DONE with revision

JPCL_revision/G2-srDFT.tex

@@ -198,8 +198,8 @@ We refer the interested reader to Ref.~\onlinecite{GinPraFerAssSavTou-JCP-18} fo
 %Let us assume we have both the energy $\E{\modY}{\Bas}$ and density $\n{\modZ}{\Bas}$ of a $\Ne$-electron system described by two methods $\modY$ and $\modZ$ (potentially identical) in an incomplete basis set $\Bas$. 
 %According to Eq.~(15) of Ref.~\onlinecite{GinPraFerAssSavTou-JCP-18}, assuming that $\E{\modY}{\Bas}$ and $\n{\modZ}{\Bas}$ are reasonable approximations of the FCI energy and density within $\Bas$, the exact ground state energy $\E{}{}$ may be approximated as
 Let us assume 
-\titou{that we have reasonable approximations of the FCI energy and density of a $\Ne$-electron system in an incomplete basis set $\Bas$, say the CCSD(T) energy $\E{\CCSDT}{\Bas}$ and the Hartree-Fock (HF) density $\n{\HF}{\Bas}$. According to Eq.~(15) of Ref.~\onlinecite{GinPraFerAssSavTou-JCP-18}, the exact ground-state energy $\E{}{}$ may be approximated as
+\titou{that we have reasonable approximations of the FCI energy and density of a $\Ne$-electron system in an incomplete basis set $\Bas$, say the CCSD(T) energy $\E{\CCSDT}{\Bas}$ and the Hartree-Fock (HF) density $\n{\HF}{\Bas}$. 
-}
+According to Eq.~(15) of Ref.~\onlinecite{GinPraFerAssSavTou-JCP-18}, the exact ground-state energy $\E{}{}$ may be approximated as}
 %we have both the energy \titou{$\E{\CCSDT}{\Bas}$ and density $\n{\HF}{\Bas}$ of a $\Ne$-electron system in an incomplete basis set $\Bas$.}
 %According to Eq.~(15) of Ref.~\onlinecite{GinPraFerAssSavTou-JCP-18}, assuming that \titou{$\E{\CCSDT}{\Bas}$ and $\n{\HF}{\Bas}$} are reasonable approximations of the FCI energy and density within $\Bas$, the exact ground state energy $\E{}{}$ may be approximated as
 \begin{equation}
@@ -428,7 +428,7 @@ iii) vanishes in the CBS limit, hence guaranteeing an unaltered CBS limit for a
 
 
 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 (X $=$ D, T, Q and 5).
-\ce{N2}, \ce{O2} and \ce{F2} are weakly correlated systems and belong to the G2 set \cite{CurRagTruPop-JCP-91} (see below), whereas \ce{C2} already contains a non-negligible amount of strong correlation. \cite{BooCleThoAla-JCP-11} 
+%\ce{N2}, \ce{O2} and \ce{F2} are weakly correlated systems and belong to the G2 set \cite{CurRagTruPop-JCP-91} (see below), whereas \ce{C2} already contains a non-negligible amount of strong correlation. \cite{BooCleThoAla-JCP-11} 
 In a second time, we compute the atomization energies of the entire G2 set \cite{CurRagTruPop-JCP-91} composed by 55 molecules with the cc-pVXZ basis set family.
 This molecular set has been intensively 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, HauKlo-JCP-12, PetTouUmr-JCP-12, FelPet-JCP-13, KesSylKohTewMar-JCP-18}) and can be considered as a representative set of small organic and inorganic molecules.
 %As a method $\modY$ we employ either CCSD(T) or exFCI.
@@ -442,7 +442,7 @@ CCSD(T) energies are computed with Gaussian09 using standard threshold values, \
 For the numerical quadratures, we employ the SG-2 grid. \cite{DasHer-JCC-17}
 Apart from 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 systematically performed and defined as such: a \ce{He} core is frozen from \ce{Li} to \ce{Ne}, while a \ce{Ne} core is frozen from \ce{Na} to \ce{Ar}.
-In the context of the basis-set correction, the set of active MOs, $\BasFC$, involved in the definition of the effective interaction [see Eq.~\eqref{eq:WFC}] refers to the non-frozen MOs.
+%In the context of the basis-set correction, the set of active MOs, $\BasFC$, involved in the definition of the effective interaction [see Eq.~\eqref{eq:WFC}] refers to the non-frozen MOs.
 The FC density-based correction is used consistently with the FC approximation in WFT methods.
 To estimate the CBS limit of each method, following Ref.~\onlinecite{HalHelJorKloKocOlsWil-CPL-98}, we perform a two-point X$^{-3}$ extrapolation of the correlation energies using the quadruple- and quintuple-$\zeta$ data that we add up to the HF energies obtained in the largest (i.e.~quintuple-$\zeta$) basis.
 
@@ -467,7 +467,8 @@ In most cases, the basis-set corrected triple-$\zeta$ atomization energies are o
 	\includegraphics[width=0.5\linewidth]{fig2}
 	\caption{
 	\titou{$\rsmu{}{\Bas}$ (top) and $\n{}{} \times \be{\text{c,md}}{\sr,\PBE}$ (bottom) along the molecular axis ($z$) for \ce{N2} for various basis sets.
-	The two nitrogen nuclei are located at $z=0$ and $z=2.076$ bohr.}
+	The two nitrogen nuclei are located at $z=0$ and $z=2.076$ bohr.
+	The calculations have been performed in the FC approximation.}
 	\label{fig:N2}}
 \end{figure}