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 \begin{abstract}
-We extend to strongly correlated systems the recently introduced basis-set correction based on density-functional theory (DFT) [E. Giner \textit{et al.}, J. Chem. Phys. \textbf{149}, 194301 (2018)]. This basis-set correction relies on a mapping between wave-function calculations in a finite basis set and range-separated DFT (RSDFT) through the definition of an effective non-divergent interaction corresponding to the Coulomb electron-electron interaction projected in the finite basis set, allowing one to use RSDFT-type complementary functionals to recover the dominant part of the short-range correlation effects missing in a finite basis set. Using as test cases the potential energy curves of the H$_{10}$, C$_2$, N$_2$, O$_2$, and F$_2$ molecules up to the dissociation limit, we systematically explore different approximations for the complementary functionals which are suited to describe strong-correlation regimes and which fulfill two very desirable properties: $S_z$ invariance and size consistency. Specifically, we investigate the dependence of the functionals on different flavors of on-top pair densities and spin polarizations. An important result is that the explicit dependence on the on-top pair density allows one to completely remove the dependence on any form of spin polarization without any significant loss of accuracy. 
-In the general context of multiconfigurational DFT, this finding shows that one can avoid the effective spin polarization whose mathematical definition is rather \textit{ad hoc} and which can become complex valued. Quantitatively, we show that the basis-set correction reaches chemical accuracy on atomization energies with triple-zeta quality basis sets for most of the systems studied. Also, the present basis-set correction provides smooth curves along the whole potential energy curves.
-%We study the potential energy surfaces (PES) of the H$_{10}$, C$_2$, N$_2$, O$_2$, and F$_2$ molecules up to the dissociation limit using increasing basis sets at near full configuration interaction (FCI) level with and without the present basis-set correction. 
+We extend to strongly correlated systems the recently introduced basis-set incompleteness correction based on density-functional theory (DFT) [E. Giner \textit{et al.}, \href{https://doi.org/10.1063/1.5052714}{J. Chem. Phys. \textbf{149}, 194301 (2018)}]. This basis-set correction relies on a mapping between wave-function calculations in a finite basis set and range-separated DFT (RSDFT) through the definition of an effective non-divergent interaction corresponding to the Coulomb electron-electron interaction projected in the finite basis set. This allows to use RSDFT-type complementary functionals to recover the dominant part of the short-range correlation effects missing in this finite basis. Using as test cases the potential energy curves of the H$_{10}$, C$_2$, N$_2$, O$_2$, and F$_2$ molecules up to the dissociation limit, we explore various approximations of complementary functionals suited to describe strong correlation. These short-range correlation functionals fulfill two very desirable properties: invariance with respect to the spin operator $S_z$ and size consistency. Specifically, we systematically investigate the dependence of the functionals on different flavors of on-top pair densities and spin polarizations. The key result of this study is that the explicit dependence on the on-top pair density allows one to completely remove the dependence on any form of spin polarization without any significant loss of accuracy. 
+In the general context of multiconfigurational DFT, this finding shows that one can avoid the effective spin polarization whose mathematical definition is rather \textit{ad hoc} and which can become complex valued. Quantitatively, we show that the basis-set correction reaches chemical accuracy on atomization energies with triple-$\zeta$ quality basis sets for most of the systems studied here. Also, the present basis-set incompleteness correction provides smooth curves along the whole potential energy surfaces.
 \end{abstract}
 
 \maketitle