added some on top
This commit is contained in:
Emmanuel Giner
parent
a63c719d6f
commit
6765fd3dbf
@ -143,6 +143,7 @@
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% effective interaction
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% effective interaction
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\newcommand{\twodm}[4]{\mel{\Psi}{\psixc{#4}\psixc{#3} \psix{#2}\psix{#1}}{\Psi}}
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\newcommand{\twodm}[4]{\mel{\Psi}{\psixc{#4}\psixc{#3} \psix{#2}\psix{#1}}{\Psi}}
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\newcommand{\murpsi}[0]{\mu_{\wf{}{\Bas}}({\bf r})}
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\newcommand{\murpsi}[0]{\mu_{\wf{}{\Bas}}({\bf r})}
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\newcommand{\murcas}[0]{\mu_{\text{CASSCF}}({\bf r})}
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\newcommand{\murpsibas}[0]{\mu_{\wf{}{\Bas}}({\bf r})}
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\newcommand{\murpsibas}[0]{\mu_{\wf{}{\Bas}}({\bf r})}
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\newcommand{\ntwo}[0]{n_{2}}
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\newcommand{\ntwo}[0]{n_{2}}
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\newcommand{\ntwohf}[0]{n_2^{\text{HF}}}
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\newcommand{\ntwohf}[0]{n_2^{\text{HF}}}
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@ -267,6 +268,11 @@
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\newcommand{\dbr}[1]{d\br{#1}}
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\newcommand{\dbr}[1]{d\br{#1}}
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\newcommand{\PBEspin}{PBEspin}
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\newcommand{\PBEspin}{PBEspin}
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\newcommand{\PBEueg}{PBE-UEG-{$\tilde{\zeta}$}}
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\newcommand{\PBEueg}{PBE-UEG-{$\tilde{\zeta}$}}
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\newcommand{\ontopcas}{\langle n_2^{\text{CAS}}(\br{},\br{}) \rangle}
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\newcommand{\ontopextrap}{\langle \mathring{n}_{2}^{\text{CAS}}(\br{},\br{}) \rangle}
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\newcommand{\ontopcipsi}{\langle n_2^{\text{CIPSI}}(\br{},\br{}) \rangle}
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\newcommand{\muaverage}{\langle \murcas \rangle}
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\newcommand{\largemu}{E_{c,md}^{\mu \rightarrow \infty}}
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\newcommand{\LCT}{Laboratoire de Chimie Th\'eorique (UMR 7616), Sorbonne Universit\'e, CNRS, Paris, France}
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\newcommand{\LCT}{Laboratoire de Chimie Th\'eorique (UMR 7616), Sorbonne Universit\'e, CNRS, Paris, France}
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\newcommand{\ISCD}{Institut des Sciences du Calcul et des Donn\'ees, Sorbonne Universit\'e, Paris, France}
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\newcommand{\ISCD}{Institut des Sciences du Calcul et des Donn\'ees, Sorbonne Universit\'e, Paris, France}
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@ -681,6 +687,55 @@ The performance of each of these functionals is tested in the following. Note th
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\end{table*}
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\end{table*}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{table*}
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\caption{Integral of the on-top pair density in real space at various levels of theory (see text for details) for N$_2$, N, O$_2$ an O in the aug-cc-pVXZ basis sets (X=D,T,Q).}
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\begin{ruledtabular}
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\begin{tabular}{lrcccccc}
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%\begin{tabular}{lrcccccc}
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System & \tabc{Basis set} &\tabc{$\ontopcas$}& \tabc{$\ontopextrap$}& \tabc{$\ontopcipsi$}& \tabc{$\muaverage$} \\
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\hline
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\ce{N2} & aug-cc-pVDZ & 0.587712 & 0.329839 & 0.513967 & 0.946 \\
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& aug-cc-pVTZ & 0.591622 & 0.385069 & 0.461386 & 1.328 \\
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& aug-cc-pVQZ & 0.592422 & 0.461393 & 0.419336 & 1.706 \\[0.1cm]
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\ce{N} & aug-cc-pVDZ & 0.172320 & 0.098115 & 0.127420 & 0.910 \\
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& aug-cc-pVTZ & 0.173022 & 0.113155 & 0.111726 & 1.263 \\
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& aug-cc-pVQZ & 0.173071 & 0.123332 & 0.106121 & 1.601 \\[0.1cm]
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\hline
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\ce{O2} & aug-cc-pVDZ & 1.164428 & 0.707757 & 0.971217 & 1.107 \\
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& aug-cc-pVTZ & 1.166676 & 0.797154 & 0.884406 & 1.545 \\
