added separaility tests
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\citation{GinPraFerAssSavTou-JCP-18}
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\citation{GinPraFerAssSavTou-JCP-18}
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\citation{GinPraFerAssSavTou-JCP-18}
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\citation{GinPraFerAssSavTou-JCP-18}
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\citation{GinPraFerAssSavTou-JCP-18}
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\citation{GinPraFerAssSavTou-JCP-18}
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\citation{LooPraSceTouGin-JCPL-19,excited}
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\citation{LooPraSceTouGin-JCPL-19,GinSceTouLoo-JCP-19}
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\citation{kato}
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\citation{kato}
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\citation{GinPraFerAssSavTou-JCP-18}
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\citation{GinPraFerAssSavTou-JCP-18}
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\citation{GinPraFerAssSavTou-JCP-18}
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\citation{GinPraFerAssSavTou-JCP-18}
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@ -81,22 +81,30 @@
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\newlabel{eq:lim_mularge}{{19}{4}{}{equation.2.19}{}}
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\newlabel{eq:lim_mularge}{{19}{4}{}{equation.2.19}{}}
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\newlabel{eq:lim_n2}{{20}{4}{}{equation.2.20}{}}
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\newlabel{eq:lim_n2}{{20}{4}{}{equation.2.20}{}}
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\newlabel{eq:lim_muinf}{{21}{4}{}{equation.2.21}{}}
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\newlabel{eq:lim_muinf}{{21}{4}{}{equation.2.21}{}}
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\@writefile{toc}{\contentsline {subsubsection}{\numberline {2}Properties of approximated functionals}{4}{section*.10}}
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\citation{GarBulHenScu-PCCP-15}
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\citation{GarBulHenScu-PCCP-15}
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\citation{LooPraSceTouGin-JCPL-19}
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\@writefile{toc}{\contentsline {subsubsection}{\numberline {2}Properties of approximated functionals}{5}{section*.10}}
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\citation{GorSav-PRA-06}
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\newlabel{eq:lim_ebasis}{{22}{5}{}{equation.2.22}{}}
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\newlabel{eq:lim_ebasis}{{22}{5}{}{equation.2.22}{}}
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\@writefile{toc}{\contentsline {subsection}{\numberline {E}Requirements for the approximated functionals in the strong correlation }{5}{section*.11}}
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\@writefile{toc}{\contentsline {subsection}{\numberline {E}Requirements for the approximated functionals in the strong correlation regime}{5}{section*.11}}
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\@writefile{toc}{\contentsline {subsubsection}{\numberline {1}Requirements: separability of the energies and $S_z$ invariance}{5}{section*.12}}
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\@writefile{toc}{\contentsline {subsubsection}{\numberline {1}Requirements: separability of the energies and $S_z$ invariance}{5}{section*.12}}
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\@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}}
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\@writefile{toc}{\contentsline {subsubsection}{\numberline {2}Condition for the functional $\mathaccentV {bar}916{E}_{\text {X}}^\mathcal {B}[{n},\xi ,s,n^{(2)},\mu _{\Psi ^{\mathcal {B}}}]$ to obtain $S_z$ invariance}{5}{section*.13}}
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\newlabel{eq:def_effspin}{{23}{5}{}{equation.2.23}{}}
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\newlabel{eq:def_effspin}{{23}{5}{}{equation.2.23}{}}
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\@writefile{toc}{\contentsline {subsection}{\numberline {F}Requirement on $\Psi ^{\mathcal {B}}$ for the extensivity}{5}{section*.14}}
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\@writefile{toc}{\contentsline {subsubsection}{\numberline {3}Conditions on $\Psi ^{\mathcal {B}}$ for the extensivity}{5}{section*.14}}
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\@writefile{toc}{\contentsline {subsection}{\numberline {G}Approximations for the strong correlation regime}{5}{section*.15}}
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\@writefile{toc}{\contentsline {subsection}{\numberline {F}Different types of approximations for the functional}{5}{section*.15}}
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\@writefile{toc}{\contentsline {subsubsection}{\numberline {1}Definition of the different types of functionals}{5}{section*.16}}
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\@writefile{toc}{\contentsline {subsubsection}{\numberline {1}Definition of the protocol to design functionals}{5}{section*.16}}
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\newlabel{eq:def_pbeueg}{{24}{5}{}{equation.2.24}{}}
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\newlabel{sec:def_func}{{II\tmspace +\thinmuskip {.1667em}F\tmspace +\thinmuskip {.1667em}1}{5}{}{section*.16}{}}
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\newlabel{eq:def_n2ueg}{{25}{5}{}{equation.2.25}{}}
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\citation{FerGinTou-JCP-18,excited}
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\citation{GorSav-PRA-06}
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\citation{GorSav-PRA-06}
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\citation{FerGinTou-JCP-18,GinSceTouLoo-JCP-19}
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\citation{GorSav-PRA-06}
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\citation{LooPraSceTouGin-JCPL-19}
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\newlabel{eq:def_n2ueg}{{25}{6}{}{equation.2.25}{}}
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\@writefile{toc}{\contentsline {subsubsection}{\numberline {2}Definition of a hierarchy of functionals}{6}{section*.17}}
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\newlabel{eq:def_pbeueg}{{27}{6}{}{equation.2.27}{}}
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\newlabel{eq:def_pbeueg}{{28}{6}{}{equation.2.28}{}}
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\newlabel{eq:def_pbeueg}{{29}{6}{}{equation.2.29}{}}
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\newlabel{eq:def_pbeueg}{{30}{6}{}{equation.2.30}{}}
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\@writefile{toc}{\contentsline {section}{\numberline {III}Results}{6}{section*.18}}
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\@writefile{toc}{\contentsline {subsection}{\numberline {A}Numerical tests of extensivity}{6}{section*.19}}
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\@writefile{toc}{\contentsline {subsubsection}{\numberline {1}Dissociation to closed shell ground states}{6}{section*.20}}
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\bibdata{srDFT_SCNotes,srDFT_SC}
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\bibdata{srDFT_SCNotes,srDFT_SC}
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\bibcite{Thom-PRL-10}{{1}{2010}{{Thom}}{{}}}
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\bibcite{Thom-PRL-10}{{1}{2010}{{Thom}}{{}}}
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\bibcite{ScoTho-JCP-17}{{2}{2017}{{Scott\ and\ Thom}}{{}}}
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\bibcite{ScoTho-JCP-17}{{2}{2017}{{Scott\ and\ Thom}}{{}}}
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@ -115,15 +123,6 @@
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\bibcite{EvaDauMal-ChemPhys-83}{{15}{1983}{{Evangelisti, Daudey,\ and\ Malrieu}}{{}}}
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\bibcite{EvaDauMal-ChemPhys-83}{{15}{1983}{{Evangelisti, Daudey,\ and\ Malrieu}}{{}}}
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\bibcite{Cim-JCP-1985}{{16}{1985}{{Cimiraglia}}{{}}}
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\bibcite{Cim-JCP-1985}{{16}{1985}{{Cimiraglia}}{{}}}
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\bibcite{Cim-JCC-1987}{{17}{1987}{{Cimiraglia\ and\ Persico}}{{}}}
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\bibcite{Cim-JCC-1987}{{17}{1987}{{Cimiraglia\ and\ Persico}}{{}}}
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\newlabel{eq:def_pbeueg}{{26}{6}{}{equation.2.26}{}}
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\newlabel{eq:def_pbeueg}{{28}{6}{}{equation.2.28}{}}
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\@writefile{toc}{\contentsline {section}{\numberline {III}Results}{6}{section*.17}}
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\@writefile{toc}{\contentsline {subsection}{\numberline {A}Numerical tests of extensivity}{6}{section*.18}}
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\newlabel{sec:results}{{III\tmspace +\thinmuskip {.1667em}A}{6}{}{table.1}{}}
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\@writefile{toc}{\contentsline {section}{\numberline {IV}Conclusion}{6}{section*.19}}
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\newlabel{sec:conclusion}{{IV}{6}{}{section*.19}{}}
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\@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}}
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\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}{}}
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\bibcite{IllRubRic-JCP-88}{{18}{1988}{{Illas, Rubio,\ and\ Ricart}}{{}}}
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\bibcite{IllRubRic-JCP-88}{{18}{1988}{{Illas, Rubio,\ and\ Ricart}}{{}}}
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\bibcite{PovRubIll-TCA-92}{{19}{1992}{{Povill, Rubio,\ and\ Illas}}{{}}}
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\bibcite{PovRubIll-TCA-92}{{19}{1992}{{Povill, Rubio,\ and\ Illas}}{{}}}
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\bibcite{BunCarRam-JCP-06}{{20}{2006}{{Bunge\ and\ Carb{\'o}-Dorca}}{{}}}
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\bibcite{BunCarRam-JCP-06}{{20}{2006}{{Bunge\ and\ Carb{\'o}-Dorca}}{{}}}
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@ -134,12 +133,6 @@
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\bibcite{CafGinScemRam-JCTC-14}{{25}{2014}{{Caffarel\ \emph {et~al.}}}{{Caffarel, Giner, Scemama,\ and\ Ram{\'\i }rez-Sol{\'\i }s}}}
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\bibcite{CafGinScemRam-JCTC-14}{{25}{2014}{{Caffarel\ \emph {et~al.}}}{{Caffarel, Giner, Scemama,\ and\ Ram{\'\i }rez-Sol{\'\i }s}}}
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\bibcite{GinSceCaf-JCP-15}{{26}{2015}{{Giner, Scemama,\ and\ Caffarel}}{{}}}
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\bibcite{GinSceCaf-JCP-15}{{26}{2015}{{Giner, Scemama,\ and\ Caffarel}}{{}}}
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\bibcite{CafAplGinScem-arxiv-16}{{27}{2016{}}{{Caffarel\ \emph {et~al.}}}{{Caffarel, Applencourt, Giner,\ and\ Scemama}}}
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\bibcite{CafAplGinScem-arxiv-16}{{27}{2016{}}{{Caffarel\ \emph {et~al.}}}{{Caffarel, Applencourt, Giner,\ and\ Scemama}}}
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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$_2$. }}{7}{table.1}}
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\newlabel{conv_He_table}{{I}{7}{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}{}}
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\@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}}
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\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}{}}
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\@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_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}{}}
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\bibcite{CafAplGinSce-JCP-16}{{28}{2016{}}{{Caffarel\ \emph {et~al.}}}{{Caffarel, Applencourt, Giner,\ and\ Scemama}}}
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\bibcite{CafAplGinSce-JCP-16}{{28}{2016{}}{{Caffarel\ \emph {et~al.}}}{{Caffarel, Applencourt, Giner,\ and\ Scemama}}}
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\bibcite{SchEva-JCP-16}{{29}{2016}{{Schriber\ and\ Evangelista}}{{}}}
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\bibcite{SchEva-JCP-16}{{29}{2016}{{Schriber\ and\ Evangelista}}{{}}}
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\bibcite{LiuHofJCTC-16}{{30}{2016}{{Liu\ and\ Hoffmann}}{{}}}
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\bibcite{LiuHofJCTC-16}{{30}{2016}{{Liu\ and\ Hoffmann}}{{}}}
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@ -148,15 +141,23 @@
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\bibcite{SchEva-JCTC-17}{{33}{2017}{{Schriber\ and\ Evangelista}}{{}}}
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\bibcite{SchEva-JCTC-17}{{33}{2017}{{Schriber\ and\ Evangelista}}{{}}}
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\bibcite{PerCle-JCP-17}{{34}{2017}{{Per\ and\ Cleland}}{{}}}
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\bibcite{PerCle-JCP-17}{{34}{2017}{{Per\ and\ Cleland}}{{}}}
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\bibcite{OhtJun-JCP-17}{{35}{2017}{{Ohtsuka\ and\ ya~Hasegawa}}{{}}}
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\bibcite{OhtJun-JCP-17}{{35}{2017}{{Ohtsuka\ and\ ya~Hasegawa}}{{}}}
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\@writefile{toc}{\contentsline {subsubsection}{\numberline {2}Dissociation to open shell ground states}{7}{section*.21}}
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\newlabel{sec:results}{{III\tmspace +\thinmuskip {.1667em}A\tmspace +\thinmuskip {.1667em}2}{7}{}{table.2}{}}
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\@writefile{toc}{\contentsline {section}{\numberline {IV}Conclusion}{7}{section*.22}}
