working on the conclusion ...
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Emmanuel Giner
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@ -5,18 +5,20 @@
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\BOOKMARK [2][-]{section*.5}{Basic formal equations}{section*.4}% 5
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\BOOKMARK [2][-]{section*.6}{Definition of an effective interaction within B}{section*.4}% 6
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\BOOKMARK [2][-]{section*.7}{Definition of a range-separation parameter varying in real space}{section*.4}% 7
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\BOOKMARK [2][-]{section*.8}{Generic form and properties of the approximations for B[n\(r\)] }{section*.4}% 8
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\BOOKMARK [3][-]{section*.9}{Generic form of the approximated functionals}{section*.8}% 9
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\BOOKMARK [3][-]{section*.10}{Properties of approximated functionals}{section*.8}% 10
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\BOOKMARK [2][-]{section*.11}{Requirements for the approximated functionals in the strong correlation regime}{section*.4}% 11
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\BOOKMARK [3][-]{section*.12}{Requirements: separability of the energies and Sz invariance}{section*.11}% 12
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\BOOKMARK [3][-]{section*.13}{Condition for the functional XB[n,,s,n\(2\),B] to obtain Sz invariance}{section*.11}% 13
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\BOOKMARK [3][-]{section*.14}{Conditions on B for the extensivity}{section*.11}% 14
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\BOOKMARK [2][-]{section*.15}{Different types of approximations for the functional}{section*.4}% 15
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\BOOKMARK [3][-]{section*.16}{Definition of the protocol to design functionals}{section*.15}% 16
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\BOOKMARK [3][-]{section*.17}{Definition of functionals with good formal properties}{section*.15}% 17
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\BOOKMARK [1][-]{section*.18}{Results for the C2, N2, O2, F2 and H10 potential energy curves}{section*.2}% 18
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\BOOKMARK [2][-]{section*.19}{Computational details}{section*.18}% 19
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\BOOKMARK [2][-]{section*.20}{Dissociation of equally distant H10 chains}{section*.18}% 20
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\BOOKMARK [2][-]{section*.21}{Dissociation of C2, N2, O2 and F2}{section*.18}% 21
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\BOOKMARK [1][-]{section*.22}{Conclusion}{section*.2}% 22
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\BOOKMARK [3][-]{section*.8}{General definition}{section*.7}% 8
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\BOOKMARK [3][-]{section*.9}{Frozen core density approximation}{section*.7}% 9
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\BOOKMARK [2][-]{section*.10}{Generic form and properties of the approximations for B[n\(r\)] }{section*.4}% 10
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\BOOKMARK [3][-]{section*.11}{Generic form of the approximated functionals}{section*.10}% 11
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\BOOKMARK [3][-]{section*.12}{Properties of approximated functionals}{section*.10}% 12
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\BOOKMARK [2][-]{section*.13}{Requirements for the approximated functionals in the strong correlation regime}{section*.4}% 13
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\BOOKMARK [3][-]{section*.14}{Requirements: separability of the energies and Sz invariance}{section*.13}% 14
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\BOOKMARK [3][-]{section*.15}{Condition for the functional XB[n,,s,n\(2\),B] to obtain Sz invariance}{section*.13}% 15
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\BOOKMARK [3][-]{section*.16}{Conditions on B for the extensivity}{section*.13}% 16
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\BOOKMARK [2][-]{section*.17}{Different types of approximations for the functional}{section*.4}% 17
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\BOOKMARK [3][-]{section*.18}{Definition of the protocol to design functionals}{section*.17}% 18
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\BOOKMARK [3][-]{section*.19}{Definition of functionals with good formal properties}{section*.17}% 19
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\BOOKMARK [1][-]{section*.20}{Results for the C2, N2, O2, F2 and H10 potential energy curves}{section*.2}% 20
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\BOOKMARK [2][-]{section*.21}{Computational details}{section*.20}% 21
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\BOOKMARK [2][-]{section*.22}{Dissociation of equally distant H10 chains}{section*.20}% 22
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\BOOKMARK [2][-]{section*.23}{Dissociation of C2, N2, O2 and F2}{section*.20}% 23
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\BOOKMARK [1][-]{section*.24}{Conclusion}{section*.2}% 24
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@ -35,6 +35,8 @@
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\newcommand{\phix}[2]{\phi_{#1}(\bfr{#2})}
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\newcommand{\phixprim}[2]{\phi_{#1}(\bfr{#2}')}
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\newcommand{\CBS}{\text{CBS}}
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%operators
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\newcommand{\elemm}[3]{{\ensuremath{\bra{#1}{#2}\ket{#3}}\xspace}}
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@ -83,6 +85,7 @@
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\newcommand{\emuldaval}[0]{\bar{\varepsilon}^{\text{sr},\text{unif}}_{\text{c,md}}\left(\denval ({\bf r});\murval;\wf{}{\Bas})\right)}
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\newcommand{\ecmd}[0]{\varepsilon^{\text{c,md}}_{\text{PBE}}}
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\newcommand{\psibasis}[0]{\Psi^{\basis}}
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\newcommand{\BasFC}{\mathcal{A}}
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%pbeuegxiHF
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\newcommand{\pbeuegxihf}{\text{PBE-UEG-}\zeta\text{-HF}^\Bas}
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@ -389,7 +392,7 @@ More specifically, the effective interaction associated to a given wave function
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\end{equation}
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where $\twodmrdiagpsi$ is the opposite spin two-body density associated to $\wf{}{\Bas}$
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\begin{equation}