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& aug-cc-pVQZ & 1.167688 & 0.861134 & 0.841366 & 1.979 \\[0.1cm]
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\ce{O} & aug-cc-pVDZ & 0.513919 & 0.314972 & 0.416040 & 1.080 \\
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& aug-cc-pVTZ & 0.516070 & 0.369056 & 0.376896 & 1.499 \\
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& aug-cc-pVQZ & 0.516288 & 0.383353 & 0.362491 & 1.924 \\[0.1cm]
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% & &\multicolumn{4}{c}{Estimated exact:\fnm[1] 665.4} \\[0.2cm]
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\hline
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\end{tabular}
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\end{ruledtabular}
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\label{tab:d1}
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\end{table*}
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%& \tabc{$\largemu$}
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%
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%& -0.0520
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%& -0.0210
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%& -0.0104
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%
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%& -0.0107
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%& -0.0064
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%& -0.0032
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%
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%& -0.0726
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%& -0.0302
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%& -0.0152
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%
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%& -0.0318
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%& -0.0138
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%& -0.0069
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\subsection{Computational details}
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\subsection{Computational details}
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We present potential energy curves of small molecules up to the dissociation limit
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We present potential energy curves of small molecules up to the dissociation limit
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@ -775,6 +830,37 @@ We report in Figs.~\ref{fig:N2}, \ref{fig:O2}, and \ref{fig:F2} the potential en
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Just as in \ce{H10}, the accuracy of the atomization energies is globally improved by adding the basis-set correction and it is remarkable that $\pbeontXi$ and $\pbeontns$ provide again very similar results. The latter observation confirms that the dependence on the on-top pair density allows one to remove the dependence of any kind of spin polarization for a quite wide range of covalent bonds and also for an open-shell system like \ce{O2}. More quantitatively, an error below 1.0 mHa compared to the estimated exact valence-only atomization energy is found for \ce{N2}, \ce{O2}, and \ce{F2} with the aug-cc-pVTZ basis set using the $\pbeontns$ functional, whereas such a feat is far from being reached within the same basis set at the near-FCI level. In the case of \ce{F2} it is clear that the addition of diffuse functions in the double- and triple-$\zeta$ basis sets strongly improves the accuracy of the results, which could have be anticipated due to the strong breathing-orbital effect induced by the ionic valence-bond forms in this molecule. \cite{HibHumByrLen-JCP-94}
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Just as in \ce{H10}, the accuracy of the atomization energies is globally improved by adding the basis-set correction and it is remarkable that $\pbeontXi$ and $\pbeontns$ provide again very similar results. The latter observation confirms that the dependence on the on-top pair density allows one to remove the dependence of any kind of spin polarization for a quite wide range of covalent bonds and also for an open-shell system like \ce{O2}. More quantitatively, an error below 1.0 mHa compared to the estimated exact valence-only atomization energy is found for \ce{N2}, \ce{O2}, and \ce{F2} with the aug-cc-pVTZ basis set using the $\pbeontns$ functional, whereas such a feat is far from being reached within the same basis set at the near-FCI level. In the case of \ce{F2} it is clear that the addition of diffuse functions in the double- and triple-$\zeta$ basis sets strongly improves the accuracy of the results, which could have be anticipated due to the strong breathing-orbital effect induced by the ionic valence-bond forms in this molecule. \cite{HibHumByrLen-JCP-94}
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It should be also noticed that when reaching the aug-cc-pVQZ basis set for \ce{N2}, the accuracy of the atomization energy slightly deteriorates for the $\pbeontXi$ and $\pbeontns$ functionals, but it remains nevertheless more accurate than the estimated FCI atomization energy and very close to chemical accuracy.