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\newlabel{sec:conclusion}{{IV}{7}{}{section*.22}{}}
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\@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. }}{7}{figure.1}}
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\newlabel{fig:N2_avdz}{{1}{7}{N$_2$, aug-cc-pvdz: Comparison between the near FCI and corrected near FCI energies and the estimated exact one}{figure.1}{}}
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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 Ne atom, F$_2$ (with F-F=1.411 angstroms) and the super non interacting system Ne--F$_2$. }}{8}{table.1}}
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\newlabel{tab:extensiv_closed}{{I}{8}{Total energies (in Hartree) for HF and $E$ in aug-cc-pvdz for the Ne atom, F$_2$ (with F-F=1.411 angstroms) and the super non interacting system Ne--F$_2$}{table.1}{}}
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\@writefile{lot}{\contentsline {table}{\numberline {II}{\ignorespaces Total energies (in Hartree) for N$_2$ in the aug-cc-pvdz basis set. }}{8}{table.2}}
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\newlabel{tab:extensiv_open}{{II}{8}{Total energies (in Hartree) for N$_2$ in the aug-cc-pvdz basis set}{table.2}{}}
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\@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. }}{8}{figure.2}}
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\newlabel{fig:N2_avtz}{{2}{8}{N$_2$, aug-cc-pvtz: Comparison between the near FCI and corrected near FCI energies and the estimated exact one}{figure.2}{}}
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\@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. }}{8}{figure.3}}
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\newlabel{fig:F2_avdz}{{3}{8}{F$_2$, aug-cc-pvdz: Comparison between the near FCI and corrected near FCI energies and the estimated exact one}{figure.3}{}}
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\bibcite{Zim-JCP-17}{{36}{2017}{{Zimmerman}}{{}}}
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\bibcite{Zim-JCP-17}{{36}{2017}{{Zimmerman}}{{}}}
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\bibcite{LiOttHolShaUmr-JCP-2018}{{37}{2018}{{Li\ \emph {et~al.}}}{{Li, Otten, Holmes, Sharma,\ and\ Umrigar}}}
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\bibcite{LiOttHolShaUmr-JCP-2018}{{37}{2018}{{Li\ \emph {et~al.}}}{{Li, Otten, Holmes, Sharma,\ and\ Umrigar}}}
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\bibcite{ChiHolOttUmrShaZim-JPCA-18}{{38}{2018}{{Chien\ \emph {et~al.}}}{{Chien, Holmes, Otten, Umrigar, Sharma,\ and\ Zimmerman}}}
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\bibcite{ChiHolOttUmrShaZim-JPCA-18}{{38}{2018}{{Chien\ \emph {et~al.}}}{{Chien, Holmes, Otten, Umrigar, Sharma,\ and\ Zimmerman}}}
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\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces F$_2$, aug-cc-pvtz: Comparison between the near FCI and corrected near FCI energies and the estimated exact one. }}{8}{figure.4}}
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\newlabel{fig:F2_avtz}{{4}{8}{F$_2$, aug-cc-pvtz: Comparison between the near FCI and corrected near FCI energies and the estimated exact one}{figure.4}{}}
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\@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}}
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\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}{}}
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\@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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\newlabel{fig:H10_vtz}{{6}{8}{H$_{10}$, cc-pvtz: Comparison between the near FCI and corrected near FCI energies and the estimated exact one}{figure.6}{}}
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\bibcite{SceBenJacCafLoo-JCP-18}{{39}{2018{}}{{Scemama\ \emph {et~al.}}}{{Scemama, Benali, Jacquemin, Caffarel,\ and\ Loos}}}
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\bibcite{SceBenJacCafLoo-JCP-18}{{39}{2018{}}{{Scemama\ \emph {et~al.}}}{{Scemama, Benali, Jacquemin, Caffarel,\ and\ Loos}}}
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\bibcite{LooSceBloGarCafJac-JCTC-18}{{40}{2018}{{Loos\ \emph {et~al.}}}{{Loos, Scemama, Blondel, Garniron, Caffarel,\ and\ Jacquemin}}}
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\bibcite{LooSceBloGarCafJac-JCTC-18}{{40}{2018}{{Loos\ \emph {et~al.}}}{{Loos, Scemama, Blondel, Garniron, Caffarel,\ and\ Jacquemin}}}
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\bibcite{GarSceGinCaffLoo-JCP-18}{{41}{2018}{{Garniron\ \emph {et~al.}}}{{Garniron, Scemama, Giner, Caffarel,\ and\ Loos}}}
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\bibcite{GarSceGinCaffLoo-JCP-18}{{41}{2018}{{Garniron\ \emph {et~al.}}}{{Garniron, Scemama, Giner, Caffarel,\ and\ Loos}}}
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@ -164,6 +165,12 @@
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\bibcite{GarGinMalSce-JCP-16}{{43}{2017}{{Garniron\ \emph {et~al.}}}{{Garniron, Giner, Malrieu,\ and\ Scemama}}}
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\bibcite{GarGinMalSce-JCP-16}{{43}{2017}{{Garniron\ \emph {et~al.}}}{{Garniron, Giner, Malrieu,\ and\ Scemama}}}
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\bibcite{LooBogSceCafJac-JCTC-19}{{44}{2019{}}{{Loos\ \emph {et~al.}}}{{Loos, Boggio-Pasqua, Scemama, Caffarel,\ and\ Jacquemin}}}
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\bibcite{LooBogSceCafJac-JCTC-19}{{44}{2019{}}{{Loos\ \emph {et~al.}}}{{Loos, Boggio-Pasqua, Scemama, Caffarel,\ and\ Jacquemin}}}
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\bibcite{Hyl-ZP-29}{{45}{1929}{{Hylleraas}}{{}}}
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\bibcite{Hyl-ZP-29}{{45}{1929}{{Hylleraas}}{{}}}
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\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces F$_2$, aug-cc-pvtz: Comparison between the near FCI and corrected near FCI energies and the estimated exact one. }}{9}{figure.4}}
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\newlabel{fig:F2_avtz}{{4}{9}{F$_2$, aug-cc-pvtz: Comparison between the near FCI and corrected near FCI energies and the estimated exact one}{figure.4}{}}
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\@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. }}{9}{figure.5}}
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\newlabel{fig:H10_vdz}{{5}{9}{H$_{10}$, cc-pvdz: Comparison between the near FCI and corrected near FCI energies and the estimated exact one}{figure.5}{}}
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\@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. }}{9}{figure.6}}
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\newlabel{fig:H10_vtz}{{6}{9}{H$_{10}$, cc-pvtz: Comparison between the near FCI and corrected near FCI energies and the estimated exact one}{figure.6}{}}
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\bibcite{Kut-TCA-85}{{46}{1985}{{Kutzelnigg}}{{}}}
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\bibcite{Kut-TCA-85}{{46}{1985}{{Kutzelnigg}}{{}}}
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\bibcite{KutKlo-JCP-91}{{47}{1991}{{Kutzelnigg\ and\ Klopper}}{{}}}
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\bibcite{KutKlo-JCP-91}{{47}{1991}{{Kutzelnigg\ and\ Klopper}}{{}}}
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\bibcite{NogKut-JCP-94}{{48}{1994}{{Noga\ and\ Kutzelnigg}}{{}}}
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\bibcite{NogKut-JCP-94}{{48}{1994}{{Noga\ and\ Kutzelnigg}}{{}}}
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@ -192,18 +199,19 @@
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\bibcite{FerGinTou-JCP-18}{{71}{2019}{{Fert{\'e}, Giner,\ and\ Toulouse}}{{}}}
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\bibcite{FerGinTou-JCP-18}{{71}{2019}{{Fert{\'e}, Giner,\ and\ Toulouse}}{{}}}
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\bibcite{GinPraFerAssSavTou-JCP-18}{{72}{2018}{{Giner\ \emph {et~al.}}}{{Giner, Pradines, Fert\'e, Assaraf, Savin,\ and\ Toulouse}}}
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\bibcite{GinPraFerAssSavTou-JCP-18}{{72}{2018}{{Giner\ \emph {et~al.}}}{{Giner, Pradines, Fert\'e, Assaraf, Savin,\ and\ Toulouse}}}
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\bibcite{LooPraSceTouGin-JCPL-19}{{73}{2019{}}{{Loos\ \emph {et~al.}}}{{Loos, Pradines, Scemama, Toulouse,\ and\ Giner}}}
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\bibcite{LooPraSceTouGin-JCPL-19}{{73}{2019{}}{{Loos\ \emph {et~al.}}}{{Loos, Pradines, Scemama, Toulouse,\ and\ Giner}}}
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\bibcite{TouGorSav-TCA-05}{{74}{2005}{{Toulouse, Gori-Giorgi,\ and\ Savin}}{{}}}
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\bibcite{GinSceTouLoo-JCP-19}{{74}{2019}{{Giner\ \emph {et~al.}}}{{Giner, Scemama, Toulouse,\ and\ Loos}}}
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\bibcite{PerBurErn-PRL-96}{{75}{1996}{{Perdew, Burke,\ and\ Ernzerhof}}{{}}}
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\bibcite{TouGorSav-TCA-05}{{75}{2005}{{Toulouse, Gori-Giorgi,\ and\ Savin}}{{}}}
|
||||||
\bibcite{GoriSav-PRA-06}{{76}{2006{}}{{Gori-Giorgi\ and\ Savin}}{{}}}
|
\bibcite{PerBurErn-PRL-96}{{76}{1996}{{Perdew, Burke,\ and\ Ernzerhof}}{{}}}
|
||||||
\bibcite{PazMorGorBac-PRB-06}{{77}{2006}{{Paziani\ \emph {et~al.}}}{{Paziani, Moroni, Gori-Giorgi,\ and\ Bachelet}}}
|
\bibcite{GoriSav-PRA-06}{{77}{2006{}}{{Gori-Giorgi\ and\ Savin}}{{}}}
|
||||||
\bibcite{GritMeePer-PRA-18}{{78}{2018}{{Gritsenko, van Meer,\ and\ Pernal}}{{}}}
|
\bibcite{PazMorGorBac-PRB-06}{{78}{2006}{{Paziani\ \emph {et~al.}}}{{Paziani, Moroni, Gori-Giorgi,\ and\ Bachelet}}}
|
||||||
\bibcite{CarTruGag-JPCA-17}{{79}{2017}{{Carlson, Truhlar,\ and\ Gagliardi}}{{}}}
|
\bibcite{GritMeePer-PRA-18}{{79}{2018}{{Gritsenko, van Meer,\ and\ Pernal}}{{}}}
|
||||||
\bibcite{GarBulHenScu-PCCP-15}{{80}{2015}{{Garza\ \emph {et~al.}}}{{Garza, Bulik, Henderson,\ and\ Scuseria}}}
|
\bibcite{CarTruGag-JPCA-17}{{80}{2017}{{Carlson, Truhlar,\ and\ Gagliardi}}{{}}}
|
||||||
\bibcite{GorSav-PRA-06}{{81}{2006{}}{{Gori-Giorgi\ and\ Savin}}{{}}}
|
\bibcite{GarBulHenScu-PCCP-15}{{81}{2015}{{Garza\ \emph {et~al.}}}{{Garza, Bulik, Henderson,\ and\ Scuseria}}}
|
||||||
|
\bibcite{GorSav-PRA-06}{{82}{2006{}}{{Gori-Giorgi\ and\ Savin}}{{}}}
|
||||||
\bibstyle{aipnum4-1}
|
\bibstyle{aipnum4-1}
|
||||||
\citation{REVTEX41Control}
|
\citation{REVTEX41Control}
|
||||||
\citation{aip41Control}
|
\citation{aip41Control}
|
||||||
\@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. }}{9}{figure.7}}
|
\@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. }}{10}{figure.7}}
|
||||||
\newlabel{fig:H10_vqz}{{7}{9}{H$_{10}$, cc-pvqz: Comparison between the near FCI and corrected near FCI energies and the estimated exact one}{figure.7}{}}
|
\newlabel{fig:H10_vqz}{{7}{10}{H$_{10}$, cc-pvqz: Comparison between the near FCI and corrected near FCI energies and the estimated exact one}{figure.7}{}}
|
||||||
\newlabel{LastBibItem}{{81}{9}{}{section*.19}{}}
|
\newlabel{LastBibItem}{{82}{10}{}{section*.22}{}}
|
||||||
\newlabel{LastPage}{{}{9}{}{}{}}
|
\newlabel{LastPage}{{}{10}{}{}{}}
|
||||||
|
@ -6,7 +6,7 @@
|
|||||||
%Control: page (0) single
|
%Control: page (0) single
|
||||||
%Control: year (1) truncated
|
%Control: year (1) truncated
|
||||||
%Control: production of eprint (0) enabled
|
%Control: production of eprint (0) enabled
|
||||||
\begin{thebibliography}{81}%
|
\begin{thebibliography}{82}%
|
||||||
\makeatletter
|
\makeatletter
|
||||||
\providecommand \@ifxundefined [1]{%
|
\providecommand \@ifxundefined [1]{%
|
||||||
\@ifx{#1\undefined}
|
\@ifx{#1\undefined}
|
||||||
@ -789,6 +789,19 @@
|
|||||||
{note} {pMID: 31090432},\ \Eprint
|
{note} {pMID: 31090432},\ \Eprint
|
||||||
{http://arxiv.org/abs/https://doi.org/10.1021/acs.jpclett.9b01176}
|
{http://arxiv.org/abs/https://doi.org/10.1021/acs.jpclett.9b01176}
|
||||||
{https://doi.org/10.1021/acs.jpclett.9b01176} \BibitemShut {NoStop}%
|
{https://doi.org/10.1021/acs.jpclett.9b01176} \BibitemShut {NoStop}%
|
||||||
|
\bibitem [{\citenamefont {Giner}\ \emph {et~al.}(2019)\citenamefont {Giner},
|
||||||
|
\citenamefont {Scemama}, \citenamefont {Toulouse},\ and\ \citenamefont
|
||||||
|
{Loos}}]{GinSceTouLoo-JCP-19}%
|
||||||
|
\BibitemOpen
|
||||||
|
\bibfield {author} {\bibinfo {author} {\bibfnamefont {E.}~\bibnamefont
|
||||||
|
{Giner}}, \bibinfo {author} {\bibfnamefont {A.}~\bibnamefont {Scemama}},
|
||||||
|
\bibinfo {author} {\bibfnamefont {J.}~\bibnamefont {Toulouse}}, \ and\
|
||||||
|
\bibinfo {author} {\bibfnamefont {P.-F.}\ \bibnamefont {Loos}},\ }\href
|
||||||
|
{\doibase 10.1063/1.5122976} {\bibfield {journal} {\bibinfo {journal} {The
|
||||||
|
Journal of Chemical Physics}\ }\textbf {\bibinfo {volume} {151}},\ \bibinfo
|
||||||
|
{pages} {144118} (\bibinfo {year} {2019})},\ \Eprint
|
||||||
|
{http://arxiv.org/abs/https://doi.org/10.1063/1.5122976}
|
||||||
|
{https://doi.org/10.1063/1.5122976} \BibitemShut {NoStop}%
|
||||||
\bibitem [{\citenamefont {Toulouse}, \citenamefont {Gori-Giorgi},\ and\
|
\bibitem [{\citenamefont {Toulouse}, \citenamefont {Gori-Giorgi},\ and\
|
||||||
\citenamefont {Savin}(2005)}]{TouGorSav-TCA-05}%
|
\citenamefont {Savin}(2005)}]{TouGorSav-TCA-05}%
|
||||||
\BibitemOpen
|
\BibitemOpen
|
||||||
|
@ -12657,3 +12657,16 @@ eprint = {https://doi.org/10.1021/acs.jpclett.9b01176}
|
|||||||
doi = {10.1103/PhysRevA.98.062510},
|
doi = {10.1103/PhysRevA.98.062510},
|
||||||
url = {https://link.aps.org/doi/10.1103/PhysRevA.98.062510}
|
url = {https://link.aps.org/doi/10.1103/PhysRevA.98.062510}
|
||||||
}
|
}
|
||||||
|
@article{GinSceTouLoo-JCP-19,
|
||||||
|
author = {Giner,Emmanuel and Scemama,Anthony and Toulouse,Julien and Loos,Pierre-François },
|
||||||
|
title = {Chemically accurate excitation energies with small basis sets},
|
||||||
|
journal = {The Journal of Chemical Physics},
|
||||||
|
volume = {151},
|
||||||
|
number = {14},
|
||||||
|
pages = {144118},
|
||||||
|
year = {2019},
|
||||||
|
doi = {10.1063/1.5122976},
|
||||||
|
URL = {https://doi.org/10.1063/1.5122976},
|
||||||
|
eprint = {https://doi.org/10.1063/1.5122976}
|
||||||
|
}
|
||||||
|
|
||||||
|
@ -12,7 +12,6 @@ Reallocated wiz_functions (elt_size=4) to 6000 items from 3000.
