diff --git a/Manuscript/CI-F12.aux b/Manuscript/CI-F12.aux deleted file mode 100644 index 4959a2d..0000000 --- a/Manuscript/CI-F12.aux +++ /dev/null @@ -1,158 +0,0 @@ -\relax -\providecommand\hyper@newdestlabel[2]{} -\providecommand\HyperFirstAtBeginDocument{\AtBeginDocument} -\HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined -\global\let\oldcontentsline\contentsline -\gdef\contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}} -\global\let\oldnewlabel\newlabel -\gdef\newlabel#1#2{\newlabelxx{#1}#2} -\gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}} -\AtEndDocument{\ifx\hyper@anchor\@undefined -\let\contentsline\oldcontentsline -\let\newlabel\oldnewlabel -\fi} -\fi} -\global\let\hyper@last\relax -\gdef\HyperFirstAtBeginDocument#1{#1} -\providecommand\HyField@AuxAddToFields[1]{} -\providecommand\HyField@AuxAddToCoFields[2]{} -\citation{Kutzelnigg85} -\citation{Kutzelnigg85,Kutzelnigg91,Termath91,Klopper91a,Klopper91b,Noga94} -\citation{Persson96,Persson97,May04,Tenno04b,Tew05,May05} -\citation{Tenno12a,Tenno12b,Hattig12,Kong12} -\citation{Tew07b} -\citation{Malrieu85} -\citation{Heully92,Garniron18} -\citation{Knowles84,Knowles89} -\citation{Huron73,Giner13,Giner15,Caffarel16,Scemama18a,Scemama18b,Loos18b,Loos19} -\citation{Shiozaki11} -\citation{Kato51,Kato57} -\citation{Pack66,Morgan93,Tew08,ExSpherium10,eee15} -\newlabel{FirstPage}{{}{1}{}{section*.1}{}} -\@writefile{toc}{\contentsline {title}{Dressing the configuration interaction matrix with explicit correlation}{1}{section*.2}\protected@file@percent } -\@writefile{toc}{\contentsline {abstract}{Abstract}{1}{section*.1}\protected@file@percent } -\@writefile{toc}{\contentsline {section}{\numberline {I}Introduction}{1}{section*.3}\protected@file@percent } -\@writefile{toc}{\contentsline {section}{\numberline {II}Ans{\"a}tz}{1}{section*.4}\protected@file@percent } -\newlabel{eq:ansatz}{{1}{1}{}{equation.2.1}{}} -\newlabel{eq:D}{{2}{1}{}{equation.2.2}{}} -\newlabel{eq:WF-F12-CIPSI}{{3}{1}{}{equation.2.3}{}} -\newlabel{eq:Ja}{{5}{1}{}{equation.2.5}{}} -\@writefile{toc}{\contentsline {section}{\numberline {III}Effective Hamiltonian}{1}{section*.5}\protected@file@percent } -\newlabel{eq:DrH}{{8}{1}{}{equation.3.8}{}} -\citation{Tenno04a} -\citation{Garniron18} -\citation{Garniron18} -\citation{SzaboBook} -\citation{Kutzelnigg91,Klopper92,Persson97,Klopper02,Manby03,Werner03,Klopper04,Tenno04a,Tenno04b,May05,Manby06,Tenno07,Komornicki11,Reine12,GG16} -\citation{Kutzelnigg91,Klopper92} -\citation{3ERI1,3ERI2,4eRR,IntF12} -\citation{Kutzelnigg91,Klopper02,Valeev04,Werner07,Hattig12} -\citation{Klopper02,Valeev04} -\citation{Garniron17b} -\newlabel{eq:IHF}{{9}{2}{}{equation.3.9}{}} -\newlabel{eq:DrH}{{10}{2}{}{equation.3.10}{}} -\@writefile{toc}{\contentsline {section}{\numberline {IV}Matrix elements}{2}{section*.6}\protected@file@percent } -\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Schematic representation of the various orbital spaces and their notation. The arrows represent the three types of excited determinants contributing to the dressing term: the pure doubles $\ket *{_{ij}^{\alpha \beta }}$ (green), the mixed doubles $\ket *{_{ij}^{a \beta }}$ (magenta) and the pure singles $\ket *{_{i}^{\alpha }}$ (orange).