From 942ba298753a1eb230d1bdf297287d0527d0b891 Mon Sep 17 00:00:00 2001 From: Emmanuel Giner Date: Wed, 20 Nov 2019 21:00:10 +0100 Subject: [PATCH] working on the conclusion ... --- Manuscript/srDFT_SC.out | 32 +- Manuscript/srDFT_SC.tex | 67 +- new/O2_avdz/plots/DFT_avdzE_error.eps | 2 +- new/O2_avdz/plots/DFT_avdzE_relat.eps | 312 ++++---- new/O2_avdz/plots/DFT_avdzE_relat_zoom.eps | 887 ++++++++++++--------- new/O2_avdz/plots/plot.sh | 6 +- new/O2_avtz/data/exact-O2 | 1 - 7 files changed, 707 insertions(+), 600 deletions(-) diff --git a/Manuscript/srDFT_SC.out b/Manuscript/srDFT_SC.out index 6d2d062..7c6d559 100644 --- a/Manuscript/srDFT_SC.out +++ b/Manuscript/srDFT_SC.out @@ -5,18 +5,20 @@ \BOOKMARK [2][-]{section*.5}{Basic formal equations}{section*.4}% 5 \BOOKMARK [2][-]{section*.6}{Definition of an effective interaction within B}{section*.4}% 6 \BOOKMARK [2][-]{section*.7}{Definition of a range-separation parameter varying in real space}{section*.4}% 7 -\BOOKMARK [2][-]{section*.8}{Generic form and properties of the approximations for B[n\(r\)] }{section*.4}% 8 -\BOOKMARK [3][-]{section*.9}{Generic form of the approximated functionals}{section*.8}% 9 -\BOOKMARK [3][-]{section*.10}{Properties of approximated functionals}{section*.8}% 10 -\BOOKMARK [2][-]{section*.11}{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*.13}{Condition for the functional XB[n,,s,n\(2\),B] to obtain Sz invariance}{section*.11}% 13 -\BOOKMARK [3][-]{section*.14}{Conditions on B for the extensivity}{section*.11}% 14 -\BOOKMARK [2][-]{section*.15}{Different types of approximations for the functional}{section*.4}% 15 -\BOOKMARK [3][-]{section*.16}{Definition of the protocol to design functionals}{section*.15}% 16 -\BOOKMARK [3][-]{section*.17}{Definition of functionals with good formal properties}{section*.15}% 17 -\BOOKMARK [1][-]{section*.18}{Results for the C2, N2, O2, F2 and H10 potential energy curves}{section*.2}% 18 -\BOOKMARK [2][-]{section*.19}{Computational details}{section*.18}% 19 -\BOOKMARK [2][-]{section*.20}{Dissociation of equally distant H10 chains}{section*.18}% 20 -\BOOKMARK [2][-]{section*.21}{Dissociation of C2, N2, O2 and F2}{section*.18}% 21 -\BOOKMARK [1][-]{section*.22}{Conclusion}{section*.2}% 22 +\BOOKMARK [3][-]{section*.8}{General definition}{section*.7}% 8 +\BOOKMARK [3][-]{section*.9}{Frozen core density approximation}{section*.7}% 9 +\BOOKMARK [2][-]{section*.10}{Generic form and properties of the approximations for B[n\(r\)] }{section*.4}% 10 +\BOOKMARK [3][-]{section*.11}{Generic form of the approximated functionals}{section*.10}% 11 +\BOOKMARK [3][-]{section*.12}{Properties of approximated functionals}{section*.10}% 12 +\BOOKMARK [2][-]{section*.13}{Requirements for the approximated functionals in the strong correlation regime}{section*.4}% 13 +\BOOKMARK [3][-]{section*.14}{Requirements: separability of the energies and Sz invariance}{section*.13}% 14 +\BOOKMARK [3][-]{section*.15}{Condition for the functional XB[n,,s,n\(2\),B] to obtain Sz invariance}{section*.13}% 15 +\BOOKMARK [3][-]{section*.16}{Conditions on B for the extensivity}{section*.13}% 16 +\BOOKMARK [2][-]{section*.17}{Different types of approximations for the functional}{section*.4}% 17 +\BOOKMARK [3][-]{section*.18}{Definition of the protocol to design functionals}{section*.17}% 18 +\BOOKMARK [3][-]{section*.19}{Definition of functionals with good formal properties}{section*.17}% 19 +\BOOKMARK [1][-]{section*.20}{Results for the C2, N2, O2, F2 and H10 potential energy curves}{section*.2}% 20 +\BOOKMARK [2][-]{section*.21}{Computational details}{section*.20}% 21 +\BOOKMARK [2][-]{section*.22}{Dissociation of equally distant H10 chains}{section*.20}% 22 +\BOOKMARK [2][-]{section*.23}{Dissociation of C2, N2, O2 and F2}{section*.20}% 23 +\BOOKMARK [1][-]{section*.24}{Conclusion}{section*.2}% 24 diff --git a/Manuscript/srDFT_SC.tex b/Manuscript/srDFT_SC.tex index 69a8454..bb717f4 100644 --- a/Manuscript/srDFT_SC.tex +++ b/Manuscript/srDFT_SC.tex @@ -35,6 +35,8 @@ \newcommand{\phix}[2]{\phi_{#1}(\bfr{#2})} \newcommand{\phixprim}[2]{\phi_{#1}(\bfr{#2}')} +\newcommand{\CBS}{\text{CBS}} + %operators \newcommand{\elemm}[3]{{\ensuremath{\bra{#1}{#2}\ket{#3}}\xspace}} @@ -83,6 +85,7 @@ \newcommand{\emuldaval}[0]{\bar{\varepsilon}^{\text{sr},\text{unif}}_{\text{c,md}}\left(\denval ({\bf r});\murval;\wf{}{\Bas})\right)} \newcommand{\ecmd}[0]{\varepsilon^{\text{c,md}}_{\text{PBE}}} \newcommand{\psibasis}[0]{\Psi^{\basis}} +\newcommand{\BasFC}{\mathcal{A}} %pbeuegxiHF \newcommand{\pbeuegxihf}{\text{PBE-UEG-}\zeta\text{-HF}^\Bas} @@ -389,7 +392,7 @@ More specifically, the effective interaction associated to a given wave function \end{equation} where $\twodmrdiagpsi$ is the opposite spin two-body density associated to $\wf{}{\Bas}$ \begin{equation} - \twodmrdiagpsi = \sum_{pqrs} \SO{p}{1} \SO{q}{2} \Gam{pq}{rs} \SO{r}{1} \SO{s}{2}, + \twodmrdiagpsi = \sum_{pqrs \in \Bas} \SO{p}{1} \SO{q}{2} \Gam{pq}{rs} \SO{r}{1} \SO{s}{2}, \end{equation} $\Gam{pq}{rs} = 2 \mel*{\wf{}{\Bas}}{ \aic{r_\downarrow}\aic{s_\uparrow}\ai{q_\uparrow}\ai{p_\downarrow}}{\wf{}{\Bas}}$ its associated two-body tensor, $\SO{p}{}$ are the spatial orthonormal orbitals, \begin{equation} @@ -411,6 +414,7 @@ The condition of equation \eqref{eq:cbs_wbasis} is fundamental as it guarantees \subsection{Definition of a range-separation parameter varying in real space} \label{sec:mur} +\subsubsection{General definition} 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 $\mu$ \begin{equation} \label{eq:weelr} @@ -432,6 +436,37 @@ Because of the very definition of $\wbasis$, one has the following properties at \end{equation} which is fundamental to guarantee the good behaviour of the theory at the CBS limit. +\subsubsection{Frozen core density approximation} +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. +We split the basis set as $\Bas = \Cor \bigcup \BasFC$ (where $\Cor$ and $\BasFC$ are the sets of core and active MOs, respectively) +and define the valence only range separation parameter +\begin{equation} + \label{eq:def_mur_val} + \murpsival = \frac{\sqrt{\pi}}{2} \wbasiscoalval, +\end{equation} +where $\wbasisval$ is the valence-only effective interaction defined as +\begin{equation} + \label{eq:wbasis_val} + \wbasisval = + \begin{cases} + \fbasisval /\twodmrdiagpsi, & \text{if $\twodmrdiagpsival \ne 0$,} +\\ + \infty, & \text{otherwise,} + \end{cases} +\end{equation} +where $\fbasisval$ is defined as +\begin{equation} + \label{eq:fbasis_val} + \fbasisval + = \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}, +\end{equation} +and $\twodmrdiagpsival$ +\begin{equation} + \label{eq:twordm_val} + \twodmrdiagpsival = \sum_{pqrs \in \BasFC} \SO{p}{1} \SO{q}{2} \Gam{pq}{rs} \SO{r}{1} \SO{s}{2}, +\end{equation} +It is noteworthy that, within the present definition, $\wbasisval$ still tends to the regular Coulomb interaction as $\Bas \to \CBS$. + \subsection{Generic form and properties of the approximations for $\efuncden{\denr}$ } \label{sec:functional} \subsubsection{Generic form of the approximated functionals} @@ -587,9 +622,11 @@ In the case of C$_2$, N$_2$, O$_2$ and F$_2$, the approximation to the FCI energ For all geometry and basis sets, the error with respect to actual FCI energies are estimated to be below 0.5 mH. 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). -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. +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. 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$_2$. +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}. + \subsection{Dissociation of equally distant H$_{10}$ chains} 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). @@ -601,16 +638,22 @@ More quantitatively, the values of $D_0$ are within the chemical accuracy (\text 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-$\tilde{\zeta}$. These observations bring two important clues on the role of the different physical ingredients used in the functionals: 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}), -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. +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. \subsection{Dissociation of C$_2$, N$_2$, O$_2$ and F$_2$} -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. +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. -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}. -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. -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. +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}. -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. + +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. +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$_2$. +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. +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. + +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. +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. \begin{table*} \label{tab:d0} @@ -756,7 +799,15 @@ F$_2$, aug-cc-pvtz & 59.3$/$2.9 & 61.2$/$1.0 & \section{Conclusion} \label{sec:conclusion} +In the present