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It should be also noticed that when reaching the aug-cc-pVQZ basis set for \ce{N2}, the accuracy of the atomization energy slightly deteriorates for the $\pbeontXi$ and $\pbeontns$ functionals, but it remains nevertheless more accurate than the estimated FCI atomization energy and very close to chemical accuracy.
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\manu{
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The overestimation of the atomization energy appearing for \ce{N2} in large basis sets reveals a kind of unbalanced treatment between the molecule and atoms in favour of the molecular system.
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As the integral of the exact on-top pair density is proportional to the correlation energy in the large $\mu$ limit\cite{PazMorGorBac-PRB-06,FerGinTou-JCP-18} (see Eq. \eqref{eq:lim_mularge}), the accuracy of a given approximation to the exact on-top pair density will have a direct influence on the accuracy of the related correlation energy.
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To quantify the quality of various flavour of on-top pair densities for a given system and a given basis set $\basis$, we define the following quantities
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}
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\begin{equation}
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\ontopcas = \int \text{d}\br{}\, n_2^{\text{CASSCF}}(\br{},\br{}),
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\end{equation}
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\begin{equation}
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\ontopextrap = \int \text{d}\br{}\, \ntwoextrap(n_2^{\text{CASSCF}}(\br{},\br{}),\murcas),
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\end{equation}
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\begin{equation}
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\ontopcipsi = \int \text{d}\br{}\,n_2^{\text{CIPSI}}(\br{},\br{}),
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\end{equation}
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%\begin{equation}
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% \largemu = \int \text{d}\br{}\, \frac{(-2+\sqrt{2})\sqrt{2\pi}}{3\left(\murcas\right)^3} \ntwoextrap(n_2^{\text{CASSCF}}(\br{},\br{}),\murcas),
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%\end{equation}
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\begin{equation}
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\muaverage = \frac{1}{N_{e}}\int \text{d}\br{}\,n^{\text{CASSCF}}(\br{}) \,\, \murcas
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\end{equation}
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\manu{
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The quantity $n_2^{\text{CIPSI}}(\br{},\br{})$ is the on-top pair density of the largest CIPSI wave function obtained for each system in a given basis, which contains here at leas $10^7$ Slater determinants. All of these three quantities were computed excluding all contributions from the $1s$ orbitals.
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We report in Table \ref{tab:d1} these quantities for N, \ce{N2}, O and \ce{O2} in different basis sets.
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From this Table \ref{tab:d1} one can notice that integral of the on-top pair density at the CIPSI level is systematically lower than that at the CASSCF level, which is expected as the short-range correlation, digging the coulomb hone in a given basis set $\basis$ at near FCI level, is missing from the valence CASSCF wave function.
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Also, the on-top pair density at the CIPSI level decreases roughly by $20\%$ between the aug-cc-pVDZ and aug-cc-pVQZ, whereas the on-top pair density at the CASSCF level is almost constant with respect to the basis set.
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In order to estimate the integral of exact on-top pair density, we take as reference the value of $\ontopcipsi$ in the aug-cc-pVQZ basis set, although it is certainly an upper bound to the exact values.
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Regarding $\ontopextrap$, such a quantity is directly linked to the basis set correction in the large $\mu$ limit.
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The lowering of $\ontopextrap$ with respect to $\ontopcas$ is noticeable in a given basis set, but such $\ontopextrap$ globally increases when enlarging the basis set. This can be understood easily by remembering Eq. \eqref{eq:def_n2extrap} and realizing that the CASSCF on-top pair density is globally constant with the basis set whereas the value of $\murcas$ globally increases (as evidenced by $\muaverage$).