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\twodmrdiagpsi = \sum_{pqrs} \SO{p}{1} \SO{q}{2} \Gam{pq}{rs} \SO{r}{1} \SO{s}{2},
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\twodmrdiagpsi = \sum_{pqrs \in \Bas} \SO{p}{1} \SO{q}{2} \Gam{pq}{rs} \SO{r}{1} \SO{s}{2},
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\end{equation}
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$\Gam{pq}{rs} = 2 \mel*{\wf{}{\Bas}}{ \aic{r_\downarrow}\aic{s_\uparrow}\ai{q_\uparrow}\ai{p_\downarrow}}{\wf{}{\Bas}}$ its associated two-body tensor, $\SO{p}{}$ are the spatial orthonormal orbitals,
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\begin{equation}
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@ -411,6 +414,7 @@ The condition of equation \eqref{eq:cbs_wbasis} is fundamental as it guarantees
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\subsection{Definition of a range-separation parameter varying in real space}
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\label{sec:mur}
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\subsubsection{General definition}
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As the effective interaction within a basis set $\wbasis$ is non divergent, one can fit such a function with a long-range interaction defined in the framework of RSDFT which depends on the range-separation parameter $\mu$
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\begin{equation}
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\label{eq:weelr}
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@ -432,6 +436,37 @@ Because of the very definition of $\wbasis$, one has the following properties at
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\end{equation}
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which is fundamental to guarantee the good behaviour of the theory at the CBS limit.
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\subsubsection{Frozen core density approximation}
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As all WFT calculations for the purpose of that work are performed within the frozen core approximation, we define the valence-only versions of the various quantities needed for the complementary basis set functional.
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We split the basis set as $\Bas = \Cor \bigcup \BasFC$ (where $\Cor$ and $\BasFC$ are the sets of core and active MOs, respectively)
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and define the valence only range separation parameter
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\begin{equation}
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\label{eq:def_mur_val}
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\murpsival = \frac{\sqrt{\pi}}{2} \wbasiscoalval,
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\end{equation}
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where $\wbasisval$ is the valence-only effective interaction defined as
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\begin{equation}
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\label{eq:wbasis_val}
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\wbasisval =
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\begin{cases}
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\fbasisval /\twodmrdiagpsi, & \text{if $\twodmrdiagpsival \ne 0$,}
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\\
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\infty, & \text{otherwise,}
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\end{cases}
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\end{equation}
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where $\fbasisval$ is defined as
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\begin{equation}
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\label{eq:fbasis_val}
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\fbasisval
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= \sum_{pq\in \Bas} \sum_{rstu \in \BasFC} \SO{p}{1} \SO{q}{2} \V{pq}{rs} \Gam{rs}{tu} \SO{t}{1} \SO{u}{2},
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\end{equation}
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and $\twodmrdiagpsival$
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\begin{equation}
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\label{eq:twordm_val}
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\twodmrdiagpsival = \sum_{pqrs \in \BasFC} \SO{p}{1} \SO{q}{2} \Gam{pq}{rs} \SO{r}{1} \SO{s}{2},
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\end{equation}
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It is noteworthy that, within the present definition, $\wbasisval$ still tends to the regular Coulomb interaction as $\Bas \to \CBS$.
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\subsection{Generic form and properties of the approximations for $\efuncden{\denr}$ }
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\label{sec:functional}
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\subsubsection{Generic form of the approximated functionals}
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@ -587,9 +622,11 @@ In the case of C$_2$, N$_2$, O$_2$ and F$_2$, the approximation to the FCI energ
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For all geometry and basis sets, the error with respect to actual FCI energies are estimated to be below 0.5 mH.
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In the case of H$_{10}$, the approximation to $\efci$ together with the estimated exact curves are obtained from the data from of Ref. \onlinecite{h10_prx} where the authors performed MRCI+Q calculations with a minimal valence active space as reference (see below for the description of the active space).
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Regarding the complementary basis set energy functional, we use CASSCF wave functions computed with the GAMESS-US software\cite{gamess} to obtain the wave functions $\psibasis$. Therefore, all density related quantities (such as the total densities, different flavors of spin polarizations and on-top pair densities) together with the $\murpsi$ of equation \eqref{eq:def_mur} are obtained at full valence CASSCF level.
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Regarding the complementary basis set energy functional, we use a full valence CASSCF wave functions computed with the GAMESS-US software\cite{gamess} to obtain the wave functions $\psibasis$. Therefore, all density related quantities (such as the total densities, different flavors of spin polarizations and on-top pair densities) together with the $\murpsi$ of equation \eqref{eq:def_mur} are obtained at full valence CASSCF level.
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These CASSCF wave functions correspond to the following active spaces: ten electrons in ten orbitals for H$_{10}$, 8 electrons in 8 electrons for C$_2$, 10 electrons in 8 orbitals for N$_2$, twelve electrons in eight orbitals for O$_2$ and forteen electrons in eight orbitals for F$_2$.