|
|||||||
Database file #1: srDFT_SCNotes.bib
|
Database file #1: srDFT_SCNotes.bib
|
||||||
Database file #2: srDFT_SC.bib
|
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 "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 "kato"
|
||||||
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{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},
|
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},
|
||||||
@ -27,45 +26,45 @@ Control: page (0) single
|
|||||||
Control: year (1) truncated
|
Control: year (1) truncated
|
||||||
Control: production of eprint (0) enabled
|
Control: production of eprint (0) enabled
|
||||||
Warning--missing journal in CafAplGinScem-arxiv-16
|
Warning--missing journal in CafAplGinScem-arxiv-16
|
||||||
You've used 83 entries,
|
You've used 84 entries,
|
||||||
5918 wiz_defined-function locations,
|
5918 wiz_defined-function locations,
|
||||||
2192 strings with 31256 characters,
|
2198 strings with 31484 characters,
|
||||||
and the built_in function-call counts, 85895 in all, are:
|
and the built_in function-call counts, 87081 in all, are:
|
||||||
= -- 5509
|
= -- 5583
|
||||||
> -- 2814
|
> -- 2853
|
||||||
< -- 524
|
< -- 531
|
||||||
+ -- 874
|
+ -- 886
|
||||||
- -- 715
|
- -- 725
|
||||||
* -- 13242
|
* -- 13437
|
||||||
:= -- 8845
|
:= -- 8963
|
||||||
add.period$ -- 82
|
add.period$ -- 83
|
||||||
call.type$ -- 83
|
call.type$ -- 84
|
||||||
change.case$ -- 327
|
change.case$ -- 331
|
||||||
chr.to.int$ -- 79
|
chr.to.int$ -- 80
|
||||||
cite$ -- 84
|
cite$ -- 85
|
||||||
duplicate$ -- 7640
|
duplicate$ -- 7745
|
||||||
empty$ -- 6094
|
empty$ -- 6179
|
||||||
format.name$ -- 1447
|
format.name$ -- 1468
|
||||||
if$ -- 17038
|
if$ -- 17274
|
||||||
int.to.chr$ -- 5
|
int.to.chr$ -- 5
|
||||||
int.to.str$ -- 90
|
int.to.str$ -- 91
|
||||||
missing$ -- 1009
|
missing$ -- 1022
|
||||||
newline$ -- 295
|
newline$ -- 298
|
||||||
num.names$ -- 243
|
num.names$ -- 246
|
||||||
pop$ -- 3272
|
pop$ -- 3312
|
||||||
preamble$ -- 1
|
preamble$ -- 1
|
||||||
purify$ -- 405
|
purify$ -- 410
|
||||||
quote$ -- 0
|
quote$ -- 0
|
||||||
skip$ -- 3031
|
skip$ -- 3072
|
||||||
stack$ -- 0
|
stack$ -- 0
|
||||||
substring$ -- 2250
|
substring$ -- 2282
|
||||||
swap$ -- 7428
|
swap$ -- 7534
|
||||||
text.length$ -- 261
|
text.length$ -- 265
|
||||||
text.prefix$ -- 0
|
text.prefix$ -- 0
|
||||||
top$ -- 10
|
top$ -- 10
|
||||||
type$ -- 1164
|
type$ -- 1179
|
||||||
warning$ -- 2
|
warning$ -- 2
|
||||||
while$ -- 322
|
while$ -- 326
|
||||||
width$ -- 0
|
width$ -- 0
|
||||||
write$ -- 710
|
write$ -- 719
|
||||||
(There were 5 warnings)
|
(There were 4 warnings)
|
||||||
|
@ -8,12 +8,15 @@
|
|||||||
\BOOKMARK [2][-]{section*.8}{Generic form and properties of the approximations for B[n\(r\)] }{section*.4}% 8
|
\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*.9}{Generic form of the approximated functionals}{section*.8}% 9
|
||||||
\BOOKMARK [3][-]{section*.10}{Properties of approximated functionals}{section*.8}% 10
|
\BOOKMARK [3][-]{section*.10}{Properties of approximated functionals}{section*.8}% 10
|
||||||
\BOOKMARK [2][-]{section*.11}{Requirements for the approximated functionals in the strong correlation }{section*.4}% 11
|
\BOOKMARK [2][-]{section*.11}{Requirements for the approximated functionals in the strong correlation regime}{section*.4}% 11
|
||||||
\BOOKMARK [3][-]{section*.12}{Requirements: separability of the energies and Sz invariance}{section*.11}% 12
|
\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*.13}{Condition for the functional XB[n,,s,n\(2\),B] to obtain Sz invariance}{section*.11}% 13
|
||||||
\BOOKMARK [2][-]{section*.14}{Requirement on B for the extensivity}{section*.4}% 14
|
\BOOKMARK [3][-]{section*.14}{Conditions on B for the extensivity}{section*.11}% 14
|
||||||
\BOOKMARK [2][-]{section*.15}{Approximations for the strong correlation regime}{section*.4}% 15
|
\BOOKMARK [2][-]{section*.15}{Different types of approximations for the functional}{section*.4}% 15
|
||||||
\BOOKMARK [3][-]{section*.16}{Definition of the different types of functionals}{section*.15}% 16
|
\BOOKMARK [3][-]{section*.16}{Definition of the protocol to design functionals}{section*.15}% 16
|
||||||
\BOOKMARK [1][-]{section*.17}{Results}{section*.2}% 17
|
\BOOKMARK [3][-]{section*.17}{Definition of a hierarchy of functionals}{section*.15}% 17
|
||||||
\BOOKMARK [2][-]{section*.18}{Numerical tests of extensivity}{section*.17}% 18
|
\BOOKMARK [1][-]{section*.18}{Results}{section*.2}% 18
|
||||||
\BOOKMARK [1][-]{section*.19}{Conclusion}{section*.2}% 19
|
\BOOKMARK [2][-]{section*.19}{Numerical tests of extensivity}{section*.18}% 19
|
||||||
|
\BOOKMARK [3][-]{section*.20}{Dissociation to closed shell ground states}{section*.19}% 20
|
||||||
|
\BOOKMARK [3][-]{section*.21}{Dissociation to open shell ground states}{section*.19}% 21
|
||||||
|
\BOOKMARK [1][-]{section*.22}{Conclusion}{section*.2}% 22
|
||||||
|
@ -66,16 +66,8 @@
|
|||||||
\newcommand{\efuncbasisfci}[0]{\bar{E}^\Bas[\denfci]}
|
\newcommand{\efuncbasisfci}[0]{\bar{E}^\Bas[\denfci]}
|
||||||
\newcommand{\efuncbasis}[0]{\bar{E}^\Bas[\den]}
|
\newcommand{\efuncbasis}[0]{\bar{E}^\Bas[\den]}
|
||||||
\newcommand{\efuncden}[1]{\bar{E}^\Bas[#1]}
|
\newcommand{\efuncden}[1]{\bar{E}^\Bas[#1]}
|
||||||
\newcommand{\efuncdenpbe}[1]{\bar{E}_{\text{PBE}}^\Bas[#1]}
|
\newcommand{\efuncdenpbe}[1]{\bar{E}_{\text{X}}^\Bas[#1]}
|
||||||
\newcommand{\ecompmodel}[0]{\bar{E}^\Bas[\denmodel]}
|
\newcommand{\ecompmodel}[0]{\bar{E}^\Bas[\denmodel]}
|
||||||
\newcommand{\argepbe}[0]{\den,\xi,s}
|
|
||||||
\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{\argepbeontxihf}[0]{\den,\xi,s,\ntwoextrap,\mu_{\text{CAS}}^{\basis}}
|
|
||||||
\newcommand{\argepbeuegXihf}[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]}
|
\newcommand{\ecmubis}[0]{\bar{E}_{\text{c,md}}^{\text{sr}}[\denr;\,\mu]}
|
||||||
\newcommand{\ecmubisldapbe}[0]{\bar{E}_{\text{c,md}\,\text{PBE}}^{\text{sr}}[\denr;\,\mu]}
|
\newcommand{\ecmubisldapbe}[0]{\bar{E}_{\text{c,md}\,\text{PBE}}^{\text{sr}}[\denr;\,\mu]}
|
||||||
\newcommand{\ecmuapprox}[0]{\bar{E}_{\text{c,md-}\mathcal{X}}^{\text{sr}}[\den;\,\mu]}
|
\newcommand{\ecmuapprox}[0]{\bar{E}_{\text{c,md-}\mathcal{X}}^{\text{sr}}[\den;\,\mu]}
|
||||||
@ -92,7 +84,36 @@
|
|||||||
\newcommand{\ecmd}[0]{\varepsilon^{\text{c,md}}_{\text{PBE}}}
|
\newcommand{\ecmd}[0]{\varepsilon^{\text{c,md}}_{\text{PBE}}}
|
||||||
\newcommand{\psibasis}[0]{\Psi^{\basis}}
|
\newcommand{\psibasis}[0]{\Psi^{\basis}}
|
||||||
|
|
||||||
|
%pbeuegxiHF
|
||||||
|
\newcommand{\pbeuegxihf}{\text{PBE-UEG-}\xi\text{-HF}^\Bas}
|
||||||
|
\newcommand{\argpbeuegxihf}[0]{\den,\xi,s,\ntwo_{\text{UEG}},\mu_{\text{HF}}^{\basis}}
|
||||||
|
\newcommand{\argrpbeuegxihf}[0]{\den(\br{}),\xi(\br{}),s(\br{}),\ntwo_{\text{UEG}}(\br{}),\mu_{\text{HF}}^{\basis}(\br{})}
|
||||||
|
%pbeuegxiCAS
|
||||||
|
\newcommand{\pbeuegxicas}{\text{PBE-UEG-}\xi\text{-CAS}^\Bas}
|
||||||
|
\newcommand{\argpbeuegxicas}[0]{\den,\xi,s,\ntwo_{\text{UEG}},\mu_{\text{CAS}}^{\basis}}
|
||||||
|
\newcommand{\argrpbeuegxicas}[0]{\den(\br{}),\xi(\br{}),s(\br{}),\ntwo_{\text{UEG}}(\br{}),\mu_{\text{CAS}}^{\basis}(\br{})}
|
||||||
|
%pbeuegXiCAS
|
||||||
|
\newcommand{\pbeuegXicas}{\text{PBE-UEG-}\Xi\text{-CAS}^\Bas}
|
||||||
|
\newcommand{\argpbeuegXicas}[0]{\den,\Xi,s,\ntwo_{\text{UEG}},\mu_{\text{CAS}}^{\basis}}
|
||||||
|
\newcommand{\argrpbeuegXicas}[0]{\den(\br{}),\Xi(\br{}),s(\br{}),\ntwo_{\text{UEG}}(\br{}),\mu_{\text{CAS}}^{\basis}(\br{})}
|
||||||
|
%pbeontxiCAS
|
||||||
|
\newcommand{\pbeontxicas}{\text{PBE-ONT-}\xi\text{-CAS}^\Bas}
|
||||||
|
\newcommand{\argpbeontxicas}[0]{\den,\xi,s,\ntwoextrapcas,\mu_{\text{CAS}}^{\basis}}
|
||||||
|
\newcommand{\argrpbeontxicas}[0]{\den(\br{}),\xi(\br{}),s(\br{}),\ntwoextrapcas(\br{}),\mu_{\text{CAS}}^{\basis}(\br{})}
|
||||||
|
%pbeontXiCAS
|
||||||
|
\newcommand{\pbeontXicas}{\text{PBE-ONT-}\Xi\text{-CAS}^\Bas}
|
||||||
|
\newcommand{\argpbeontXicas}[0]{\den,\Xi,s,\ntwoextrapcas,\mu_{\text{CAS}}^{\basis}}
|
||||||
|
\newcommand{\argrpbeontXicas}[0]{\den(\br{}),\Xi(\br{}),s(\br{}),\ntwoextrapcas(\br{}),\mu_{\text{CAS}}^{\basis}(\br{})}
|
||||||
|
|
||||||
|
%%%%%% arguments
|
||||||
|
|
||||||
|
\newcommand{\argepbe}[0]{\den,\xi,s}
|
||||||
|
\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{\argepbeontxicas}[0]{\den,\xi,s,\ntwoextrapcas,\mu_{\text{CAS}}^{\basis}}
|
||||||
|
\newcommand{\argepbeuegXihf}[0]{\den,\Xi,s,\ntwo_{\text{UEG}},\mu_{\Psi^{\basis}}}
|
||||||
|
\newcommand{\argrebasis}[0]{\denr,\xi(\br{}),s,\ntwo(\br{}),\mu_{\Psi^{\basis}}(\br{})}
|
||||||
|
|
||||||
|
|
||||||
% numbers
|
% numbers
|
||||||
@ -108,7 +129,9 @@
|
|||||||
\newcommand{\twodm}[4]{\elemm{\Psi}{\psixc{#4}\psixc{#3} \psix{#2}\psix{#1}}{\Psi}}
|
\newcommand{\twodm}[4]{\elemm{\Psi}{\psixc{#4}\psixc{#3} \psix{#2}\psix{#1}}{\Psi}}
|
||||||
\newcommand{\murpsi}[0]{\mu({\bf r};\wf{}{\Bas})}
|
\newcommand{\murpsi}[0]{\mu({\bf r};\wf{}{\Bas})}
|
||||||
\newcommand{\ntwo}[0]{n^{(2)}}
|
\newcommand{\ntwo}[0]{n^{(2)}}
|
||||||
|
\newcommand{\ntwohf}[0]{n^{(2),\text{HF}}}
|
||||||
\newcommand{\ntwoextrap}[0]{\tilde{n}^{(2)}_{\psibasis}}
|
\newcommand{\ntwoextrap}[0]{\tilde{n}^{(2)}_{\psibasis}}
|
||||||
|
\newcommand{\ntwoextrapcas}[0]{\tilde{n}^{(2)\,\basis}_{\text{CAS}}}
|
||||||
\newcommand{\mur}[0]{\mu({\bf r})}
|
\newcommand{\mur}[0]{\mu({\bf r})}
|
||||||
\newcommand{\murr}[1]{\mu({\bf r}_{#1})}
|
\newcommand{\murr}[1]{\mu({\bf r}_{#1})}
|
||||||
\newcommand{\murval}[0]{\mu_{\text{val}}({\bf r})}
|
\newcommand{\murval}[0]{\mu_{\text{val}}({\bf r})}
|
||||||
@ -339,7 +362,7 @@ Assuming that the density $\denFCI$ associated to the ground state FCI wave func
|
|||||||
\label{eq:e0approx}
|
\label{eq:e0approx}
|
||||||
E_0 = \efci + \efuncbasisFCI
|
E_0 = \efci + \efuncbasisFCI
|
||||||
\end{equation}
|
\end{equation}
|
||||||
where $\efci$ is the ground state FCI energy within $\Bas$. As it was originally shown in Ref. \onlinecite{GinPraFerAssSavTou-JCP-18} and further emphasized in Ref. \onlinecite{LooPraSceTouGin-JCPL-19,excited}, the main role of $\efuncbasisFCI$ is to correct for the basis set incompleteness errors, a large part of which originates from the lack of cusp in any wave function developed in an incomplete basis set.
|
where $\efci$ is the ground state FCI energy within $\Bas$. As it was originally shown in Ref. \onlinecite{GinPraFerAssSavTou-JCP-18} and further emphasized in Ref. \onlinecite{LooPraSceTouGin-JCPL-19,GinSceTouLoo-JCP-19}, the main role of $\efuncbasisFCI$ is to correct for the basis set incompleteness errors, a large part of which originates from the lack of cusp in any wave function developed in an incomplete basis set.
|
||||||
The whole purpose of this paper is to determine approximations for $\efuncbasisFCI$ which are suited for treating strong correlation regimes. The two requirement for such conditions are that i) it can be defined for multi-reference wave functions, ii) it must provide size extensive energies, iii) it is invariant of the $S_z$ component of a given spin multiplicity.
|
The whole purpose of this paper is to determine approximations for $\efuncbasisFCI$ which are suited for treating strong correlation regimes. The two requirement for such conditions are that i) it can be defined for multi-reference wave functions, ii) it must provide size extensive energies, iii) it is invariant of the $S_z$ component of a given spin multiplicity.
|
||||||
|
|
||||||
\subsection{Definition of an effective interaction within $\Bas$}
|
\subsection{Definition of an effective interaction within $\Bas$}
|
||||||
@ -406,8 +429,8 @@ which is fundamental to guarantee the good behaviour of the theory at the CBS li
|
|||||||
\subsection{Generic form and properties of the approximations for $\efuncden{\denr}$ }
|
\subsection{Generic form and properties of the approximations for $\efuncden{\denr}$ }
|
||||||
\subsubsection{Generic form of the approximated functionals}
|
\subsubsection{Generic form of the approximated functionals}
|
||||||
As originally proposed and motivated in Ref. \onlinecite{GinPraFerAssSavTou-JCP-18}, we approximate the complementary basis set functional $\efuncden{\denr}$ by using the so-called multi-determinant correlation functional (ECMD) introduced by Toulouse and co-workers\cite{TouGorSav-TCA-05}.
|
As originally proposed and motivated in Ref. \onlinecite{GinPraFerAssSavTou-JCP-18}, we approximate the complementary basis set functional $\efuncden{\denr}$ by using the so-called multi-determinant correlation functional (ECMD) introduced by Toulouse and co-workers\cite{TouGorSav-TCA-05}.
|
||||||
Following the recent work of some of the present authors\cite{LooPraSceTouGin-JCPL-19}, we propose to use a PBE-like functional which uses the total density $\denr$, the spin polarisation $\xi(\br{}) = n_{\alpha}(\br{}) - n_{\beta}(\br{})$, reduced density gradient $s(\br{}) = \nabla \denr/\denr^{4/3}$ and the on-top pair density $\ntwo(\br{})$. In the present work, the quantities $\denr$, $\xi(\br{})$, $s(\br{})$ and $\ntwo(\br{})$ are be computed from the same wave function $\psibasis$ used to define $\murpsi$.
|
Following the recent work of some of the present authors\cite{LooPraSceTouGin-JCPL-19}, we propose to use a PBE-like functional which uses the total density $\denr$, the spin polarisation $\xi(\br{}) = n_{\alpha}(\br{}) - n_{\beta}(\br{})$, reduced density gradient $s(\br{}) = \nabla \denr/\denr^{4/3}$ and the on-top pair density $\ntwo(\br{})$. In the present work, all the density-related quantities are computed with the same wave function $\psibasis$ used to define $\murpsi$.
|
||||||
The generic form for the approximations to $\efuncden{\denr}$ proposed here reads
|
Therefore, a given approximation X of $\efuncden{\denr}$ have the following generic form
|
||||||
\begin{equation}
|
\begin{equation}
|
||||||
\begin{aligned}
|
\begin{aligned}
|
||||||
\label{eq:def_ecmdpbebasis}
|
\label{eq:def_ecmdpbebasis}
|
||||||
@ -424,7 +447,8 @@ with
|
|||||||
\label{eq:def_beta}
|
\label{eq:def_beta}
|
||||||
\beta(\argebasis) = \frac{3}{2\sqrt{\pi}(1 - \sqrt{2})}\frac{\varepsilon_{\text{c,PBE}}(\argepbe)}{\ntwo/\den},
|
\beta(\argebasis) = \frac{3}{2\sqrt{\pi}(1 - \sqrt{2})}\frac{\varepsilon_{\text{c,PBE}}(\argepbe)}{\ntwo/\den},
|
||||||
\end{equation}
|
\end{equation}
|
||||||
and where $\varepsilon_{\text{c,PBE}}(\argepbe)$ is the usual PBE correlation energy density\cite{PerBurErn-PRL-96}.