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By comparing $\ontopextrap$ to the $\ontopcipsi$ in the aug-cc-pVQZ basis set, it is quite clear that the error
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}
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Regarding now the performance of the basis-set correction along the whole potential energy curve, it is interesting to notice that it fails to provide a noticeable improvement far from the equilibrium geometry. Acknowledging that the weak-correlation effects in these regions are dominated by dispersion interactions which are long-range effects, the failure of the present approximations for the complementary functional can be understood easily. Indeed, the whole scheme designed here is based on the physics of correlation near the electron-electron coalescence point: the local range-separation function $\mu(\br{})$ is based on the value of the effective electron-electron interaction at coalescence and the ECMD functionals are suited for short-range correlation effects. Therefore, the failure of the present basis-set correction to describe dispersion interactions is theoretically expected.
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Regarding now the performance of the basis-set correction along the whole potential energy curve, it is interesting to notice that it fails to provide a noticeable improvement far from the equilibrium geometry. Acknowledging that the weak-correlation effects in these regions are dominated by dispersion interactions which are long-range effects, the failure of the present approximations for the complementary functional can be understood easily. Indeed, the whole scheme designed here is based on the physics of correlation near the electron-electron coalescence point: the local range-separation function $\mu(\br{})$ is based on the value of the effective electron-electron interaction at coalescence and the ECMD functionals are suited for short-range correlation effects. Therefore, the failure of the present basis-set correction to describe dispersion interactions is theoretically expected.
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We hope to report further on this in the near future.
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We hope to report further on this in the near future.
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@ -1,29 +1,29 @@
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=========================
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=========================
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N2
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N2
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CAS CAS-extrap CIPSI
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CAS CAS-extrap CIPSI CIPSI-extrap
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avdz
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avdz
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N2 0.587712 0.337529 0.513967
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N2 0.58771 0.32983 0.51397
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N 0.172320 0.100855 0.127420
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N 0.17232 0.09811 0.12742 0.07343
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-------------------------------------
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------------- ---------- -------------------------
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avtz
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avtz
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N2 0.591622 0.388739 0.461386
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N2 0.59162 0.38506 0.46139
