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added some more stuffs for extensivity

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Emmanuel Giner 2019-10-13 23:22:30 +08:00
parent 0dc8ce505e
commit 6b9ed78ede
11 changed files with 1458 additions and 92 deletions
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69
Manuscript/srDFT_SC.aux
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@ -84,7 +84,17 @@
\@writefile{toc}{\contentsline {subsubsection}{\numberline {2}Properties of approximated functionals}{4}{section*.10}}
\newlabel{eq:lim_ebasis}{{22}{4}{}{equation.2.22}{}}
\citation{GarBulHenScu-PCCP-15}
\citation{LooPraSceTouGin}
\citation{LooPraSceTouGin-JCPL-19}
\citation{GorSav-PRA-06}
\@writefile{toc}{\contentsline {subsection}{\numberline {E}Requirements for the approximated functionals in the strong correlation }{5}{section*.11}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {1}Requirements: separability of the energies and $S_z$ invariance}{5}{section*.12}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {2}Condition for the functional $\mathaccentV {bar}916{E}_{\text {PBE}}^\mathcal {B}[{n},\xi ,s,n^{(2)},\mu _{\Psi ^{\mathcal {B}}}]$ to obtain $S_z$ invariance}{5}{section*.13}}
\newlabel{eq:def_effspin}{{23}{5}{}{equation.2.23}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {F}Requirement on $\Psi ^{\mathcal {B}}$ for the extensivity}{5}{section*.14}}
\@writefile{toc}{\contentsline {subsection}{\numberline {G}Approximations for the strong correlation regime}{5}{section*.15}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {1}Definition of the different types of functionals}{5}{section*.16}}
\newlabel{eq:def_pbeueg}{{24}{5}{}{equation.2.24}{}}
\newlabel{eq:def_n2ueg}{{25}{5}{}{equation.2.25}{}}
\bibdata{srDFT_SCNotes,srDFT_SC}
\bibcite{Thom-PRL-10}{{1}{2010}{{Thom}}{{}}}
\bibcite{ScoTho-JCP-17}{{2}{2017}{{Scott\ and\ Thom}}{{}}}
@ -98,20 +108,6 @@
\bibcite{WerKno-JCP-88}{{10}{1988}{{Werner\ and\ Knowles}}{{}}}
\bibcite{KnoWer-CPL-88}{{11}{1988}{{Knowles\ and\ Werner}}{{}}}
\bibcite{BenErn-PhysRev-1969}{{12}{1969}{{Bender\ and\ Davidson}}{{}}}
\@writefile{toc}{\contentsline {subsection}{\numberline {E}Approximations for the strong correlation regime}{5}{section*.11}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {1}Requirements: separability of the energies and $S_z$ invariance}{5}{section*.12}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {2}Condition for the functional $\mathaccentV {bar}916{E}_{\text {PBE}}^\mathcal {B}[{n},\xi ,s,n^{(2)},\mu _{\Psi ^{\mathcal {B}}}]$ to obtain $S_z$ invariance}{5}{section*.13}}
\newlabel{eq:def_effspin}{{23}{5}{}{equation.2.23}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {3}Functionals for strong correlation}{5}{section*.14}}
\newlabel{eq:def_pbeueg}{{24}{5}{}{equation.2.24}{}}
\newlabel{eq:def_n2ueg}{{25}{5}{}{equation.2.25}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {F}Requirement on $\Psi ^{\mathcal {B}}$ for the extensivity of $\mu ({\bf r};\Psi _{}^{\mathcal {B}})$}{5}{section*.15}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {1}Introduction of the effective spin-density}{5}{section*.16}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {2}Requirement for $\Psi _{}^{\mathcal {B}}$ for size extensivity}{5}{section*.17}}
\@writefile{toc}{\contentsline {section}{\numberline {III}Results}{5}{section*.18}}
\newlabel{sec:results}{{III}{5}{}{section*.18}{}}
\@writefile{toc}{\contentsline {section}{\numberline {IV}Conclusion}{5}{section*.19}}
\newlabel{sec:conclusion}{{IV}{5}{}{section*.19}{}}
\bibcite{WhiHac-JCP-1969}{{13}{1969}{{Whitten\ and\ Hackmeyer}}{{}}}
\bibcite{HurMalRan-1973}{{14}{1973}{{Huron, Malrieu,\ and\ Rancurel}}{{}}}
\bibcite{EvaDauMal-ChemPhys-83}{{15}{1983}{{Evangelisti, Daudey,\ and\ Malrieu}}{{}}}
@ -120,12 +116,6 @@
\bibcite{IllRubRic-JCP-88}{{18}{1988}{{Illas, Rubio,\ and\ Ricart}}{{}}}
\bibcite{PovRubIll-TCA-92}{{19}{1992}{{Povill, Rubio,\ and\ Illas}}{{}}}
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\@writefile{lot}{\contentsline {table}{\numberline {I}{\ignorespaces Total energies (in Hartree) for HF and $E$ in aug-cc-pvdz for the He atom, F$_2$ (with F-F=1.411 angstroms) and the super non interacting system He--F$_2$. }}{6}{table.1}}
\newlabel{conv_He_table}{{I}{6}{Total energies (in Hartree) for HF and $E$ in aug-cc-pvdz for the He atom, F$_2$ (with F-F=1.411 angstroms) and the super non interacting system He--F$_2$}{table.1}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces N$_2$, aug-cc-pvdz: Comparison between the near FCI and corrected near FCI energies and the estimated exact one. }}{6}{figure.1}}
\newlabel{fig:N2_avdz}{{1}{6}{N$_2$, aug-cc-pvdz: Comparison between the near FCI and corrected near FCI energies and the estimated exact one}{figure.1}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces N$_2$, aug-cc-pvtz: Comparison between the near FCI and corrected near FCI energies and the estimated exact one. }}{6}{figure.2}}
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\bibcite{AbrSheDav-CPL-05}{{21}{2005}{{Abrams\ and\ Sherrill}}{{}}}
\bibcite{MusEngels-JCC-06}{{22}{2006}{{Musch\ and\ Engels}}{{}}}
\bibcite{BytRue-CP-09}{{23}{2009}{{Bytautas\ and\ Ruedenberg}}{{}}}
@ -144,15 +134,21 @@
\bibcite{Zim-JCP-17}{{36}{2017}{{Zimmerman}}{{}}}
\bibcite{LiOttHolShaUmr-JCP-2018}{{37}{2018}{{Li\ \emph {et~al.}}}{{Li, Otten, Holmes, Sharma,\ and\ Umrigar}}}
\bibcite{ChiHolOttUmrShaZim-JPCA-18}{{38}{2018}{{Chien\ \emph {et~al.}}}{{Chien, Holmes, Otten, Umrigar, Sharma,\ and\ Zimmerman}}}
\@writefile{lot}{\contentsline {table}{\numberline {I}{\ignorespaces Total energies (in Hartree) for HF and $E$ in aug-cc-pvdz for the He atom, F$_2$ (with F-F=1.411 angstroms) and the super non interacting system He--F$_2$. }}{6}{table.1}}
\newlabel{conv_He_table}{{I}{6}{Total energies (in Hartree) for HF and $E$ in aug-cc-pvdz for the He atom, F$_2$ (with F-F=1.411 angstroms) and the super non interacting system He--F$_2$}{table.1}{}}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {2}Introduction of the effective spin-density}{6}{section*.17}}
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\@writefile{toc}{\contentsline {section}{\numberline {IV}Conclusion}{6}{section*.20}}
\newlabel{sec:conclusion}{{IV}{6}{}{section*.20}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces N$_2$, aug-cc-pvdz: Comparison between the near FCI and corrected near FCI energies and the estimated exact one. }}{6}{figure.1}}
\newlabel{fig:N2_avdz}{{1}{6}{N$_2$, aug-cc-pvdz: Comparison between the near FCI and corrected near FCI energies and the estimated exact one}{figure.1}{}}
\bibcite{SceBenJacCafLoo-JCP-18}{{39}{2018{}}{{Scemama\ \emph {et~al.}}}{{Scemama, Benali, Jacquemin, Caffarel,\ and\ Loos}}}
\bibcite{LooSceBloGarCafJac-JCTC-18}{{40}{2018}{{Loos\ \emph {et~al.}}}{{Loos, Scemama, Blondel, Garniron, Caffarel,\ and\ Jacquemin}}}
\bibcite{GarSceGinCaffLoo-JCP-18}{{41}{2018}{{Garniron\ \emph {et~al.}}}{{Garniron, Scemama, Giner, Caffarel,\ and\ Loos}}}
\bibcite{SceGarCafLoo-JCTC-18}{{42}{2018{}}{{Scemama\ \emph {et~al.}}}{{Scemama, Garniron, Caffarel,\ and\ Loos}}}
\bibcite{GarGinMalSce-JCP-16}{{43}{2017}{{Garniron\ \emph {et~al.}}}{{Garniron, Giner, Malrieu,\ and\ Scemama}}}
\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces F$_2$, aug-cc-pvdz: Comparison between the near FCI and corrected near FCI energies and the estimated exact one. }}{7}{figure.3}}
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\newlabel{fig:F2_avtz}{{4}{7}{F$_2$, aug-cc-pvtz: Comparison between the near FCI and corrected near FCI energies and the estimated exact one}{figure.4}{}}
\bibcite{LooBogSceCafJac-JCTC-19}{{44}{2019{}}{{Loos\ \emph {et~al.}}}{{Loos, Boggio-Pasqua, Scemama, Caffarel,\ and\ Jacquemin}}}
\bibcite{Hyl-ZP-29}{{45}{1929}{{Hylleraas}}{{}}}
\bibcite{Kut-TCA-85}{{46}{1985}{{Kutzelnigg}}{{}}}
@ -170,34 +166,41 @@
\bibcite{TouColSav-PRA-04}{{58}{2004}{{Toulouse, Colonna,\ and\ Savin}}{{}}}
\bibcite{FraMusLupTou-JCP-15}{{59}{2015}{{Franck\ \emph {et~al.}}}{{Franck, Mussard, Luppi,\ and\ Toulouse}}}
\bibcite{AngGerSavTou-PRA-05}{{60}{2005}{{\'Angy\'an\ \emph {et~al.}}}{{\'Angy\'an, Gerber, Savin,\ and\ Toulouse}}}
\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces N$_2$, aug-cc-pvtz: Comparison between the near FCI and corrected near FCI energies and the estimated exact one. }}{7}{figure.2}}
\newlabel{fig:N2_avtz}{{2}{7}{N$_2$, aug-cc-pvtz: Comparison between the near FCI and corrected near FCI energies and the estimated exact one}{figure.2}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces F$_2$, aug-cc-pvdz: Comparison between the near FCI and corrected near FCI energies and the estimated exact one. }}{7}{figure.3}}
\newlabel{fig:F2_avdz}{{3}{7}{F$_2$, aug-cc-pvdz: Comparison between the near FCI and corrected near FCI energies and the estimated exact one}{figure.3}{}}
\bibcite{GolWerSto-PCCP-05}{{61}{2005}{{Goll, Werner,\ and\ Stoll}}{{}}}
\bibcite{TouGerJanSavAng-PRL-09}{{62}{2009}{{Toulouse\ \emph {et~al.}}}{{Toulouse, Gerber, Jansen, Savin,\ and\ \'Angy\'an}}}
\bibcite{JanHenScu-JCP-09}{{63}{2009}{{Janesko, Henderson,\ and\ Scuseria}}{{}}}
\bibcite{TouZhuSavJanAng-JCP-11}{{64}{2011}{{Toulouse\ \emph {et~al.}}}{{Toulouse, Zhu, Savin, Jansen,\ and\ \'Angy\'an}}}
