ \bibinfo {pages} {369} (\bibinfo {year} {1996})}\BibitemShut {NoStop}% +\bibitem [{\citenamefont {Paw{\l}owski}\ \emph + {et~al.}(2019{\natexlab{a}})\citenamefont {Paw{\l}owski}, \citenamefont + {Olsen},\ and\ \citenamefont {J{\o}rgensen}}]{Pawlowski_2019a}% + \BibitemOpen + \bibfield {author} {\bibinfo {author} {\bibfnamefont {F.}~\bibnamefont + {Paw{\l}owski}}, \bibinfo {author} {\bibfnamefont {J.}~\bibnamefont {Olsen}}, + \ and\ \bibinfo {author} {\bibfnamefont {P.}~\bibnamefont {J{\o}rgensen}},\ + }\href {\doibase 10.1063/1.5004037} {\bibfield {journal} {\bibinfo + {journal} {J. Chem. Phys.}\ }\textbf {\bibinfo {volume} {150}},\ \bibinfo + {pages} {134108} (\bibinfo {year} {2019}{\natexlab{a}})}\BibitemShut + {NoStop}% +\bibitem [{\citenamefont {Paw{\l}owski}\ \emph + {et~al.}(2019{\natexlab{b}})\citenamefont {Paw{\l}owski}, \citenamefont + {Olsen},\ and\ \citenamefont {J{\o}rgensen}}]{Pawlowski_2019b}% + \BibitemOpen + \bibfield {author} {\bibinfo {author} {\bibfnamefont {F.}~\bibnamefont + {Paw{\l}owski}}, \bibinfo {author} {\bibfnamefont {J.}~\bibnamefont {Olsen}}, + \ and\ \bibinfo {author} {\bibfnamefont {P.}~\bibnamefont {J{\o}rgensen}},\ + }\href {\doibase 10.1063/1.5053167} {\bibfield {journal} {\bibinfo + {journal} {J. Chem. Phys.}\ }\textbf {\bibinfo {volume} {150}},\ \bibinfo + {pages} {134109} (\bibinfo {year} {2019}{\natexlab{b}})}\BibitemShut + {NoStop}% +\bibitem [{\citenamefont {Baudin}\ \emph {et~al.}(2019)\citenamefont {Baudin}, + \citenamefont {Paw{\l}owski}, \citenamefont {Bykov}, \citenamefont {Liakh}, + \citenamefont {Kristensen}, \citenamefont {Olsen},\ and\ \citenamefont + {J{\o}rgensen}}]{Pawlowski_2019c}% + \BibitemOpen + \bibfield {author} {\bibinfo {author} {\bibfnamefont {P.}~\bibnamefont + {Baudin}}, \bibinfo {author} {\bibfnamefont {F.}~\bibnamefont + {Paw{\l}owski}}, \bibinfo {author} {\bibfnamefont {D.}~\bibnamefont {Bykov}}, + \bibinfo {author} {\bibfnamefont {D.}~\bibnamefont {Liakh}}, \bibinfo + {author} {\bibfnamefont {K.}~\bibnamefont {Kristensen}}, \bibinfo {author} + {\bibfnamefont {J.}~\bibnamefont {Olsen}}, \ and\ \bibinfo {author} + {\bibfnamefont {P.}~\bibnamefont {J{\o}rgensen}},\ }\href {\doibase + 10.1063/1.5046935} {\bibfield {journal} {\bibinfo {journal} {J. Chem. + Phys.}\ }\textbf {\bibinfo {volume} {150}},\ \bibinfo {pages} {134110} + (\bibinfo {year} {2019})}\BibitemShut {NoStop}% +\bibitem [{\citenamefont {Paw{\l}owski}\ \emph + {et~al.}(2019{\natexlab{c}})\citenamefont {Paw{\l}owski}, \citenamefont + {Olsen},\ and\ \citenamefont {J{\o}rgensen}}]{Pawlowski_2019d}% + \BibitemOpen + \bibfield {author} {\bibinfo {author} {\bibfnamefont {F.}~\bibnamefont + {Paw{\l}owski}}, \bibinfo {author} {\bibfnamefont {J.}~\bibnamefont {Olsen}}, + \ and\ \bibinfo {author} {\bibfnamefont {P.}~\bibnamefont {J{\o}rgensen}},\ + }\href {\doibase 10.1063/1.5053622} {\bibfield {journal} {\bibinfo + {journal} {J. Chem. Phys.}\ }\textbf {\bibinfo {volume} {150}},\ \bibinfo + {pages} {134111} (\bibinfo {year} {2019}{\natexlab{c}})}\BibitemShut + {NoStop}% +\bibitem [{\citenamefont {Paw{\l}owski}\ \emph + {et~al.}(2019{\natexlab{d}})\citenamefont {Paw{\l}owski}, \citenamefont + {Olsen},\ and\ \citenamefont {J{\o}rgensen}}]{Pawlowski_2019e}% + \BibitemOpen + \bibfield {author} {\bibinfo {author} {\bibfnamefont {F.