paper we have extended the recently proposed DFT-based basis set correction to strongly correlated systems. +We studied the H$_{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. +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. +In the present paper, we investigated points i) and iii) in order to to properly investigate atomization energies. +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. + +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. +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. \bibliography{srDFT_SC} diff --git a/new/O2_avdz/plots/DFT_avdzE_error.eps b/new/O2_avdz/plots/DFT_avdzE_error.eps index 02724e8..855c545 100644 --- a/new/O2_avdz/plots/DFT_avdzE_error.eps +++ b/new/O2_avdz/plots/DFT_avdzE_error.eps @@ -1,6 +1,6 @@ %!PS-Adobe-3.0 EPSF-3.0 %%Creator: cairo 1.14.6 (http://cairographics.org) -%%CreationDate: Tue Nov 19 15:22:41 2019 +%%CreationDate: Wed Nov 20 17:22:36 2019 %%Pages: 1 %%DocumentData: Clean7Bit %%LanguageLevel: 2 diff --git a/new/O2_avdz/plots/DFT_avdzE_relat.eps b/new/O2_avdz/plots/DFT_avdzE_relat.eps index 7262ca8..b8c5883 100644 --- a/new/O2_avdz/plots/DFT_avdzE_relat.eps +++ b/new/O2_avdz/plots/DFT_avdzE_relat.eps @@ -1,6 +1,6 @@ %!PS-Adobe-3.0 EPSF-3.0 %%Creator: cairo 1.14.6 (http://cairographics.org) -%%CreationDate: Tue Nov 19 15:22:40 2019 +%%CreationDate: Wed Nov 20 17:22:35 2019 %%Pages: 1 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+731,42 @@ BT ET 0.901961 0.623529 0 rg q 1 0 0 -1 0 216 cm -67.898 174.25 3 3 re S Q +88.301 130.199 3 3 re S Q q 1 0 0 -1 0 216 cm -190.449 99.648 3 3 re S Q +181.051 169.949 3 3 re S Q q 1 0 0 -1 0 216 cm -141.102 36.199 3 3 re S Q +241.5 162.199 3 3 re S Q +q 1 0 0 -1 0 216 cm +343.648 120.398 3 3 re S Q +q 1 0 0 -1 0 216 cm +321.398 36.199 3 3 re S Q 0 g q 1 0 0 -1 0 216 cm -38.75 190.102 m 41.852 188.648 l 44.949 187.199 l 48.051 185.699 l 51.148 - 184.199 l 54.199 182.602 l 57.301 181 l 60.398 179.398 l 63.5 177.75 l -66.602 176.051 l 69.699 174.352 l 72.801 172.648 l 75.898 170.898 l 82.102 - 167.398 l 85.148 165.602 l 91.352 162 l 94.449 160.148 l 97.551 158.352 - l 100.648 156.5 l 103.75 154.602 l 106.852 152.75 l 109.949 150.852 l 113.051 - 148.949 l 116.102 147.051 l 119.199 145.148 l 122.301 143.25 l 125.398 -141.301 l 128.5 139.398 l 131.602 137.449 l 134.699 135.5 l 137.801 133.551 - l 140.898 131.648 l 144 129.699 l 147.051 127.75 l 150.148 125.801 l 153.25 - 123.852 l 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Q +38.75 58.801 m 41.852 63.801 l 44.949 68.801 l 48.051 73.699 l 51.148 78.5 + l 54.199 83.25 l 57.301 87.898 l 60.398 92.449 l 63.5 96.898 l 66.602 101.25 + l 69.699 105.449 l 72.801 109.551 l 75.898 113.551 l 79 117.398 l 82.102 + 121.051 l 85.148 124.602 l 88.25 128 l 91.352 131.25 l 94.449 134.301 l + 97.551 137.199 l 100.648 139.949 l 103.75 142.551 l 106.852 144.949 l 109.949 + 147.25 l 113.051 149.449 l 116.102 151.449 l 119.199 153.352 l 122.301 +155.102 l 125.398 156.75 l 128.5 158.25 l 131.602 159.648 l 134.699 160.949 + l 137.801 162.102 