\@writefile{lof}{\contentsline {figure}{\numberline {5}{\ignorespaces H$_{10}$, cc-pvdz: Comparison between the near FCI and corrected near FCI energies and the estimated exact one. }}{8}{figure.5}}
\newlabel{fig:H10_vdz}{{5}{8}{H$_{10}$, cc-pvdz: Comparison between the near FCI and corrected near FCI energies and the estimated exact one}{figure.5}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {6}{\ignorespaces H$_{10}$, cc-pvtz: Comparison between the near FCI and corrected near FCI energies and the estimated exact one. }}{8}{figure.6}}
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\@writefile{lof}{\contentsline {figure}{\numberline {7}{\ignorespaces H$_{10}$, cc-pvqz: Comparison between the near FCI and corrected near FCI energies and the estimated exact one. }}{8}{figure.7}}
\newlabel{fig:H10_vqz}{{7}{8}{H$_{10}$, cc-pvqz: Comparison between the near FCI and corrected near FCI energies and the estimated exact one}{figure.7}{}}
\bibcite{MusReiAngTou-JCP-15}{{65}{2015}{{Mussard\ \emph {et~al.}}}{{Mussard, Reinhardt, \'Angy\'an,\ and\ Toulouse}}}
\bibcite{LeiStoWerSav-CPL-97}{{66}{1997}{{Leininger\ \emph {et~al.}}}{{Leininger, Stoll, Werner,\ and\ Savin}}}
\bibcite{FroTouJen-JCP-07}{{67}{2007}{{Fromager, Toulouse,\ and\ Jensen}}{{}}}
\bibcite{FroCimJen-PRA-10}{{68}{2010}{{Fromager, Cimiraglia,\ and\ Jensen}}{{}}}
\bibcite{HedKneKieJenRei-JCP-15}{{69}{2015}{{Hedeg{\r a}rd\ \emph {et~al.}}}{{Hedeg{\r a}rd, Knecht, Kielberg, Jensen,\ and\ Reiher}}}
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\bibcite{HedTouJen-JCP-18}{{70}{2018}{{Hedeg{\r a}rd, Toulouse,\ and\ Jensen}}{{}}}
\bibcite{FerGinTou-JCP-18}{{71}{2019}{{Fert{\'e}, Giner,\ and\ Toulouse}}{{}}}
\bibcite{GinPraFerAssSavTou-JCP-18}{{72}{2018}{{Giner\ \emph {et~al.}}}{{Giner, Pradines, Fert\'e, Assaraf, Savin,\ and\ Toulouse}}}
\bibcite{LooPraSceTouGin-JCPL-19}{{73}{2019{}}{{Loos\ \emph {et~al.}}}{{Loos, Pradines, Scemama, Toulouse,\ and\ Giner}}}
\bibcite{TouGorSav-TCA-05}{{74}{2005}{{Toulouse, Gori-Giorgi,\ and\ Savin}}{{}}}
\bibcite{PerBurErn-PRL-96}{{75}{1996}{{Perdew, Burke,\ and\ Ernzerhof}}{{}}}
\bibcite{GoriSav-PRA-06}{{76}{2006}{{Gori-Giorgi\ and\ Savin}}{{}}}
\bibcite{GoriSav-PRA-06}{{76}{2006{}}{{Gori-Giorgi\ and\ Savin}}{{}}}
\bibcite{PazMorGorBac-PRB-06}{{77}{2006}{{Paziani\ \emph {et~al.}}}{{Paziani, Moroni, Gori-Giorgi,\ and\ Bachelet}}}
\bibcite{GritMeePer-PRA-18}{{78}{2018}{{Gritsenko, van Meer,\ and\ Pernal}}{{}}}
\bibcite{CarTruGag-JPCA-17}{{79}{2017}{{Carlson, Truhlar,\ and\ Gagliardi}}{{}}}
\bibcite{GarBulHenScu-PCCP-15}{{80}{2015}{{Garza\ \emph {et~al.}}}{{Garza, Bulik, Henderson,\ and\ Scuseria}}}
\bibcite{GorSav-PRA-06}{{81}{2006{}}{{Gori-Giorgi\ and\ Savin}}{{}}}
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Manuscript/srDFT_SC.bbl
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@ -6,7 +6,7 @@
%Control: page (0) single
%Control: year (1) truncated
%Control: production of eprint (0) enabled
\begin{thebibliography}{80}%
\begin{thebibliography}{81}%
\makeatletter
\providecommand \@ifxundefined [1]{%
\@ifx{#1\undefined}
@ -808,13 +808,14 @@
}\textbf {\bibinfo {volume} {77}},\ \bibinfo {pages} {3865} (\bibinfo {year}
{1996})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Gori-Giorgi}\ and\ \citenamefont
{Savin}(2006)}]{GoriSav-PRA-06}%
{Savin}(2006{\natexlab{a}})}]{GoriSav-PRA-06}%
\BibitemOpen
\bibfield {author} {\bibinfo {author} {\bibfnamefont {P.}~\bibnamefont
{Gori-Giorgi}}\ and\ \bibinfo {author} {\bibfnamefont {A.}~\bibnamefont
{Savin}},\ }\href {\doibase 10.1103/PhysRevA.73.032506} {\bibfield {journal}
{\bibinfo {journal} {Phys. Rev. A}\ }\textbf {\bibinfo {volume} {73}},\
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\bibinfo {pages} {032506} (\bibinfo {year} {2006}{\natexlab{a}})}\BibitemShut
{NoStop}%
\bibitem [{\citenamefont {Paziani}\ \emph {et~al.}(2006)\citenamefont
{Paziani}, \citenamefont {Moroni}, \citenamefont {Gori-Giorgi},\ and\
\citenamefont {Bachelet}}]{PazMorGorBac-PRB-06}%
@ -855,4 +856,13 @@
}\href@noop {} {\bibfield {journal} {\bibinfo {journal} {Phys. Chem. Chem.
Phys.}\ }\textbf {\bibinfo {volume} {17}},\ \bibinfo {pages} {22412}
(\bibinfo {year} {2015})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Gori-Giorgi}\ and\ \citenamefont
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\BibitemOpen
\bibfield {author} {\bibinfo {author} {\bibfnamefont {P.}~\bibnamefont
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{\bibinfo {journal} {Phys. Rev. A}\ }\textbf {\bibinfo {volume} {73}},\
\bibinfo {pages} {032506} (\bibinfo {year} {2006}{\natexlab{b}})}\BibitemShut
{NoStop}%
\end{thebibliography}%

67
Manuscript/srDFT_SC.blg
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@ -14,7 +14,6 @@ Database file #2: srDFT_SC.bib
Warning--I didn't find a database entry for "exicted"
Warning--I didn't find a database entry for "excited"
Warning--I didn't find a database entry for "kato"
Warning--I didn't find a database entry for "LooPraSceTouGin"
control{REVTEX41Control}, control.key{N/A}, control.author{N/A}, control.editor{N/A}, control.title{N/A}, control.pages{N/A}, control.year{N/A}, control.eprint{N/A},
control{aip41Control}, control.key{N/A}, control.author{N/A}, control.editor{N/A}, control.title{}, control.pages{0}, control.year{N/A}, control.eprint{N/A},
Warning--jnrlst (dependency: not reversed) set 1
@ -28,45 +27,45 @@ Control: page (0) single
Control: year (1) truncated
Control: production of eprint (0) enabled
Warning--missing journal in CafAplGinScem-arxiv-16
You've used 82 entries,
You've used 83 entries,
5918 wiz_defined-function locations,
2192 strings with 31260 characters,
and the built_in function-call counts, 84952 in all, are:
= -- 5441
> -- 2788
< -- 519
+ -- 865
- -- 709
* -- 13106
:= -- 8744
add.period$ -- 81
call.type$ -- 82
change.case$ -- 323
2192 strings with 31256 characters,
and the built_in function-call counts, 85895 in all, are:
= -- 5509
> -- 2814
< -- 524
+ -- 874
- -- 715
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:= -- 8845
add.period$ -- 82
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int.to.chr$ -- 5
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(There were 6 warnings)
write$ -- 710
(There were 5 warnings)

15
Manuscript/srDFT_SC.out
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@ -8,12 +8,13 @@
\BOOKMARK [2][-]{section*.8}{Generic form and properties of the approximations for B[n\(r\)] }{section*.4}% 8
\BOOKMARK [3][-]{section*.9}{Generic form of the approximated functionals}{section*.8}% 9
\BOOKMARK [3][-]{section*.10}{Properties of approximated functionals}{section*.8}% 10
\BOOKMARK [2][-]{section*.11}{Approximations for the strong correlation regime}{section*.4}% 11
\BOOKMARK [2][-]{section*.11}{Requirements for the approximated functionals in the strong correlation }{section*.4}% 11
\BOOKMARK [3][-]{section*.12}{Requirements: separability of the energies and Sz invariance}{section*.11}% 12
\BOOKMARK [3][-]{section*.13}{Condition for the functional PBEB[n,,s,n\(2\),B] to obtain Sz invariance}{section*.11}% 13
\BOOKMARK [3][-]{section*.14}{Functionals for strong correlation}{section*.11}% 14
\BOOKMARK [2][-]{section*.15}{Requirement on B for the extensivity of \(r;B\)}{section*.4}% 15
\BOOKMARK [3][-]{section*.16}{Introduction of the effective spin-density}{section*.15}% 16
\BOOKMARK [3][-]{section*.17}{Requirement for B for size extensivity}{section*.15}% 17
\BOOKMARK [1][-]{section*.18}{Results}{section*.2}% 18
\BOOKMARK [1][-]{section*.19}{Conclusion}{section*.2}% 19
\BOOKMARK [2][-]{section*.14}{Requirement on B for the extensivity}{section*.4}% 14
\BOOKMARK [2][-]{section*.15}{Approximations for the strong correlation regime}{section*.4}% 15
\BOOKMARK [3][-]{section*.16}{Definition of the different types of functionals}{section*.15}% 16
\BOOKMARK [3][-]{section*.17}{Introduction of the effective spin-density}{section*.15}% 17
\BOOKMARK [3][-]{section*.18}{Requirement for B for size extensivity}{section*.15}% 18
\BOOKMARK [1][-]{section*.19}{Results}{section*.2}% 19
\BOOKMARK [1][-]{section*.20}{Conclusion}{section*.2}% 20

41
Manuscript/srDFT_SC.tex
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@ -72,6 +72,7 @@
\newcommand{\argebasis}[0]{\den,\xi,s,\ntwo,\mu_{\Psi^{\basis}}}
\newcommand{\argecmd}[0]{\den,\xi,s,\ntwo,\mu}
\newcommand{\argepbeueg}[0]{\den,\xi,s,\ntwo_{\text{UEG}},\mu_{\Psi^{\basis}}}
\newcommand{\argepbeuegxihf}[0]{\den,\xi,s,\ntwo_{\text{UEG}},\mu_{\text{HF}}^{\basis}}
\newcommand{\argepbeuegspin}[0]{\den,\Xi,s,\ntwo_{\text{UEG}},\mu_{\Psi^{\basis}}}
\newcommand{\argrebasis}[0]{\denr,\xi(\br{}),s,\ntwo(\br{}),\mu_{\Psi^{\basis}}(\br{})}
\newcommand{\ecmubis}[0]{\bar{E}_{\text{c,md}}^{\text{sr}}[\denr;\,\mu]}
@ -220,6 +221,7 @@
\newcommand{\bx}[1]{\mathbf{x}_{#1}}
\newcommand{\dbr}[1]{d\br{#1}}
\newcommand{\PBEspin}{PBEspin}
\newcommand{\PBEueg}{PBE-UEG-{$\Xi$}}
\newcommand{\LCPQ}{Laboratoire de Chimie et Physique Quantiques (UMR 5626), Universit\'e de Toulouse, CNRS, UPS, France}
\newcommand{\LCT}{Laboratoire de Chimie Th\'eorique, Universit\'e Pierre et Marie Curie, Sorbonne Universit\'e, CNRS, Paris, France}
@ -375,6 +377,7 @@ As it was shown in Ref. \onlinecite{GinPraFerAssSavTou-JCP-18}, the effective in
\lim_{\Bas \rightarrow \text{CBS}} \wbasis = \frac{1}{|\br{1}-\br{2}|}\quad \forall\,\psibasis.