}~\bibnamefont + {Paw{\l}owski}}, \bibinfo {author} {\bibfnamefont {J.}~\bibnamefont {Olsen}}, + \ and\ \bibinfo {author} {\bibfnamefont {P.}~\bibnamefont {J{\o}rgensen}},\ + }\href {\doibase 10.1063/1.5053627} {\bibfield {journal} {\bibinfo + {journal} {J. Chem. Phys.}\ }\textbf {\bibinfo {volume} {150}},\ \bibinfo + {pages} {134112} (\bibinfo {year} {2019}{\natexlab{d}})}\BibitemShut + {NoStop}% \bibitem [{\citenamefont {Sergeev}\ \emph {et~al.}(2005)\citenamefont {Sergeev}, \citenamefont {Goodson}, \citenamefont {Wheeler},\ and\ \citenamefont {Allen}}]{Sergeev_2005}% diff --git a/Manuscript/EPAWTFT.bib b/Manuscript/EPAWTFT.bib index 1cf6784..a038f3f 100644 --- a/Manuscript/EPAWTFT.bib +++ b/Manuscript/EPAWTFT.bib @@ -1,13 +1,79 @@ %% This BibTeX bibliography file was created using BibDesk. %% http://bibdesk.sourceforge.net/ -%% Created for Pierre-Francois Loos at 2020-11-12 14:54:07 +0100 +%% Created for Pierre-Francois Loos at 2020-11-12 15:34:01 +0100 %% Saved with string encoding Unicode (UTF-8) +@article{Pawlowski_2019a, + author = {Paw{\l}owski,Filip and Olsen,Jeppe and J{\o}rgensen,Poul}, + date-added = {2020-11-12 15:24:23 +0100}, + date-modified = {2020-11-12 15:33:57 +0100}, + doi = {10.1063/1.5004037}, + journal = {J. Chem. Phys.}, + number = {13}, + pages = {134108}, + title = {Cluster perturbation theory. I. Theoretical foundation for a coupled cluster target state and ground-state energies}, + volume = {150}, + year = {2019}, + Bdsk-Url-1 = {https://doi.org/10.1063/1.5004037}} + +@article{Pawlowski_2019e, + author = {Paw{\l}owski,Filip and Olsen,Jeppe and J{\o}rgensen,Poul}, + date-added = {2020-11-12 15:24:15 +0100}, + date-modified = {2020-11-12 15:33:38 +0100}, + doi = {10.1063/1.5053627}, + journal = {J. Chem. Phys.}, + number = {13}, + pages = {134112}, + title = {Cluster perturbation theory. V. Theoretical foundation for cluster linear target states}, + url = {https://doi.org/10.1063/1.5053627}, + volume = {150}, + year = {2019}, + Bdsk-Url-1 = {https://doi.org/10.1063/1.5053627}} + +@article{Pawlowski_2019d, + author = {Paw{\l}owski,Filip and Olsen,Jeppe and J{\o}rgensen,Poul}, + date-added = {2020-11-12 15:24:12 +0100}, + date-modified = {2020-11-12 15:33:46 +0100}, + doi = {10.1063/1.5053622}, + journal = {J. Chem. Phys.}, + number = {13}, + pages = {134111}, + title = {Cluster perturbation theory. IV. Convergence of cluster perturbation series for energies and molecular properties}, + volume = {150}, + year = {2019}, + Bdsk-Url-1 = {https://doi.org/10.1063/1.5053622}} + +@article{Pawlowski_2019c, + author = {Baudin,Pablo and Paw{\l}owski,Filip and Bykov,Dmytro and Liakh,Dmitry and Kristensen,Kasper and Olsen,Jeppe and J{\o}rgensen,Poul}, + date-added = {2020-11-12 15:24:07 +0100}, + date-modified = {2020-11-12 15:33:50 +0100}, + doi = {10.1063/1.5046935}, + journal = {J. Chem. Phys.}, + number = {13}, + pages = {134110}, + title = {Cluster perturbation theory. III. Perturbation series for coupled cluster singles and doubles excitation energies}, + volume = {150}, + year = {2019}, + Bdsk-Url-1 = {https://doi.org/10.1063/1.5046935}} + +@article{Pawlowski_2019b, + author = {Paw{\l}owski,Filip and Olsen,Jeppe and J{\o}rgensen,Poul}, + date-added = {2020-11-12 15:24:02 +0100}, + date-modified = {2020-11-12 15:33:53 +0100}, + doi = {10.1063/1.5053167}, + journal = {J. Chem. Phys.