diff --git a/Manuscript/CSF_RCV.pdf b/Manuscript/CSF_RCV.pdf deleted file mode 100644 index 7963c41..0000000 Binary files a/Manuscript/CSF_RCV.pdf and /dev/null differ diff --git a/Manuscript/EMP_RHF_R10.pdf b/Manuscript/EMP_RHF_R10.pdf deleted file mode 100644 index 5ef9cae..0000000 Binary files a/Manuscript/EMP_RHF_R10.pdf and /dev/null differ diff --git a/Manuscript/EMP_UHF_R10.pdf b/Manuscript/EMP_UHF_R10.pdf deleted file mode 100644 index 13f5410..0000000 Binary files a/Manuscript/EMP_UHF_R10.pdf and /dev/null differ diff --git a/Manuscript/EPAWTFT.aux b/Manuscript/EPAWTFT.aux index 3768c25..6ec196e 100644 --- a/Manuscript/EPAWTFT.aux +++ b/Manuscript/EPAWTFT.aux @@ -75,12 +75,16 @@ \citation{Lepetit_1988} \citation{Cremer_1996} \citation{Cremer_1996} +\citation{Mihalka_2017a} +\citation{Mihalka_2017b} +\citation{Surjan_2018} +\citation{Mihalka_2019} \citation{Olsen_1996} \citation{Olsen_1996,Christiansen_1996} -\citation{Olsen_2000} \@writefile{toc}{\contentsline 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\emph {et~al.}}}{{Leininger, Allen, Schaefer,\ and\ Sherrill}}} @@ -160,32 +164,33 @@ \bibcite{Epstein_1926}{{50}{1926}{{Epstein}}{{}}} \bibcite{Seidl_2018}{{51}{2018}{{Seidl\ \emph {et~al.}}}{{Seidl, Giarrusso, Vuckovic, Fabiano,\ and\ Gori-Giorgi}}} \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{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}}{{}}} 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+\bibcite{Pawlowski_2019b}{{56}{2019{}}{{Paw{\l }owski\ \emph {et~al.}}}{{Paw{\l }owski, Olsen,\ and\ J{\o }rgensen}}} +\bibcite{Pawlowski_2019c}{{57}{2019}{{Baudin\ \emph {et~al.}}}{{Baudin, Paw{\l }owski, Bykov, Liakh, Kristensen, Olsen,\ and\ J{\o }rgensen}}} +\bibcite{Pawlowski_2019d}{{58}{2019{}}{{Paw{\l }owski\ \emph {et~al.}}}{{Paw{\l }owski, Olsen,\ and\ J{\o }rgensen}}} +\bibcite{Pawlowski_2019e}{{59}{2019{}}{{Paw{\l }owski\ \emph {et~al.}}}{{Paw{\l }owski, Olsen,\ and\ J{\o }rgensen}}} +\bibcite{Sergeev_2005}{{60}{2005}{{Sergeev\ \emph {et~al.}}}{{Sergeev, Goodson, Wheeler,\ and\ Allen}}} +\bibcite{Sergeev_2006}{{61}{2006}{{Sergeev\ and\ Goodson}}{{}}} +\bibcite{Stillinger_2000}{{62}{2000}{{Stillinger}}{{}}} +\bibcite{Baker_1971}{{63}{1971}{{{Baker}}}{{}}} +\bibcite{Goodson_2004}{{64}{2004}{{Goodson\ and\ Sergeev}}{{}}} +\bibcite{Heiss_2002}{{65}{2002}{{Heiss\ and\ M{\"u}ller}}{{}}} +\bibcite{Cejnar_2005}{{66}{2005}{{Cejnar\ \emph {et~al.}}}{{Cejnar, Heinze,\ and\ Dobe{\v s}}}} +\bibcite{Cejnar_2007}{{67}{2007}{{Cejnar\ \emph {et~al.}}}{{Cejnar, Heinze,\ and\ Macek}}} +\bibcite{Cejnar_2009}{{68}{2009}{{Cejnar\ and\ Jolie}}{{}}} +\bibcite{Borisov_2015}{{69}{2015}{{Borisov\ \emph {et~al.}}}{{Borisov, Ru{\v z}i{\v c}ka,\ and\ Znojil}}} +\bibcite{Sindelka_2017}{{70}{2017}{{{\v S}indelka\ \emph {et~al.}}}{{{\v S}indelka, Santos,\ and\ Moiseyev}}} +\bibcite{Sachdev_2011}{{71}{2011}{{Sachdev}}{{}}} +\bibcite{Cejnar_2015}{{72}{2015}{{Cejnar\ \emph {et~al.}}}{{Cejnar, Str{\'a}nsk{\'y},\ and\ Kloc}}} +\bibcite{Cejnar_2016}{{73}{2016}{{Cejnar\ and\ Str{\'a}nsk{\'y}}}{{}}} +\bibcite{Caprio_2008}{{74}{2008}{{Caprio\ \emph {et~al.}}}{{Caprio, Cejnar,\ and\ Iachello}}} +\bibcite{Macek_2019}{{75}{2019}{{Macek\ \emph {et~al.}}}{{Macek, Str{\'a}nsk{\'y}, Leviatan,\ and\ Cejnar}}} +\bibcite{Stransky_2018}{{76}{2018}{{Str{\'a}nsk{\'y}\ \emph {et~al.}}}{{Str{\'a}nsk{\'y}, Dvo{\v r}{\'a}k,\ and\ Cejnar}}} +\bibcite{Lipkin_1965}{{77}{1965}{{Lipkin\ \emph {et~al.