}}{2}{figure.1}\protected@file@percent } -\newlabel{fig:CBS}{{1}{2}{Schematic representation of the various orbital spaces and their notation. The arrows represent the three types of excited determinants contributing to the dressing term: the pure doubles $\ket *{_{ij}^{\alpha \beta }}$ (green), the mixed doubles $\ket *{_{ij}^{a \beta }}$ (magenta) and the pure singles $\ket *{_{i}^{\alpha }}$ (orange)}{figure.1}{}} -\newlabel{eq:RI}{{11}{2}{}{equation.4.11}{}} -\newlabel{eq:IHF-RI}{{12}{2}{}{equation.4.12}{}} -\citation{Kutzelnigg91} -\citation{Tenno04a} -\citation{Persson96,Persson97,May04,Tenno04b,Tew05,May05} -\citation{Tew05} -\citation{Kong12} -\citation{Nakashima07} -\citation{Puchalski09} -\citation{Sharkey11} -\citation{Bubin11} -\citation{Sharkey10} -\citation{Klopper10} -\citation{Pachucki10} -\citation{Giner15} -\citation{Cleland12} -\citation{Caffarel16} -\citation{AlmoraDiaz14} -\citation{Yousaf08,Yousaf09} -\citation{Giner13,Giner15,Caffarel16} -\@writefile{toc}{\contentsline {section}{\numberline {V}Computational details}{3}{section*.7}\protected@file@percent } -\@writefile{toc}{\contentsline {section}{\numberline {VI}Results}{3}{section*.8}\protected@file@percent } -\@writefile{toc}{\contentsline {section}{\numberline {VII}Conclusion}{3}{section*.9}\protected@file@percent } -\@writefile{lot}{\contentsline {table}{\numberline {I}{\ignorespaces FCI-F12 and FCI total ground-state energy of the neutral atoms for $Z = 2$ to $10$ calculated with Dunning's cc-pCVXZ and cc-pVXZ basis sets. \leavevmode {\color {red}The corresponding cc-pVXZ\_OPTRI or cc-pCVXZ\_OPTRI auxiliary basis is used as CABS.}}}{3}{table.1}\protected@file@percent } -\newlabel{tab:atoms}{{I}{3}{FCI-F12 and FCI total ground-state energy of the neutral atoms for $Z = 2$ to $10$ calculated with Dunning's cc-pCVXZ and cc-pVXZ basis sets. \alert {The corresponding cc-pVXZ\_OPTRI or cc-pCVXZ\_OPTRI auxiliary basis is used as CABS.}}{table.1}{}} -\bibdata{CI-F12Notes,CI-F12,CI-F12-control} -\bibcite{Kutzelnigg85}{{1}{1985}{{Kutzelnigg}}{{}}} -\bibcite{Kutzelnigg91}{{2}{1991}{{Kutzelnigg\ and\ Klopper}}{{}}} -\bibcite{Termath91}{{3}{1991}{{Termath, Klopper,\ and\ Kutzelnigg}}{{}}} -\bibcite{Klopper91a}{{4}{1991}{{Klopper\ and\ Kutzelnigg}}{{}}} -\bibcite{Klopper91b}{{5}{1991}{{Klopper, Rohse,\ and\ Kutzelnigg}}{{}}} -\bibcite{Noga94}{{6}{1994}{{Noga\ and\ Kutzelnigg}}{{}}} -\bibcite{Persson96}{{7}{1996}{{Persson\ and\ Taylor}}{{}}} -\bibcite{Persson97}{{8}{1997}{{Persson\ and\ Taylor}}{{}}} -\bibcite{May04}{{9}{2004}{{May\ and\ Manby}}{{}}} -\bibcite{Tenno04b}{{10}{2004{}}{{Ten-no}}{{}}} -\bibcite{Tew05}{{11}{2005}{{Tew\ and\ Klopper}}{{}}} -\bibcite{May05}{{12}{2005}{{May\ \emph {et~al.}}}{{May, Valeev, Polly,\ and\ Manby}}} -\bibcite{Tenno12a}{{13}{2012}{{Ten-no\ and\ Noga}}{{}}} -\bibcite{Tenno12b}{{14}{2012}{{Ten-no}}{{}}} -\bibcite{Hattig12}{{15}{2012}{{Hattig\ \emph {et~al.