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N 0.173022 0.114365 0.111726
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N 0.17302 0.11315 0.11173 0.07414
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-------------------------------------
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------------- ---------- -------------------------
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avqz
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avqz
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N2 0.592422 0.423673 0.419336
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N2 0.59242 0.42006 0.41934
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0.173071 0.124562 0.106121
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N 0.17307 0.12333 0.10612 0.07582
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======================================
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============= ====================================
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======================================
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============= ====================================
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O2
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O2
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CAS CAS-extrap CIPSI
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CAS CAS-extrap CIPSI
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avdz
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avdz
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O2 1.164428 0.70775731 0.97121
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O2 1.16443 0.69100 0.97121
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O 0.513919 0.31497205 0.41604
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O 0.51391 0.30623 0.41604 0.24934
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--------------------------------------
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--------------------------------------------------
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avtz
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avtz
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O2 1.166676 0.79715452 0.88440
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O2 1.16668 0.78996 0.88440
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O 0.516070 0.36905624 0.37689
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O 0.51607 0.35068 0.37689 0.25768
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--------------------------------------
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--------------------------------------------------
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avqz
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avqz
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O2 1.167688 0.861134291 0.84136
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O2 1.16769 0.85386 0.84136
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O 0.516288 0.398760190 0.36249
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O 0.51628 0.37922 0.36249 0.26283
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|
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|
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|
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|
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end readonly def
|
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|
||||||
|
7d03d5d44705d57d03d44703d3d21b05d3fe03d21b03d1fe03d0fe03cffe03cefe03cd9603cc
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||||||
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cb1e05ccfe03cb1e03ca3203c9fe03c6851105c61c03c51603c4fe03c3fe03c2fe03c1fe03c0