\end{equation}
The condition of equation \eqref{eq:cbs_wbasis} is fundamental as it guarantees the good behaviour of all the theory in the limit of a complete basis set.
\subsection{Definition of a range-separation parameter varying in real space}
\label{sec:mur}
As the effective interaction within a basis set $\wbasis$ is non divergent, one can fit such a function with a long-range interaction defined in the framework of RSDFT which depends on the range-separation parameter $\mu$
@ -455,7 +458,7 @@ which guarantees an unaltered limit when reaching the CBS limit.
Also, the $\efuncdenpbe{\argecmd}$ vanishes for systems with vanishing on-top pair density, which guarantees the good limit in the case of stretched H$_2$ and for one-electron system.
Such a property is guaranteed independently by i) the definition of the effective interaction $\wbasis$ (see equation \eqref{eq:wbasis}) together with the condition \eqref{eq:lim_muinf}, ii) the fact that the $\ecmd(\argecmd)$ vanishes when the on-top pair density vanishes (see equation \eqref{eq:lim_n2}).
\subsection{Approximations for the strong correlation regime}
\subsection{Requirements for the approximated functionals in the strong correlation }
\subsubsection{Requirements: separability of the energies and $S_z$ invariance}
An important requirement for any electronic structure method is the extensivity of the energy, \textit{i. e.} the additivity of the energies in the case of non interacting fragments, which is particularly important to avoid any ambiguity in computing interaction energies.
When two subsystems $A$ and $B$ dissociate in closed shell systems, as in the case of weak interactions for instance, a simple HF wave function leads to extensive energies.
@ -464,8 +467,7 @@ Another important requirement is the independence of the energy with respect to
Such a property is also important in the context of covalent bond breaking where the ground state of the super system $A+B$ is in general of low spin while the ground states of the fragments $A$ and $B$ are in high spin which can have multiple $S_z$ components.
\subsubsection{Condition for the functional $\efuncdenpbe{\argebasis}$ to obtain $S_z$ invariance}
A sufficient condition to achieve $S_z$ invariance is to eliminate all dependency to any quantity related to $S_z$, which is the spin density $s(\b{})$ in the case of the definition $\ecmd(\argecmd)$.
The spin density is involved in the usual PBE correlation functional $\varepsilon_{\text{c,PBE}}(\argepbe)$ which contributes to the definition of $\ecmd(\argecmd)$ (see equation \eqref{eq:def_ecmdpbe}). A possible way to eliminate the $S_z$ dependency would be then to simply set $\xi(\br{})=0$, but this would lower the accuracy of the usual PBE correlation functional $\varepsilon_{\text{c,PBE}}(\argepbe)$. Therefore, we use the proposal by Scuseria and co-workers\cite{GarBulHenScu-PCCP-15} which introduce an effective spin density depending on the on-top pair density and the total density
A sufficient condition to achieve $S_z$ invariance is to eliminate all dependency to $S_z$, which for the $\ecmd(\argecmd)$, is the spin density $s(\br{})$ involved in the correlation energy density $\varepsilon_{\text{c,PBE}}(\argepbe)$ (see equation \eqref{eq:def_ecmdpbe}). A possible way to eliminate the $S_z$ dependency would be to simply set $\xi(\br{})=0$, but this would lower the accuracy of the usual PBE correlation functional $\varepsilon_{\text{c,PBE}}(\argepbe)$. Therefore, we use the effective spin density depending on the on-top pair density and the total density introduced by Scuseria and co-workers\cite{GarBulHenScu-PCCP-15} which reads
\begin{equation}
\label{eq:def_effspin}
\Xi(n,\ntwo) =
@ -474,26 +476,39 @@ The spin density is involved in the usual PBE correlation functional $\varepsilo
0 & \text{otherwise.}
\end{cases}
\end{equation}
The definition of equation \eqref{eq:def_effspin} is exact when $n$ and $\ntwo$ are obtained from a single Slater determinant.
Such a definition is inspired by the spin density of a single determinant, which has precisely the form of \eqref{eq:def_effspin}.
With this definition, the $\Xi(n,\ntwo)$ depends only on $S_z$ invariants quantities, which naturally makes it $S_z$ invariant.
We also propose
\subsubsection{Functionals for strong correlation}
The first one, referred as the \PBEspin functional, is a natural extension with effective spin density of the previously introduced PBE\cite{LooPraSceTouGin},
\subsection{Requirement on $\psibasis$ for the extensivity}
In the case of the present basis set correction, as $\efuncdenpbe{\argebasis}$ depends only on local quantities, one sufficient condition for the extensivity is that these quantities must be the same on the system $A$ that in the subsystem $A$ of the super system $A+B$ in the limit of non interacting fragments.
As all these quantities are properties of the wave function $\psibasis$, the extensivity requires that the wave function factorise in the limit of non-interacting fragments, that is $\Psi_{A\ldots B}^{\basis} = \Psi_A^{\basis} \Psi_B^{\basis}$.
In the case where the two subsystems $A$ and $B$ dissociate in closed shell systems, a simple HF wave function ensures this property, but when one or several covalent bonds are broken, the use of a properly chosen CASSCF wave function is sufficient to recover this property, as will be numerically illustrated in section \ref{sec:separability}.
The condition for the active space involved in the CASSCF wave function is that it has to lead to extensive energies in the limit of dissociated fragments.
\subsection{Approximations for the strong correlation regime}
\subsubsection{Definition of the different types of functionals}
As the present work proposes to investigate the performance of different flavours of functionals by varying different physical ingredients, we propose here a general nomenclature in order to make things easier.
The functionals $\efuncdenpbe{\argebasis}$ depends on: i) the wave function $\psibasis$ used to determine the $\murpsi$ and the various density related quantities, ii) the flavour of on-top pair density used, iii) the type of spin density used.
Therefore, we propose to use the following notations: PBE-"on-top"-"spin-density"-$\psibasis$.
For instance, within this convention the PBE-UEG-$\xi$-HF is the functional which was introduced in Ref. \onlinecite{LooPraSceTouGin-JCPL-19} and which reads
\begin{equation}
\label{eq:def_pbeueg}
\begin{aligned}
\efuncdenpbe{\argepbeuegspin} = &\int d\br{} \,\denr \\ & \ecmd(\argepbeuegspin)
\efuncdenpbe{\argepbeuegxihf} = &\int d\br{} \,\denr \\ & \ecmd(\argepbeuegxihf)
\end{aligned}
\end{equation}
where $\ntwo_{\text{UEG}}$ is the on-top pair density of the UEG defined as
where $\ntwo_{\text{UEG}}$ is an approximation of the on-top pair density of the uniform electron gas (UEG) defined as
\begin{equation}
\label{eq:def_n2ueg}
\ntwo_{\text{UEG}}(n,\xi) = n^2(1-\xi)g_0(n).
\ntwo_{\text{UEG}}(n,\xi) = n^2(1-\xi)g_0(n)
\end{equation}
Therefore, such a functional used the on-top pair density of the UEG computed with the total density and effective spin density which depends on the on-top pair density.
using the pair-distribution function $g_0(n)$ of equation (46) of Ref. \onlinecite{GorSav-PRA-06}.
Therefore, such a functional uses a HF wave function to define; i)the $\murpsi$, ii) the total density, reduced density gradients, regular spin density $\xi$ and uses the UEG-like on-top pair density.
\subsection{Requirement on $\psibasis$ for the extensivity of $\murpsi$}
\begin{table*}
\caption{Total energies (in Hartree) for HF and $E$ in aug-cc-pvdz for the He atom, F$_2$ (with F-F=1.411 angstroms) and the super non interacting system He--F$_2$. }
\begin{tabular}{lcc}
@ -510,8 +525,6 @@ Error to additivity & 1.2 $\times 10^{-12}$ & 7 $\times 10^{-15}$
\end{table*}
In the case of the present basis set correction, as $\murpsi$ is a local quantity, one of the necessary but not sufficient requirements for extensivity is that $\murpsi$ must be the same on the system $A$ that in the subsystem $A$ of the super system $A+B$ in the limit of non interacting fragments.
\subsubsection{Introduction of the effective spin-density}

270
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@ -0,0 +1,270 @@
Date: 13/10/2019 22:24:33
===============
Quantum Package
===============
Git Commit: trying to fix the casscf
Git Date : Wed Sep 18 13:55:16 2019 +0200
Git SHA1 : c8cd1611626d12424fa9776ad42e17a0ce2ce228
EZFIO Dir : n.ezfio
Task server running : tcp://127.0.1.1:41279
.. >>>>> [ IO READ: no_core_density ] <<<<< ..
.. >>>>> [ RES MEM : 0.004505 GB ] [ VIRT MEM : 0.041687 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.000199 s ] [ CPU TIME: 0.001915 s ] <<<<< ..
.. >>>>> [ IO READ: on_top_from_cas ] <<<<< ..
.. >>>>> [ RES MEM : 0.004765 GB ] [ VIRT MEM : 0.041687 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.000384 s ] [ CPU TIME: 0.002039 s ] <<<<< ..
