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Manuscript/srDFT_SC.bbl
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@ -897,12 +897,11 @@
{\bibinfo {journal} {J. Chem. Phys.}\ }\textbf {\bibinfo {volume} {122}},\
\bibinfo {pages} {154110} (\bibinfo {year} {2005})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {{P. C. Hiberty S. Humbel, C. P. Byrman and J. H. van
Lenthe}}()}]{HibHumByrLen-JCP-94}%
Lenthe}}(1994)}]{HibHumByrLen-JCP-94}%
\BibitemOpen
\bibfield {author} {\bibinfo {author} {\bibnamefont {{P. C. Hiberty S.
Humbel, C. P. Byrman and J. H. van Lenthe}}},\ }\href {\doibase
10.1063/1.468459} {\bibfield {journal} {\bibinfo {journal} {J. Chem.
Phys.}\ }\textbf {\bibinfo {volume} {101}},\ \bibinfo {pages} {5969}},\
\Eprint {http://arxiv.org/abs/https://doi.org/10.1063/1.468459}
{https://doi.org/10.1063/1.468459} \BibitemShut {NoStop}%
Phys.}\ }\textbf {\bibinfo {volume} {101}},\ \bibinfo {pages} {5969}
(\bibinfo {year} {1994})}\BibitemShut {NoStop}%
\end{thebibliography}%

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Manuscript/srDFT_SC.bib
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@ -5250,7 +5250,6 @@ eprint = {https://doi.org/10.1063/1.2800017}
Volume = {101},
doi = {10.1063/1.468459},
URL = {https://doi.org/10.1063/1.468459},
eprint = {https://doi.org/10.1063/1.468459}
Year = {1994}}
@article{HibHum-JCP-94,

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Manuscript/srDFT_SC.tex
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@ -697,7 +697,7 @@ Regarding the computational cost of the present approach, it should be stressed
\hline
\ce{F2} & aug-cc-pVDZ & 49.6 [12.6] & 54.8 [7.4] & 54.9 [7.3] & 54.8 [7.4] \\
& aug-cc-pVTZ & 59.3 [2.9] & 61.2 [1.0] & 61.5 [0.7] & 61.5 [0.7] \\[0.1cm]
& aug-cc-pVTZ & 60.1 [ ] & 61.0 [1.2] & 61.3 [0.9] & 61.3 [0.9] \\[0.1cm]
& aug-cc-pVQZ & 60.1 [ ] & 61.0 [1.2] & 61.3 [0.9] & 61.3 [0.9] \\[0.1cm]
\hline
& & \tabc{CEEIS\fnm[3]} & \tabc{CEEIS\fnm[3]+$\pbeuegXi$} & \tabc{CEEIS\fnm[3]+$\pbeontXi$} & \tabc{CEEIS\fnm[3]+$\pbeontns$}\\
\hline
@ -784,7 +784,7 @@ The \ce{N2}, \ce{O2} and \ce{F2} molecules are complementary to the \ce{H10} sys
We report in Figs~\ref{fig:N2}, \ref{fig:O2} the potential energy curves of \ce{N2}, \ce{O2}, and computed at various approximation levels using the aug-cc-pVDZ and aug-cc-pVTZ basis sets, and in Fig~\ref{fig:F2} the potential energy surface of \ce{F2} using the cc-pVXZ (X=D,T,Q) basis set. The computation of the atomization energies $D_0$ at each level of theory is reported in Table \ref{tab:d0}.
Just as in \ce{H10}, the quality of $D_0$ 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 dependency on the on-top pair density allows one to remove the dependency of any kind of spin polarization for a quite wide range of electron density and also for \titou{open-shell} systems like \ce{O2}. More quantitatively, an error below 1.0 mHa on the estimated exact valence-only $D_0$ 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 presence of diffuse function strongly improves the results, which is somehow understandable due to the strong breathing-orbital effect in this molecule induced by the ionic valence bond forms\cite{HibHumByrLen-JCP-94}.
Just as in \ce{H10}, the quality of $D_0$ 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 dependency on the on-top pair density allows one to remove the dependency of any kind of spin polarization for a quite wide range of electron density and also for \titou{open-shell} systems like \ce{O2}. More quantitatively, an error below 1.0 mHa on the estimated exact valence-only $D_0$ 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 presence of diffuse functions in for double- and triple-zeta types basis sets strongly improves the results, which is somehow understandable due to the strong breathing-orbital effect in this molecule induced by the ionic valence bond forms\cite{HibHumByrLen-JCP-94}.
It should be also noticed that when reaching the aug-cc-pVQZ basis set for \ce{N2}, the quality of $D_0$ slightly deteriorates for the $\pbeontXi$ and $\pbeontns$ functionals, but it remains nevertheless more accurate than the estimated FCI $D_0$ and very close the to chemical accuracy.
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 \titou{complementary basis functionals} 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 designed thanks to the universal condition provided by the electron-electron cusp 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 and predictable.