}}}{{Hattig, Klopper, Kohn,\ and\ Tew}}} -\bibcite{Kong12}{{16}{2012}{{Kong, Bischo,\ and\ Valeev}}{{}}} -\bibcite{Tew07b}{{17}{2007}{{Tew\ \emph {et~al.}}}{{Tew, Klopper, Neiss,\ and\ Hattig}}} -\bibcite{Malrieu85}{{18}{1985}{{Malrieu, Durand,\ and\ Daudey}}{{}}} -\bibcite{Heully92}{{19}{1992}{{Heuilly\ and\ Malrieu}}{{}}} -\bibcite{Garniron18}{{20}{2018}{{Garniron\ \emph {et~al.}}}{{Garniron, Scemama, Giner, Caffarel,\ and\ Loos}}} -\bibcite{Knowles84}{{21}{1984}{{Knowles\ and\ Handy}}{{}}} -\bibcite{Knowles89}{{22}{1989}{{Knowles\ and\ Handy}}{{}}} -\bibcite{Huron73}{{23}{1973}{{Huron, Malrieu,\ and\ Rancurel}}{{}}} -\bibcite{Giner13}{{24}{2013}{{Giner, Scemama,\ and\ Caffarel}}{{}}} -\bibcite{Giner15}{{25}{2015}{{Giner, Scemama,\ and\ Caffarel}}{{}}} -\bibcite{Caffarel16}{{26}{2016}{{Caffarel\ \emph {et~al.}}}{{Caffarel, Applencourt, Giner,\ and\ Scemama}}} -\bibcite{Scemama18a}{{27}{2018}{{Scemama\ \emph {et~al.}}}{{Scemama, Garniron, Caffarel,\ and\ Loos}}} -\bibcite{Scemama18b}{{28}{ress}{{Scemama\ \emph {et~al.}}}{{Scemama, Benali, Jacquemin, Caffarel,\ and\ Loos}}} -\bibcite{Loos18b}{{29}{2018}{{Loos\ \emph {et~al.}}}{{Loos, Scemama, Blondel, Garniron, Caffarel,\ and\ Jacquemin}}} -\bibcite{Loos19}{{30}{2019}{{Loos\ \emph {et~al.}}}{{Loos, Boggio-Pasqua, Scemama, Caffarel,\ and\ Jacquemin}}} -\bibcite{Shiozaki11}{{31}{2011}{{Shiozaki, Knizia,\ and\ Werner}}{{}}} -\bibcite{Kato51}{{32}{1951}{{Kato}}{{}}} -\bibcite{Kato57}{{33}{1957}{{Kato}}{{}}} -\bibcite{Pack66}{{34}{1966}{{Pack\ and\ {Byers Brown}}}{{}}} -\bibcite{Morgan93}{{35}{1993}{{{Morgan III}\ and\ Kutzelnigg}}{{}}} -\bibcite{Tew08}{{36}{2008}{{Tew}}{{}}} -\bibcite{ExSpherium10}{{37}{2010}{{Loos\ and\ Gill}}{{}}} -\bibcite{eee15}{{38}{2015}{{Loos, Bloomfield,\ and\ Gill}}{{}}} -\bibcite{Tenno04a}{{39}{2004{}}{{Ten-no}}{{}}} -\bibcite{SzaboBook}{{40}{1989}{{Szabo\ and\ Ostlund}}{{}}} -\bibcite{Klopper92}{{41}{1992}{{Klopper\ and\ Rohse}}{{}}} -\bibcite{Klopper02}{{42}{2002}{{Klopper\ and\ Samson}}{{}}} -\bibcite{Manby03}{{43}{2003}{{Manby}}{{}}} -\bibcite{Werner03}{{44}{2003}{{Werner, Manby,\ and\ Knowles}}{{}}} -\bibcite{Klopper04}{{45}{2004}{{Klopper}}{{}}} -\bibcite{Manby06}{{46}{2006}{{Manby\ \emph {et~al.}}}{{Manby, Werner, Adler,\ and\ May}}} -\bibcite{Tenno07}{{47}{2007}{{Ten-no}}{{}}} -\bibcite{Komornicki11}{{48}{2011}{{Komornicki\ and\ King}}{{}}} -\bibcite{Reine12}{{49}{2012}{{Reine, Helgaker,\ and\ Lind}}{{}}} -\bibcite{GG16}{{50}{2016}{{Barca\ and\ Gill}}{{}}} -\bibcite{3ERI1}{{51}{2016}{{Barca, Loos,\ and\ Gill}}{{}}} -\bibcite{3ERI2}{{52}{tion}{{Barca, Loos,\ and\ Gill}}{{}}} -\bibcite{4eRR}{{53}{ress}{{Barca\ and\ Loos}}{{}}} -\bibcite{IntF12}{{54}{2017}{{Barca\ and\ Loos}}{{}}} -\bibcite{Valeev04}{{55}{2004}{{Valeev}}{{}}} -\bibcite{Werner07}{{56}{2007}{{Werner, Adler,\ and\ Manby}}{{}}} -\bibcite{Garniron17b}{{57}{2017}{{Garniron\ \emph {et~al.