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||||||
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||||||
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||||||
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03ae6403ad0e03acab2505ac6403abaa1205ab2503aa1203a98a4105a9fa03a8fe03a7fe03a6
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||||||
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fe03a51203a4fe03a3a20e05a33203a20e03a16403a08a4105a096039ffe039e9d0c059efe03
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||||||
|
9d0c039c9b19059c64039b9a10059b19039a1003990a0398fe0397960d0597fe03960d03958a
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||||||
|
410595960394930e05942803930e0392fa039190bb0591fe03908f5d0590bb039080048f8e25
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||||||
|
058f5d038f40048e25038dfe038c8b2e058cfe038b2e038a8625058a410389880b0589140388
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||||||
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0b03878625058764038685110586250385110384fe038382110583fe0382110381fe0380fe03
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||||||
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7ffe0340ff7e7d7d057efe037d7d037c64037b5415057b25037afe0379fe03780e03770c0376
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||||||
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0a0375fe0374fa0373fa0372fa0371fa0370fe036ffe036efe036c21036bfe036a1142056a53
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||||||
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0369fe03687d036711420566fe0365fe0364fe0363fe0362fe03613a0360fa035e0c035dfe03
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||||||
|
5bfe035afe0359580a0559fa03580a035716190557320356fe03555415055542035415035301
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||||||
|
1005531803521403514a130551fe03500b034ffe034e4d10054efe034d10034cfe034b4a1305
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||||||
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4bfe034a4910054a1303491d0d05491003480d0347fe0346960345960344fe0343022d0543fa
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||||||
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0342bb03414b0340fe033ffe033e3d12053e14033d3c0f053d12033c3b0d053c40ff0f033b0d
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||||||
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033afe0339fe033837140538fa033736100537140336350b05361003350b03341e03330d0332
|
||||||
|
310b0532fe03310b03302f0b05300d032f0b032e2d09052e10032d09032c32032b2a25052b64
|
||||||
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032a2912052a25032912032827250528410327250326250b05260f03250b0324fe0323fe0322
|
||||||
|
0f03210110052112032064031ffa031e1d0d051e64031d0d031c1142051cfe031bfa031a4203
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||||||
|
1911420519fe031864031716190517fe031601100516190315fe0314fe0313fe031211420512
|
||||||
|
fe0311022d05114203107d030f64030efe030d0c16050dfe030c0110050c16030bfe030a1003
|
||||||
|
09fe0308022d0508fe030714030664030401100504fe03401503022d0503fe0302011005022d
|
||||||
|
0301100300fe0301b80164858d012b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b
|
||||||
|
2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b
|
||||||
|
2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b
|
||||||
|
2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b
|
||||||
|
2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b002b2b2b2b2b2b2b2b2b2b
|
||||||
|
2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b
|
||||||
|
2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b
|
||||||
|
2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b
|
||||||
|
2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b2b1d00>
|