}, + number = {13}, + pages = {134109}, + title = {Cluster perturbation theory. II. Excitation energies for a coupled cluster target state}, + volume = {150}, + year = {2019}, + Bdsk-Url-1 = {https://doi.org/10.1063/1.5053167}} + @article{Leininger_2000, author = {Leininger,Matthew L. and Allen,Wesley D. and Schaefer,Henry F. and Sherrill,C. David}, date-added = {2020-11-12 14:50:57 +0100}, diff --git a/Manuscript/EPAWTFT.blg b/Manuscript/EPAWTFT.blg index 5362b8d..1f0b03d 100644 --- a/Manuscript/EPAWTFT.blg +++ b/Manuscript/EPAWTFT.blg @@ -23,45 +23,45 @@ Control: production of article title (-1) disabled Control: page (0) single Control: year (1) truncated Control: production of eprint (0) enabled -You've used 73 entries, +You've used 78 entries, 5847 wiz_defined-function locations, - 2142 strings with 28296 characters, -and the built_in function-call counts, 71165 in all, are: -= -- 4543 -> -- 1883 -< -- 488 -+ -- 595 -- -- 461 -* -- 11019 -:= -- 7005 -add.period$ -- 71 -call.type$ -- 73 -change.case$ -- 286 -chr.to.int$ -- 79 -cite$ -- 73 -duplicate$ -- 6622 -empty$ -- 5299 -format.name$ -- 1097 -if$ -- 14200 -int.to.chr$ -- 3 -int.to.str$ -- 80 -missing$ -- 873 -newline$ -- 265 -num.names$ -- 213 -pop$ -- 2728 + 2171 strings with 29296 characters, +and the built_in function-call counts, 76591 in all, are: += -- 4882 +> -- 2041 +< -- 522 ++ -- 646 +- -- 499 +* -- 11895 +:= -- 7522 +add.period$ -- 76 +call.type$ -- 78 +change.case$ -- 306 +chr.to.int$ -- 81 +cite$ -- 78 +duplicate$ -- 7109 +empty$ -- 5698 +format.name$ -- 1188 +if$ -- 15295 +int.to.chr$ -- 6 +int.to.str$ -- 85 +missing$ -- 937 +newline$ -- 280 +num.names$ -- 228 +pop$ -- 2921 preamble$ -- 1 -purify$ -- 355 +purify$ -- 380 quote$ -- 0 -skip$ -- 2608 +skip$ -- 2801 stack$ -- 0 -substring$ -- 1889 -swap$ -- 6281 -text.length$ -- 223 +substring$ -- 2049 +swap$ -- 6764 +text.length$ -- 242 text.prefix$ -- 0 top$ -- 10 -type$ -- 1008 +type$ -- 1082 warning$ -- 1 -while$ -- 218 +while$ -- 233 width$ -- 0 -write$ -- 615 +write$ -- 655 (There was 1 warning) diff --git a/Manuscript/EPAWTFT.log b/Manuscript/EPAWTFT.log index 02b653f..65189e8 100644 --- a/Manuscript/EPAWTFT.log +++ b/Manuscript/EPAWTFT.log @@ -1,4 +1,4 @@ -This is pdfTeX, Version 3.14159265-2.6-1.40.21 (TeX Live 2020) (preloaded format=pdflatex 2020.6.14) 12 NOV 2020 15:03 +This is pdfTeX, Version 3.14159265-2.6-1.40.21 (TeX Live 2020) (preloaded format=pdflatex 2020.6.14) 12 NOV 2020 15:45 entering extended mode restricted \write18 enabled. file:line:error style messages enabled. @@ -853,21 +853,21 @@ Class revtex4-1 Warning: Environment acknowledgements is obsolete; Use acknowledgments instead. [8] -Package atveryend Info: Empty hook `AfterLastShipout' on input line 754. +Package atveryend Info: Empty hook `AfterLastShipout' on input line 759. (./EPAWTFT.aux) -Package atveryend Info: Executing hook `AtVeryEndDocument' on input line 754. -Package atveryend Info: Executing hook `AtEndAfterFileList' on input line 754. +Package atveryend Info: Executing hook `AtVeryEndDocument' on input line 759. +Package atveryend Info: Executing hook `AtEndAfterFileList' on input line 759. Package rerunfilecheck Info: File `EPAWTFT.out' has not