|
and where $\varepsilon_{\text{c,PBE}}(\argepbe)$ is the usual PBE correlation energy density\cite{PerBurErn-PRL-96}. Before introducing the different flavour of approximated functionals that we will use here (see \ref{sec:def_func}), we would like to give some motivations based on physical requirements for the such a choice of functional form.
|
||||||
|
|
||||||
The actual functional form of $\ecmd(\argecmd)$ have been originally proposed by some of the present authors in the context of RSDFT~\cite{FerGinTou-JCP-18} in order to fulfill the two following limits
|
The actual functional form of $\ecmd(\argecmd)$ have been originally proposed by some of the present authors in the context of RSDFT~\cite{FerGinTou-JCP-18} in order to fulfill the two following limits
|
||||||
\begin{equation}
|
\begin{equation}
|
||||||
\lim_{\mu \rightarrow 0} \ecmd(\argecmd) = \varepsilon_{\text{c,PBE}}(\argepbe),
|
\lim_{\mu \rightarrow 0} \ecmd(\argecmd) = \varepsilon_{\text{c,PBE}}(\argepbe),
|
||||||
@ -441,7 +465,7 @@ Also, $\ecmd(\argecmd) $ vanishes when $\ntwo$ vanishes
|
|||||||
\label{eq:lim_n2}
|
\label{eq:lim_n2}
|
||||||
\lim_{\ntwo \rightarrow 0} \ecmd(\argecmd) = 0
|
\lim_{\ntwo \rightarrow 0} \ecmd(\argecmd) = 0
|
||||||
\end{equation}
|
\end{equation}
|
||||||
which is exact for systems with vanishing spin density, such as the totally dissociated H$_2$ which is the archetype of strongly correlated systems.
|
which is exact for systems with a vanishing on-top pair density, such as the totally dissociated H$_2$ which is the archetype of strongly correlated systems.
|
||||||
Of course, as all RSDFT functionals the function $\ecmd(\argecmd)$ vanishes when $\mu \rightarrow \infty$
|
Of course, as all RSDFT functionals the function $\ecmd(\argecmd)$ vanishes when $\mu \rightarrow \infty$
|
||||||
\begin{equation}
|
\begin{equation}
|
||||||
\label{eq:lim_muinf}
|
\label{eq:lim_muinf}
|
||||||
@ -449,7 +473,7 @@ Of course, as all RSDFT functionals the function $\ecmd(\argecmd)$ vanishes when
|
|||||||
\end{equation}
|
\end{equation}
|
||||||
|
|
||||||
\subsubsection{Properties of approximated functionals}
|
\subsubsection{Properties of approximated functionals}
|
||||||
Within the definition of \eqref{eq:def_mur} and \eqref{eq:def_ecmdpbebasis}, the approximated complementary basis set functionals $\efuncdenpbe{\argecmd}$ satisfies two important properties.
|
Within the definition of \eqref{eq:def_mur} and \eqref{eq:def_ecmdpbebasis}, any approximated complementary basis set functionals $\efuncdenpbe{\argecmd}$ satisfies two important properties.
|
||||||
Because of the properties \eqref{eq:cbs_mu} and \eqref{eq:lim_muinf}, $\efuncdenpbe{\argecmd}$ vanishes when reaching the complete basis set limit, whatever the wave function $\psibasis$ used to define the range separation parameter $\mu_{\Psi^{\basis}}$:
|
Because of the properties \eqref{eq:cbs_mu} and \eqref{eq:lim_muinf}, $\efuncdenpbe{\argecmd}$ vanishes when reaching the complete basis set limit, whatever the wave function $\psibasis$ used to define the range separation parameter $\mu_{\Psi^{\basis}}$:
|
||||||
\begin{equation}
|
\begin{equation}
|
||||||
\label{eq:lim_ebasis}
|
\label{eq:lim_ebasis}
|
||||||
@ -459,7 +483,7 @@ 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.
|
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}).
|
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{Requirements for the approximated functionals in the strong correlation }
|
\subsection{Requirements for the approximated functionals in the strong correlation regime}
|
||||||
\subsubsection{Requirements: separability of the energies and $S_z$ invariance}
|
\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.
|
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.
|
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.
|
||||||
@ -468,88 +492,141 @@ 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.
|
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}
|
\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 $S_z$, 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
|
A sufficient condition to achieve $S_z$ invariance is to eliminate all dependency to $S_z$, which in the case of $\ecmd(\argecmd)$ is the spin polarisation $\xi(\br{})$ 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 polarisation introduced by Scuseria and co-workers\cite{GarBulHenScu-PCCP-15} which depends on the on-top pair density and the total density of a general multi configurational wave function $\psibasis$:
|
||||||
\begin{equation}
|
\begin{equation}
|
||||||
\label{eq:def_effspin}
|
\label{eq:def_effspin}
|
||||||
\Xi(n,\ntwo) =
|
\Xi(n,\ntwo_{\psibasis}) =
|
||||||
\begin{cases}
|
\begin{cases}
|
||||||
\sqrt{ n^2 - 4 \ntwo }. & \text{if $n^2 - 4 \ntwo > 0$,} \\
|
\sqrt{ n^2 - 4 \ntwo_{\psibasis} } & \text{if $n^2 - 4 \ntwo_{\psibasis} > 0$,} \\
|
||||||
0 & \text{otherwise.}
|
0 & \text{otherwise.}
|
||||||
\end{cases}
|
\end{cases}
|
||||||
\end{equation}
|
\end{equation}
|
||||||
Such a definition is inspired by the spin density of a single determinant, which has precisely the form of \eqref{eq:def_effspin}.
|
If the density $n$ and on-top pair density $\ntwo_{\psibasis}$ are obtained from a single HF determinant, the definition \eqref{eq:def_effspin} is equivalent to the usual one
|
||||||
With this definition, the $\Xi(n,\ntwo)$ depends only on $S_z$ invariants quantities, which naturally makes it $S_z$ invariant.
|
\begin{equation}
|
||||||
|
\Xi(n^{\text{HF}},\ntwohf) = n_{\alpha}^{\text{HF}} - n_{\beta}^{\text{HF}},
|
||||||
|
\end{equation}
|
||||||
|
but when $n$ and $\ntwo_{\psibasis}$ are obtained from a general multi configurational wave function $\psibasis$, the definition of the usual spin polarisation and the equation \eqref{eq:def_effspin} do not coincide.
|
||||||
|
As equation \eqref{eq:def_effspin} depends only on $S_z$ invariants quantities, $\Xi$ is therefore $S_z$ invariant.
|
||||||
|
|
||||||
\subsection{Requirement on $\psibasis$ for the extensivity}
|
\subsubsection{Conditions 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.
|
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 are the same on the system $A$ that in the subsystem $A$ of the super system $A\ldots B$ in the limit of non interacting fragments $A$ and $B$.
|
||||||
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 $\Psi_{A\ldots B}^{\basis} = \Psi_A^{\basis} \Psi_B^{\basis}$.
|
As $\efuncdenpbe{\argebasis}$ depends only on quantities which are properties of the wave function $\psibasis$, a sufficient condition for the extensivity of these quantities is that the 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}.
|
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.
|
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}
|
\subsection{Different types of approximations for the functional}
|
||||||
\subsubsection{Definition of the different types of functionals}
|
\subsubsection{Definition of the protocol to design 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.
|
\label{sec:def_func}
|
||||||
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.
|
As the present work proposes to investigate how different physical quantities impact the description of correlation, we propose here a general protocol and a corresponding nomenclature in order to make things as clear as possible.
|
||||||
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
|
Here we propose to investigate the dependency of the functionals $\efuncdenpbe{\argebasis}$ 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 polarisation used.
|
||||||
\begin{equation}
|
Therefore, we propose to use the following notations: PBE-"on-top"-"spin polarisation"-$\psibasis$.
|
||||||
\label{eq:def_pbeueg}
|
|
||||||
\begin{aligned}
|
Regarding the spin polarisation, we will use two different types of formula: i) the usual spin polarisation $\xi = n_{\alpha} - n_{\beta}$ which \textit{is not} $S_z$ invariant, ii) $\Xi$ defined in equation \eqref{eq:def_effspin} which \textit{is} $S_z$ invariant.
|
||||||
\efuncdenpbe{\argepbeuegxihf} = &\int d\br{} \,\denr \\ & \ecmd(\argepbeuegxihf)
|
|
||||||
\end{aligned}
|
For the wave function $\psibasis$, we will use either i) a simple RHF/ROHF wave function, ii) a minimal CASSCF leading to additive energies in the case of dissociated covalent bonds.
|
||||||
\end{equation}
|
|
||||||
where $\ntwo_{\text{UEG}}$ is an approximation of the on-top pair density of the uniform electron gas (UEG) defined as
|
Regarding the approximation to the \textit{exact} on-top pair density, we use two different approximations. The first one is based on the uniform electron gas (UEG) and reads
|
||||||
\begin{equation}
|
\begin{equation}
|
||||||
\label{eq:def_n2ueg}
|
\label{eq:def_n2ueg}
|
||||||
\ntwo_{\text{UEG}}(n,\xi) = n^2(1-\xi)g_0(n)
|
\ntwo_{\text{UEG}}(n,\xi,\br{}) = n(\br{})^2\big(1-\xi(\br{})\big)g_0\big(n(\br{})\big)
|
||||||
\end{equation}
|
\end{equation}
|
||||||
using the pair-distribution function $g_0(n)$ of equation (46) of Ref. \onlinecite{GorSav-PRA-06}.
|
where the pair-distribution function $g_0(n)$ is taken from equation (46) of Ref. \onlinecite{GorSav-PRA-06}. The approximation of equation \eqref{eq:def_n2ueg} depends on the density and some spin polarisation. Notice that, when using a CASSCF wave function and $\Xi$ as spin polarization, the $\ntwo_{\text{UEG}}$ will depend indirectly on the on-top pair density as $\Xi$ depends on the on-top pair density.
|
||||||
The function $\ntwo_{\text{UEG}}$ in an approximation of the \text{exact} on-top pair density based on informations of the UEG.
|
|
||||||
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.
|
Another approach consists in taking advantage of the on-top pair density of the wave function $\psibasis$. Following the work of some of the previous authors\cite{FerGinTou-JCP-18,GinSceTouLoo-JCP-19} we introduce the extrapolated on-top pair density $\ntwoextrap$ as
|
||||||
Of course, because of the use of an HF wave function as $\psibasis$, the density related quantities are extensive only in the case of dissociation in closed shell system.
|
|
||||||
By changing the definition of $\psibasis=\text{HF}$ to $\psibasis=\text{CAS}$ on obtains the PBE-UEG-$\xi$-CAS where all the quantities are computed from a CASSCF wave function. Therfore, the $\murpsi$, density, reduced density gradient, and on-top pair density are extensive in that functional. Nevertheless, the use of the regular spin density $\xi$ leads to non $S_z$ invariance.
|
|
||||||
One can change the spin density to the effective spin density $\Xi$ to obtain the PBE-UEG-$\Xi$-CAS which is $S_z$ invariant, and therefore this functional will reads to
|
|
||||||
\begin{equation}
|
\begin{equation}
|
||||||
\label{eq:def_pbeueg}
|
\ntwoextrap(\ntwo_{\psibasis},\mu,\br{}) = \ntwo_{\wf{}{\Bas}}(\br{}) \bigg( 1 + \frac{2}{\sqrt{\pi}\murpsi} \bigg)^{-1}
|
||||||
\begin{aligned}
|
|
||||||
\efuncdenpbe{\argepbeuegXihf} = &\int d\br{} \,\denr \\ & \ecmd(\argepbeuegXihf).
|
|
||||||
\end{aligned}
|
|
||||||
\end{equation}
|
|
||||||
One can also change the flavour of the on-top pair density by taking using the on-top pair density $\ntwo_{\wf{}{\Bas}}(\br{})$ computed with $\psibasis$.
|
|
||||||
Following the work of some of the previous authors\cite{FerGinTou-JCP-18,excited} we introduce the extrapolated on-top pair density $\ntwoextrap$ as
|
|
||||||
\begin{equation}
|
|
||||||
\ntwoextrap(\ntwo,\mu,\br{}) = \ntwo_{\wf{}{\Bas}}(\br{}) \bigg( 1 + \frac{2}{\sqrt{\pi}\murpsi} \bigg)^{-1}
|
|
||||||
\end{equation}
|
\end{equation}
|
||||||
which directly follows from the large-$\mu$ extrapolation of the exact on-top pair density proposed by Gori-Giorgi and Savin\cite{GorSav-PRA-06}.
|
which directly follows from the large-$\mu$ extrapolation of the exact on-top pair density proposed by Gori-Giorgi and Savin\cite{GorSav-PRA-06}.
|
||||||
When using $\ntwoextrap(\ntwo,\mu,\br{})$ in a functional, we will refer simply refer it as "ont".
|
When using $\ntwoextrap(\ntwo,\mu,\br{})$ in a functional, we will refer simply refer it as "ont".
|
||||||
Therefore, one can define the PBE-ont-$\xi$-CAS as
|
|
||||||
|
\subsubsection{Definition of a hierarchy of functionals}
|
||||||
|
Within the convention proposed in the section \ref{sec:def_func}, the PBE-UEG-$\xi$-HF is the functional which was introduced in Ref. \onlinecite{LooPraSceTouGin-JCPL-19} and which reads
|
||||||
\begin{equation}
|
\begin{equation}
|
||||||
\label{eq:def_pbeueg}
|
\label{eq:def_pbeueg}
|
||||||
\begin{aligned}
|
\begin{aligned}
|
||||||
\efuncdenpbe{\argepbeontxihf} = &\int d\br{} \,\denr \\ & \ecmd(\argepbeontxihf).
|
\pbeuegxihf &\equiv \int d\br{} \,\denr \\ & \ecmd\big(\argrpbeuegxihf\big)
|
||||||
\end{aligned}
|
\end{aligned}
|
||||||
\end{equation}
|
\end{equation}
|
||||||
Such a functional can be further improved by using the effective spin density $\Xi$ to give the PBE-ont-$\Xi$-CAS.
|
Therefore, such a functional uses a HF wave function to define; i) the $\murpsi$, ii) the total density, reduced density gradients, usual spin polarisation $\xi$ and uses the UEG-like on-top pair density with the usual spin polarisation $\xi$.
|
||||||
|
Of course, because of the use of an HF wave function as $\psibasis$, the density related quantities are extensive only in the case of dissociation in closed shell system. Also, one can notice that changing the spin polarisation from $\xi$ to $\Xi$ does not change the results as by definition, $\Xi = \xi$ for a single Slater determinant.
|
||||||
|
|
||||||
|
By changing the definition of $\psibasis=\text{HF}$ to $\psibasis=\text{CASSCF}$ on obtains the PBE-UEG-$\xi$-CAS which reads
|
||||||
|
\begin{equation}
|
||||||
|
\label{eq:def_pbeueg}
|
||||||
|
\begin{aligned}
|
||||||
|
\pbeuegxicas &\equiv \int d\br{} \,\denr \\ & \ecmd\big(\argrpbeuegxicas\big)
|
||||||
|
\end{aligned}
|
||||||
|
\end{equation}
|
||||||
|
where the density, reduced density gradients, usual spin polarisation and UEG on-top pair density are computed from a CASSCF wave function. Therefore, the $\murpsi$, density, reduced density gradient are extensive in the case of dissociated covalent bonding. Nevertheless, the use of the regular spin polarisation $\xi$ leads to non $S_z$ invariance.
|
||||||
|
|
||||||
|
One can change the spin polarisation to the effective spin polarisation $\Xi$ to obtain the PBE-UEG-$\Xi$-CAS which is $S_z$ invariant, and therefore this functional will reads to
|
||||||
|
\begin{equation}
|
||||||
|
\label{eq:def_pbeueg}
|
||||||
|
\begin{aligned}
|
||||||
|
\pbeuegXicas = &\int d\br{} \,\denr \\ & \ecmd(\argrpbeuegXicas).
|
||||||
|
\end{aligned}
|
||||||
|
\end{equation}
|
||||||
|
One can also change the flavour of the on-top pair density by taking advantage of the on-top pair density $\ntwo_{\wf{}{\Bas}}(\br{})$ computed with $\psibasis$.
|
||||||
|
Therefore, one can define the PBE-ONT-$\xi$-CAS as
|
||||||
|
\begin{equation}
|
||||||
|
\label{eq:def_pbeueg}
|
||||||
|
\begin{aligned}
|
||||||
|
\pbeontXicas = &\int d\br{} \,\denr \\ & \ecmd(\argrpbeontXicas).
|
||||||
|
\end{aligned}
|
||||||
|
\end{equation}
|
||||||
|
Such a functional can be further improved by using the $S_z$ invariant effective spin polarisation $\Xi$ to give the PBE-ONT-$\Xi$-CAS.