l 140.898 163.199 l 144 164.148 l 147.051 165.051 l 150.148 + 165.801 l 153.25 166.5 l 156.352 167.148 l 159.449 167.648 l 162.551 168.102 + l 165.648 168.5 l 168.75 168.801 l 171.852 169.051 l 174.949 169.25 l 178 + 169.352 l 181.102 169.449 l 184.199 169.5 l 187.301 169.449 l 190.398 169.398 + l 193.5 169.301 l 196.602 169.148 l 199.699 168.949 l 202.801 168.699 l + 205.898 168.398 l 208.949 168.102 l 212.051 167.699 l 215.148 167.301 l + 218.25 166.852 l 221.352 166.352 l 224.449 165.801 l 227.551 165.25 l 230.648 + 164.602 l 233.75 163.949 l 236.852 163.25 l 239.898 162.5 l 243 161.75 +l 246.102 160.949 l 249.199 160.102 l 252.301 159.199 l 255.398 158.301 +l 258.5 157.352 l 261.602 156.352 l 264.699 155.301 l 267.801 154.25 l 270.852 + 153.199 l 273.949 152.051 l 277.051 150.949 l 280.148 149.75 l 286.352 +147.352 l 289.449 146.102 l 292.551 144.801 l 295.648 143.5 l 298.75 142.148 + l 301.801 140.801 l 304.898 139.449 l 308 138.051 l 311.102 136.648 l 314.199 + 135.199 l 317.301 133.75 l 320.398 132.301 l 326.602 129.301 l 329.699 +127.801 l 332.75 126.25 l 335.852 124.699 l 338.949 123.148 l 342.051 121.551 + l 345.148 119.949 l S Q BT -8 0 0 8 51.75 165.972656 Tm +8 0 0 8 232.050781 165.972656 Tm /f-0-0 1 Tf (FCI+PBEot0)Tj /f-0-1 1 Tf @@ -699,60 +775,77 @@ BT (/avdz)Tj ET q 1 0 0 -1 0 216 cm -67.898 175.051 m 69.398 173.051 l 70.898 175.051 l h -67.898 175.051 m S Q +88.301 130.148 m 89.801 128.148 l 91.301 130.148 l h +88.301 130.148 m S Q q 1 0 0 -1 0 216 cm -190.449 100.5 m 191.949 98.5 l 193.449 100.5 l h -190.449 100.5 m S Q +181.051 169.949 m 182.551 167.949 l 184.051 169.949 l h +181.051 169.949 m S Q q 1 0 0 -1 0 216 cm -141.102 47.5 m 142.602 45.5 l 144.102 47.5 l h -141.102 47.5 m S Q +241.5 162.25 m 243 160.25 l 244.5 162.25 l h +241.5 162.25 m S Q +q 1 0 0 -1 0 216 cm +343.648 120.449 m 345.148 118.449 l 346.648 120.449 l h +343.648 120.449 m S Q +q 1 0 0 -1 0 216 cm +321.398 47.5 m 322.898 45.5 l 324.398 47.5 l h +321.398 47.5 m S Q 0.898039 0.117647 0.0627451 rg q 1 0 0 -1 0 216 cm -38.75 195.148 m 41.852 193.648 l 44.949 192.148 l 48.051 190.602 l 51.148 - 189 l 54.199 187.398 l 57.301 185.75 l 60.398 184.051 l 63.5 182.352 l -66.602 180.602 l 69.699 178.898 l 72.801 177.102 l 75.898 175.352 l 79 173.551 - l 82.102 171.699 l 85.148 169.898 l 88.25 168.051 l 91.352 166.199 l 94.449 - 164.352 l 97.551 162.449 l 100.648 160.551 l 103.75 158.648 l 106.852 156.75 - l 109.949 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295.648 52.5 l 298.75 51.199 l 301.801 49.898 l 304.898 48.602 l 311.102 - 46.102 l 314.199 44.852 l 317.301 43.648 l 320.398 42.449 l 326.602 40.051 - l 329.699 38.852 l 332.75 37.699 l 335.852 36.551 l 338.949 35.449 l 342.051 - 34.301 l 345.148 33.199 l S Q +38.75 81.102 m 41.852 85.801 l 44.949 90.398 l 48.051 95 l 51.148 99.449 + l 54.199 103.898 l 57.301 108.199 l 60.398 112.449 l 63.5 116.551 l 66.602 + 120.602 l 69.699 124.5 l 72.801 128.301 l 75.898 131.949 l 79 135.5 l 82.102 + 138.898 l 85.148 142.148 l 88.25 145.25 l 91.352 148.199 