||||||
|
] def
|
||||||
|
/f-0-0 currentdict end definefont pop
|
||||||
|
%%EndResource
|
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|
%%EndSetup
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|
%%Page: 1 1
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||||||
|
%%BeginPageSetup
|
||||||
|
%%PageBoundingBox: 0 0 360 216
|
||||||
|
%%EndPageSetup
|
||||||
|
q 4 2 349 207 rectclip q
|
||||||
|
0 g
|
||||||
|
0.25 w
|
||||||
|
0 J
|
||||||
|
0 j
|
||||||
|
[] 0.0 d
|
||||||
|
3.8 M q 1 0 0 -1 0 216 cm
|
||||||
|
48.051 186.75 m 51.75 186.75 l S Q
|
||||||
|
q 1 0 0 -1 0 216 cm
|
||||||
|
345.148 186.75 m 341.449 186.75 l S Q
|
||||||
|
BT
|
||||||
|
8 0 0 8 22.570312 26.25 Tm
|
||||||
|
/f-0-0 1 Tf
|
||||||
|
( 0.09)Tj
|
||||||
|
ET
|
||||||
|
q 1 0 0 -1 0 216 cm
|
||||||
|
48.051 157.398 m 51.75 157.398 l S Q
|
||||||
|
q 1 0 0 -1 0 216 cm
|
||||||
|
345.148 157.398 m 341.449 157.398 l S Q
|
||||||
|
BT
|
||||||
|
8 0 0 8 27.660156 55.597656 Tm
|
||||||
|
/f-0-0 1 Tf
|
||||||
|
( 0.1)Tj
|
||||||
|
ET
|
||||||
|
q 1 0 0 -1 0 216 cm
|
||||||
|
48.051 128.102 m 51.75 128.102 l S Q
|
||||||
|
q 1 0 0 -1 0 216 cm
|
||||||
|
345.148 128.102 m 341.449 128.102 l S Q
|
||||||
|
BT
|
||||||
|
8 0 0 8 22.570312 84.898438 Tm
|
||||||
|
/f-0-0 1 Tf
|
||||||
|
( 0.11)Tj
|
||||||
|
ET
|
||||||
|
q 1 0 0 -1 0 216 cm
|
||||||
|
48.051 98.75 m 51.75 98.75 l S Q
|
||||||
|
q 1 0 0 -1 0 216 cm
|
||||||
|
345.148 98.75 m 341.449 98.75 l S Q
|
||||||
|
BT
|
||||||
|
8 0 0 8 22.570312 114.25 Tm
|
||||||
|
/f-0-0 1 Tf
|
||||||
|
( 0.12)Tj
|
||||||
|
ET
|
||||||
|
q 1 0 0 -1 0 216 cm
|
||||||
|
48.051 69.398 m 51.75 69.398 l S Q
|
||||||
|
q 1 0 0 -1 0 216 cm
|
||||||
|
345.148 69.398 m 341.449 69.398 l S Q
|
||||||
|
BT
|
||||||
|
8 0 0 8 22.570312 143.597656 Tm
|
||||||
|
/f-0-0 1 Tf
|
||||||
|
( 0.13)Tj
|
||||||
|
ET
|
||||||
|
q 1 0 0 -1 0 216 cm
|
||||||
|
48.051 40.102 m 51.75 40.102 l S Q
|
||||||
|
q 1 0 0 -1 0 216 cm
|
||||||
|
345.148 40.102 m 341.449 40.102 l S Q
|
||||||
|
BT
|
||||||
|
8 0 0 8 22.570312 172.898438 Tm
|
||||||
|
/f-0-0 1 Tf
|
||||||
|
( 0.14)Tj
|
||||||
|
ET
|
||||||
|
q 1 0 0 -1 0 216 cm
|
||||||
|
48.051 10.75 m 51.75 10.75 l S Q
|
||||||
|
q 1 0 0 -1 0 216 cm
|
||||||
|
345.148 10.75 m 341.449 10.75 l S Q
|
||||||
|
BT
|
||||||
|
8 0 0 8 22.570312 202.25 Tm
|
||||||
|
/f-0-0 1 Tf
|
||||||
|
( 0.15)Tj
|
||||||
|
ET
|
||||||
|
q 1 0 0 -1 0 216 cm
|
||||||
|
48.051 186.75 m 48.051 183.051 l S Q
|
||||||
|
q 1 0 0 -1 0 216 cm
|
||||||
|
48.051 10.75 m 48.051 14.449 l S Q
|
||||||
|
BT
|
||||||
|
8 0 0 8 37.847656 16.949219 Tm
|
||||||
|
/f-0-0 1 Tf
|
||||||
|
( 0.15)Tj
|
||||||
|
ET
|
||||||
|
q 1 0 0 -1 0 216 cm
|
||||||
|
90.5 186.75 m 90.5 183.051 l S Q
|
||||||
|
q 1 0 0 -1 0 216 cm
|
||||||
|
90.5 10.75 m 90.5 14.449 l S Q
|
||||||
|
BT
|
||||||
|
8 0 0 8 82.84375 16.949219 Tm
|
||||||
|
/f-0-0 1 Tf
|
||||||
|
( 0.2)Tj
|
||||||
|
ET
|
||||||
|
q 1 0 0 -1 0 216 cm
|
||||||
|
132.949 186.75 m 132.949 183.051 l S Q
|
||||||
|
q 1 0 0 -1 0 216 cm
|
||||||
|
132.949 10.75 m 132.949 14.449 l S Q
|
||||||
|
BT
|
||||||
|
8 0 0 8 122.746094 16.949219 Tm
|
||||||
|
/f-0-0 1 Tf
|
||||||
|
( 0.25)Tj
|
||||||
|
ET
|
||||||
|
q 1 0 0 -1 0 216 cm
|
||||||
|
175.398 186.75 m 175.398 183.051 l S Q
|
||||||
|
q 1 0 0 -1 0 216 cm
|
||||||
|
175.398 10.75 m 175.398 14.449 l S Q
|
||||||
|
BT
|
||||||
|
8 0 0 8 167.742188 16.949219 Tm
|
||||||
|
/f-0-0 1 Tf
|
||||||
|
( 0.3)Tj
|
||||||
|
ET
|
||||||
|
q 1 0 0 -1 0 216 cm
|
||||||
|
217.801 186.75 m 217.801 183.051 l S Q
|
||||||
|
q 1 0 0 -1 0 216 cm
|
||||||
|
217.801 10.75 m 217.801 14.449 l S Q
|
||||||
|
BT
|
||||||
|
8 0 0 8 207.597656 16.949219 Tm
|
||||||
|
/f-0-0 1 Tf
|
||||||
|
( 0.35)Tj
|
||||||
|
ET
|
||||||
|
q 1 0 0 -1 0 216 cm
|
||||||
|
260.25 186.75 m 260.25 183.051 l S Q