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
%%%%%%%%%%%%%%%%%%%%%%%%
|
%%%%%%%%%%%%%%%%%%%%%%%%
|
||||||
\section{Results}
|
\section{Results}
|
||||||
\subsection{Numerical tests of extensivity}
|
\subsection{Numerical tests of extensivity}
|
||||||
|
The first numerical results investigated are the numerical tests of extensivity of the various functionals.
|
||||||
|
As mentioned before, when considering a super system $A+B$ dissociating into non interacting fragments $A\ldots B$, there are two different situations regarding the extensivity of the energy: when the subsystems $A$ and $B$ dissociate in closed or open shell systems.
|
||||||
|
Therefore, we shall consider two systems $A$ and $B$ and compare the sum of the energies obtained with the super system $A\ldots B$ in the limit of non interactive fragments. The error to additivity for a given method $Y$ is therefore defined as $E_Y(A) + E_Y(B) - E_Y(A\ldots B)$.
|
||||||
|
|
||||||
|
\subsubsection{Dissociation to closed shell ground states}
|
||||||
|
We begin our study by giving numerical evidence for the extensivity of the present basis set correction for systems dissociating in closed shell systems.
|
||||||
|
In these cases, the use a HF wave function is sufficient to guarantee the extensivity of the basis set correction, and therefore we use the simple $\pbeuegxihf$ functional. The system under study is $A=\text{F}_2$ at experimental equilibrium geometry (F-F=1.411 angstroms) and $B=\text{Ne}$.
|
||||||
|
We report in table \ref{tab:extensiv_closed} the error to additivity for the HF energy and for $\pbeuegxihf$ using the aug-cc-pvdz basis set and using a He core to define the $\mu_{\text{HF}}^{\basis}(\br{})$ and the frozen core densities.
|
||||||
|
The numbers in table \ref{tab:extensiv_closed} clearly show that when HF energies are additive, the $\pbeuegxihf$ is also additive.
|
||||||
|
Also, the error to additivity using the usual spin polarisation $\xi$ and the extrapolated on-top pair density are much lowered compared to that using UEG on-top pair density, highlighting the important role played by the on-top pair density of the CASSCF wave function.
|
||||||
|
|
||||||
\begin{table*}
|
\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$_2$. }
|
\caption{Total energies (in Hartree) for HF and $E$ in aug-cc-pvdz for the Ne atom, F$_2$ (with F-F=1.411 angstroms) and the super non interacting system Ne--F$_2$. }
|
||||||
\begin{tabular}{lcc}
|
\begin{tabular}{lcc}
|
||||||
%\hline
|
%\hline
|
||||||
System & HF & $E$ \\
|
System & HF & $\pbeuegxihf$ \\
|
||||||
\hline
|
\hline
|
||||||
F$_2$ & -2.85570466771188 & -0.0112667838948910 \\
|
Ne & -128.4963497306184 & -0.1039022285466806 \\
|
||||||
He & -198.698792752661 & -0.1596345827582842 \\
|
F$_2$ & -198.698792752661 & -0.1596345827582842 \\
|
||||||
He $\ldots$ F$_2$ & -201.554497420371 & -0.1709013666531826 \\
|
Ne $\ldots$ F$_2$ & -201.554497420371 & -0.2635368113049532 \\
|
||||||
\hline
|
\hline
|
||||||
Error to additivity & 1.2 $\times 10^{-12}$ & 7 $\times 10^{-15}$ \\
|
Error to additivity & 3.4 $\times 10^{-13}$ & 1.1 $\times 10^{-14}$ \\
|
||||||
\end{tabular}
|
\end{tabular}
|
||||||
\label{conv_He_table}
|
\label{tab:extensiv_closed}
|
||||||
|
\end{table*}
|
||||||
|
|
||||||
|
\subsubsection{Dissociation to open shell ground states}
|
||||||
|
The system studied to investigate the extensivity in the case of dissociation to open shell systems is the completely dissociated N$_2$ molecule which imply the breaking of three covalent bonds.
|
||||||
|
As the HF wave function does not lead to extensive energy, it is clear that it cannot be used as $\psibasis$ and therefore for N$_2$ we use a minimal valence CASSCF(6,6) involving the three bonding orbitals ($\sigma$, $\pi_x$, $\pi_y$) and corresponding anti-bonding orbitals and a ROHF wave function for the N atom.
|
||||||
|
The numerical results for the extensivity of the various flavours of functionals are given in table \ref{tab:extensiv_open}. From these numbers, one can clearly notice that only the functionals using the effective spin polarisation $\Xi$ are size extensive, whatever the type of on-top pair density used.
|
||||||
|
|
||||||
|
\begin{table*}
|
||||||
|
\caption{Total energies (in Hartree) for N$_2$ in the aug-cc-pvdz basis set. }
|
||||||
|
\begin{tabular}{lccccc}
|
||||||
|
%\hline
|
||||||
|
System & ROHF/CASSCF(6,6) & $\pbeuegxicas$ & $\pbeuegXicas$ & $\pbeontxicas$ & $\pbeontXicas$ \\
|
||||||
|
\hline
|
||||||
|
N & -128.496349730618 & -0.0230740500348705 & -0.0230740500348705 & -0.0247392466968251 & -0.0247392466968251 \\
|
||||||
|
N$\ldots$N & -198.698792752661 & -0.0691133629633014 & -0.0461481000697329 & -0.0509457188492165 & -0.0494784933936403 \\
|
||||||
|
\hline
|
||||||
|
Error to additivity & 1.0 $\times 10^{-13}$ & 0.02296 & 8.0 $\times 10^{-15}$ & 0.0015 & 9.9 $\times 10^{-15}$ \\
|
||||||
|
\end{tabular}
|
||||||
|
\label{tab:extensiv_open}
|
||||||
\end{table*}
|
\end{table*}
|
||||||
|
|
||||||
\label{sec:results}
|
\label{sec:results}
|
||||||
|
@ -1,4 +1,4 @@
|
|||||||
Date: 13/10/2019 22:24:33
|
Date: 16/10/2019 11:59:09
|
||||||
===============
|
===============
|
||||||
Quantum Package
|
Quantum Package
|
||||||
===============
|
===============
|
||||||
@ -12,28 +12,28 @@ EZFIO Dir : n.ezfio
|
|||||||
Task server running : tcp://127.0.1.1:41279
|
Task server running : tcp://127.0.1.1:41279
|
||||||
.. >>>>> [ IO READ: no_core_density ] <<<<< ..
|
.. >>>>> [ IO READ: no_core_density ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ RES MEM : 0.004505 GB ] [ VIRT MEM : 0.041687 GB ] <<<<< ..
|
.. >>>>> [ RES MEM : 0.004578 GB ] [ VIRT MEM : 0.041687 GB ] <<<<< ..
|
||||||
.. >>>>> [ WALL TIME: 0.000199 s ] [ CPU TIME: 0.001915 s ] <<<<< ..
|
.. >>>>> [ WALL TIME: 0.000197 s ] [ CPU TIME: 0.002052 s ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ IO READ: on_top_from_cas ] <<<<< ..
|
.. >>>>> [ IO READ: on_top_from_cas ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ RES MEM : 0.004765 GB ] [ VIRT MEM : 0.041687 GB ] <<<<< ..
|
.. >>>>> [ RES MEM : 0.004898 GB ] [ VIRT MEM : 0.041687 GB ] <<<<< ..
|
||||||
.. >>>>> [ WALL TIME: 0.000384 s ] [ CPU TIME: 0.002039 s ] <<<<< ..
|
.. >>>>> [ WALL TIME: 0.000711 s ] [ CPU TIME: 0.002260 s ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ IO READ: mu_of_r_potential ] <<<<< ..
|
.. >>>>> [ IO READ: mu_of_r_potential ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ RES MEM : 0.004841 GB ] [ VIRT MEM : 0.041679 GB ] <<<<< ..
|
.. >>>>> [ RES MEM : 0.004974 GB ] [ VIRT MEM : 0.041679 GB ] <<<<< ..
|
||||||
.. >>>>> [ WALL TIME: 0.000553 s ] [ CPU TIME: 0.002147 s ] <<<<< ..
|
.. >>>>> [ WALL TIME: 0.000886 s ] [ CPU TIME: 0.002369 s ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ IO READ: read_wf ] <<<<< ..
|
.. >>>>> [ IO READ: read_wf ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ RES MEM : 0.004841 GB ] [ VIRT MEM : 0.041679 GB ] <<<<< ..
|
.. >>>>> [ RES MEM : 0.004974 GB ] [ VIRT MEM : 0.041679 GB ] <<<<< ..
|
||||||
.. >>>>> [ WALL TIME: 0.000719 s ] [ CPU TIME: 0.002252 s ] <<<<< ..
|
.. >>>>> [ WALL TIME: 0.001055 s ] [ CPU TIME: 0.002477 s ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ IO READ: mu_of_r_functional ] <<<<< ..
|
.. >>>>> [ IO READ: mu_of_r_functional ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ RES MEM : 0.004841 GB ] [ VIRT MEM : 0.041679 GB ] <<<<< ..
|
.. >>>>> [ RES MEM : 0.004974 GB ] [ VIRT MEM : 0.041679 GB ] <<<<< ..
|
||||||
.. >>>>> [ WALL TIME: 0.000907 s ] [ CPU TIME: 0.002379 s ] <<<<< ..
|
.. >>>>> [ WALL TIME: 0.001251 s ] [ CPU TIME: 0.002613 s ] <<<<< ..
|
||||||
|
|
||||||
LDA, PBE and PBE-on-top / mu(r) PSI coallescence with frozen core interaction
|
LDA, PBE and PBE-on-top / mu(r) PSI coallescence with frozen core interaction
|
||||||
****************************************
|
****************************************
|
||||||
@ -43,27 +43,27 @@ Task server running : tcp://127.0.1.1:41279
|
|||||||
MR DFT energy with pure correlation part for the DFT
|
MR DFT energy with pure correlation part for the DFT
|
||||||
.. >>>>> [ IO READ: grid_type_sgn ] <<<<< ..
|
.. >>>>> [ IO READ: grid_type_sgn ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ RES MEM : 0.004841 GB ] [ VIRT MEM : 0.041679 GB ] <<<<< ..
|
.. >>>>> [ RES MEM : 0.004974 GB ] [ VIRT MEM : 0.041679 GB ] <<<<< ..
|
||||||
.. >>>>> [ WALL TIME: 0.001095 s ] [ CPU TIME: 0.002507 s ] <<<<< ..
|
.. >>>>> [ WALL TIME: 0.001447 s ] [ CPU TIME: 0.002747 s ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ IO READ: nucl_num ] <<<<< ..
|
.. >>>>> [ IO READ: nucl_num ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ RES MEM : 0.004841 GB ] [ VIRT MEM : 0.041679 GB ] <<<<< ..
|
.. >>>>> [ RES MEM : 0.004974 GB ] [ VIRT MEM : 0.041679 GB ] <<<<< ..
|
||||||
.. >>>>> [ WALL TIME: 0.001283 s ] [ CPU TIME: 0.002633 s ] <<<<< ..
|
.. >>>>> [ WALL TIME: 0.001637 s ] [ CPU TIME: 0.002876 s ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ IO READ: nucl_charge ] <<<<< ..
|
.. >>>>> [ IO READ: nucl_charge ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ RES MEM : 0.004841 GB ] [ VIRT MEM : 0.065128 GB ] <<<<< ..
|
.. >>>>> [ RES MEM : 0.004974 GB ] [ VIRT MEM : 0.065128 GB ] <<<<< ..
|
||||||
.. >>>>> [ WALL TIME: 0.004089 s ] [ CPU TIME: 0.008215 s ] <<<<< ..
|
.. >>>>> [ WALL TIME: 0.006209 s ] [ CPU TIME: 0.011878 s ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ IO READ: nucl_label ] <<<<< ..
|
.. >>>>> [ IO READ: nucl_label ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ RES MEM : 0.004841 GB ] [ VIRT MEM : 0.065128 GB ] <<<<< ..
|
.. >>>>> [ RES MEM : 0.004974 GB ] [ VIRT MEM : 0.065128 GB ] <<<<< ..
|
||||||
.. >>>>> [ WALL TIME: 0.004391 s ] [ CPU TIME: 0.008912 s ] <<<<< ..
|
.. >>>>> [ WALL TIME: 0.006486 s ] [ CPU TIME: 0.012531 s ] <<<<< ..
|
||||||
|
|
||||||
|
|
||||||
.. >>>>> [ RES MEM : 0.004841 GB ] [ VIRT MEM : 0.190128 GB ] <<<<< ..
|
.. >>>>> [ RES MEM : 0.004974 GB ] [ VIRT MEM : 0.190128 GB ] <<<<< ..
|
||||||
.. >>>>> [ WALL TIME: 0.004694 s ] [ CPU TIME: 0.009648 s ] <<<<< ..
|
.. >>>>> [ WALL TIME: 0.006776 s ] [ CPU TIME: 0.013777 s ] <<<<< ..
|
||||||
|
|
||||||
|
|
||||||
Nuclear Coordinates (Angstroms)
|
Nuclear Coordinates (Angstroms)
|
||||||
@ -77,24 +77,24 @@ N 7.000000 0.000000 0.000000 0.000000
|
|||||||
|
|
||||||
.. >>>>> [ IO READ: thresh_grid ] <<<<< ..
|
.. >>>>> [ IO READ: thresh_grid ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ RES MEM : 0.006584 GB ] [ VIRT MEM : 0.190979 GB ] <<<<< ..
|
.. >>>>> [ RES MEM : 0.006603 GB ] [ VIRT MEM : 0.190979 GB ] <<<<< ..
|
||||||
.. >>>>> [ WALL TIME: 0.007206 s ] [ CPU TIME: 0.020426 s ] <<<<< ..
|
.. >>>>> [ WALL TIME: 0.009469 s ] [ CPU TIME: 0.020608 s ] <<<<< ..
|
||||||
|
|
||||||
n_points_final_grid = 22046
|
n_points_final_grid = 22046
|
||||||
n max point = 22348
|
n max point = 22348
|
||||||
.. >>>>> [ IO READ: n_states ] <<<<< ..
|
.. >>>>> [ IO READ: n_states ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ RES MEM : 0.006584 GB ] [ VIRT MEM : 0.190979 GB ] <<<<< ..
|
.. >>>>> [ RES MEM : 0.006603 GB ] [ VIRT MEM : 0.190979 GB ] <<<<< ..
|
||||||
.. >>>>> [ WALL TIME: 0.007513 s ] [ CPU TIME: 0.020911 s ] <<<<< ..
|
.. >>>>> [ WALL TIME: 0.009797 s ] [ CPU TIME: 0.021038 s ] <<<<< ..
|
||||||
|
|
||||||
providing the mu_of_r ...
|
providing the mu_of_r ...
|
||||||
* mo_num 23
|
* mo_num 23
|
||||||
.. >>>>> [ IO READ: mo_class ] <<<<< ..
|
.. >>>>> [ IO READ: mo_class ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ RES MEM : 0.007782 GB ] [ VIRT MEM : 0.254852 GB ] <<<<< ..