l 94.449 151 l + 97.551 153.602 l 100.648 156.051 l 103.75 158.398 l 106.852 160.602 l 109.949 + 162.602 l 113.051 164.551 l 116.102 166.301 l 119.199 167.949 l 122.301 + 169.449 l 125.398 170.852 l 128.5 172.148 l 131.602 173.352 l 134.699 174.398 + l 137.801 175.352 l 140.898 176.25 l 144 177 l 147.051 177.699 l 150.148 + 178.25 l 153.25 178.801 l 156.352 179.199 l 159.449 179.551 l 162.551 179.852 + l 165.648 180.051 l 168.75 180.199 l 171.852 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8 103.199219 156.699219 Tm +8 0 0 8 283.5 156.699219 Tm /f-0-0 1 Tf (Exact)Tj ET 0.898039 0.117647 0.0627451 rg -70.898 36.949 m 70.898 34.949 67.898 34.949 67.898 36.949 c 67.898 38.949 - 70.898 38.949 70.898 36.949 c f +91.301 69.25 m 91.301 67.25 88.301 67.25 88.301 69.25 c 88.301 71.25 91.301 + 71.25 91.301 69.25 c f q 1 0 0 -1 0 216 cm -70.898 179.051 m 70.898 181.051 67.898 181.051 67.898 179.051 c 67.898 -177.051 70.898 177.051 70.898 179.051 c S Q -193.449 111.699 m 193.449 109.699 190.449 109.699 190.449 111.699 c 190.449 - 113.699 193.449 113.699 193.449 111.699 c f +91.301 146.75 m 91.301 148.75 88.301 148.75 88.301 146.75 c 88.301 144.75 + 91.301 144.75 91.301 146.75 c S Q +184.051 35.801 m 184.051 33.801 181.051 33.801 181.051 35.801 c 181.051 + 37.801 184.051 37.801 184.051 35.801 c f q 1 0 0 -1 0 216 cm -193.449 104.301 m 193.449 106.301 190.449 106.301 190.449 104.301 c 190.449 - 102.301 193.449 102.301 193.449 104.301 c S Q -144.102 159.699 m 144.102 157.699 141.102 157.699 141.102 159.699 c 141.102 - 161.699 144.102 161.699 144.102 159.699 c f +184.051 180.199 m 184.051 182.199 181.051 182.199 181.051 180.199 c 181.051 + 178.199 184.051 178.199 184.051 180.199 c S Q +244.5 45.352 m 244.5 43.352 241.5 43.352 241.5 45.352 c 241.5 47.352 244.5 + 47.352 244.5 45.352 c f q 1 0 0 -1 0 216 cm -144.102 56.301 m 144.102 58.301 141.102 58.301 141.102 56.301 c 141.102 - 54.301 144.102 54.301 144.102 56.301 c S Q +244.5 170.648 m 244.5 172.648 241.5 172.648 241.5 170.648 c 241.5 168.648 + 244.5 168.648 244.5 170.648 c S Q +346.648 89 m 346.648 87 343.648 87 343.648 89 c 343.648 91 346.648 91 346.648 + 89 c f +q 1 0 0 -1 0 216 cm +346.648 127 m 346.648 129 343.648 129 343.648 127 c 343.648 125 346.648 + 125 346.648 127 c S Q +324.398 159.699 m 324.398 157.699 321.398 157.699 321.398 159.699 c 321.398 + 161.699 324.398 161.699 324.398 159.699 c f +q 1 0 0 -1 0 216 cm +324.398 56.301 m 324.398 58.301 321.398 58.301 321.398 56.301 c 321.398 + 54.301 324.398 54.301 324.398 56.301 c S Q 0 g q 1 0 0 -1 0 216 cm 38.75 10.75 306.398 187.148 re S Q diff --git a/new/O2_avdz/plots/plot.sh b/new/O2_avdz/plots/plot.sh index 5d8a6f8..03def99 100755 --- a/new/O2_avdz/plots/plot.sh +++ b/new/O2_avdz/plots/plot.sh @@ -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" diff --git a/new/O2_avtz/data/exact-O2 b/new/O2_avtz/data/exact-O2 index 935380c..f3d8293 100644 --- a/new/O2_avtz/data/exact-O2 +++ b/new/O2_avtz/data/exact-O2 @@ -6,4 +6,3 @@ 3.00 -150.2314 4.00 -150.1476 5.00 -150.1274 -10.0 -150.1214