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Also, as the frozen core approximation is used in all near FCI calculations, we use the corresponding valence-only complementary functionals. Therefore, all density related quantities exclude any contribution from the core $1s$ orbitals, and the range-separation parameter is taken as the one defined in equation \eqref{eq:def_mur_val}.
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\subsection{Dissociation of equally distant H$_{10}$ chains}
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The study of equally distant H$_{10}$ chains is a good prototype for the study of strong correlation regime as it consists in the simultaneous breaking of 10 covalent $\sigma$ bonds which all interact with each other. Also, being a relatively small system, benchmark calculations can be performed at near CBS values can be obtained (see Ref. \onlinecite{h10_prx} for detailed study of that problem).
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@ -601,16 +638,22 @@ More quantitatively, the values of $D_0$ are within the chemical accuracy (\text
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Regarding in more details the performance of the different types of approximated functionals, the results show that the PBE-ot-$\tilde{\zeta}$ and PBE-ot-$0{\zeta}$ are very similar (the maximal difference being 0.3 mH on $D_0$), and they give slightly more accurate than the PBE-UEG-$\tilde{\zeta}$.
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These observations bring two important clues on the role of the different physical ingredients used in the functionals:
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i) the explicit use of the on-top pair density coming from the CASSCF wave function (see equation \eqref{eq:def_n2extrap}) is preferable to the use of the on-top pair density based on the UEG (see equation \eqref{eq:def_n2ueg}),
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ii) removing the dependence on any kind of spin polarizations does not lead to significant loss of accuracy once that a minimal description of the on-top pair density of the system is used.
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ii) removing the dependence on any kind of spin polarizations does not lead to significant loss of accuracy provided that one uses a qualitatively correct on-top pair density. The point ii) is important as it shows that the use of the spin-polarization in density functional approximations (DFA) essentially plays the role of the effect of the on-top pair density.
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\subsection{Dissociation of C$_2$, N$_2$, O$_2$ and F$_2$}
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The study of C$_2$, N$_2$, O$_2$ and F$_2$ molecules are complementary to the H$_{10}$ system for the present study as the level of strong correlation increases while stretching the bond similarly to the case of H$_{10}$, but also these systems exhibit more important and versatile types of weak correlations due to the larger number of electrons. Indeed, the short-range correlation effects are known to play a strong differential effect on the computation of $D_0$, while the shape of the curve far from the equilibrium geometry is governed by dispersion forces which are medium to long-range weak correlation effects. Also, O$_2$ exhibit a triplet ground state and therefore is good check for the performance of the dependence on the spin polarization of various types of functionals proposed here.
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The study of C$_2$, N$_2$, O$_2$ and F$_2$ molecules are complementary to the H$_{10}$ system for the present study as the level of strong correlation increases while stretching the bond similarly to the case of H$_{10}$, but also these systems exhibit more important and versatile types of weak correlations due to the larger number of electrons. Indeed, the short-range correlation effects are known to play a strong differential effect on the computation of $D_0$, while the shape of the curve far from the equilibrium geometry is governed by dispersion forces which are medium to long-range weak correlation effects.
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Also, O$_2$ exhibit a triplet ground state and therefore is good check for the performance of the dependence on the spin polarization of various types of functionals proposed here.
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We report in figures \ref{fig:C2_avdz}, \ref{fig:N2_avdz}, \ref{fig:O2_avdz} and \ref{fig:F2_avdz} (\ref{fig:C2_avtz}, \ref{fig:N2_avtz}, \ref{fig:O2_avtz} and \ref{fig:F2_avtz}) the potential energy curves computed using the aug-cc-pVDZ (aug-cc-pVTZ) basis sets of N$_2$, O$_2$ and N$_2$, respectively, for different levels of computations. The computation of the atomization energies $D_0$ at each level of theory used here is reported in table \ref{tab:d0}.
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Just as the case of H$_{10}$, the quality of $D_0$ are globally improved and the chemical accuracy is reached at the aug-cc-pVTZ using the PBE-ot-$\tilde{\zeta}$ and PBE-ot-$0{\zeta}$ functionals, which also give very similar results.
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The latter observation confirms that even in the presence of higher electron density, the dependence on the on-top pair density allows to remove the dependence of any kind of spin polarizations.
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We report in figures \ref{fig:C2_avdz}, \ref{fig:N2_avdz}, \ref{fig:O2_avdz} and \ref{fig:F2_avdz} (\ref{fig:C2_avtz}, \ref{fig:N2_avtz}, \ref{fig:O2_avtz} and \ref{fig:F2_avtz}) the potential energy curves computed using the aug-cc-pVDZ (aug-cc-pVTZ) basis sets of C$_2$, N$_2$, O$_2$ and N$_2$, respectively, for different levels of computations. The computation of the atomization energies $D_0$ at each level of theory used here is reported in table \ref{tab:d0}.
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Interestingly, the complementary basis set functional fail provide a noticeable improvement of the PES near twice the equilibrium geometry, both for F$_2$ and N$_2$. Acknowledging that the weak correlation effects in these regions are dominated by dispersion forces which are long-range effects, the failure of the present approximations for the complementary basis set functionals can be understood easily. Indeed, the whole scheme designed here is based on the physics near the electron-electron cusp: the $\murpsi$ is designed by looking at the electron coalescence point and the ECMD functionals are suited for short-range correlation effects. Therefore, the failure of the present basis set correction to describe dispersion forces can be considered as a good behaviour.