.. >>>>> [ IO READ: mu_of_r_potential ] <<<<< ..
.. >>>>> [ RES MEM : 0.004841 GB ] [ VIRT MEM : 0.041679 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.000553 s ] [ CPU TIME: 0.002147 s ] <<<<< ..
.. >>>>> [ IO READ: read_wf ] <<<<< ..
.. >>>>> [ RES MEM : 0.004841 GB ] [ VIRT MEM : 0.041679 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.000719 s ] [ CPU TIME: 0.002252 s ] <<<<< ..
.. >>>>> [ IO READ: mu_of_r_functional ] <<<<< ..
.. >>>>> [ RES MEM : 0.004841 GB ] [ VIRT MEM : 0.041679 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.000907 s ] [ CPU TIME: 0.002379 s ] <<<<< ..
LDA, PBE and PBE-on-top / mu(r) PSI coallescence with frozen core interaction
****************************************
Functional used = basis_set_on_top_PBE
****************************************
mu_of_r_potential = psi_cas_ful
MR DFT energy with pure correlation part for the DFT
.. >>>>> [ IO READ: grid_type_sgn ] <<<<< ..
.. >>>>> [ RES MEM : 0.004841 GB ] [ VIRT MEM : 0.041679 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.001095 s ] [ CPU TIME: 0.002507 s ] <<<<< ..
.. >>>>> [ IO READ: nucl_num ] <<<<< ..
.. >>>>> [ RES MEM : 0.004841 GB ] [ VIRT MEM : 0.041679 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.001283 s ] [ CPU TIME: 0.002633 s ] <<<<< ..
.. >>>>> [ IO READ: nucl_charge ] <<<<< ..
.. >>>>> [ RES MEM : 0.004841 GB ] [ VIRT MEM : 0.065128 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.004089 s ] [ CPU TIME: 0.008215 s ] <<<<< ..
.. >>>>> [ IO READ: nucl_label ] <<<<< ..
.. >>>>> [ RES MEM : 0.004841 GB ] [ VIRT MEM : 0.065128 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.004391 s ] [ CPU TIME: 0.008912 s ] <<<<< ..
.. >>>>> [ RES MEM : 0.004841 GB ] [ VIRT MEM : 0.190128 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.004694 s ] [ CPU TIME: 0.009648 s ] <<<<< ..
Nuclear Coordinates (Angstroms)
===============================
================ ============ ============ ============ ============
Atom Charge X Y Z
================ ============ ============ ============ ============
N 7.000000 0.000000 0.000000 0.000000
================ ============ ============ ============ ============
.. >>>>> [ IO READ: thresh_grid ] <<<<< ..
.. >>>>> [ RES MEM : 0.006584 GB ] [ VIRT MEM : 0.190979 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.007206 s ] [ CPU TIME: 0.020426 s ] <<<<< ..
n_points_final_grid = 22046
n max point = 22348
.. >>>>> [ IO READ: n_states ] <<<<< ..
.. >>>>> [ RES MEM : 0.006584 GB ] [ VIRT MEM : 0.190979 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.007513 s ] [ CPU TIME: 0.020911 s ] <<<<< ..
providing the mu_of_r ...
* mo_num 23
.. >>>>> [ IO READ: mo_class ] <<<<< ..
.. >>>>> [ RES MEM : 0.007782 GB ] [ VIRT MEM : 0.254852 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.009572 s ] [ CPU TIME: 0.028539 s ] <<<<< ..
* Number of active MOs 4
* Number of core MOs 1
* Number of inactive MOs 0
* mo_label Canonical
* Number of determinants 1
* Dimension of the psi arrays 100000
providing core_inact_act_two_bod_alpha_beta_mo ...
* N_int 1
.. >>>>> [ IO READ: ao_num ] <<<<< ..
.. >>>>> [ RES MEM : 0.008533 GB ] [ VIRT MEM : 0.255600 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.011494 s ] [ CPU TIME: 0.033719 s ] <<<<< ..
Read mo_coef
.. >>>>> [ IO READ: elec_beta_num ] <<<<< ..
.. >>>>> [ RES MEM : 0.008533 GB ] [ VIRT MEM : 0.255600 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.013069 s ] [ CPU TIME: 0.037688 s ] <<<<< ..
.. >>>>> [ IO READ: elec_alpha_num ] <<<<< ..
.. >>>>> [ RES MEM : 0.008533 GB ] [ VIRT MEM : 0.255600 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.013702 s ] [ CPU TIME: 0.038646 s ] <<<<< ..
* Number of unique alpha determinants 1
* Number of unique beta determinants 1
core_inact_act_two_bod_alpha_beta_mo provided in 7.2065409985953011E-003
Core MOs:
1
USING THE VALENCE ONLY TWO BODY DENSITY
providing core_inact_act_two_bod_alpha_beta_mo_physicist ...
core_inact_act_two_bod_alpha_beta_mo_physicist provided in 1.6240010154433548E-006
providing the core_inact_act_on_top_of_r
.. >>>>> [ IO READ: ao_prim_num ] <<<<< ..
.. >>>>> [ RES MEM : 0.010159 GB ] [ VIRT MEM : 0.275307 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.018106 s ] [ CPU TIME: 0.057134 s ] <<<<< ..
.. >>>>> [ IO READ: ao_expo ] <<<<< ..
.. >>>>> [ RES MEM : 0.010159 GB ] [ VIRT MEM : 0.275307 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.018569 s ] [ CPU TIME: 0.057815 s ] <<<<< ..
.. >>>>> [ IO READ: ao_coef ] <<<<< ..
.. >>>>> [ RES MEM : 0.010159 GB ] [ VIRT MEM : 0.275307 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.019022 s ] [ CPU TIME: 0.059222 s ] <<<<< ..
.. >>>>> [ IO READ: ao_power ] <<<<< ..
.. >>>>> [ RES MEM : 0.010159 GB ] [ VIRT MEM : 0.275307 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.019376 s ] [ CPU TIME: 0.060144 s ] <<<<< ..
.. >>>>> [ IO READ: ao_nucl ] <<<<< ..
.. >>>>> [ RES MEM : 0.010159 GB ] [ VIRT MEM : 0.275307 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.019883 s ] [ CPU TIME: 0.061265 s ] <<<<< ..
mo_num,n_points_final_grid 23 22046
* Number of virtual MOs 18
* Number of deleted MOs 0
Active MOs:
2 3 4 5
0 1 2 3
Virtual MOs:
6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Core, Inactive and Active MOs:
1 2 3 4 5
provided the core_inact_act_on_top_of_r
Time to provide : 4.1155614999297541E-002
MO map initialized: 38226
.. >>>>> [ IO READ: io_mo_two_e_integrals ] <<<<< ..
.. >>>>> [ RES MEM : 0.057476 GB ] [ VIRT MEM : 0.313763 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.191075 s ] [ CPU TIME: 0.400365 s ] <<<<< ..
.. >>>>> [ IO READ: io_ao_two_e_integrals ] <<<<< ..
.. >>>>> [ RES MEM : 0.057476 GB ] [ VIRT MEM : 0.313763 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.191326 s ] [ CPU TIME: 0.400910 s ] <<<<< ..
AO map initialized : 52975
.. >>>>> [ IO READ: ao_integrals_threshold ] <<<<< ..
.. >>>>> [ RES MEM : 0.057476 GB ] [ VIRT MEM : 0.313763 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.191596 s ] [ CPU TIME: 0.401487 s ] <<<<< ..
Providing the AO integrals
Sorting the map
AO integrals provided:
Size of AO map : 8.5845947265625000E-002 MB
Number of AO integrals : 7966
cpu time : 0.13432800000000000 s
wall time : 8.3950192001793766E-002 s ( x 1.6000916352535539 )
AO -> MO integrals transformation
---------------------------------
.. >>>>> [ IO READ: mo_integrals_threshold ] <<<<< ..
.. >>>>> [ RES MEM : 0.060123 GB ] [ VIRT MEM : 0.524979 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.276098 s ] [ CPU TIME: 0.536419 s ] <<<<< ..
Buffers : 0.459625244 MB / core
Molecular integrals provided:
Size of MO map 0.36037063598632812 MB
Number of MO integrals: 18472
cpu time : 0.18962299999999999 s
wall time : 5.7800987000518944E-002 s ( x 3.2806187202010499 )
Providing core_inact_act_V_kl_contracted_transposed .....
Time to provide core_inact_act_V_kl_contracted_transposed = 0.10545316999923671
Providing core_inact_act_rho2_kl_contracted_transposed .....
Time to provide core_inact_act_rho2_kl_contracted_transposed = 1.6968988002190599E-002
Providing core_inact_act_f_psi_ab .....
Time to provide core_inact_act_f_psi_ab = 3.2415269997727592E-003
providing the cas_full_mu_of_r_psi_coal_vector ...
Time to provide cas_full_mu_of_r_psi_coal_vector = 5.8083600015379488E-004
Time to provide mu_of_r = 0.47625986300045042
Providing Energy_c_md_n_and_PBE_mu_of_r ...
.. >>>>> [ IO READ: density_for_dft ] <<<<< ..
.. >>>>> [ RES MEM : 0.083530 GB ] [ VIRT MEM : 0.658264 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.484660 s ] [ CPU TIME: 1.212247 s ] <<<<< ..
.. >>>>> [ IO READ: normalize_dm ] <<<<< ..
.. >>>>> [ RES MEM : 0.083530 GB ] [ VIRT MEM : 0.658264 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.484885 s ] [ CPU TIME: 1.212841 s ] <<<<< ..
Time for the Energy_c_md_n_and_PBE_mu_of_r : 0.11964879900187952
Providing Energy_c_md_LDA_mu_of_r ...
Time for Energy_c_md_LDA_mu_of_r : 2.9454646002704976E-002
Providing Energy_c_md_LDA_mu_of_r ...
Time for Energy_c_md_n_and_LDA_mu_of_r : 2.9101256001013098E-002
Providing Energy_c_md_n_and_on_top_PBE_mu_of_r ...
Time for the Energy_c_md_n_and_on_top_PBE_mu_of_r : 6.3777867999306181E-002
.. >>>>> [ IO READ: ontop_approx ] <<<<< ..
.. >>>>> [ RES MEM : 0.084538 GB ] [ VIRT MEM : 0.659248 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.773004 s ] [ CPU TIME: 1.541545 s ] <<<<< ..
Inactive MOs:
providing the core_inact_act_on_top_of_r_new
providint all_states_act_two_rdm_alpha_beta_mo
ispin = 3
USING THE VALENCE ONLY TWO BODY DENSITY
provided the core_inact_act_on_top_of_r_new
Time to provide : 3.5796539996226784E-003
Providing Energy_c_md_mu_of_r_PBE_on_top ...
Time for the Energy_c_md_on_top_PBE_mu_of_r: 0.27439229000083287
Providing Energy_c_md_PBE_mu_of_r ...