}}}{{Garniron, Scemama, Loos,\ and\ Caffarel}}} -\bibcite{Nakashima07}{{58}{2007}{{Nakashima\ and\ Nakatsuji}}{{}}} -\bibcite{Puchalski09}{{59}{2009}{{Puchalski, Kedziera,\ and\ Pachucki}}{{}}} -\bibcite{Sharkey11}{{60}{2011}{{Sharkey\ and\ Adamowicz}}{{}}} -\bibcite{Bubin11}{{61}{2011}{{Bubin\ and\ Adamowicz}}{{}}} -\bibcite{Sharkey10}{{62}{2010}{{Sharkey, Bubin,\ and\ Adamowicz}}{{}}} -\@writefile{lot}{\contentsline {table}{\numberline {II}{\ignorespaces CIPSI, FCI-F12, i-FCIQMC and FCI total ground-state energy of the \ce {H2}, \ce {F2} and \ce {H2)} molecules at experimental geometry with Dunning's cc-pVXZ basis set. The corresponding cc-pVXZ\_OPTRI auxiliary basis is used as CABS.}}{4}{table.2}\protected@file@percent } -\newlabel{tab:molecules}{{II}{4}{CIPSI, FCI-F12, i-FCIQMC and FCI total ground-state energy of the \ce {H2}, \ce {F2} and \ce {H2)} molecules at experimental geometry with Dunning's cc-pVXZ basis set. The corresponding cc-pVXZ\_OPTRI auxiliary basis is used as CABS}{table.2}{}} -\@writefile{toc}{\contentsline {section}{\numberline {}Acknowledgments}{4}{section*.10}\protected@file@percent } -\bibcite{Klopper10}{{63}{2010}{{Klopper\ \emph {et~al.}}}{{Klopper, Bachorz, Tew,\ and\ Hattig}}} -\bibcite{Pachucki10}{{64}{2010}{{Pachucki}}{{}}} -\bibcite{Cleland12}{{65}{2012}{{Cleland\ \emph {et~al.}}}{{Cleland, Booth, Overy,\ and\ Alavi}}} -\bibcite{AlmoraDiaz14}{{66}{2014}{{Almora-Diaz}}{{}}} -\bibcite{Yousaf08}{{67}{2008}{{Yousaf\ and\ Peterson}}{{}}} -\bibcite{Yousaf09}{{68}{2009}{{Yousaf\ and\ Peterson}}{{}}} -\bibstyle{aipnum4-1} -\citation{REVTEX41Control} -\citation{aip41Control} -\newlabel{LastBibItem}{{68}{5}{}{section*.10}{}} -\newlabel{LastPage}{{}{5}{}{}{}} diff --git a/Manuscript/CI-F12.out b/Manuscript/CI-F12.out index e8d78ee..110cd70 100644 --- a/Manuscript/CI-F12.out +++ b/Manuscript/CI-F12.out @@ -1,7 +1,7 @@ \BOOKMARK [0][-]{section*.2}{Dressing the configuration interaction matrix with explicit correlation}{}% 2 \BOOKMARK [1][-]{section*.1}{Abstract}{section*.2}% 1 \BOOKMARK [1][-]{section*.3}{Introduction}{section*.2}% 3 -\BOOKMARK [1][-]{section*.4}{Ans\344tz}{section*.2}% 4 +\BOOKMARK [1][-]{section*.4}{Ansatz}{section*.2}% 4 \BOOKMARK [1][-]{section*.5}{Effective Hamiltonian}{section*.2}% 5 \BOOKMARK [1][-]{section*.6}{Matrix elements}{section*.2}% 6 \BOOKMARK [1][-]{section*.7}{Computational details}{section*.2}% 7 diff --git a/Manuscript/CI-F12.tex b/Manuscript/CI-F12.tex index c54dbe3..2e98fe7 100644 --- a/Manuscript/CI-F12.tex +++ b/Manuscript/CI-F12.tex @@ -108,7 +108,8 @@ However, for the sake of generality, we will discuss here the dressing of the fu Atomic units are used throughout. %---------------------------------------------------------------- -\section{Ans{\"a}tz} +%\section{Ans{\"a}tz} : Ca prend un trema au pluriel seulement : Ans{\"a}tze +\section{Ansatz} %---------------------------------------------------------------- Inspired by a number of previous research (see Ref.~\onlinecite{Shiozaki11} and references therein), our electronic wave function \emph{ans{\"a}tz} \begin{equation}