changed. (rerunfilecheck) Checksum: 81A90960DB67E307FACD10337C344D5D;1233. ) Here is how much of TeX's memory you used: - 16604 strings out of 480478 - 283054 string characters out of 5899595 - 610721 words of memory out of 5000000 - 31769 multiletter control sequences out of 15000+600000 + 16624 strings out of 480478 + 283499 string characters out of 5899595 + 622138 words of memory out of 5000000 + 31784 multiletter control sequences out of 15000+600000 619636 words of font info for 469 fonts, out of 8000000 for 9000 1141 hyphenation exceptions out of 8191 - 44i,18n,58p,1757b,994s stack positions out of 5000i,500n,10000p,200000b,80000s + 44i,18n,58p,1757b,980s stack positions out of 5000i,500n,10000p,200000b,80000s {/usr/local/texlive/2020/texmf-dist/fonts/enc/dvips/base/8r.enc} -Output written on EPAWTFT.pdf (8 pages, 135947 bytes). +Output written on EPAWTFT.pdf (8 pages, 138049 bytes). PDF statistics: - 462 PDF objects out of 1000 (max. 8388607) - 435 compressed objects within 5 object streams - 122 named destinations out of 1000 (max. 500000) + 485 PDF objects out of 1000 (max. 8388607) + 458 compressed objects within 5 object streams + 127 named destinations out of 1000 (max. 500000) 52873 words of extra memory for PDF output out of 61914 (max. 10000000) diff --git a/Manuscript/EPAWTFT.pdf b/Manuscript/EPAWTFT.pdf index fbc3c1c..1be289d 100644 Binary files a/Manuscript/EPAWTFT.pdf and b/Manuscript/EPAWTFT.pdf differ diff --git a/Manuscript/EPAWTFT.synctex.gz b/Manuscript/EPAWTFT.synctex.gz index 3a81c6b..6ade691 100644 Binary files a/Manuscript/EPAWTFT.synctex.gz and b/Manuscript/EPAWTFT.synctex.gz differ diff --git a/Manuscript/EPAWTFT.tex b/Manuscript/EPAWTFT.tex index ccf5749..7c9a980 100644 --- a/Manuscript/EPAWTFT.tex +++ b/Manuscript/EPAWTFT.tex @@ -366,15 +366,6 @@ A singularity in the unit circle is designated as an intruder state, more precis \end{equation} where the diagonal matrix is the unperturbed Hamiltonian matrix $\bH^{(0)}$ and the second matrix in the right-hand-side $\bV$ is the perturbation. -In Ref.~\onlinecite{Olsen_2019}, the simple two-state model proposed by Olsen \textit{et al.} is generalized to a non-symmetric Hamiltonian -\begin{equation} - \underbrace{\mqty(\alpha & \delta_1 \\ \delta_2 & \beta)}_{\bH} = \underbrace{\mqty(\alpha & 0 \\ 0 & \beta + \gamma )}_{\bH^{(0)}} + \underbrace{\mqty( 0 & \delta_2 \\ \delta_1 & - \gamma)}_{\bV}. -\end{equation} -allowing an analysis of various choice of perturbation (not only the MP partioning) such as coupled cluster perturbation expansions and other non-Hermitian perturbation methods. -It is worth noting that only cases where $\text{sgn}(\delta_1) = - \text{sgn}(\delta_2)$ leads to new forms of perturbation expansions. -Interestingly, they showed that the convergence pattern of a given perturbation method can be characterized by its archetype which defines the overall ``shape'' of the energy convergence and can be subdivided in five classes for Hermitian Hamiltonians (zigzag, interspersed zigzag, triadic, ripples, and geometric), while two additional archetypes (zigzag-geometric and convex-geometric) are observed in non-Hermitian Hamiltonians. -Other features characterizing the convergence behavior of a perturbation method are its rate of convergence, its length