updated manuscript

Manuscript/G2-srDFT.bib

@@ -12233,3 +12233,15 @@
 	Year = {1998},
 	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0009261498001110},
 	Bdsk-Url-2 = {https://doi.org/10.1016/S0009-2614(98)00111-0}}
+
+@article{DasHer-JCC-17,
+author = {Dasgupta, Saswata and Herbert, John M.},
+title = {Standard grids for high-precision integration of modern density functionals: SG-2 and SG-3},
+journal = {Journal of Computational Chemistry},
+volume = {38},
+number = {12},
+pages = {869-882},
+doi = {10.1002/jcc.24761},
+eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/jcc.24761},
+year = {2017}
+}

Manuscript/G2-srDFT.tex

@@ -703,28 +703,27 @@ iii) it vanishes in the limit of a complete basis set and thus garentees the cor
 We begin our investigation of the performance of the basis set correction by computing the atomization energies of \ce{C2}, \ce{N2}, \ce{O2} and \ce{F2} obtained with Dunning's cc-pVXZ basis sets (X $=$ D, T, Q and 5).
 In the case of \ce{C2} and \ce{N2}, we also perform calculations with the cc-pCVXZ family.
 \ce{N2}, \ce{O2} and \ce{F2} are weakly correlated systems and belong to the G2 set, whereas \ce{C2} already contains a non-negligible amount of strong correlation. \cite{BooCleThoAla-JCP-11} 
-In a second time, we compute the entire atomization energies of the G2 set \cite{CurRagTruPop-JCP-91} composed by 55 molecules with the cc-pVXZ family.
+In a second time, we compute the entire atomization energies of the G2 set \cite{CurRagTruPop-JCP-91} composed by 55 molecules with the cc-pVXZ family, except for Li, Be and Na for which we use the cc-pCVXZ basis sets.
 This molecular set has been exhausively studied in the last 20 years (see, for example, Refs.~\onlinecite{FelPetDix-JCP-08,Gro-JCP-09,FelPet-JCP-09,NemTowNee-JCP-10,FelPetHil-JCP-11,PetTouUmr-JCP-12,FelPet-JCP-13,KesSylKohTewMar-JCP-18}).
 %The reference values for the atomization energies are extracted from Ref.~\onlinecite{HauKlo-JCP-12} and corresponds to frozen-core non-relativistic atomization energies obtained at the CCSD(T)(F12)/cc-pVQZ-F12 level of theory corrected for higher-excitation contributions ($E_\text{CCSDT(Q)/cc-pV(D+d)Z} - E_\text{CCSD(T)/cc-pV(D+d)Z})$.
 As a method $\modX$ we employ either CCSD(T) or exFCI.
 Here, exFCI stands for extrapolated FCI energies computed with the CIPSI algorithm. \cite{HurMalRan-JCP-73, GinSceCaf-CJC-13, GinSceCaf-JCP-15}
 We refer the interested reader to Refs.~\onlinecite{HolUmrSha-JCP-17, SceGarCafLoo-JCTC-18, LooSceBloGarCafJac-JCTC-18, SceBenJacCafLoo-JCP-18, LooBogSceCafJAc-JCTC-19} for more details.
 In the case of the CCSD(T) calculations, we have $\modY = \HF$ as we use the Restricted Open Shel Hartree-Fock (ROHF) one-electron density to compute the complementary energy, and for the CIPSI calculations we use the density of a converged variational wave function. 
-For the definition of the interaction, we use a single Slater determinant in the ROHF basis. 
+For the definition of the interaction, we use a single Slater determinant built in the ROHF basis for the CCSD(T) calculations, and built with the natural orbitals of the converged variational wave function for the exFCI calculations. 
 The CCSD(T) calculations have been performed with Gaussian09 with standard threshold values. \cite{g09}
 RS-DFT and exFCI calculations are performed with {\QP}. \cite{QP2}
-\titou{For the quadrature grid, we employ ... radial and angular points.}
+For the quadrature grid, we employ the radial and angular points of the SG2 grid\cite{DasHer-JCC-17}.
 Except for the carbon dimer where we have taken the experimental equilibrium bond length (\InAA{1.2425}), all geometries have been extracted from Ref.~\onlinecite{HauJanScu-JCP-09} and have been obtained at the B3LYP/6-31G(2df,p) level of theory.
 Frozen core calculations are defined as such: an \ce{He} core is frozen from \ce{B} to \ce{Mg}, while a \ce{Ne} core is frozen from \ce{Al} to \ce{Xe}.
-In the context of the basis set correction, the set of valence spinorbitals $\Val$ involved in the definition of the effective interaction [see Eq.~\eqref{eq:Wval}] refers to the non-frozen spinorbitals.
+In the context of the basis set correction, the set of valence spinorbitals $\Val$ involved in the definition of the effective interaction refers to the non-frozen spinorbitals.
 The ``valence'' correction was used consistently when the FC approximation was applied.
 In order to estimate the complete basis set (CBS) limit for each model, we employed the two-point extrapolation proposed in Ref.~\onlinecite{HalHelJorKloKocOlsWil-CPL-98} for the correlation energies. 
 We refer to these atomization energies as $\CBS$. 
 
 %\subsection{Convergence of the atomization energies with the WFT models }
 As the exFCI calculations were converged with a precision of about 0.1 {\kcal}, we can consider these atomization energies as near-FCI values.
-They will be our references for a given system in a given basis. 
-The results for four diatomics mentioned above are reported in Table \ref{tab:diatomics}. 
+They will be our references for \ce{C2}, \ce{N2}, \ce{O2} and \ce{F2} in a given basis, and the results for these diatomics are reported in Table \ref{tab:diatomics}. 
 As one can see, the convergence of the exFCI atomization energies is, as expected, slow with respect to the basis set: chemical accuracy (error below 1 {\kcal}) is barely reached for \ce{C2}, \ce{O2} and \ce{F2} even with cc-pV5Z. 
 Also, the atomization energies are consistently underestimated, reflecting that, in a given basis, the atom is always better described than the molecule due to the larger number of interacting electron pairs in the molecular system. 
 A similar trend holds for CCSD(T).
@@ -738,6 +737,7 @@ Nevertheless, the deviation observed for the largest basis set is typically with
 %Also, the values obtained with the largest basis sets tends to converge toward a value close to the estimated CBS values. 
 Importantly, the sensitivity with respect to the SR-DFT functional is quite large for the double- and triple-$\zeta$ basis sets, where clearly the PBE functional performs better. 
 However, from the quadruple-$\zeta$ basis, the LDA and PBE functionals agree within a few tenths of a {\kcal}. 
+Such weak sensitivity to the approximated functionals in the DFT part when reaching large basis sets shows the robustness of the approach. 
 
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 \section*{Supporting information}