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Just as the case of H$_{10}$, the quality of $D_0$ are globally improved by adding the basis set correction and it is remarkable that the PBE-ot-$\tilde{\zeta}$ and PBE-ot-$0{\zeta}$ functionals give very similar results.
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The latter observation confirms that the dependence on the on-top pair density allows to remove the dependence of any kind of spin polarizations for a quite wide spread of electron density and also for purely high spin systems as O$_2$.
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More quantitatively, an error below 1.0 mH on the estimated exact valence-only $D_0$ is found for N$_2$, O$_2$ and F$_2$ in aug-cc-pVTZ with the PBE-ot-$0{\zeta}$ functional, whereas such a result is far from reach within the same basis set at near FCI level.
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In the case of C$_2$ in the aug-cc-pVTZ basis set, an error of about 5.5 mH is found with respect to the estimated exact $D_0$. Such an error is remarkably large with respect to the other diatomic molecules studied here and might be associated to the level of strong correlation of the C$_2$ molecule.
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Regarding now the performance of the basis set correction along the whole PES, it is interesting to notice that it fails to provide a noticeable improvement of the PES far from the equilibrium geometry.
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Acknowledging that the weak correlation effects in these regions are dominated by dispersion forces which are long-range effects, the failure of the present approximations for the complementary basis set functionals can be understood easily. Indeed, the whole scheme designed here is based on the physics near the electron-electron cusp: the $\murpsi$ is designed by looking at the electron coalescence point and the ECMD functionals are suited for short-range correlation effects. Therefore, the failure of the present basis set correction to describe dispersion forces can be considered as a good behaviour.
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\begin{table*}
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\label{tab:d0}
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@ -756,7 +799,15 @@ F$_2$, aug-cc-pvtz & 59.3$/$2.9 & 61.2$/$1.0 &
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\section{Conclusion}
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\label{sec:conclusion}
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In the present paper we have extended the recently proposed DFT-based basis set correction to strongly correlated systems.
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We studied the H$_{10}$, C$_2$, N$_2$, O$_2$ and F$_2$ linear molecules up to full dissociation limits at near FCI level in increasing basis sets, and investigated how the basis set correction affect the convergence toward the CBS limits of the PES of these molecular systems.
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The DFT-based basis set correction rely on three aspects: i) the definition of an effective non-divergent electron-electron interaction obtained from the expectation value over a wave function $\psibasis$ of the regular coulomb interaction projected into an incomplete basis set $\basis$, ii) the fitting of such effective interaction with a long-range interaction used in RS-DFT, iii) the use of complementary correlation functional of RS-DFT.
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In the present paper, we investigated points i) and iii) in order to to properly investigate atomization energies.
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In this context, we propose a new scheme to design functionals fulfilling a) $S_z$ invariance, b) size extensivity. To achieve such requirements we proposed to use CASSCF wave functions leading to extensive energies, and to develop functionals using only $S_z$ invariant density-related quantities.
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The development of new $S_z$ invariant and size extensive functionals has lead us to investigate the role of two related quantities: the spin-polarization and the on-top pair density.