|
.. >>>>> [ RES MEM : 0.007782 GB ] [ VIRT MEM : 0.254852 GB ] <<<<< ..
|
||||||
.. >>>>> [ WALL TIME: 0.009572 s ] [ CPU TIME: 0.028539 s ] <<<<< ..
|
.. >>>>> [ WALL TIME: 0.012069 s ] [ CPU TIME: 0.026409 s ] <<<<< ..
|
||||||
|
|
||||||
* Number of active MOs 4
|
* Number of active MOs 22
|
||||||
* Number of core MOs 1
|
* Number of core MOs 1
|
||||||
* Number of inactive MOs 0
|
* Number of inactive MOs 0
|
||||||
* mo_label Canonical
|
* mo_label Canonical
|
||||||
@ -104,136 +104,134 @@ N 7.000000 0.000000 0.000000 0.000000
|
|||||||
* N_int 1
|
* N_int 1
|
||||||
.. >>>>> [ IO READ: ao_num ] <<<<< ..
|
.. >>>>> [ IO READ: ao_num ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ RES MEM : 0.008533 GB ] [ VIRT MEM : 0.255600 GB ] <<<<< ..
|
.. >>>>> [ RES MEM : 0.010548 GB ] [ VIRT MEM : 0.257687 GB ] <<<<< ..
|
||||||
.. >>>>> [ WALL TIME: 0.011494 s ] [ CPU TIME: 0.033719 s ] <<<<< ..
|
.. >>>>> [ WALL TIME: 0.015830 s ] [ CPU TIME: 0.043224 s ] <<<<< ..
|
||||||
|
|
||||||
Read mo_coef
|
Read mo_coef
|
||||||
.. >>>>> [ IO READ: elec_beta_num ] <<<<< ..
|
.. >>>>> [ IO READ: elec_beta_num ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ RES MEM : 0.008533 GB ] [ VIRT MEM : 0.255600 GB ] <<<<< ..
|
.. >>>>> [ RES MEM : 0.010548 GB ] [ VIRT MEM : 0.257687 GB ] <<<<< ..
|
||||||
.. >>>>> [ WALL TIME: 0.013069 s ] [ CPU TIME: 0.037688 s ] <<<<< ..
|
.. >>>>> [ WALL TIME: 0.016646 s ] [ CPU TIME: 0.044626 s ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ IO READ: elec_alpha_num ] <<<<< ..
|
.. >>>>> [ IO READ: elec_alpha_num ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ RES MEM : 0.008533 GB ] [ VIRT MEM : 0.255600 GB ] <<<<< ..
|
.. >>>>> [ RES MEM : 0.010548 GB ] [ VIRT MEM : 0.257687 GB ] <<<<< ..
|
||||||
.. >>>>> [ WALL TIME: 0.013702 s ] [ CPU TIME: 0.038646 s ] <<<<< ..
|
.. >>>>> [ WALL TIME: 0.016878 s ] [ CPU TIME: 0.044900 s ] <<<<< ..
|
||||||
|
|
||||||
* Number of unique alpha determinants 1
|
* Number of unique alpha determinants 1
|
||||||
* Number of unique beta determinants 1
|
* Number of unique beta determinants 1
|
||||||
core_inact_act_two_bod_alpha_beta_mo provided in 7.2065409985953011E-003
|
core_inact_act_two_bod_alpha_beta_mo provided in 3.6840269995082053E-003
|
||||||
Core MOs:
|
Core MOs:
|
||||||
1
|
1
|
||||||
USING THE VALENCE ONLY TWO BODY DENSITY
|
USING THE VALENCE ONLY TWO BODY DENSITY
|
||||||
providing core_inact_act_two_bod_alpha_beta_mo_physicist ...
|
providing core_inact_act_two_bod_alpha_beta_mo_physicist ...
|
||||||
core_inact_act_two_bod_alpha_beta_mo_physicist provided in 1.6240010154433548E-006
|
core_inact_act_two_bod_alpha_beta_mo_physicist provided in 9.4613800047227414E-004
|
||||||
providing the core_inact_act_on_top_of_r
|
providing the core_inact_act_on_top_of_r
|
||||||
.. >>>>> [ IO READ: ao_prim_num ] <<<<< ..
|
.. >>>>> [ IO READ: ao_prim_num ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ RES MEM : 0.010159 GB ] [ VIRT MEM : 0.275307 GB ] <<<<< ..
|
.. >>>>> [ RES MEM : 0.014290 GB ] [ VIRT MEM : 0.279480 GB ] <<<<< ..
|
||||||
.. >>>>> [ WALL TIME: 0.018106 s ] [ CPU TIME: 0.057134 s ] <<<<< ..
|
.. >>>>> [ WALL TIME: 0.021762 s ] [ CPU TIME: 0.059488 s ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ IO READ: ao_expo ] <<<<< ..
|
.. >>>>> [ IO READ: ao_expo ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ RES MEM : 0.010159 GB ] [ VIRT MEM : 0.275307 GB ] <<<<< ..
|
.. >>>>> [ RES MEM : 0.014290 GB ] [ VIRT MEM : 0.279480 GB ] <<<<< ..
|
||||||
.. >>>>> [ WALL TIME: 0.018569 s ] [ CPU TIME: 0.057815 s ] <<<<< ..
|
.. >>>>> [ WALL TIME: 0.022218 s ] [ CPU TIME: 0.068037 s ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ IO READ: ao_coef ] <<<<< ..
|
.. >>>>> [ IO READ: ao_coef ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ RES MEM : 0.010159 GB ] [ VIRT MEM : 0.275307 GB ] <<<<< ..
|
.. >>>>> [ RES MEM : 0.014290 GB ] [ VIRT MEM : 0.279480 GB ] <<<<< ..
|
||||||
.. >>>>> [ WALL TIME: 0.019022 s ] [ CPU TIME: 0.059222 s ] <<<<< ..
|
.. >>>>> [ WALL TIME: 0.025070 s ] [ CPU TIME: 0.073913 s ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ IO READ: ao_power ] <<<<< ..
|
.. >>>>> [ IO READ: ao_power ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ RES MEM : 0.010159 GB ] [ VIRT MEM : 0.275307 GB ] <<<<< ..
|
.. >>>>> [ RES MEM : 0.014290 GB ] [ VIRT MEM : 0.279480 GB ] <<<<< ..
|
||||||
.. >>>>> [ WALL TIME: 0.019376 s ] [ CPU TIME: 0.060144 s ] <<<<< ..
|
.. >>>>> [ WALL TIME: 0.029855 s ] [ CPU TIME: 0.086789 s ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ IO READ: ao_nucl ] <<<<< ..
|
.. >>>>> [ IO READ: ao_nucl ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ RES MEM : 0.010159 GB ] [ VIRT MEM : 0.275307 GB ] <<<<< ..
|
.. >>>>> [ RES MEM : 0.014694 GB ] [ VIRT MEM : 0.279480 GB ] <<<<< ..
|
||||||
.. >>>>> [ WALL TIME: 0.019883 s ] [ CPU TIME: 0.061265 s ] <<<<< ..
|
.. >>>>> [ WALL TIME: 0.032773 s ] [ CPU TIME: 0.100059 s ] <<<<< ..
|
||||||
|
|
||||||
mo_num,n_points_final_grid 23 22046
|
mo_num,n_points_final_grid 23 22046
|
||||||
* Number of virtual MOs 18
|
* Number of virtual MOs 0
|
||||||
* Number of deleted MOs 0
|
* Number of deleted MOs 0
|
||||||
Active MOs:
|
Active MOs:
|
||||||
2 3 4 5
|
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
|
||||||
0 1 2 3
|
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
|
||||||
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:
|
Core, Inactive and Active MOs:
|
||||||
1 2 3 4 5
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
|
||||||
provided the core_inact_act_on_top_of_r
|
provided the core_inact_act_on_top_of_r
|
||||||
Time to provide : 4.1155614999297541E-002
|
Time to provide : 7.5939346880004450
|
||||||
MO map initialized: 38226
|
MO map initialized: 38226
|
||||||
.. >>>>> [ IO READ: io_mo_two_e_integrals ] <<<<< ..
|
.. >>>>> [ IO READ: io_mo_two_e_integrals ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ RES MEM : 0.057476 GB ] [ VIRT MEM : 0.313763 GB ] <<<<< ..
|
.. >>>>> [ RES MEM : 0.076382 GB ] [ VIRT MEM : 0.415508 GB ] <<<<< ..
|
||||||
.. >>>>> [ WALL TIME: 0.191075 s ] [ CPU TIME: 0.400365 s ] <<<<< ..
|
.. >>>>> [ WALL TIME: 7.788660 s ] [ CPU TIME: 30.008055 s ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ IO READ: io_ao_two_e_integrals ] <<<<< ..
|
.. >>>>> [ IO READ: io_ao_two_e_integrals ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ RES MEM : 0.057476 GB ] [ VIRT MEM : 0.313763 GB ] <<<<< ..
|
.. >>>>> [ RES MEM : 0.076382 GB ] [ VIRT MEM : 0.415508 GB ] <<<<< ..
|
||||||
.. >>>>> [ WALL TIME: 0.191326 s ] [ CPU TIME: 0.400910 s ] <<<<< ..
|
.. >>>>> [ WALL TIME: 7.788863 s ] [ CPU TIME: 30.008745 s ] <<<<< ..
|
||||||
|
|
||||||
AO map initialized : 52975
|
AO map initialized : 52975
|
||||||
.. >>>>> [ IO READ: ao_integrals_threshold ] <<<<< ..
|
.. >>>>> [ IO READ: ao_integrals_threshold ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ RES MEM : 0.057476 GB ] [ VIRT MEM : 0.313763 GB ] <<<<< ..
|
.. >>>>> [ RES MEM : 0.076382 GB ] [ VIRT MEM : 0.415508 GB ] <<<<< ..
|
||||||
.. >>>>> [ WALL TIME: 0.191596 s ] [ CPU TIME: 0.401487 s ] <<<<< ..
|
.. >>>>> [ WALL TIME: 7.789088 s ] [ CPU TIME: 30.009449 s ] <<<<< ..
|
||||||
|
|
||||||
Providing the AO integrals
|
Providing the AO integrals
|
||||||
Sorting the map
|
Sorting the map
|
||||||
AO integrals provided:
|
AO integrals provided:
|
||||||
Size of AO map : 8.5845947265625000E-002 MB
|
Size of AO map : 8.5845947265625000E-002 MB
|
||||||
Number of AO integrals : 7966
|
Number of AO integrals : 7966
|
||||||
cpu time : 0.13432800000000000 s
|
cpu time : 0.10205699999999851 s
|
||||||
wall time : 8.3950192001793766E-002 s ( x 1.6000916352535539 )
|
wall time : 6.4726441999482631E-002 s ( x 1.5767435509712440 )
|
||||||
|
|
||||||
AO -> MO integrals transformation
|
AO -> MO integrals transformation
|
||||||
---------------------------------
|
---------------------------------
|
||||||
|
|
||||||
.. >>>>> [ IO READ: mo_integrals_threshold ] <<<<< ..
|
.. >>>>> [ IO READ: mo_integrals_threshold ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ RES MEM : 0.060123 GB ] [ VIRT MEM : 0.524979 GB ] <<<<< ..
|
.. >>>>> [ RES MEM : 0.078991 GB ] [ VIRT MEM : 0.626755 GB ] <<<<< ..
|
||||||
.. >>>>> [ WALL TIME: 0.276098 s ] [ CPU TIME: 0.536419 s ] <<<<< ..
|
.. >>>>> [ WALL TIME: 7.854217 s ] [ CPU TIME: 30.112367 s ] <<<<< ..
|
||||||
|
|
||||||
Buffers : 0.459625244 MB / core
|
Buffers : 0.459625244 MB / core
|
||||||
Molecular integrals provided:
|
Molecular integrals provided:
|
||||||
Size of MO map 0.36037063598632812 MB
|
Size of MO map 0.36027526855468750 MB
|
||||||
Number of MO integrals: 18472
|
Number of MO integrals: 18894
|
||||||
cpu time : 0.18962299999999999 s
|
cpu time : 0.19265299999999996 s
|
||||||
wall time : 5.7800987000518944E-002 s ( x 3.2806187202010499 )
|
wall time : 6.1197967000225617E-002 s ( x 3.1480294108346722 )
|
||||||
Providing core_inact_act_V_kl_contracted_transposed .....
|
Providing core_inact_act_V_kl_contracted_transposed .....
|
||||||
Time to provide core_inact_act_V_kl_contracted_transposed = 0.10545316999923671
|
Time to provide core_inact_act_V_kl_contracted_transposed = 1.6614129850004247
|
||||||
Providing core_inact_act_rho2_kl_contracted_transposed .....
|
Providing core_inact_act_rho2_kl_contracted_transposed .....
|
||||||
Time to provide core_inact_act_rho2_kl_contracted_transposed = 1.6968988002190599E-002
|
Time to provide core_inact_act_rho2_kl_contracted_transposed = 1.6492683180003951
|
||||||
Providing core_inact_act_f_psi_ab .....
|
Providing core_inact_act_f_psi_ab .....
|
||||||
Time to provide core_inact_act_f_psi_ab = 3.2415269997727592E-003
|
Time to provide core_inact_act_f_psi_ab = 1.2572189999445982E-002
|
||||||
providing the cas_full_mu_of_r_psi_coal_vector ...
|
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 cas_full_mu_of_r_psi_coal_vector = 1.4178099991113413E-004
|
||||||
Time to provide mu_of_r = 0.47625986300045042
|
Time to provide mu_of_r = 11.600998191999679
|
||||||
Providing Energy_c_md_n_and_PBE_mu_of_r ...
|
Providing Energy_c_md_n_and_PBE_mu_of_r ...
|
||||||
.. >>>>> [ IO READ: density_for_dft ] <<<<< ..
|
.. >>>>> [ IO READ: density_for_dft ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ RES MEM : 0.083530 GB ] [ VIRT MEM : 0.658264 GB ] <<<<< ..
|
.. >>>>> [ RES MEM : 0.264374 GB ] [ VIRT MEM : 0.841324 GB ] <<<<< ..
|
||||||
.. >>>>> [ WALL TIME: 0.484660 s ] [ CPU TIME: 1.212247 s ] <<<<< ..
|
.. >>>>> [ WALL TIME: 11.612689 s ] [ CPU TIME: 43.103987 s ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ IO READ: normalize_dm ] <<<<< ..
|
.. >>>>> [ IO READ: normalize_dm ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ RES MEM : 0.083530 GB ] [ VIRT MEM : 0.658264 GB ] <<<<< ..
|
.. >>>>> [ RES MEM : 0.264374 GB ] [ VIRT MEM : 0.841324 GB ] <<<<< ..
|
||||||
.. >>>>> [ WALL TIME: 0.484885 s ] [ CPU TIME: 1.212841 s ] <<<<< ..
|
.. >>>>> [ WALL TIME: 11.613163 s ] [ CPU TIME: 43.107534 s ] <<<<< ..
|
||||||
|
|
||||||
Time for the Energy_c_md_n_and_PBE_mu_of_r : 0.11964879900187952
|
Time for the Energy_c_md_n_and_PBE_mu_of_r : 0.12555567500021425
|
||||||
Providing Energy_c_md_LDA_mu_of_r ...
|
Providing Energy_c_md_LDA_mu_of_r ...
|
||||||
Time for Energy_c_md_LDA_mu_of_r : 2.9454646002704976E-002
|
Time for Energy_c_md_LDA_mu_of_r : 2.6958546000059869E-002
|
||||||
Providing Energy_c_md_LDA_mu_of_r ...
|
Providing Energy_c_md_LDA_mu_of_r ...
|
||||||
Time for Energy_c_md_n_and_LDA_mu_of_r : 2.9101256001013098E-002
|
Time for Energy_c_md_n_and_LDA_mu_of_r : 2.6924847999907797E-002
|
||||||
Providing Energy_c_md_n_and_on_top_PBE_mu_of_r ...
|
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
|
Time for the Energy_c_md_n_and_on_top_PBE_mu_of_r : 6.1856046000684728E-002
|
||||||
.. >>>>> [ IO READ: ontop_approx ] <<<<< ..