Time for the Energy_c_md_PBE_mu_of_r: 6.7258312999911141E-002
Corrections using Multi determinant mu
Functionals with UEG ontop pair density at large mu
ECMD LDA regular spin dens = -0.0265407099448326
ECMD LDA effective spin dens = -0.0265407099448326
ECMD PBE regular spin dens = -0.0230740500348705
ECMD PBE effective spin dens = -0.0230740500348705
Functionals with extrapolated exact ontop based on current wave function
ECMD PBE/ontop regular spin dens = -0.0247392466968251
ECMD PBE/ontop effective spin dens = -0.0247392466968251
mu_average for basis set = 0.9116337460
Wall time: 0:00:02

1
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@ -0,0 +1 @@
N

273
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@ -0,0 +1,273 @@
Date: 13/10/2019 22:24:49
===============
Quantum Package
===============
Git Commit: trying to fix the casscf
Git Date : Wed Sep 18 13:55:16 2019 +0200
Git SHA1 : c8cd1611626d12424fa9776ad42e17a0ce2ce228
EZFIO Dir : n2.ezfio
Task server running : tcp://127.0.1.1:41279
.. >>>>> [ IO READ: no_core_density ] <<<<< ..
.. >>>>> [ RES MEM : 0.004436 GB ] [ VIRT MEM : 0.041679 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.000193 s ] [ CPU TIME: 0.001977 s ] <<<<< ..
.. >>>>> [ IO READ: on_top_from_cas ] <<<<< ..
.. >>>>> [ RES MEM : 0.004436 GB ] [ VIRT MEM : 0.041679 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.000368 s ] [ CPU TIME: 0.002092 s ] <<<<< ..
.. >>>>> [ IO READ: mu_of_r_potential ] <<<<< ..
.. >>>>> [ RES MEM : 0.004436 GB ] [ VIRT MEM : 0.041679 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.000533 s ] [ CPU TIME: 0.002196 s ] <<<<< ..
.. >>>>> [ IO READ: read_wf ] <<<<< ..
.. >>>>> [ RES MEM : 0.004436 GB ] [ VIRT MEM : 0.041679 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.000696 s ] [ CPU TIME: 0.002298 s ] <<<<< ..
.. >>>>> [ IO READ: mu_of_r_functional ] <<<<< ..
.. >>>>> [ RES MEM : 0.004436 GB ] [ VIRT MEM : 0.041679 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.000880 s ] [ CPU TIME: 0.002422 s ] <<<<< ..
LDA, PBE and PBE-on-top / mu(r) PSI coallescence with frozen core interaction
****************************************
Functional used = basis_set_on_top_PBE
****************************************
mu_of_r_potential = psi_cas_ful
MR DFT energy with pure correlation part for the DFT
.. >>>>> [ IO READ: grid_type_sgn ] <<<<< ..
.. >>>>> [ RES MEM : 0.004436 GB ] [ VIRT MEM : 0.041679 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.001067 s ] [ CPU TIME: 0.002548 s ] <<<<< ..
.. >>>>> [ IO READ: nucl_num ] <<<<< ..
.. >>>>> [ RES MEM : 0.004436 GB ] [ VIRT MEM : 0.041679 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.001253 s ] [ CPU TIME: 0.002673 s ] <<<<< ..
.. >>>>> [ IO READ: nucl_charge ] <<<<< ..
.. >>>>> [ RES MEM : 0.005276 GB ] [ VIRT MEM : 0.127628 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.006438 s ] [ CPU TIME: 0.014247 s ] <<<<< ..
.. >>>>> [ IO READ: nucl_label ] <<<<< ..
.. >>>>> [ RES MEM : 0.005276 GB ] [ VIRT MEM : 0.127628 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.006731 s ] [ CPU TIME: 0.015202 s ] <<<<< ..
.. >>>>> [ RES MEM : 0.005276 GB ] [ VIRT MEM : 0.252628 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.007020 s ] [ CPU TIME: 0.015901 s ] <<<<< ..
Nuclear Coordinates (Angstroms)
===============================
================ ============ ============ ============ ============
Atom Charge X Y Z
================ ============ ============ ============ ============
N 7.000000 0.000000 0.000000 -1000.000072
N 7.000000 0.000000 0.000000 1000.000072
================ ============ ============ ============ ============
.. >>>>> [ IO READ: thresh_grid ] <<<<< ..
.. >>>>> [ RES MEM : 0.007256 GB ] [ VIRT MEM : 0.254322 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.018087 s ] [ CPU TIME: 0.054428 s ] <<<<< ..
n_points_final_grid = 44092
n max point = 44998
.. >>>>> [ IO READ: n_states ] <<<<< ..
.. >>>>> [ RES MEM : 0.007256 GB ] [ VIRT MEM : 0.254322 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.018397 s ] [ CPU TIME: 0.057538 s ] <<<<< ..
providing the mu_of_r ...
* mo_num 46
.. >>>>> [ IO READ: mo_class ] <<<<< ..
.. >>>>> [ RES MEM : 0.009270 GB ] [ VIRT MEM : 0.256981 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.019785 s ] [ CPU TIME: 0.061670 s ] <<<<< ..
* Number of active MOs 8
* Number of core MOs 2
* Number of inactive MOs 0
* mo_label Canonical
* Number of determinants 400
* Dimension of the psi arrays 100000
Read psi_coef 400 1
providing core_inact_act_two_bod_alpha_beta_mo ...
* N_int 1
.. >>>>> [ IO READ: ao_num ] <<<<< ..
.. >>>>> [ RES MEM : 0.010387 GB ] [ VIRT MEM : 0.257874 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.020953 s ] [ CPU TIME: 0.064729 s ] <<<<< ..
Read mo_coef
.. >>>>> [ IO READ: elec_beta_num ] <<<<< ..
.. >>>>> [ RES MEM : 0.010387 GB ] [ VIRT MEM : 0.257874 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.022999 s ] [ CPU TIME: 0.074050 s ] <<<<< ..
.. >>>>> [ IO READ: elec_alpha_num ] <<<<< ..
.. >>>>> [ RES MEM : 0.010387 GB ] [ VIRT MEM : 0.257874 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.023209 s ] [ CPU TIME: 0.074364 s ] <<<<< ..
Read psi_det
* Number of unique alpha determinants 20
* Number of unique beta determinants 20
core_inact_act_two_bod_alpha_beta_mo provided in 1.0138563997315941E-002
Core MOs:
1 2
USING THE VALENCE ONLY TWO BODY DENSITY
providing core_inact_act_two_bod_alpha_beta_mo_physicist ...
core_inact_act_two_bod_alpha_beta_mo_physicist provided in 3.8632999348919839E-005
providing the core_inact_act_on_top_of_r
.. >>>>> [ IO READ: ao_prim_num ] <<<<< ..
.. >>>>> [ RES MEM : 0.012398 GB ] [ VIRT MEM : 0.315315 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.032296 s ] [ CPU TIME: 0.104271 s ] <<<<< ..
.. >>>>> [ IO READ: ao_expo ] <<<<< ..
.. >>>>> [ RES MEM : 0.012398 GB ] [ VIRT MEM : 0.315315 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.033598 s ] [ CPU TIME: 0.110293 s ] <<<<< ..
.. >>>>> [ IO READ: ao_coef ] <<<<< ..
.. >>>>> [ RES MEM : 0.012398 GB ] [ VIRT MEM : 0.315315 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.034755 s ] [ CPU TIME: 0.114448 s ] <<<<< ..
.. >>>>> [ IO READ: ao_power ] <<<<< ..
.. >>>>> [ RES MEM : 0.012398 GB ] [ VIRT MEM : 0.315315 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.035587 s ] [ CPU TIME: 0.117060 s ] <<<<< ..
.. >>>>> [ IO READ: ao_nucl ] <<<<< ..
.. >>>>> [ RES MEM : 0.012398 GB ] [ VIRT MEM : 0.315315 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.036767 s ] [ CPU TIME: 0.120070 s ] <<<<< ..
mo_num,n_points_final_grid 46 44092
* Number of virtual MOs 36
* Number of deleted MOs 0
Active MOs:
3 4 5 6 7 8 9 10
0 0 1 2 3 4 5 6
Virtual MOs:
11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46
Core, Inactive and Active MOs:
1 2 3 4 5 6 7 8 9 10
provided the core_inact_act_on_top_of_r
Time to provide : 0.70096241300052498
MO map initialized: 584821
.. >>>>> [ IO READ: io_mo_two_e_integrals ] <<<<< ..
.. >>>>> [ RES MEM : 0.200268 GB ] [ VIRT MEM : 0.485504 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 1.265357 s ] [ CPU TIME: 3.473769 s ] <<<<< ..
.. >>>>> [ IO READ: io_ao_two_e_integrals ] <<<<< ..
.. >>>>> [ RES MEM : 0.200268 GB ] [ VIRT MEM : 0.485504 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 1.265604 s ] [ CPU TIME: 3.474068 s ] <<<<< ..
AO map initialized : 813450
.. >>>>> [ IO READ: ao_integrals_threshold ] <<<<< ..
.. >>>>> [ RES MEM : 0.200573 GB ] [ VIRT MEM : 0.485504 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 1.265888 s ] [ CPU TIME: 3.474393 s ] <<<<< ..
Providing the AO integrals
Sorting the map
AO integrals provided:
Size of AO map : 0.44347000122070312 MB
Number of AO integrals : 38257
cpu time : 1.0639589999999997 s
wall time : 0.41615004599952954 s ( x 2.5566715905185853 )
AO -> MO integrals transformation
---------------------------------
.. >>>>> [ IO READ: mo_integrals_threshold ] <<<<< ..
.. >>>>> [ RES MEM : 0.203552 GB ] [ VIRT MEM : 0.697113 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 1.682451 s ] [ CPU TIME: 4.539011 s ] <<<<< ..
Buffers : 3.63958740 MB / core
Molecular integrals provided:
Size of MO map 9.6878700256347656 MB
Number of MO integrals: 473042
cpu time : 2.2190269999999996 s
wall time : 0.80212339799982146 s ( x 2.7664409310754126 )
Providing core_inact_act_V_kl_contracted_transposed .....
Time to provide core_inact_act_V_kl_contracted_transposed = 1.7762000410002656
Providing core_inact_act_rho2_kl_contracted_transposed .....
Time to provide core_inact_act_rho2_kl_contracted_transposed = 0.22741315399980522
Providing core_inact_act_f_psi_ab .....
Time to provide core_inact_act_f_psi_ab = 4.9875350014190190E-003
providing the cas_full_mu_of_r_psi_coal_vector ...
Time to provide cas_full_mu_of_r_psi_coal_vector = 1.9037699894397520E-004
Time to provide mu_of_r = 4.6907960499993351
Providing Energy_c_md_n_and_PBE_mu_of_r ...
.. >>>>> [ IO READ: density_for_dft ] <<<<< ..
.. >>>>> [ RES MEM : 0.352638 GB ] [ VIRT MEM : 0.860363 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 4.710455 s ] [ CPU TIME: 14.149410 s ] <<<<< ..
.. >>>>> [ IO READ: normalize_dm ] <<<<< ..