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To achieve $S_z$ invariant in the context of DFT based on multi-configurational wave functions, an effective spin polarization depending on the total density and on-top pair density is commonly used. Nevertheless, such an effective spin density can be considered as \textit{ad hoc} as its expression is formally valid only for a single-determinant wave function and it can become complex for multi-configurational wave functions. Based on the previous work of some of the present authors, we use functionals depending \textit{explicitly} on the on-top pair density.
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\bibliography{srDFT_SC}
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345.148 197.898 m 345.148 194.199 l S Q
|
||||
q 1 0 0 -1 0 216 cm
|
||||
345.148 10.75 m 345.148 14.449 l S Q
|
||||
BT
|
||||
8 0 0 8 341.308594 5.800781 Tm
|
||||
/f-0-0 1 Tf
|
||||
( 5)Tj
|
||||
( 4)Tj
|
||||
ET
|
||||
q 1 0 0 -1 0 216 cm
|
||||
38.75 10.75 306.398 187.148 re S Q
|
||||
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|
||||
q 1 0 0 -1 0 216 cm
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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||||
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|
||||
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||||
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||||
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|
||||
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||||
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||||
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||||
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||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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||||
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|
||||
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||||
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||||
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|
||||
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|
||||
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||||
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|
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||||
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|
||||
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||||
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|
||||
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|
||||
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|
||||
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|
||||
l 339.398 23.551 l 342.25 22.699 l 345.148 21.852 l S Q
|
||||
0 g
|
||||
BT
|
||||
8 0 0 8 271.570312 42.050781 Tm
|
||||
@ -615,66 +588,62 @@ BT
|
||||
ET
|
||||
0 0.619608 0.45098 rg
|
||||
q 1 0 0 -1 0 216 cm
|
||||
76.648 94.352 m 79.648 97.352 l S Q
|
||||
58.148 94.352 m 61.148 97.352 l S Q
|
||||
q 1 0 0 -1 0 216 cm
|
||||
76.648 97.352 m 79.648 94.352 l S Q
|
||||
58.148 97.352 m 61.148 94.352 l S Q
|
||||
q 1 0 0 -1 0 216 cm
|
||||
89.801 148.648 m 92.801 151.648 l S Q
|
||||
79.051 148.648 m 82.051 151.648 l S Q
|
||||
q 1 0 0 -1 0 216 cm
|
||||
89.801 151.648 m 92.801 148.648 l S Q
|
||||
79.051 151.648 m 82.051 148.648 l S Q
|
||||
q 1 0 0 -1 0 216 cm
|
||||
105.648 169.449 m 108.648 172.449 l S Q
|
||||
104.301 169.449 m 107.301 172.449 l S Q
|
||||
q 1 0 0 -1 0 216 cm
|
||||
105.648 172.449 m 108.648 169.449 l S Q
|
||||
104.301 172.449 m 107.301 169.449 l S Q
|
||||
q 1 0 0 -1 0 216 cm
|
||||
116.051 167.5 m 119.051 170.5 l S Q
|
||||
120.801 167.5 m 123.801 170.5 l S Q
|
||||
q 1 0 0 -1 0 216 cm
|
||||
116.051 170.5 m 119.051 167.5 l S Q
|
||||
120.801 170.5 m 123.801 167.5 l S Q
|
||||
q 1 0 0 -1 0 216 cm
|
||||
133.551 150.801 m 136.551 153.801 l S Q
|
||||
148.648 150.801 m 151.648 153.801 l S Q
|
||||
q 1 0 0 -1 0 216 cm
|
||||
133.551 153.801 m 136.551 150.801 l S Q
|
||||
148.648 153.801 m 151.648 150.801 l S Q
|
||||
q 1 0 0 -1 0 216 cm
|
||||
168.551 101.699 m 171.551 104.699 l S Q
|
||||
204.398 101.699 m 207.398 104.699 l S Q
|
||||
q 1 0 0 -1 0 216 cm
|
||||
168.551 104.699 m 171.551 101.699 l S Q
|
||||
204.398 104.699 m 207.398 101.699 l S Q
|
||||
q 1 0 0 -1 0 216 cm
|
||||
256.102 20.352 m 259.102 23.352 l S Q
|
||||
343.648 20.352 m 346.648 23.352 l S Q
|
||||
q 1 0 0 -1 0 216 cm
|
||||