|
||||||
|
q 1 0 0 -1 0 216 cm
|
||||||
|
260.25 10.75 m 260.25 14.449 l S Q
|
||||||
|
BT
|
||||||
|
8 0 0 8 252.59375 16.949219 Tm
|
||||||
|
/f-0-0 1 Tf
|
||||||
|
( 0.4)Tj
|
||||||
|
ET
|
||||||
|
q 1 0 0 -1 0 216 cm
|
||||||
|
302.699 186.75 m 302.699 183.051 l S Q
|
||||||
|
q 1 0 0 -1 0 216 cm
|
||||||
|
302.699 10.75 m 302.699 14.449 l S Q
|
||||||
|
BT
|
||||||
|
8 0 0 8 292.496094 16.949219 Tm
|
||||||
|
/f-0-0 1 Tf
|
||||||
|
( 0.45)Tj
|
||||||
|
ET
|
||||||
|
q 1 0 0 -1 0 216 cm
|
||||||
|
345.148 186.75 m 345.148 183.051 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 8 337.492188 16.949219 Tm
|
||||||
|
/f-0-0 1 Tf
|
||||||
|
( 0.5)Tj
|
||||||
|
ET
|
||||||
|
q 1 0 0 -1 0 216 cm
|
||||||
|
48.051 10.75 297.098 176 re S Q
|
||||||
|
BT
|
||||||
|
0 8 -8 0 10.699219 74.636719 Tm
|
||||||
|
/f-0-0 1 Tf
|
||||||
|
(integral of the on-top)Tj
|
||||||
|
8 0 0 8 189.941406 3 Tm
|
||||||
|
(1/Z)Tj
|
||||||
|
2.63916 23.862305 Td
|
||||||
|
[(FCI e)18(xtrapolated on-top)]TJ
|
||||||
|
ET
|
||||||
|
0.580392 0 0.827451 rg
|
||||||
|
q 1 0 0 -1 0 216 cm
|
||||||
|
310.852 19.102 m 334.949 19.102 l S Q
|
||||||
|
q 1 0 0 -1 0 216 cm
|
||||||
|
345.148 179.699 m 203.648 169.301 l 132.949 161.75 l 90.5 157.449 l 62.199
|
||||||
|
154.648 l S Q
|
||||||
|
q 1 0 0 -1 0 216 cm
|
||||||
|
342.148 179.699 m 348.148 179.699 l S Q
|
||||||
|
q 1 0 0 -1 0 216 cm
|
||||||
|
345.148 176.699 m 345.148 182.699 l S Q
|
||||||
|
q 1 0 0 -1 0 216 cm
|
||||||
|
200.648 169.301 m 206.648 169.301 l S Q
|
||||||
|
q 1 0 0 -1 0 216 cm
|
||||||
|
203.648 166.301 m 203.648 172.301 l S Q
|
||||||
|
q 1 0 0 -1 0 216 cm
|
||||||
|
129.949 161.75 m 135.949 161.75 l S Q
|
||||||
|
q 1 0 0 -1 0 216 cm
|
||||||
|
132.949 158.75 m 132.949 164.75 l S Q
|
||||||
|
q 1 0 0 -1 0 216 cm
|
||||||
|
87.5 157.449 m 93.5 157.449 l S Q
|
||||||
|
q 1 0 0 -1 0 216 cm
|
||||||
|
90.5 154.449 m 90.5 160.449 l S Q
|
||||||
|
q 1 0 0 -1 0 216 cm
|
||||||
|
59.199 154.648 m 65.199 154.648 l S Q
|
||||||
|
q 1 0 0 -1 0 216 cm
|
||||||
|
62.199 151.648 m 62.199 157.648 l S Q
|
||||||
|
q 1 0 0 -1 0 216 cm
|
||||||
|
319.898 19.102 m 325.898 19.102 l S Q
|
||||||
|
q 1 0 0 -1 0 216 cm
|
||||||
|
322.898 16.102 m 322.898 22.102 l S Q
|
||||||
|
0 g
|
||||||
|
BT
|
||||||
|
8 0 0 8 264.675781 184.597656 Tm
|
||||||
|
/f-0-0 1 Tf
|
||||||
|
(FCI on-top)Tj
|
||||||
|
ET
|
||||||
|
0 0.619608 0.45098 rg
|
||||||
|
q 1 0 0 -1 0 216 cm
|
||||||
|
310.852 28.398 m 334.949 28.398 l S Q
|
||||||
|
q 1 0 0 -1 0 216 cm
|
||||||
|
345.148 22.75 m 203.648 64.25 l 132.949 85.398 l 90.5 97.25 l 62.199 104.699
|
||||||
|
l S Q
|
||||||
|
q 1 0 0 -1 0 216 cm
|
||||||
|
342.148 19.75 m 348.148 25.75 l S Q
|
||||||
|
q 1 0 0 -1 0 216 cm
|
||||||
|
342.148 25.75 m 348.148 19.75 l S Q
|
||||||
|
q 1 0 0 -1 0 216 cm
|
||||||
|
200.648 61.25 m 206.648 67.25 l S Q
|
||||||
|
q 1 0 0 -1 0 216 cm
|
||||||
|
200.648 67.25 m 206.648 61.25 l S Q
|
||||||
|
q 1 0 0 -1 0 216 cm
|
||||||
|
129.949 82.398 m 135.949 88.398 l S Q
|
||||||
|
q 1 0 0 -1 0 216 cm
|
||||||
|
129.949 88.398 m 135.949 82.398 l S Q
|
||||||
|
q 1 0 0 -1 0 216 cm
|
||||||
|
87.5 94.25 m 93.5 100.25 l S Q
|
||||||
|
q 1 0 0 -1 0 216 cm
|
||||||
|
87.5 100.25 m 93.5 94.25 l S Q
|
||||||
|
q 1 0 0 -1 0 216 cm
|
||||||
|
59.199 101.699 m 65.199 107.699 l S Q
|
||||||
|
q 1 0 0 -1 0 216 cm
|
||||||
|
59.199 107.699 m 65.199 101.699 l S Q
|
||||||
|
q 1 0 0 -1 0 216 cm
|
||||||
|
319.898 25.398 m 325.898 31.398 l S Q
|
||||||
|
q 1 0 0 -1 0 216 cm
|
||||||
|
319.898 31.398 m 325.898 25.398 l S Q
|
||||||
|
0 g
|
||||||
|
q 1 0 0 -1 0 216 cm
|
||||||
|
48.051 10.75 297.098 176 re S Q
|
||||||
|
Q Q
|
||||||
|
showpage
|
||||||
|
%%Trailer
|
||||||
|
end restore
|
||||||
|
%%EOF
|
||||||
Loading…
Reference in New Issue
Block a user