.. >>>>> [ RES MEM : 0.352638 GB ] [ VIRT MEM : 0.860363 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 4.710757 s ] [ CPU TIME: 14.150161 s ] <<<<< ..
Time for the Energy_c_md_n_and_PBE_mu_of_r : 0.37609190000148374
Providing Energy_c_md_LDA_mu_of_r ...
Time for Energy_c_md_LDA_mu_of_r : 5.3449625997018302E-002
Providing Energy_c_md_LDA_mu_of_r ...
Time for Energy_c_md_n_and_LDA_mu_of_r : 5.2238627999031451E-002
Providing Energy_c_md_n_and_on_top_PBE_mu_of_r ...
Time for the Energy_c_md_n_and_on_top_PBE_mu_of_r : 0.12120974099889281
.. >>>>> [ IO READ: ontop_approx ] <<<<< ..
.. >>>>> [ RES MEM : 0.361450 GB ] [ VIRT MEM : 0.864967 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 5.529283 s ] [ CPU TIME: 15.013616 s ] <<<<< ..
Inactive MOs:
providing the core_inact_act_on_top_of_r_new
providint all_states_act_two_rdm_alpha_beta_mo
ispin = 3
USING THE VALENCE ONLY TWO BODY DENSITY
provided the core_inact_act_on_top_of_r_new
Time to provide : 9.8473186000774149E-002
Providing Energy_c_md_mu_of_r_PBE_on_top ...
Time for the Energy_c_md_on_top_PBE_mu_of_r: 0.95842244199957349
Providing Energy_c_md_PBE_mu_of_r ...
Time for the Energy_c_md_PBE_mu_of_r: 0.12124202900304226
Corrections using Multi determinant mu
Functionals with UEG ontop pair density at large mu
ECMD LDA regular spin dens = -0.0678669003007728
ECMD LDA effective spin dens = -0.0530814198896590
ECMD PBE regular spin dens = -0.0691133629633015
ECMD PBE effective spin dens = -0.0461481000697329
Functionals with extrapolated exact ontop based on current wave function
ECMD PBE/ontop regular spin dens = -0.0509457188492165
ECMD PBE/ontop effective spin dens = -0.0494784933936403
mu_average for basis set = 0.9116337460
Wall time: 0:00:08

787
calcs/extensivity/n2.ezfio.casci.out Normal file
View File

@ -0,0 +1,787 @@
Date: 13/10/2019 22:18:11
===============
Quantum Package
===============
Git Commit: trying to fix the casscf
Git Date : Wed Sep 18 13:55:16 2019 +0200
Git SHA1 : c8cd1611626d12424fa9776ad42e17a0ce2ce228
EZFIO Dir : n2.ezfio
Task server running : tcp://127.0.1.1:41279
* mo_num 46
.. >>>>> [ IO READ: mo_class ] <<<<< ..
.. >>>>> [ RES MEM : 0.004566 GB ] [ VIRT MEM : 0.251705 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.000330 s ] [ CPU TIME: 0.012040 s ] <<<<< ..
.. >>>>> [ IO READ: io_mo_two_e_integrals ] <<<<< ..
.. >>>>> [ RES MEM : 0.004566 GB ] [ VIRT MEM : 0.251705 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.000661 s ] [ CPU TIME: 0.012783 s ] <<<<< ..
* N_int 1
MO map initialized: 584821
.. >>>>> [ IO READ: io_ao_two_e_integrals ] <<<<< ..
.. >>>>> [ RES MEM : 0.004566 GB ] [ VIRT MEM : 0.251705 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.001302 s ] [ CPU TIME: 0.014906 s ] <<<<< ..
.. >>>>> [ IO READ: ao_num ] <<<<< ..
.. >>>>> [ RES MEM : 0.004566 GB ] [ VIRT MEM : 0.251705 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.001641 s ] [ CPU TIME: 0.015667 s ] <<<<< ..
AO map initialized : 813450
.. >>>>> [ IO READ: ao_power ] <<<<< ..
.. >>>>> [ RES MEM : 0.004566 GB ] [ VIRT MEM : 0.251705 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.002248 s ] [ CPU TIME: 0.017195 s ] <<<<< ..
.. >>>>> [ IO READ: ao_prim_num ] <<<<< ..
.. >>>>> [ RES MEM : 0.004566 GB ] [ VIRT MEM : 0.251705 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.003513 s ] [ CPU TIME: 0.021442 s ] <<<<< ..
.. >>>>> [ IO READ: ao_expo ] <<<<< ..
.. >>>>> [ RES MEM : 0.004566 GB ] [ VIRT MEM : 0.251705 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.004434 s ] [ CPU TIME: 0.023313 s ] <<<<< ..
.. >>>>> [ IO READ: ao_coef ] <<<<< ..
.. >>>>> [ RES MEM : 0.004566 GB ] [ VIRT MEM : 0.251705 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.006587 s ] [ CPU TIME: 0.028598 s ] <<<<< ..
.. >>>>> [ IO READ: ao_nucl ] <<<<< ..
.. >>>>> [ RES MEM : 0.005543 GB ] [ VIRT MEM : 0.251705 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.008006 s ] [ CPU TIME: 0.030702 s ] <<<<< ..
.. >>>>> [ IO READ: ao_integrals_threshold ] <<<<< ..
.. >>>>> [ RES MEM : 0.005543 GB ] [ VIRT MEM : 0.251705 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.008525 s ] [ CPU TIME: 0.031353 s ] <<<<< ..
Providing the AO integrals
.. >>>>> [ IO READ: nucl_num ] <<<<< ..
.. >>>>> [ RES MEM : 0.005543 GB ] [ VIRT MEM : 0.400280 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.018219 s ] [ CPU TIME: 0.065993 s ] <<<<< ..
.. >>>>> [ IO READ: nucl_label ] <<<<< ..
.. >>>>> [ RES MEM : 0.005543 GB ] [ VIRT MEM : 0.400280 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.019145 s ] [ CPU TIME: 0.066277 s ] <<<<< ..
.. >>>>> [ IO READ: nucl_charge ] <<<<< ..
.. >>>>> [ RES MEM : 0.005543 GB ] [ VIRT MEM : 0.400280 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.019401 s ] [ CPU TIME: 0.066472 s ] <<<<< ..
.. >>>>> [ RES MEM : 0.005543 GB ] [ VIRT MEM : 0.400280 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.019638 s ] [ CPU TIME: 0.066648 s ] <<<<< ..
Nuclear Coordinates (Angstroms)
===============================
================ ============ ============ ============ ============
Atom Charge X Y Z
================ ============ ============ ============ ============
N 7.000000 0.000000 0.000000 -1000.000072
N 7.000000 0.000000 0.000000 1000.000072
================ ============ ============ ============ ============
Sorting the map
AO integrals provided:
Size of AO map : 0.44347000122070312 MB
Number of AO integrals : 38257
cpu time : 1.0255760000000000 s
wall time : 0.39576729399777832 s ( x 2.5913611749983496 )
AO -> MO integrals transformation
---------------------------------
Read mo_coef
.. >>>>> [ IO READ: mo_integrals_threshold ] <<<<< ..
.. >>>>> [ RES MEM : 0.007996 GB ] [ VIRT MEM : 0.463428 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.406879 s ] [ CPU TIME: 1.068523 s ] <<<<< ..
Buffers : 2.91943359 MB / core
Molecular integrals provided:
Size of MO map 2.8884887695312500E-002 MB
Number of MO integrals: 1467
cpu time : 0.41741099999999998 s
wall time : 0.29118732999995700 s ( x 1.4334792657361213 )
.. >>>>> [ IO READ: n_states ] <<<<< ..
.. >>>>> [ RES MEM : 0.075394 GB ] [ VIRT MEM : 0.588432 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.696199 s ] [ CPU TIME: 1.488003 s ] <<<<< ..
* mo_label Canonical
.. >>>>> [ IO READ: read_wf ] <<<<< ..
.. >>>>> [ RES MEM : 0.075394 GB ] [ VIRT MEM : 0.588432 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.696403 s ] [ CPU TIME: 1.488470 s ] <<<<< ..
* Number of determinants 118
* Dimension of the psi arrays 100000
Read psi_coef 118 1
.. >>>>> [ IO READ: elec_beta_num ] <<<<< ..
.. >>>>> [ RES MEM : 0.075893 GB ] [ VIRT MEM : 0.589176 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.697194 s ] [ CPU TIME: 1.494597 s ] <<<<< ..
.. >>>>> [ IO READ: elec_alpha_num ] <<<<< ..
.. >>>>> [ RES MEM : 0.075893 GB ] [ VIRT MEM : 0.589176 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.697367 s ] [ CPU TIME: 1.494990 s ] <<<<< ..
Read psi_det
.. >>>>> [ IO READ: do_pt2 ] <<<<< ..
.. >>>>> [ RES MEM : 0.077404 GB ] [ VIRT MEM : 0.590668 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.699137 s ] [ CPU TIME: 1.500094 s ] <<<<< ..
.. >>>>> [ RES MEM : 0.077656 GB ] [ VIRT MEM : 0.590851 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.700237 s ] [ CPU TIME: 1.506425 s ] <<<<< ..
.. >>>>> [ IO READ: io_nuclear_repulsion ] <<<<< ..
.. >>>>> [ RES MEM : 0.077656 GB ] [ VIRT MEM : 0.590851 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.700416 s ] [ CPU TIME: 1.506818 s ] <<<<< ..
.. >>>>> [ RES MEM : 0.077656 GB ] [ VIRT MEM : 0.590851 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.700578 s ] [ CPU TIME: 1.507172 s ] <<<<< ..
* Nuclear repulsion energy 0.1296484166754000E-01
.. >>>>> [ IO READ: distributed_davidson ] <<<<< ..
.. >>>>> [ RES MEM : 0.077656 GB ] [ VIRT MEM : 0.590851 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.700802 s ] [ CPU TIME: 1.508225 s ] <<<<< ..
.. >>>>> [ IO READ: n_det_max_full ] <<<<< ..
.. >>>>> [ RES MEM : 0.077656 GB ] [ VIRT MEM : 0.590851 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.700992 s ] [ CPU TIME: 1.508612 s ] <<<<< ..
.. >>>>> [ IO READ: io_mo_integrals_e_n ] <<<<< ..
.. >>>>> [ RES MEM : 0.109283 GB ] [ VIRT MEM : 2.467323 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.776437 s ] [ CPU TIME: 1.793946 s ] <<<<< ..
.. >>>>> [ IO READ: io_ao_integrals_e_n ] <<<<< ..
.. >>>>> [ RES MEM : 0.109283 GB ] [ VIRT MEM : 2.467323 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.776657 s ] [ CPU TIME: 1.794447 s ] <<<<< ..
.. >>>>> [ IO READ: io_mo_integrals_kinetic ] <<<<< ..
.. >>>>> [ RES MEM : 0.109283 GB ] [ VIRT MEM : 2.467323 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.777556 s ] [ CPU TIME: 1.800996 s ] <<<<< ..