256.102 23.352 m 259.102 20.352 l S Q
|
||||
q 1 0 0 -1 0 216 cm
|
||||
343.648 11.352 m 346.648 14.352 l S Q
|
||||
q 1 0 0 -1 0 216 cm
|
||||
343.648 14.352 m 346.648 11.352 l S Q
|
||||
343.648 23.352 m 346.648 20.352 l S Q
|
||||
q 1 0 0 -1 0 216 cm
|
||||
321.398 169.449 m 324.398 172.449 l S Q
|
||||
q 1 0 0 -1 0 216 cm
|
||||
321.398 172.449 m 324.398 169.449 l S Q
|
||||
0 g
|
||||
q 1 0 0 -1 0 216 cm
|
||||
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||||
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||||
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|
||||
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||||
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||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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||||
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||||
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||||
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|
||||
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||||
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||||
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|
||||
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|
||||
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|
||||
13.801 l 334.352 13.949 l 337.051 14.102 l 342.449 14.398 l 345.148 14.551
|
||||
l S Q
|
||||
59.648 115.949 m 62.5 124.051 l 65.398 132.051 l 68.301 139.801 l 71.199
|
||||
147.199 l 74.051 154.102 l 76.949 160.398 l 79.852 165.949 l 82.699 170.699
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
134.602 174.801 l 137.5 172.801 l 140.398 170.699 l 143.25 168.5 l 146.148
|
||||
166.148 l 149.051 163.801 l 151.949 161.352 l 154.801 158.852 l 157.699
|
||||
156.25 l 160.602 153.648 l 163.449 151.051 l 166.352 148.352 l 169.25 145.648
|
||||
l 172.102 142.949 l 175 140.199 l 177.898 137.398 l 180.75 134.648 l 183.648
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
29.148 l 333.602 28.148 l 336.5 27.148 l 339.398 26.199 l 342.25 25.25
|
||||
l 345.148 24.398 l S Q
|
||||
BT
|
||||
8 0 0 8 232.050781 32.722656 Tm
|
||||
/f-0-0 1 Tf
|
||||
@ -685,56 +654,54 @@ BT
|
||||
(/avdz)Tj
|
||||
ET
|
||||
q 1 0 0 -1 0 216 cm
|
||||
76.648 116.449 m 78.148 114.449 l 79.648 116.449 l h
|
||||
76.648 116.449 m S Q
|
||||
58.148 116.449 m 59.648 114.449 l 61.148 116.449 l h
|
||||
58.148 116.449 m S Q
|
||||
q 1 0 0 -1 0 216 cm
|
||||
89.801 167.699 m 91.301 165.699 l 92.801 167.699 l h
|
||||
89.801 167.699 m S Q
|
||||
79.051 167.699 m 80.551 165.699 l 82.051 167.699 l h
|
||||
79.051 167.699 m S Q
|
||||
q 1 0 0 -1 0 216 cm
|
||||
105.648 185.602 m 107.148 183.602 l 108.648 185.602 l h
|
||||
105.648 185.602 m S Q
|
||||
104.301 185.602 m 105.801 183.602 l 107.301 185.602 l h
|
||||
104.301 185.602 m S Q
|
||||
q 1 0 0 -1 0 216 cm
|
||||
116.051 182.148 m 117.551 180.148 l 119.051 182.148 l h
|
||||
116.051 182.148 m S Q
|
||||
120.801 182.148 m 122.301 180.148 l 123.801 182.148 l h
|
||||
120.801 182.148 m S Q
|
||||
q 1 0 0 -1 0 216 cm
|
||||
133.551 163.352 m 135.051 161.352 l 136.551 163.352 l h
|
||||
133.551 163.352 m S Q
|
||||
148.648 163.352 m 150.148 161.352 l 151.648 163.352 l h
|
||||
148.648 163.352 m S Q
|
||||
q 1 0 0 -1 0 216 cm
|
||||
168.551 111.148 m 170.051 109.148 l 171.551 111.148 l h
|
||||
168.551 111.148 m S Q
|
||||
204.398 111.148 m 205.898 109.148 l 207.398 111.148 l h
|
||||
204.398 111.148 m S Q
|
||||
q 1 0 0 -1 0 216 cm
|
||||
256.102 24.898 m 257.602 22.898 l 259.102 24.898 l h
|
||||
256.102 24.898 m S Q
|
||||
q 1 0 0 -1 0 216 cm
|
||||
343.648 15.051 m 345.148 13.051 l 346.648 15.051 l h
|
||||
343.648 15.051 m S Q
|
||||
343.648 24.898 m 345.148 22.898 l 346.648 24.898 l h
|
||||
343.648 24.898 m S Q
|
||||
q 1 0 0 -1 0 216 cm
|
||||
321.398 180.75 m 322.898 178.75 l 324.398 180.75 l h
|
||||
321.398 180.75 m S Q
|
||||
0.898039 0.117647 0.0627451 rg
|
||||
q 1 0 0 -1 0 216 cm
|
||||
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|
||||
168.352 l 91.648 175.75 l 94.352 181.352 l 97 185.301 l 99.699 187.949 l
|
||||
102.398 189.398 l 105.102 189.949 l 107.801 189.898 l 110.5 189.301 l 113.199
|
||||
188.25 l 115.898 186.75 l 118.602 184.852 l 121.301 182.5 l 124 179.801
|
||||
l 126.699 176.801 l 129.398 173.5 l 132.102 170 l 134.801 166.352 l 137.5
|
||||