|
.. >>>>> [ IO READ: ontop_approx ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ RES MEM : 0.084538 GB ] [ VIRT MEM : 0.659248 GB ] <<<<< ..
|
.. >>>>> [ RES MEM : 0.268711 GB ] [ VIRT MEM : 0.843632 GB ] <<<<< ..
|
||||||
.. >>>>> [ WALL TIME: 0.773004 s ] [ CPU TIME: 1.541545 s ] <<<<< ..
|
.. >>>>> [ WALL TIME: 11.897411 s ] [ CPU TIME: 43.435523 s ] <<<<< ..
|
||||||
|
|
||||||
Inactive MOs:
|
Inactive MOs:
|
||||||
|
|
||||||
@ -245,11 +243,11 @@ N 7.000000 0.000000 0.000000 0.000000
|
|||||||
ispin = 3
|
ispin = 3
|
||||||
USING THE VALENCE ONLY TWO BODY DENSITY
|
USING THE VALENCE ONLY TWO BODY DENSITY
|
||||||
provided the core_inact_act_on_top_of_r_new
|
provided the core_inact_act_on_top_of_r_new
|
||||||
Time to provide : 3.5796539996226784E-003
|
Time to provide : 1.2705452380005227
|
||||||
Providing Energy_c_md_mu_of_r_PBE_on_top ...
|
Providing Energy_c_md_mu_of_r_PBE_on_top ...
|
||||||
Time for the Energy_c_md_on_top_PBE_mu_of_r: 0.27439229000083287
|
Time for the Energy_c_md_on_top_PBE_mu_of_r: 0.27205234399934852
|
||||||
Providing Energy_c_md_PBE_mu_of_r ...
|
Providing Energy_c_md_PBE_mu_of_r ...
|
||||||
Time for the Energy_c_md_PBE_mu_of_r: 6.7258312999911141E-002
|
Time for the Energy_c_md_PBE_mu_of_r: 6.1262960999556526E-002
|
||||||
|
|
||||||
Corrections using Multi determinant mu
|
Corrections using Multi determinant mu
|
||||||
|
|
||||||
@ -266,5 +264,5 @@ N 7.000000 0.000000 0.000000 0.000000
|
|||||||
ECMD PBE/ontop effective spin dens = -0.0247392466968251
|
ECMD PBE/ontop effective spin dens = -0.0247392466968251
|
||||||
|
|
||||||
mu_average for basis set = 0.9116337460
|
mu_average for basis set = 0.9116337460
|
||||||
Wall time: 0:00:02
|
Wall time: 0:00:14
|
||||||
|
|
||||||
|
@ -1,4 +1,4 @@
|
|||||||
Date: 13/10/2019 22:24:49
|
Date: 16/10/2019 11:56:08
|
||||||
===============
|
===============
|
||||||
Quantum Package
|
Quantum Package
|
||||||
===============
|
===============
|
||||||
@ -12,28 +12,28 @@ EZFIO Dir : n2.ezfio
|
|||||||
Task server running : tcp://127.0.1.1:41279
|
Task server running : tcp://127.0.1.1:41279
|
||||||
.. >>>>> [ IO READ: no_core_density ] <<<<< ..
|
.. >>>>> [ IO READ: no_core_density ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ RES MEM : 0.004436 GB ] [ VIRT MEM : 0.041679 GB ] <<<<< ..
|
.. >>>>> [ RES MEM : 0.004402 GB ] [ VIRT MEM : 0.041679 GB ] <<<<< ..
|
||||||
.. >>>>> [ WALL TIME: 0.000193 s ] [ CPU TIME: 0.001977 s ] <<<<< ..
|
.. >>>>> [ WALL TIME: 0.002034 s ] [ CPU TIME: 0.003212 s ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ IO READ: on_top_from_cas ] <<<<< ..
|
.. >>>>> [ IO READ: on_top_from_cas ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ RES MEM : 0.004436 GB ] [ VIRT MEM : 0.041679 GB ] <<<<< ..
|
.. >>>>> [ RES MEM : 0.004402 GB ] [ VIRT MEM : 0.041679 GB ] <<<<< ..
|
||||||
.. >>>>> [ WALL TIME: 0.000368 s ] [ CPU TIME: 0.002092 s ] <<<<< ..
|
.. >>>>> [ WALL TIME: 0.002577 s ] [ CPU TIME: 0.003531 s ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ IO READ: mu_of_r_potential ] <<<<< ..
|
.. >>>>> [ IO READ: mu_of_r_potential ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ RES MEM : 0.004436 GB ] [ VIRT MEM : 0.041679 GB ] <<<<< ..
|
.. >>>>> [ RES MEM : 0.004402 GB ] [ VIRT MEM : 0.041679 GB ] <<<<< ..
|
||||||
.. >>>>> [ WALL TIME: 0.000533 s ] [ CPU TIME: 0.002196 s ] <<<<< ..
|
.. >>>>> [ WALL TIME: 0.003005 s ] [ CPU TIME: 0.003764 s ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ IO READ: read_wf ] <<<<< ..
|
.. >>>>> [ IO READ: read_wf ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ RES MEM : 0.004436 GB ] [ VIRT MEM : 0.041679 GB ] <<<<< ..
|
.. >>>>> [ RES MEM : 0.004402 GB ] [ VIRT MEM : 0.041679 GB ] <<<<< ..
|
||||||
.. >>>>> [ WALL TIME: 0.000696 s ] [ CPU TIME: 0.002298 s ] <<<<< ..
|
.. >>>>> [ WALL TIME: 0.003391 s ] [ CPU TIME: 0.003967 s ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ IO READ: mu_of_r_functional ] <<<<< ..
|
.. >>>>> [ IO READ: mu_of_r_functional ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ RES MEM : 0.004436 GB ] [ VIRT MEM : 0.041679 GB ] <<<<< ..
|
.. >>>>> [ RES MEM : 0.004402 GB ] [ VIRT MEM : 0.041679 GB ] <<<<< ..
|
||||||
.. >>>>> [ WALL TIME: 0.000880 s ] [ CPU TIME: 0.002422 s ] <<<<< ..
|
.. >>>>> [ WALL TIME: 0.003801 s ] [ CPU TIME: 0.004181 s ] <<<<< ..
|
||||||
|
|
||||||
LDA, PBE and PBE-on-top / mu(r) PSI coallescence with frozen core interaction
|
LDA, PBE and PBE-on-top / mu(r) PSI coallescence with frozen core interaction
|
||||||
****************************************
|
****************************************
|
||||||
@ -43,27 +43,27 @@ Task server running : tcp://127.0.1.1:41279
|
|||||||
MR DFT energy with pure correlation part for the DFT
|
MR DFT energy with pure correlation part for the DFT
|
||||||
.. >>>>> [ IO READ: grid_type_sgn ] <<<<< ..
|
.. >>>>> [ IO READ: grid_type_sgn ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ RES MEM : 0.004436 GB ] [ VIRT MEM : 0.041679 GB ] <<<<< ..
|
.. >>>>> [ RES MEM : 0.004402 GB ] [ VIRT MEM : 0.041679 GB ] <<<<< ..
|
||||||
.. >>>>> [ WALL TIME: 0.001067 s ] [ CPU TIME: 0.002548 s ] <<<<< ..
|
.. >>>>> [ WALL TIME: 0.006199 s ] [ CPU TIME: 0.005540 s ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ IO READ: nucl_num ] <<<<< ..
|
.. >>>>> [ IO READ: nucl_num ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ RES MEM : 0.004436 GB ] [ VIRT MEM : 0.041679 GB ] <<<<< ..
|
.. >>>>> [ RES MEM : 0.004402 GB ] [ VIRT MEM : 0.041679 GB ] <<<<< ..
|
||||||
.. >>>>> [ WALL TIME: 0.001253 s ] [ CPU TIME: 0.002673 s ] <<<<< ..
|
.. >>>>> [ WALL TIME: 0.008730 s ] [ CPU TIME: 0.007199 s ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ IO READ: nucl_charge ] <<<<< ..
|
.. >>>>> [ IO READ: nucl_charge ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ RES MEM : 0.005276 GB ] [ VIRT MEM : 0.127628 GB ] <<<<< ..
|
.. >>>>> [ RES MEM : 0.005180 GB ] [ VIRT MEM : 0.127628 GB ] <<<<< ..
|
||||||
.. >>>>> [ WALL TIME: 0.006438 s ] [ CPU TIME: 0.014247 s ] <<<<< ..
|
.. >>>>> [ WALL TIME: 0.015577 s ] [ CPU TIME: 0.024745 s ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ IO READ: nucl_label ] <<<<< ..
|
.. >>>>> [ IO READ: nucl_label ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ RES MEM : 0.005276 GB ] [ VIRT MEM : 0.127628 GB ] <<<<< ..
|
.. >>>>> [ RES MEM : 0.005180 GB ] [ VIRT MEM : 0.127628 GB ] <<<<< ..
|
||||||
.. >>>>> [ WALL TIME: 0.006731 s ] [ CPU TIME: 0.015202 s ] <<<<< ..
|
.. >>>>> [ WALL TIME: 0.015887 s ] [ CPU TIME: 0.025467 s ] <<<<< ..
|
||||||
|
|
||||||
|
|
||||||
.. >>>>> [ RES MEM : 0.005276 GB ] [ VIRT MEM : 0.252628 GB ] <<<<< ..
|
.. >>>>> [ RES MEM : 0.005180 GB ] [ VIRT MEM : 0.252628 GB ] <<<<< ..
|
||||||
.. >>>>> [ WALL TIME: 0.007020 s ] [ CPU TIME: 0.015901 s ] <<<<< ..
|
.. >>>>> [ WALL TIME: 0.016192 s ] [ CPU TIME: 0.026211 s ] <<<<< ..
|
||||||
|
|
||||||
|
|
||||||
Nuclear Coordinates (Angstroms)
|
Nuclear Coordinates (Angstroms)
|
||||||
@ -78,22 +78,22 @@ N 7.000000 0.000000 0.000000 1000.000072
|
|||||||
|
|
||||||
.. >>>>> [ IO READ: thresh_grid ] <<<<< ..
|
.. >>>>> [ IO READ: thresh_grid ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ RES MEM : 0.007256 GB ] [ VIRT MEM : 0.254322 GB ] <<<<< ..
|
.. >>>>> [ RES MEM : 0.007378 GB ] [ VIRT MEM : 0.254322 GB ] <<<<< ..
|
||||||
.. >>>>> [ WALL TIME: 0.018087 s ] [ CPU TIME: 0.054428 s ] <<<<< ..
|
.. >>>>> [ WALL TIME: 0.031278 s ] [ CPU TIME: 0.071872 s ] <<<<< ..
|
||||||
|
|
||||||
n_points_final_grid = 44092
|
n_points_final_grid = 44092
|
||||||
n max point = 44998
|
n max point = 44998
|
||||||
.. >>>>> [ IO READ: n_states ] <<<<< ..
|
.. >>>>> [ IO READ: n_states ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ RES MEM : 0.007256 GB ] [ VIRT MEM : 0.254322 GB ] <<<<< ..
|
.. >>>>> [ RES MEM : 0.007378 GB ] [ VIRT MEM : 0.254322 GB ] <<<<< ..
|
||||||
.. >>>>> [ WALL TIME: 0.018397 s ] [ CPU TIME: 0.057538 s ] <<<<< ..
|
.. >>>>> [ WALL TIME: 0.031616 s ] [ CPU TIME: 0.076421 s ] <<<<< ..
|
||||||
|
|
||||||
providing the mu_of_r ...
|
providing the mu_of_r ...
|
||||||
* mo_num 46
|
* mo_num 46
|
||||||
.. >>>>> [ IO READ: mo_class ] <<<<< ..
|
.. >>>>> [ IO READ: mo_class ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ RES MEM : 0.009270 GB ] [ VIRT MEM : 0.256981 GB ] <<<<< ..
|
.. >>>>> [ RES MEM : 0.009392 GB ] [ VIRT MEM : 0.256981 GB ] <<<<< ..
|
||||||
.. >>>>> [ WALL TIME: 0.019785 s ] [ CPU TIME: 0.061670 s ] <<<<< ..
|
.. >>>>> [ WALL TIME: 0.033638 s ] [ CPU TIME: 0.081802 s ] <<<<< ..
|
||||||
|
|
||||||
* Number of active MOs 8
|
* Number of active MOs 8
|
||||||
* Number of core MOs 2
|
* Number of core MOs 2
|
||||||
@ -106,54 +106,54 @@ N 7.000000 0.000000 0.000000 1000.000072
|
|||||||
* N_int 1
|
* N_int 1
|
||||||
.. >>>>> [ IO READ: ao_num ] <<<<< ..
|
.. >>>>> [ IO READ: ao_num ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ RES MEM : 0.010387 GB ] [ VIRT MEM : 0.257874 GB ] <<<<< ..
|
.. >>>>> [ RES MEM : 0.010250 GB ] [ VIRT MEM : 0.257874 GB ] <<<<< ..
|
||||||
.. >>>>> [ WALL TIME: 0.020953 s ] [ CPU TIME: 0.064729 s ] <<<<< ..
|
.. >>>>> [ WALL TIME: 0.035617 s ] [ CPU TIME: 0.088608 s ] <<<<< ..
|
||||||
|
|
||||||
Read mo_coef
|
Read mo_coef
|
||||||
.. >>>>> [ IO READ: elec_beta_num ] <<<<< ..
|
.. >>>>> [ IO READ: elec_beta_num ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ RES MEM : 0.010387 GB ] [ VIRT MEM : 0.257874 GB ] <<<<< ..
|
.. >>>>> [ RES MEM : 0.010250 GB ] [ VIRT MEM : 0.257874 GB ] <<<<< ..
|
||||||
.. >>>>> [ WALL TIME: 0.022999 s ] [ CPU TIME: 0.074050 s ] <<<<< ..
|
.. >>>>> [ WALL TIME: 0.037877 s ] [ CPU TIME: 0.097141 s ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ IO READ: elec_alpha_num ] <<<<< ..
|
.. >>>>> [ IO READ: elec_alpha_num ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ RES MEM : 0.010387 GB ] [ VIRT MEM : 0.257874 GB ] <<<<< ..
|
.. >>>>> [ RES MEM : 0.010250 GB ] [ VIRT MEM : 0.257874 GB ] <<<<< ..
|
||||||
.. >>>>> [ WALL TIME: 0.023209 s ] [ CPU TIME: 0.074364 s ] <<<<< ..
|
.. >>>>> [ WALL TIME: 0.038110 s ] [ CPU TIME: 0.097643 s ] <<<<< ..
|
||||||
|
|
||||||
Read psi_det
|
Read psi_det
|
||||||
* Number of unique alpha determinants 20
|
* Number of unique alpha determinants 20
|
||||||
* Number of unique beta determinants 20
|
* Number of unique beta determinants 20
|
||||||
core_inact_act_two_bod_alpha_beta_mo provided in 1.0138563997315941E-002
|
core_inact_act_two_bod_alpha_beta_mo provided in 8.8323440004387521E-003
|
||||||
Core MOs:
|
Core MOs:
|
||||||
1 2
|
1 2
|
||||||
USING THE VALENCE ONLY TWO BODY DENSITY
|
USING THE VALENCE ONLY TWO BODY DENSITY
|
||||||
providing core_inact_act_two_bod_alpha_beta_mo_physicist ...
|
providing core_inact_act_two_bod_alpha_beta_mo_physicist ...
|
||||||
core_inact_act_two_bod_alpha_beta_mo_physicist provided in 3.8632999348919839E-005
|
core_inact_act_two_bod_alpha_beta_mo_physicist provided in 1.4993999684520531E-005
|
||||||
providing the core_inact_act_on_top_of_r
|
providing the core_inact_act_on_top_of_r
|
||||||
.. >>>>> [ IO READ: ao_prim_num ] <<<<< ..
|
.. >>>>> [ IO READ: ao_prim_num ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ RES MEM : 0.012398 GB ] [ VIRT MEM : 0.315315 GB ] <<<<< ..
|
.. >>>>> [ RES MEM : 0.012318 GB ] [ VIRT MEM : 0.315315 GB ] <<<<< ..