.. >>>>> [ IO READ: io_ao_integrals_kinetic ] <<<<< ..
.. >>>>> [ RES MEM : 0.109283 GB ] [ VIRT MEM : 2.467323 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.777743 s ] [ CPU TIME: 1.801265 s ] <<<<< ..
.. >>>>> [ IO READ: io_mo_one_e_integrals ] <<<<< ..
.. >>>>> [ RES MEM : 0.109283 GB ] [ VIRT MEM : 2.467323 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.780765 s ] [ CPU TIME: 1.814206 s ] <<<<< ..
Providing the one-electron integrals
.. >>>>> [ IO READ: do_pseudo ] <<<<< ..
.. >>>>> [ RES MEM : 0.109283 GB ] [ VIRT MEM : 2.467323 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.780978 s ] [ CPU TIME: 1.814650 s ] <<<<< ..
.. >>>>> [ IO READ: selection_factor ] <<<<< ..
.. >>>>> [ RES MEM : 0.109283 GB ] [ VIRT MEM : 2.467323 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.782052 s ] [ CPU TIME: 1.817685 s ] <<<<< ..
.. >>>>> [ IO READ: pt2_max ] <<<<< ..
.. >>>>> [ RES MEM : 0.110638 GB ] [ VIRT MEM : 2.469215 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.782616 s ] [ CPU TIME: 1.820578 s ] <<<<< ..
.. >>>>> [ IO READ: correlation_energy_ratio_max ] <<<<< ..
.. >>>>> [ RES MEM : 0.110638 GB ] [ VIRT MEM : 2.469215 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.782817 s ] [ CPU TIME: 1.820999 s ] <<<<< ..
.. >>>>> [ IO READ: s2_eig ] <<<<< ..
.. >>>>> [ RES MEM : 0.110638 GB ] [ VIRT MEM : 2.469215 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.783246 s ] [ CPU TIME: 1.821527 s ] <<<<< ..
.. >>>>> [ IO READ: variance_max ] <<<<< ..
.. >>>>> [ RES MEM : 0.110638 GB ] [ VIRT MEM : 2.469215 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.783517 s ] [ CPU TIME: 1.821880 s ] <<<<< ..
.. >>>>> [ IO READ: pt2_relative_error ] <<<<< ..
.. >>>>> [ RES MEM : 0.110638 GB ] [ VIRT MEM : 2.469215 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.783775 s ] [ CPU TIME: 1.822222 s ] <<<<< ..
.. >>>>> [ RES MEM : 0.110638 GB ] [ VIRT MEM : 2.469215 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.784003 s ] [ CPU TIME: 1.822533 s ] <<<<< ..
Read n_states_diag
* N_generators_bitmask 1
.. >>>>> [ IO READ: weight_one_e_dm ] <<<<< ..
.. >>>>> [ RES MEM : 0.110638 GB ] [ VIRT MEM : 2.469215 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.784352 s ] [ CPU TIME: 1.823015 s ] <<<<< ..
.. >>>>> [ IO READ: n_det_max ] <<<<< ..
.. >>>>> [ RES MEM : 0.114918 GB ] [ VIRT MEM : 2.473316 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.789245 s ] [ CPU TIME: 1.842909 s ] <<<<< ..
.. >>>>> [ IO READ: threshold_generators ] <<<<< ..
.. >>>>> [ RES MEM : 0.114918 GB ] [ VIRT MEM : 2.473316 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.789515 s ] [ CPU TIME: 1.843273 s ] <<<<< ..
* Target maximum memory (GB) 2000
* Number of occupation patterns 46
.. >>>>> [ RES MEM : 0.114918 GB ] [ VIRT MEM : 2.474808 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.793300 s ] [ CPU TIME: 1.856314 s ] <<<<< ..
.. >>>>> [ IO READ: threshold_davidson ] <<<<< ..
.. >>>>> [ RES MEM : 0.114918 GB ] [ VIRT MEM : 2.474808 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.794625 s ] [ CPU TIME: 1.859001 s ] <<<<< ..
Diagonalization of H using Lapack
.. >>>>> [ IO READ: only_expected_s2 ] <<<<< ..
.. >>>>> [ RES MEM : 0.114918 GB ] [ VIRT MEM : 2.474808 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.795211 s ] [ CPU TIME: 1.859623 s ] <<<<< ..
.. >>>>> [ RES MEM : 0.115280 GB ] [ VIRT MEM : 2.475330 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.821105 s ] [ CPU TIME: 1.947158 s ] <<<<< ..
* Energy of state 1 -108.5308307944447
* S^2 of state 1 0.9661852136846990E-17
* Saved determinants 118
--------------------------------------------------------------------------------
* Number of unique beta determinants 19
* Number of unique alpha determinants 19
.. >>>>> [ IO READ: weight_selection ] <<<<< ..
.. >>>>> [ RES MEM : 0.116127 GB ] [ VIRT MEM : 2.477955 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.823563 s ] [ CPU TIME: 1.953964 s ] <<<<< ..
Using pt2-matching weight in selection
.. >>>>> [ IO READ: pseudo_sym ] <<<<< ..
.. >>>>> [ RES MEM : 0.116127 GB ] [ VIRT MEM : 2.477959 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.823738 s ] [ CPU TIME: 1.954365 s ] <<<<< ..
.. >>>>> [ IO READ: h0_type ] <<<<< ..
.. >>>>> [ RES MEM : 0.116127 GB ] [ VIRT MEM : 2.477959 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.823991 s ] [ CPU TIME: 1.954970 s ] <<<<< ..
.. >>>>> [ RES MEM : 0.116127 GB ] [ VIRT MEM : 2.477959 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.824201 s ] [ CPU TIME: 1.955252 s ] <<<<< ..
* Number of generators 112
.. >>>>> [ RES MEM : 0.116127 GB ] [ VIRT MEM : 2.477959 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.824406 s ] [ CPU TIME: 1.955522 s ] <<<<< ..
* Number of selectors 112
* Number of comb teeth 1
* Number of core MOs 4
* pt2_n_tasks_max 1
* PT2 Energy denominator -108.5308307944447
Using pt2-matching weight in selection
.. >>>>> [ RES MEM : 0.118645 GB ] [ VIRT MEM : 2.483547 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.828493 s ] [ CPU TIME: 1.969680 s ] <<<<< ..
* Number of generators 112
.. >>>>> [ RES MEM : 0.118645 GB ] [ VIRT MEM : 2.483547 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.828731 s ] [ CPU TIME: 1.976181 s ] <<<<< ..
* Number of selectors 112
* Number of comb teeth 1
* pt2_n_tasks_max 1
* Number of tasks 112
* Number of fragmented tasks 0
* Number of threads for PT2 4
* Memory (Gb) 0.1157009601593018E-03
========== ================= =========== =============== =============== =================
Samples Energy Stat. Err Variance Norm Seconds
========== ================= =========== =============== =============== =================
105 -108.6064355336 0.00 0.0050234074 5.9837485349 0.0226
========== ================= =========== =============== =============== =================
Using pt2-matching weight in selection
.. >>>>> [ RES MEM : 0.119499 GB ] [ VIRT MEM : 2.484295 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.874318 s ] [ CPU TIME: 2.090736 s ] <<<<< ..
* Number of generators 112
.. >>>>> [ RES MEM : 0.119499 GB ] [ VIRT MEM : 2.484295 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.874969 s ] [ CPU TIME: 2.091514 s ] <<<<< ..
* Number of selectors 112
* Number of comb teeth 1
* pt2_n_tasks_max 1
# PT2 weight 1.00000000
# var weight 1.00000000
Using pt2-matching weight in selection
* Correlation ratio 1.000000000000000
Summary at N_det = 118
-----------------------------------
# ============ =============================
State 1
# ============ =============================
# E -108.53083079
# PT2 -0.07560474 0.00000000
# rPT2 -0.01082581 0.00000000
#
# E+PT2 -108.60643553 0.00000000
# E+rPT2 -108.54165661 0.00000000
# ============ =============================
N_det = 118
N_states = 1
N_sop = 46
* State 1
< S^2 > = 9.6618521368469904E-018
E = -108.53083079444467
Variance = 5.0234073593933221E-003
PT norm = 2.4461701770151949
PT2 = -7.5604739131960072E-002
rPT2 = -1.0825810630772065E-002
E+PT2 = -108.60643553357663 +/- 0.0000000000000000
E+rPT2 = -108.54165660507545 +/- 0.0000000000000000
-----
.. >>>>> [ IO READ: io_mo_integrals_pseudo ] <<<<< ..
.. >>>>> [ RES MEM : 0.119499 GB ] [ VIRT MEM : 2.484295 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.881109 s ] [ CPU TIME: 2.113780 s ] <<<<< ..
Energy components
=================
Vnn : Nucleus-Nucleus potential energy
Ven : Electron-Nucleus potential energy
Vee : Electron-Electron potential energy
Vecp : Potential energy of the pseudo-potentials
T : Electronic kinetic energy
State 1
---------
Vnn = 1.2964841667540000E-002
Ven = -256.56312312502530
Vee = 39.292362035255408
Vecp = 0.0000000000000000
T = 108.72696545365768
.. >>>>> [ IO READ: energy_iterations ] <<<<< ..
.. >>>>> [ RES MEM : 0.119499 GB ] [ VIRT MEM : 2.484295 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.882128 s ] [ CPU TIME: 2.116795 s ] <<<<< ..
.. >>>>> [ IO READ: pt2_iterations ] <<<<< ..
.. >>>>> [ RES MEM : 0.119499 GB ] [ VIRT MEM : 2.484295 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.882490 s ] [ CPU TIME: 2.117355 s ] <<<<< ..
.. >>>>> [ IO READ: n_det_iterations ] <<<<< ..
.. >>>>> [ RES MEM : 0.119499 GB ] [ VIRT MEM : 2.484295 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.882833 s ] [ CPU TIME: 2.119319 s ] <<<<< ..
* Saved determinants 238
Diagonalization of H using Lapack
.. >>>>> [ RES MEM : 0.122677 GB ] [ VIRT MEM : 2.486561 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.941655 s ] [ CPU TIME: 2.261400 s ] <<<<< ..
* Energy of state 1 -108.7121464339008
* S^2 of state 1 -0.4329368308534452E-16
* Saved determinants 238
--------------------------------------------------------------------------------
* Number of unique beta determinants 20
* Number of unique alpha determinants 20
Using pt2-matching weight in selection
.. >>>>> [ RES MEM : 0.122677 GB ] [ VIRT MEM : 2.486561 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.944830 s ] [ CPU TIME: 2.275229 s ] <<<<< ..
* Number of generators 238
.. >>>>> [ RES MEM : 0.122677 GB ] [ VIRT MEM : 2.486561 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.945042 s ] [ CPU TIME: 2.275493 s ] <<<<< ..
* Number of selectors 238
* Number of comb teeth 1
* pt2_n_tasks_max 1
* PT2 Energy denominator -108.7121464339008
Using pt2-matching weight in selection
.. >>>>> [ RES MEM : 0.122677 GB ] [ VIRT MEM : 2.486561 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.948178 s ] [ CPU TIME: 2.281238 s ] <<<<< ..