162.551 l 140.199 158.699 l 142.852 154.699 l 145.551 150.648 l 148.25
|
||||
146.551 l 150.949 142.449 l 153.648 138.301 l 156.352 134.148 l 159.051
|
||||
130 l 161.75 125.898 l 164.449 121.852 l 167.148 117.898 l 169.852 114 l
|
||||
172.551 110.199 l 175.25 106.5 l 177.949 102.898 l 180.648 99.398 l 183.352
|
||||
96 l 186.051 92.699 l 188.699 89.5 l 191.398 86.398 l 194.102 83.352 l
|
||||
196.801 80.398 l 199.5 77.602 l 202.199 74.801 l 204.898 72.148 l 207.602
|
||||
69.551 l 210.301 67.051 l 213 64.648 l 215.699 62.301 l 218.398 60.051
|
||||
l 221.102 57.852 l 223.801 55.75 l 226.5 53.699 l 229.199 51.75 l 231.852
|
||||
49.852 l 234.551 48.051 l 237.25 46.301 l 239.949 44.648 l 242.648 43 l
|
||||
245.352 41.5 l 248.051 40 l 250.75 38.602 l 253.449 37.25 l 256.148 35.949
|
||||
l 258.852 34.699 l 261.551 33.551 l 264.25 32.398 l 266.949 31.352 l 269.648
|
||||
30.352 l 272.352 29.352 l 275.051 28.449 l 277.699 27.602 l 280.398 26.75
|
||||
l 283.102 26 l 285.801 25.25 l 288.5 24.551 l 291.199 23.898 l 293.898
|
||||
23.301 l 296.602 22.699 l 299.301 22.148 l 304.699 21.148 l 307.398 20.699
|
||||
l 310.102 20.25 l 312.801 19.852 l 315.5 19.449 l 318.199 19.102 l 320.898
|
||||
18.75 l 323.551 18.449 l 326.25 18.148 l 328.949 17.852 l 331.648 17.602
|
||||
l 334.352 17.352 l 337.051 17.051 l 339.75 16.852 l 345.148 16.352 l S Q
|
||||
59.648 127.25 m 62.5 134.852 l 65.398 142.301 l 68.301 149.551 l 71.199
|
||||
156.398 l 74.051 162.801 l 76.949 168.648 l 79.852 173.75 l 82.699 178.051
|
||||
l 85.602 181.551 l 88.5 184.352 l 91.352 186.5 l 94.25 188.051 l 97.148
|
||||
189.102 l 100 189.75 l 102.898 190 l 105.801 189.949 l 108.648 189.699
|
||||
l 111.551 189.199 l 114.449 188.551 l 117.301 187.648 l 120.199 186.551
|
||||
l 123.102 185.301 l 125.949 183.801 l 128.852 182.148 l 131.75 180.352 l
|
||||
134.602 178.398 l 137.5 176.301 l 140.398 174.102 l 143.25 171.801 l 146.148
|
||||
169.449 l 149.051 166.949 l 151.949 164.449 l 154.801 161.898 l 157.699
|
||||
159.25 l 160.602 156.602 l 163.449 153.898 l 166.352 151.199 l 169.25 148.449
|
||||
l 172.102 145.699 l 175 142.898 l 177.898 140.148 l 180.75 137.352 l 183.648
|
||||
134.551 l 186.551 131.75 l 189.398 129 l 192.301 126.25 l 195.199 123.5
|
||||
l 198.051 120.801 l 200.949 118.148 l 203.852 115.5 l 206.699 112.949 l
|
||||
209.602 110.398 l 212.5 107.898 l 215.352 105.449 l 218.25 103.051 l 221.148
|
||||
100.648 l 224 98.352 l 226.898 96.051 l 229.801 93.852 l 232.699 91.648
|
||||
l 235.551 89.5 l 238.449 87.398 l 241.352 85.352 l 244.199 83.301 l 247.102
|
||||
81.352 l 250 79.398 l 252.852 77.5 l 255.75 75.602 l 258.648 73.801 l 261.5
|
||||
72 l 264.398 70.25 l 267.301 68.551 l 270.148 66.898 l 273.051 65.25 l
|
||||
275.949 63.648 l 278.801 62.102 l 281.699 60.602 l 284.602 59.102 l 287.449
|
||||
57.648 l 290.352 56.199 l 293.25 54.852 l 296.102 53.5 l 299 52.148 l 301.898
|
||||
50.898 l 304.75 49.602 l 307.648 48.398 l 310.551 47.199 l 313.449 46.051
|
||||
l 316.301 44.949 l 319.199 43.852 l 322.102 42.75 l 324.949 41.75 l 327.852
|
||||
40.699 l 330.75 39.75 l 333.602 38.801 l 336.5 37.852 l 339.398 37 l 342.25
|
||||
36.102 l 345.148 35.25 l S Q
|
||||
0 g
|
||||
BT
|
||||
8 0 0 8 283.5 23.449219 Tm
|
||||
@ -742,46 +709,41 @@ BT
|
||||
(Exact)Tj
|
||||
ET
|
||||
0.898039 0.117647 0.0627451 rg
|
||||
79.648 88.75 m 79.648 86.75 76.648 86.75 76.648 88.75 c 76.648 90.75 79.648
|
||||
90.75 79.648 88.75 c f
|
||||
61.148 88.75 m 61.148 86.75 58.148 86.75 58.148 88.75 c 58.148 90.75 61.148
|
||||
90.75 61.148 88.75 c f
|
||||
q 1 0 0 -1 0 216 cm
|
||||
79.648 127.25 m 79.648 129.25 76.648 129.25 76.648 127.25 c 76.648 125.25
|
||||
79.648 125.25 79.648 127.25 c S Q
|
||||
92.801 41.102 m 92.801 39.102 89.801 39.102 89.801 41.102 c 89.801 43.102
|
||||
92.801 43.102 92.801 41.102 c f
|
||||
61.148 127.25 m 61.148 129.25 58.148 129.25 58.148 127.25 c 58.148 125.25
|
||||
61.148 125.25 61.148 127.25 c S Q
|
||||
82.051 41.102 m 82.051 39.102 79.051 39.102 79.051 41.102 c 79.051 43.102
|
||||
82.051 43.102 82.051 41.102 c f
|
||||
q 1 0 0 -1 0 216 cm
|
||||
92.801 174.898 m 92.801 176.898 89.801 176.898 89.801 174.898 c 89.801
|
||||
172.898 92.801 172.898 92.801 174.898 c S Q
|
||||
108.648 26.051 m 108.648 24.051 105.648 24.051 105.648 26.051 c 105.648
|
||||
28.051 108.648 28.051 108.648 26.051 c f
|
||||