of recurring period, and its sign pattern. - They first studied molecules with low-lying doubly-excited states of the same spatial and spin symmetry. The exact wave function has a non-negligible contribution from the doubly-excited states, so these low-lying excited states were good candidates for being intruder states. \titou{For \ce{CH_2} in a large basis set, the series is convergent up to the 50th order. They showed that the dominant singularity lies outside the unit circle but close to it causing the slow convergence.} @@ -385,6 +376,20 @@ Moreover they proved that the extrapolation formulas of Cremer and He \cite{Crem For example, the hydrogen fluoride molecule contains both back-door intruder states and low-lying doubly-excited states which results in alternated terms up to 10th order. For higher orders, the series is monotonically convergent. This surprising behavior is due to the fact that two pairs of singularities are approximately at the same distance from the origin. + +In Ref.~\onlinecite{Olsen_2019}, the simple two-state model proposed by Olsen \textit{et al.} is generalized to a non-symmetric Hamiltonian +\begin{equation} + \underbrace{\mqty(\alpha & \delta_1 \\ \delta_2 & \beta)}_{\bH} = \underbrace{\mqty(\alpha & 0 \\ 0 & \beta + \gamma )}_{\bH^{(0)}} + \underbrace{\mqty( 0 & \delta_2 \\ \delta_1 & - \gamma)}_{\bV}. +\end{equation} +allowing an analysis of various choice of perturbation (not only the MP partioning) such as coupled cluster perturbation expansions \cite{Pawlowski_2019a,Pawlowski_2019b,Pawlowski_2019c,Pawlowski_2019d,Pawlowski_2019e} and other non-Hermitian perturbation methods. +It is worth noting that only cases where $\text{sgn}(\delta_1) = - \text{sgn}(\delta_2)$ leads to new forms of perturbation expansions. +Interestingly, they showed that the convergence pattern of a given perturbation method can be characterized by its archetype which defines the overall ``shape'' of the energy convergence. These so-called archetypes can be subdivided in five classes for Hermitian Hamiltonians (zigzag, interspersed zigzag, triadic, ripples, and geometric), while two additional archetypes (zigzag-geometric and convex-geometric) are observed in non-Hermitian Hamiltonians. +Importantly, they observed that the the geometric archetype is the most common for MP expansions but that the ripples archetype sometimes occurs. \cite{Handy_1985,Lepetit_1988,Leininger_2000} +Other features characterizing the convergence behavior of a perturbation method are its rate of convergence, its length of recurring period, and its sign pattern; +the three remaining archetypes seem to be rarely observed in MP perturbation theory. +However, in the non-Hermitian setting of coupled cluster perturbation theory, \cite{Pawlowski_2019a,Pawlowski_2019b,Pawlowski_2019c,Pawlowski_2019d,Pawlowski_2019e} on can encounter interspersed zigzag, triadic, ripple, geometric, and zigzag-geometric archetypes. +One of main take-home messages of Olsen's study is that the primary critical point defines the high-order convergence, irrespective of whether this point is inside or outside the complex unit circle. \cite{Handy_1985,Olsen_2000} + %======================================= \subsection{The singularity structure} %=======================================