* Number of generators 238
.. >>>>> [ RES MEM : 0.122677 GB ] [ VIRT MEM : 2.486561 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 0.948361 s ] [ CPU TIME: 2.281468 s ] <<<<< ..
* Number of selectors 238
* Number of comb teeth 1
* pt2_n_tasks_max 1
* Number of tasks 238
* Number of fragmented tasks 0
* Number of threads for PT2 4
* Memory (Gb) 0.1673931628465653E-03
========== ================= =========== =============== =============== =================
Samples Energy Stat. Err Variance Norm Seconds
========== ================= =========== =============== =============== =================
232 -108.7694757844 0.00 0.0365959034 0.0937532190 0.0584
========== ================= =========== =============== =============== =================
Using pt2-matching weight in selection
.. >>>>> [ RES MEM : 0.122757 GB ] [ VIRT MEM : 2.486561 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 1.025478 s ] [ CPU TIME: 2.478538 s ] <<<<< ..
* Number of generators 238
.. >>>>> [ RES MEM : 0.122757 GB ] [ VIRT MEM : 2.486561 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 1.025668 s ] [ CPU TIME: 2.478832 s ] <<<<< ..
* Number of selectors 238
* Number of comb teeth 1
* pt2_n_tasks_max 1
# PT2 weight 1.00000000
# var weight 1.00000000
Using pt2-matching weight in selection
* Correlation ratio 1.000000000000000
Summary at N_det = 238
-----------------------------------
# ============ =============================
State 1
# ============ =============================
# E -108.71214643
# PT2 -0.05732935 0.00000000
# rPT2 -0.05241525 0.00000000
#
# E+PT2 -108.76947578 0.00000000
# E+rPT2 -108.76456169 0.00000000
# ============ =============================
N_det = 238
N_states = 1
N_sop = 77
* State 1
< S^2 > = -4.3293683085344516E-017
E = -108.71214643390083
Variance = 3.6595903431384941E-002
PT norm = 0.30619147444113620
PT2 = -5.7329350545754762E-002
rPT2 = -5.2415251949702889E-002
E+PT2 = -108.76947578444658 +/- 0.0000000000000000
E+rPT2 = -108.76456168585052 +/- 0.0000000000000000
-----
Energy components
=================
State 1
---------
Vnn = 1.2964841667540000E-002
Ven = -256.56312312524665
Vee = 39.111046396020740
Vecp = 0.0000000000000000
T = 108.72696545365754
Extrapolated energies
------------------------
State 1
=========== ===================
minimum PT2 Extrapolated energy
=========== ===================
-0.0108 -108.48363399
=========== ===================
* Saved determinants 400
Diagonalization of H using Lapack
.. >>>>> [ RES MEM : 0.126030 GB ] [ VIRT MEM : 2.486824 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 1.260993 s ] [ CPU TIME: 3.048135 s ] <<<<< ..
* Energy of state 1 -108.7797414582286
* S^2 of state 1 0.9071010226647818E-17
* Saved determinants 400
--------------------------------------------------------------------------------
* Number of unique beta determinants 20
* Number of unique alpha determinants 20
Using pt2-matching weight in selection
.. >>>>> [ RES MEM : 0.126030 GB ] [ VIRT MEM : 2.486824 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 1.265556 s ] [ CPU TIME: 3.064943 s ] <<<<< ..
* Number of generators 394
.. >>>>> [ RES MEM : 0.126030 GB ] [ VIRT MEM : 2.486824 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 1.265819 s ] [ CPU TIME: 3.065317 s ] <<<<< ..
* Number of selectors 394
* Number of comb teeth 1
* pt2_n_tasks_max 1
* PT2 Energy denominator -108.7797414582286
Using pt2-matching weight in selection
.. >>>>> [ RES MEM : 0.126030 GB ] [ VIRT MEM : 2.486824 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 1.269735 s ] [ CPU TIME: 3.080012 s ] <<<<< ..
* Number of generators 394
.. >>>>> [ RES MEM : 0.126030 GB ] [ VIRT MEM : 2.486824 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 1.269985 s ] [ CPU TIME: 3.080350 s ] <<<<< ..
* Number of selectors 394
* Number of comb teeth 1
* pt2_n_tasks_max 1
* Number of tasks 394
* Number of fragmented tasks 0
* Number of threads for PT2 4
* Memory (Gb) 0.2367957681417465E-03
========== ================= =========== =============== =============== =================
Samples Energy Stat. Err Variance Norm Seconds
========== ================= =========== =============== =============== =================
385 -108.7797414582 0.00 0.0000000000 0.0000000000 0.0927
========== ================= =========== =============== =============== =================
Using pt2-matching weight in selection
.. >>>>> [ RES MEM : 0.127384 GB ] [ VIRT MEM : 2.488316 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 1.385304 s ] [ CPU TIME: 3.367108 s ] <<<<< ..
* Number of generators 394
.. >>>>> [ RES MEM : 0.127384 GB ] [ VIRT MEM : 2.488316 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 1.385462 s ] [ CPU TIME: 3.367500 s ] <<<<< ..
* Number of selectors 394
* Number of comb teeth 1
* pt2_n_tasks_max 1
# PT2 weight 1.50000000
# var weight 1.50000000
Using pt2-matching weight in selection
* Correlation ratio 1.000000000000000
Summary at N_det = 400
-----------------------------------
# ============ =============================
State 1
# ============ =============================
# E -108.77974146
# PT2 0.00000000 0.00000000
# rPT2 0.00000000 0.00000000
#
# E+PT2 -108.77974146 0.00000000
# E+rPT2 -108.77974146 0.00000000
# ============ =============================
N_det = 400
N_states = 1
N_sop = 141
* State 1
< S^2 > = 9.0710102266478180E-018
E = -108.77974145822864
Variance = 0.0000000000000000
PT norm = 0.0000000000000000
PT2 = 0.0000000000000000
rPT2 = 0.0000000000000000
E+PT2 = -108.77974145822864 +/- 0.0000000000000000
E+rPT2 = -108.77974145822864 +/- 0.0000000000000000
-----
Energy components
=================
State 1
---------
Vnn = 1.2964841667540000E-002
Ven = -256.56312312522454
Vee = 39.043451371670429
Vecp = 0.0000000000000000
T = 108.72696545365794
Extrapolated energies
------------------------
State 1
=========== ===================
minimum PT2 Extrapolated energy
=========== ===================
-0.0524 -108.77974146
-0.0108 -108.66826016
=========== ===================
* Saved determinants 400
Diagonalization of H using Lapack
.. >>>>> [ RES MEM : 0.126148 GB ] [ VIRT MEM : 2.486824 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 1.613008 s ] [ CPU TIME: 3.947564 s ] <<<<< ..
* Energy of state 1 -108.7797414582289
* S^2 of state 1 0.6807512035418938E-16
* Saved determinants 400
* Saved determinants 400
* Number of unique beta determinants 20
* Number of unique alpha determinants 20
Using pt2-matching weight in selection
.. >>>>> [ RES MEM : 0.126148 GB ] [ VIRT MEM : 2.486824 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 1.621452 s ] [ CPU TIME: 3.979345 s ] <<<<< ..
* Number of generators 394
.. >>>>> [ RES MEM : 0.126148 GB ] [ VIRT MEM : 2.486824 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 1.621675 s ] [ CPU TIME: 3.979628 s ] <<<<< ..
* Number of selectors 394
* Number of comb teeth 1
* pt2_n_tasks_max 1
* PT2 Energy denominator -108.7797414582289
Using pt2-matching weight in selection
.. >>>>> [ RES MEM : 0.126148 GB ] [ VIRT MEM : 2.486824 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 1.626670 s ] [ CPU TIME: 3.997720 s ] <<<<< ..
* Number of generators 394
.. >>>>> [ RES MEM : 0.126148 GB ] [ VIRT MEM : 2.486824 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 1.626931 s ] [ CPU TIME: 3.998050 s ] <<<<< ..
* Number of selectors 394
* Number of comb teeth 1
* pt2_n_tasks_max 1
* Number of tasks 394
* Number of fragmented tasks 0
* Number of threads for PT2 4
* Memory (Gb) 0.2189590781927109E-03
========== ================= =========== =============== =============== =================
Samples Energy Stat. Err Variance Norm Seconds
========== ================= =========== =============== =============== =================
385 -108.7797414582 0.00 0.0000000000 0.0000000000 0.1010
========== ================= =========== =============== =============== =================
Using pt2-matching weight in selection
.. >>>>> [ RES MEM : 0.127441 GB ] [ VIRT MEM : 2.488316 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 1.750181 s ] [ CPU TIME: 4.300568 s ] <<<<< ..
* Number of generators 394
.. >>>>> [ RES MEM : 0.127441 GB ] [ VIRT MEM : 2.488316 GB ] <<<<< ..
.. >>>>> [ WALL TIME: 1.750393 s ] [ CPU TIME: 4.301085 s ] <<<<< ..
* Number of selectors 394
* Number of comb teeth 1
* pt2_n_tasks_max 1
# PT2 weight 2.25000000
# var weight 2.25000000
Using pt2-matching weight in selection
Summary at N_det = 400
-----------------------------------
# ============ =============================
State 1
# ============ =============================
# E -108.77974146
# PT2 0.00000000 0.00000000
# rPT2 0.00000000 0.00000000
#
# E+PT2 -108.77974146 0.00000000
# E+rPT2 -108.77974146 0.00000000
# ============ =============================
N_det = 400
N_states = 1
N_sop = 141
* State 1
< S^2 > = 6.8075120354189381E-017
E = -108.77974145822886
Variance = 0.0000000000000000
PT norm = 0.0000000000000000
PT2 = 0.0000000000000000
rPT2 = 0.0000000000000000
E+PT2 = -108.77974145822886 +/- 0.0000000000000000
E+rPT2 = -108.77974145822886 +/- 0.0000000000000000
-----
Energy components
=================
State 1
---------
Vnn = 1.2964841667540000E-002
Ven = -256.56312312522522
Vee = 39.043451371670628
Vecp = 0.0000000000000000
T = 108.72696545365820
Extrapolated energies
------------------------
State 1
=========== ===================
minimum PT2 Extrapolated energy
=========== ===================
0.0000 -108.77974146
-0.0524 -108.77974146
-0.0108 -108.71107465
=========== ===================
Wall time: 0:00:03

4
calcs/extensivity/n2.xyz Normal file
View File

@ -0,0 +1,4 @@
2
N 0. 0. -1000.
N 0. 0. 1000.

7
calcs/extensivity/scf_energies
View File

@ -1,4 +1,9 @@
## F2 + He
# HF correction PBE
-2.85570466771188 -0.0112667838948910
-198.698792752661 -0.1596345827582842
-201.554497420371 -0.1709013666531826
1.9 10^-12 7 10^-15
1.9 10^-12 7 10^-15
# N2
-54.3898707291144
-108.779741458229