}}}{{Lipkin, Meshkov,\ and\ Glick}}} \bibstyle{apsrev4-1} \citation{REVTEX41Control} \citation{apsrev41Control} -\newlabel{LastBibItem}{{76}{8}{}{section*.17}{}} +\newlabel{LastBibItem}{{77}{8}{}{section*.17}{}} \newlabel{LastPage}{{}{8}{}{}{}} diff --git a/Manuscript/EPAWTFT.bbl b/Manuscript/EPAWTFT.bbl index f8b3bc7..c6a0181 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}{76}% +\begin{thebibliography}{77}% \makeatletter \providecommand \@ifxundefined [1]{% \@ifx{#1\undefined} @@ -575,6 +575,17 @@ }\href {\doibase 10.1021/jp952815d} {\bibfield {journal} {\bibinfo {journal} {J. Phys. Chem.}\ }\textbf {\bibinfo {volume} {100}},\ \bibinfo {pages} {6173} (\bibinfo {year} {1996})}\BibitemShut {NoStop}% +\bibitem [{\citenamefont {Surj{\'a}n}\ \emph {et~al.}(2018)\citenamefont + {Surj{\'a}n}, \citenamefont {Mih{\'a}lka},\ and\ \citenamefont + {Szabados}}]{Surjan_2018}% + \BibitemOpen + \bibfield {author} {\bibinfo {author} {\bibfnamefont {P.~R.}\ \bibnamefont + {Surj{\'a}n}}, \bibinfo {author} {\bibfnamefont {Z.~{\'E}.}\ \bibnamefont + {Mih{\'a}lka}}, \ and\ \bibinfo {author} {\bibfnamefont {{\'A}.}~\bibnamefont + {Szabados}},\ }\href {\doibase 10.1007/s00214-018-2372-3} {\bibfield + {journal} {\bibinfo {journal} {Theor. Chem. Acc.}\ }\textbf {\bibinfo + {volume} {137}},\ \bibinfo {pages} {149} (\bibinfo {year} + {2018})}\BibitemShut {NoStop}% \bibitem [{\citenamefont {Christiansen}\ \emph {et~al.}(1996)\citenamefont {Christiansen}, \citenamefont {Olsen}, \citenamefont {J{\o}rgensen}, \citenamefont {Koch},\ and\ \citenamefont {Malmqvist}}]{Christiansen_1996}% diff --git a/Manuscript/EPAWTFT.bib b/Manuscript/EPAWTFT.bib index a038f3f..b42a54e 100644 --- a/Manuscript/EPAWTFT.bib +++ b/Manuscript/EPAWTFT.bib @@ -1,13 +1,25 @@ %% This BibTeX bibliography file was created using BibDesk. %% http://bibdesk.sourceforge.net/ -%% Created for Pierre-Francois Loos at 2020-11-12 15:34:01 +0100 +%% Created for Pierre-Francois Loos at 2020-11-12 16:42:11 +0100 %% Saved with string encoding Unicode (UTF-8) +@article{Surjan_2018, + author = {Surj{\'a}n,P{\'e}ter R. and Mih{\'a}lka,Zsuzsanna {\'E}. and Szabados,{\'A}gnes }, + date-added = {2020-11-12 16:40:48 +0100}, + date-modified = {2020-11-12 16:42:07 +0100}, + doi = {10.1007/s00214-018-2372-3}, + journal = {Theor. Chem. Acc.}, + pages = {149}, + title = {The inverse boundary value problem: application in many-body perturbation theory}, + volume = {137}, + year = {2018}, + Bdsk-Url-1 = {https://doi.org/10.1063/1.5083191}} + @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}, diff --git a/Manuscript/EPAWTFT.blg b/Manuscript/EPAWTFT.blg index 1f0b03d..283f071 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 78 entries, +You've used 79 entries, 5847 wiz_defined-function locations, - 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 + 2178 strings with 29522 characters, +and the built_in function-call counts, 77568 in all, are: += -- 4946 +> -- 2067 +< -- 528 ++ -- 656 +- -- 505 +* -- 12048 +:= -- 7618 +add.period$ -- 77 +call.type$ -- 79 +change.case$ -- 310 +chr.to.int$ -- 82 +cite$ -- 79 +duplicate$ -- 7200 +empty$ -- 5770 +format.name$ -- 1203 +if$ -- 15489 int.to.chr$ -- 6 -int.to.str$ -- 85 -missing$ -- 937 -newline$ -- 280 -num.names$ -- 228 -pop$ -- 2921 +int.to.str$ -- 86 +missing$ -- 949 +newline$ -- 283 +num.names$ -- 231 +pop$ -- 2958 preamble$ -- 1 -purify$ -- 380 +purify$ -- 385 quote$ -- 0 -skip$ -- 2801 +skip$ -- 2836 stack$ -- 0 -substring$ -- 2049 -swap$ -- 6764 -text.length$ -- 242 +substring$ -- 2074 +swap$ -- 6851 +text.length$ -- 245 text.prefix$ -- 0 top$ -- 10 -type$ -- 1082 +type$ -- 1096 warning$ -- 1 -while$ -- 233 +while$ -- 236 width$ -- 0 -write$ -- 655 +write$ -- 663 (There was 1 warning) diff --git a/Manuscript/EPAWTFT.log b/Manuscript/EPAWTFT.log index 65189e8..f42344a 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 15:45 +This is pdfTeX, Version 3.14159265-2.6-1.40.21 (TeX Live 2020) (preloaded format=pdflatex 2020.6.14) 12 NOV 2020 17:07 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. 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The mean absolute deviation taking the FCI correlation energies as reference is $0.3$ millihartree with the class-specific formula whereas the deviation increases to 12 millihartree using the general formula. Even if there were still shaded areas in their analysis and that their classification was incomplete, the work of Cremer and He clearly evidenced that understanding the origin of the different modes of convergence could potentially lead to a more rationalized use of MP perturbation theory and, hence, to more accurate correlation energy estimates. -%===============================% -\subsection{Cases of divergence} -%===============================% +Recently, Mih\'alka \textit{et al.} studied the partitioning effect on the convergence properties of Rayleigh-Schr\"odinger perturbation theory by considering the MP and the EN partitioning as well as an alternative partitioning. \cite{Mihalka_2017a} +Taking as an example (in particular) the water molecule at equilibrium and at stretched geometries, they could estimate the radius of the convergence via a quadratic Pad\'e approximant and convert divergent perturbation expansions to convergent ones in some cases thanks to a judicious choice of the level shift parameter. +In a subsequent study by the same group, \cite{Mihalka_2017b} they use analytic continuation techniques to resum divergent series taking again as an example the water molecule in a stretched geometry. +In a nutshell, their idea consists in calculating the energy of the system for several values of $\lambda$ for which the MP series is rapidly convergent, and to extrapolate the final energy to the physical system at $\lambda = 1$ via a polynomial- or Pad\'e-based fit. +However, the choice of the functional form of the fit remains a subtle task. +This technique was first generalized by using complex scaling parameters and applying analytic continuation by solving the Laplace equation, \cite{Surjan_2018} and then further improved thanks to Cauchy's integral formula +\begin{equation} + \frac{1}{2\pi i} \oint \frac{E(z)}{z - a} = E(a) +\end{equation} +instead of the solution of the Laplace equation. \cite{Mihalka_2019} + +%==========================================% +\subsection{Insights from a two-state model} +%==========================================% In the late 90's, Olsen \textit{et al.}~discovered an even more preoccupying behavior of the MP series. \cite{Olsen_1996} They showed that the series could be divergent even in systems that they considered as well understood like \ce{Ne} and \ce{HF}. \cite{Olsen_1996, Christiansen_1996} Cremer and He had already studied these two systems and classified them as \textit{class B} systems. However, the analysis of Olsen and coworkers was performed in larger basis sets containing diffuse functions. 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