82.051 174.898 m 82.051 176.898 79.051 176.898 79.051 174.898 c 79.051
|
||||
172.898 82.051 172.898 82.051 174.898 c S Q
|
||||
107.301 26.051 m 107.301 24.051 104.301 24.051 104.301 26.051 c 104.301
|
||||
28.051 107.301 28.051 107.301 26.051 c f
|
||||
q 1 0 0 -1 0 216 cm
|
||||
108.648 189.949 m 108.648 191.949 105.648 191.949 105.648 189.949 c 105.648
|
||||
187.949 108.648 187.949 108.648 189.949 c S Q
|
||||
119.051 30.352 m 119.051 28.352 116.051 28.352 116.051 30.352 c 116.051
|
||||
32.352 119.051 32.352 119.051 30.352 c f
|
||||
107.301 189.949 m 107.301 191.949 104.301 191.949 104.301 189.949 c 104.301
|
||||
187.949 107.301 187.949 107.301 189.949 c S Q
|
||||
123.801 30.352 m 123.801 28.352 120.801 28.352 120.801 30.352 c 120.801
|
||||
32.352 123.801 32.352 123.801 30.352 c f
|
||||
q 1 0 0 -1 0 216 cm
|
||||
119.051 185.648 m 119.051 187.648 116.051 187.648 116.051 185.648 c 116.051
|
||||
183.648 119.051 183.648 119.051 185.648 c S Q
|
||||
136.551 50 m 136.551 48 133.551 48 133.551 50 c 133.551 52 136.551 52 136.551
|
||||
123.801 185.648 m 123.801 187.648 120.801 187.648 120.801 185.648 c 120.801
|
||||
183.648 123.801 183.648 123.801 185.648 c S Q
|
||||
151.648 50 m 151.648 48 148.648 48 148.648 50 c 148.648 52 151.648 52 151.648
|
||||
50 c f
|
||||
q 1 0 0 -1 0 216 cm
|
||||
136.551 166 m 136.551 168 133.551 168 133.551 166 c 133.551 164 136.551
|
||||
164 136.551 166 c S Q
|
||||
171.551 102.301 m 171.551 100.301 168.551 100.301 168.551 102.301 c 168.551
|
||||
104.301 171.551 104.301 171.551 102.301 c f
|
||||
151.648 166 m 151.648 168 148.648 168 148.648 166 c 148.648 164 151.648
|
||||
164 151.648 166 c S Q
|
||||
207.398 102.301 m 207.398 100.301 204.398 100.301 204.398 102.301 c 204.398
|
||||
104.301 207.398 104.301 207.398 102.301 c f
|
||||
q 1 0 0 -1 0 216 cm
|
||||
171.551 113.699 m 171.551 115.699 168.551 115.699 168.551 113.699 c 168.551
|
||||
111.699 171.551 111.699 171.551 113.699 c S Q
|
||||
259.102 180.75 m 259.102 178.75 256.102 178.75 256.102 180.75 c 256.102
|
||||
182.75 259.102 182.75 259.102 180.75 c f
|
||||
207.398 113.699 m 207.398 115.699 204.398 115.699 204.398 113.699 c 204.398
|
||||
111.699 207.398 111.699 207.398 113.699 c S Q
|
||||
346.648 180.75 m 346.648 178.75 343.648 178.75 343.648 180.75 c 343.648
|
||||
182.75 346.648 182.75 346.648 180.75 c f
|
||||
q 1 0 0 -1 0 216 cm
|
||||
259.102 35.25 m 259.102 37.25 256.102 37.25 256.102 35.25 c 256.102 33.25
|
||||
259.102 33.25 259.102 35.25 c S Q
|
||||
346.648 199.648 m 346.648 197.648 343.648 197.648 343.648 199.648 c 343.648
|
||||
201.648 346.648 201.648 346.648 199.648 c f
|
||||
q 1 0 0 -1 0 216 cm
|
||||
346.648 16.352 m 346.648 18.352 343.648 18.352 343.648 16.352 c 343.648
|
||||
14.352 346.648 14.352 346.648 16.352 c S Q
|
||||
346.648 35.25 m 346.648 37.25 343.648 37.25 343.648 35.25 c 343.648 33.25
|
||||
346.648 33.25 346.648 35.25 c S Q
|
||||
324.398 26.449 m 324.398 24.449 321.398 24.449 321.398 26.449 c 321.398
|
||||
28.449 324.398 28.449 324.398 26.449 c f
|
||||
q 1 0 0 -1 0 216 cm
|
||||
|
||||
File diff suppressed because it is too large
Load Diff
@ -8,7 +8,7 @@ FILE=data_${METHOD}_${BASIS}E_${TYPE}
|
||||
OUT=${METHOD}_${BASIS}E_${TYPE}
|
||||
#lt -1
|
||||
cat << EOF > pouet.gp
|
||||
set xrange [:5]
|
||||
set xrange [1.8:4]
|
||||
set key bottom
|
||||
plot '${FILE}' using 1:2 smooth cspline notitle lt 2 , "" using 1:2 w p lt 2 ps 0.5 title "${WF}/$BASIS"
|
||||
replot '${FILE}' using 1:5 smooth cspline notitle lt 8 , "" using 1:5 w p lt 8 ps 0.5 title "${WF}+PBEot0{/Symbol z}/$BASIS"
|
||||
@ -24,8 +24,8 @@ if [[ $METHOD == "DFT" ]]; then
|
||||
|
||||
OUT=${METHOD}_${BASIS}E_${TYPE}_zoom
|
||||
cat << EOF > pouet.gp
|
||||
set xrange [2.5:3.5]
|
||||
set key left
|
||||
set xrange [2.:2.6]
|
||||
set key right
|
||||
plot '${FILE}' using 1:2 smooth cspline notitle lt 2 , "" using 1:2 w p lt 2 ps 0.5 title "${WF}/$BASIS"
|
||||
replot '${FILE}' using 1:3 smooth cspline notitle lt 9 , "" using 1:3 w p lt 9 ps 0.5 title "${WF}+PBE-UEG~{/Symbol z}{.8-}/$BASIS"
|
||||
replot '${FILE}' using 1:4 smooth cspline notitle lt 4 , "" using 1:4 w p lt 4 ps 0.5 title "${WF}+PBEot~{/Symbol z}{.8-}/$BASIS"
|
||||
|
||||
@ -6,4 +6,3 @@
|
||||
3.00 -150.2314
|
||||
4.00 -150.1476
|
||||
5.00 -150.1274
|
||||
10.0 -150.1214
|
||||
|
||||
Loading…
Reference in New Issue
Block a user