|
||||||
.. >>>>> [ WALL TIME: 0.032296 s ] [ CPU TIME: 0.104271 s ] <<<<< ..
|
.. >>>>> [ WALL TIME: 0.044121 s ] [ CPU TIME: 0.119986 s ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ IO READ: ao_expo ] <<<<< ..
|
.. >>>>> [ IO READ: ao_expo ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ RES MEM : 0.012398 GB ] [ VIRT MEM : 0.315315 GB ] <<<<< ..
|
.. >>>>> [ RES MEM : 0.012318 GB ] [ VIRT MEM : 0.315315 GB ] <<<<< ..
|
||||||
.. >>>>> [ WALL TIME: 0.033598 s ] [ CPU TIME: 0.110293 s ] <<<<< ..
|
.. >>>>> [ WALL TIME: 0.044656 s ] [ CPU TIME: 0.121388 s ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ IO READ: ao_coef ] <<<<< ..
|
.. >>>>> [ IO READ: ao_coef ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ RES MEM : 0.012398 GB ] [ VIRT MEM : 0.315315 GB ] <<<<< ..
|
.. >>>>> [ RES MEM : 0.012318 GB ] [ VIRT MEM : 0.315315 GB ] <<<<< ..
|
||||||
.. >>>>> [ WALL TIME: 0.034755 s ] [ CPU TIME: 0.114448 s ] <<<<< ..
|
.. >>>>> [ WALL TIME: 0.045176 s ] [ CPU TIME: 0.122740 s ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ IO READ: ao_power ] <<<<< ..
|
.. >>>>> [ IO READ: ao_power ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ RES MEM : 0.012398 GB ] [ VIRT MEM : 0.315315 GB ] <<<<< ..
|
.. >>>>> [ RES MEM : 0.012318 GB ] [ VIRT MEM : 0.315315 GB ] <<<<< ..
|
||||||
.. >>>>> [ WALL TIME: 0.035587 s ] [ CPU TIME: 0.117060 s ] <<<<< ..
|
.. >>>>> [ WALL TIME: 0.045528 s ] [ CPU TIME: 0.123594 s ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ IO READ: ao_nucl ] <<<<< ..
|
.. >>>>> [ IO READ: ao_nucl ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ RES MEM : 0.012398 GB ] [ VIRT MEM : 0.315315 GB ] <<<<< ..
|
.. >>>>> [ RES MEM : 0.012318 GB ] [ VIRT MEM : 0.315315 GB ] <<<<< ..
|
||||||
.. >>>>> [ WALL TIME: 0.036767 s ] [ CPU TIME: 0.120070 s ] <<<<< ..
|
.. >>>>> [ WALL TIME: 0.046367 s ] [ CPU TIME: 0.125622 s ] <<<<< ..
|
||||||
|
|
||||||
mo_num,n_points_final_grid 46 44092
|
mo_num,n_points_final_grid 46 44092
|
||||||
* Number of virtual MOs 36
|
* Number of virtual MOs 36
|
||||||
@ -166,77 +166,77 @@ N 7.000000 0.000000 0.000000 1000.000072
|
|||||||
Core, Inactive and Active MOs:
|
Core, Inactive and Active MOs:
|
||||||
1 2 3 4 5 6 7 8 9 10
|
1 2 3 4 5 6 7 8 9 10
|
||||||
provided the core_inact_act_on_top_of_r
|
provided the core_inact_act_on_top_of_r
|
||||||
Time to provide : 0.70096241300052498
|
Time to provide : 0.70333999699960259
|
||||||
MO map initialized: 584821
|
MO map initialized: 584821
|
||||||
.. >>>>> [ IO READ: io_mo_two_e_integrals ] <<<<< ..
|
.. >>>>> [ IO READ: io_mo_two_e_integrals ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ RES MEM : 0.200268 GB ] [ VIRT MEM : 0.485504 GB ] <<<<< ..
|
.. >>>>> [ RES MEM : 0.200497 GB ] [ VIRT MEM : 0.485504 GB ] <<<<< ..
|
||||||
.. >>>>> [ WALL TIME: 1.265357 s ] [ CPU TIME: 3.473769 s ] <<<<< ..
|
.. >>>>> [ WALL TIME: 1.286127 s ] [ CPU TIME: 3.479892 s ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ IO READ: io_ao_two_e_integrals ] <<<<< ..
|
.. >>>>> [ IO READ: io_ao_two_e_integrals ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ RES MEM : 0.200268 GB ] [ VIRT MEM : 0.485504 GB ] <<<<< ..
|
.. >>>>> [ RES MEM : 0.200497 GB ] [ VIRT MEM : 0.485504 GB ] <<<<< ..
|
||||||
.. >>>>> [ WALL TIME: 1.265604 s ] [ CPU TIME: 3.474068 s ] <<<<< ..
|
.. >>>>> [ WALL TIME: 1.289062 s ] [ CPU TIME: 3.489111 s ] <<<<< ..
|
||||||
|
|
||||||
AO map initialized : 813450
|
AO map initialized : 813450
|
||||||
.. >>>>> [ IO READ: ao_integrals_threshold ] <<<<< ..
|
.. >>>>> [ IO READ: ao_integrals_threshold ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ RES MEM : 0.200573 GB ] [ VIRT MEM : 0.485504 GB ] <<<<< ..
|
.. >>>>> [ RES MEM : 0.200497 GB ] [ VIRT MEM : 0.485504 GB ] <<<<< ..
|
||||||
.. >>>>> [ WALL TIME: 1.265888 s ] [ CPU TIME: 3.474393 s ] <<<<< ..
|
.. >>>>> [ WALL TIME: 1.289537 s ] [ CPU TIME: 3.489272 s ] <<<<< ..
|
||||||
|
|
||||||
Providing the AO integrals
|
Providing the AO integrals
|
||||||
Sorting the map
|
Sorting the map
|
||||||
AO integrals provided:
|
AO integrals provided:
|
||||||
Size of AO map : 0.44347000122070312 MB
|
Size of AO map : 0.44347000122070312 MB
|
||||||
Number of AO integrals : 38257
|
Number of AO integrals : 38257
|
||||||
cpu time : 1.0639589999999997 s
|
cpu time : 1.0522440000000004 s
|
||||||
wall time : 0.41615004599952954 s ( x 2.5566715905185853 )
|
wall time : 0.40554916499968385 s ( x 2.5946151313141543 )
|
||||||
|
|
||||||
AO -> MO integrals transformation
|
AO -> MO integrals transformation
|
||||||
---------------------------------
|
---------------------------------
|
||||||
|
|
||||||
.. >>>>> [ IO READ: mo_integrals_threshold ] <<<<< ..
|
.. >>>>> [ IO READ: mo_integrals_threshold ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ RES MEM : 0.203552 GB ] [ VIRT MEM : 0.697113 GB ] <<<<< ..
|
.. >>>>> [ RES MEM : 0.203278 GB ] [ VIRT MEM : 0.697235 GB ] <<<<< ..
|
||||||
.. >>>>> [ WALL TIME: 1.682451 s ] [ CPU TIME: 4.539011 s ] <<<<< ..
|
.. >>>>> [ WALL TIME: 1.695592 s ] [ CPU TIME: 4.542076 s ] <<<<< ..
|
||||||
|
|
||||||
Buffers : 3.63958740 MB / core
|
Buffers : 3.63958740 MB / core
|
||||||
Molecular integrals provided:
|
Molecular integrals provided:
|
||||||
Size of MO map 9.6878700256347656 MB
|
Size of MO map 9.6795730590820312 MB
|
||||||
Number of MO integrals: 473042
|
Number of MO integrals: 469580
|
||||||
cpu time : 2.2190269999999996 s
|
cpu time : 2.2609360000000001 s
|
||||||
wall time : 0.80212339799982146 s ( x 2.7664409310754126 )
|
wall time : 0.81856668300042656 s ( x 2.7620669726168439 )
|
||||||
Providing core_inact_act_V_kl_contracted_transposed .....
|
Providing core_inact_act_V_kl_contracted_transposed .....
|
||||||
Time to provide core_inact_act_V_kl_contracted_transposed = 1.7762000410002656
|
Time to provide core_inact_act_V_kl_contracted_transposed = 1.7736809010002617
|
||||||
Providing core_inact_act_rho2_kl_contracted_transposed .....
|
Providing core_inact_act_rho2_kl_contracted_transposed .....
|
||||||
Time to provide core_inact_act_rho2_kl_contracted_transposed = 0.22741315399980522
|
Time to provide core_inact_act_rho2_kl_contracted_transposed = 0.25144742500015127
|
||||||
Providing core_inact_act_f_psi_ab .....
|
Providing core_inact_act_f_psi_ab .....
|
||||||
Time to provide core_inact_act_f_psi_ab = 4.9875350014190190E-003
|
Time to provide core_inact_act_f_psi_ab = 4.9547449998499360E-003
|
||||||
providing the cas_full_mu_of_r_psi_coal_vector ...
|
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 cas_full_mu_of_r_psi_coal_vector = 2.6400199931231327E-004
|
||||||
Time to provide mu_of_r = 4.6907960499993351
|
Time to provide mu_of_r = 4.7140897310000582
|
||||||
Providing Energy_c_md_n_and_PBE_mu_of_r ...
|
Providing Energy_c_md_n_and_PBE_mu_of_r ...
|
||||||
.. >>>>> [ IO READ: density_for_dft ] <<<<< ..
|
.. >>>>> [ IO READ: density_for_dft ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ RES MEM : 0.352638 GB ] [ VIRT MEM : 0.860363 GB ] <<<<< ..
|
.. >>>>> [ RES MEM : 0.349529 GB ] [ VIRT MEM : 0.868500 GB ] <<<<< ..
|
||||||
.. >>>>> [ WALL TIME: 4.710455 s ] [ CPU TIME: 14.149410 s ] <<<<< ..
|
.. >>>>> [ WALL TIME: 4.746935 s ] [ CPU TIME: 14.221149 s ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ IO READ: normalize_dm ] <<<<< ..
|
.. >>>>> [ IO READ: normalize_dm ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ RES MEM : 0.352638 GB ] [ VIRT MEM : 0.860363 GB ] <<<<< ..
|
.. >>>>> [ RES MEM : 0.349529 GB ] [ VIRT MEM : 0.868500 GB ] <<<<< ..
|
||||||
.. >>>>> [ WALL TIME: 4.710757 s ] [ CPU TIME: 14.150161 s ] <<<<< ..
|
.. >>>>> [ WALL TIME: 4.747532 s ] [ CPU TIME: 14.229911 s ] <<<<< ..
|
||||||
|
|
||||||
Time for the Energy_c_md_n_and_PBE_mu_of_r : 0.37609190000148374
|
Time for the Energy_c_md_n_and_PBE_mu_of_r : 0.38293596199946478
|
||||||
Providing Energy_c_md_LDA_mu_of_r ...
|
Providing Energy_c_md_LDA_mu_of_r ...
|
||||||
Time for Energy_c_md_LDA_mu_of_r : 5.3449625997018302E-002
|
Time for Energy_c_md_LDA_mu_of_r : 5.3972198999872489E-002
|
||||||
Providing Energy_c_md_LDA_mu_of_r ...
|
Providing Energy_c_md_LDA_mu_of_r ...
|
||||||
Time for Energy_c_md_n_and_LDA_mu_of_r : 5.2238627999031451E-002
|
Time for Energy_c_md_n_and_LDA_mu_of_r : 5.2259051999499206E-002
|
||||||
Providing Energy_c_md_n_and_on_top_PBE_mu_of_r ...
|
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
|
Time for the Energy_c_md_n_and_on_top_PBE_mu_of_r : 0.12262305900003412
|
||||||
.. >>>>> [ IO READ: ontop_approx ] <<<<< ..
|
.. >>>>> [ IO READ: ontop_approx ] <<<<< ..
|
||||||
|
|
||||||
.. >>>>> [ RES MEM : 0.361450 GB ] [ VIRT MEM : 0.864967 GB ] <<<<< ..
|
.. >>>>> [ RES MEM : 0.358109 GB ] [ VIRT MEM : 0.873108 GB ] <<<<< ..
|
||||||
.. >>>>> [ WALL TIME: 5.529283 s ] [ CPU TIME: 15.013616 s ] <<<<< ..
|
.. >>>>> [ WALL TIME: 5.576314 s ] [ CPU TIME: 15.102221 s ] <<<<< ..
|
||||||
|
|
||||||
Inactive MOs:
|
Inactive MOs:
|
||||||
|
|
||||||
@ -248,11 +248,11 @@ N 7.000000 0.000000 0.000000 1000.000072
|
|||||||
ispin = 3
|
ispin = 3
|
||||||
USING THE VALENCE ONLY TWO BODY DENSITY
|
USING THE VALENCE ONLY TWO BODY DENSITY
|
||||||
provided the core_inact_act_on_top_of_r_new
|
provided the core_inact_act_on_top_of_r_new
|
||||||
Time to provide : 9.8473186000774149E-002
|
Time to provide : 0.10430047200043191
|
||||||
Providing Energy_c_md_mu_of_r_PBE_on_top ...
|
Providing Energy_c_md_mu_of_r_PBE_on_top ...
|
||||||
Time for the Energy_c_md_on_top_PBE_mu_of_r: 0.95842244199957349
|
Time for the Energy_c_md_on_top_PBE_mu_of_r: 0.96463285200024984
|
||||||
Providing Energy_c_md_PBE_mu_of_r ...
|
Providing Energy_c_md_PBE_mu_of_r ...
|
||||||
Time for the Energy_c_md_PBE_mu_of_r: 0.12124202900304226
|
Time for the Energy_c_md_PBE_mu_of_r: 0.12067553599990788
|
||||||
|
|
||||||
Corrections using Multi determinant mu
|
Corrections using Multi determinant mu
|
||||||
|
|
||||||
@ -260,7 +260,7 @@ N 7.000000 0.000000 0.000000 1000.000072
|
|||||||
|
|
||||||
ECMD LDA regular spin dens = -0.0678669003007728
|
ECMD LDA regular spin dens = -0.0678669003007728
|
||||||
ECMD LDA effective spin dens = -0.0530814198896590
|
ECMD LDA effective spin dens = -0.0530814198896590
|
||||||
ECMD PBE regular spin dens = -0.0691133629633015
|
ECMD PBE regular spin dens = -0.0691133629633014
|
||||||
ECMD PBE effective spin dens = -0.0461481000697329
|
ECMD PBE effective spin dens = -0.0461481000697329
|
||||||
|
|
||||||
Functionals with extrapolated exact ontop based on current wave function
|
Functionals with extrapolated exact ontop based on current wave function
|
||||||
|
@ -4,6 +4,18 @@
|
|||||||
-198.698792752661 -0.1596345827582842
|
-198.698792752661 -0.1596345827582842
|
||||||
-201.554497420371 -0.1709013666531826
|
-201.554497420371 -0.1709013666531826
|
||||||
1.9 10^-12 7 10^-15
|
1.9 10^-12 7 10^-15
|
||||||
# N2
|
# F2 + Ne
|
||||||
-54.3898707291144
|
# HF
|
||||||
-108.779741458229
|
-128.4963497306184 -0.1039022285466806
|
||||||
|
-198.698792752661 -0.1596345827582842
|
||||||
|
-327.195142483279 -0.2635368113049532
|
||||||
|
3.4 10^-13 1.1 10^-14
|
||||||
|
|
||||||
|
# N2 ROHF PBE-UEG-xi-ROHF PBE-ONT-xi-ROHF
|
||||||
|
-54.3898707291144 -0.0230740500348705 -0.0247392466968251
|
||||||
|
-108.1790794412006 -0.0715505833610001
|
||||||
|
-0.60066 0.0254024832912591
|
||||||
|
# CASSCF PBE-UEG-xi-CAS PBE-UEG-Xi-CAS PBE-ONT-xi-CAS PBE-ONT-Xi-CAS
|
||||||
|
-108.779741458229 -0.0691133629633014 -0.0461481000697329 -0.0509457188492165 -0.0494784933936403
|
||||||
|
2 10^-13 0.0229652628935603 8. 10^-15 0.0014672254555662 9.9 10^{-15}
|
||||||
|
|
||||||
|
Loading…
Reference in New Issue
Block a user