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 \begin{abstract}
 The present work proposes an application and extension to strongly correlated systems of the recently proposed basis set correction based on density functional theory (DFT). 
 We study the potential energy surfaces (PES) of the H$_{10}$, C$_2$, N$_2$, O$_2$ and F$_2$ molecules up to full dissociation limit in increasing basis sets at near full configuration interaction (FCI) level with and without the present basis set correction. 
-Such basis set correction relies on a mapping between range-separated DFT (RSDFT) and wave function calculations in a finite basis set through the definition of an effective non-divergent interaction mimicking the coulomb operator projected in a finite basis set. From that mapping, RSDFT-types functionals are used to recover the dominant the short-range correlation effects  missing in a finite basis set. 
+Such basis set correction relies on a mapping between range-separated DFT (RSDFT) and wave function calculations in a finite basis set through the definition of an effective non-divergent interaction mimicking the coulomb operator projected in a finite basis set. From that mapping, RSDFT-types functionals are used to recover the dominant part of the short-range correlation effects  missing in a finite basis set. 
 The scope of the present work is to develop new 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 extensivity. 
 In that context, we investigate the dependence of the functionals on different flavours 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 multi-configurational DFT, such findings show that one can avoid the effective spin polarization whose mathematical definition is rather \textit{ad hoc} and which can become complex valued.