correction manu

Manuscript/G2-srDFT.tex

@@ -138,8 +138,7 @@
 We report a universal density-based basis set incompleteness correction that can be applied to any wave function method.
 The present correction, which appropriately vanishes in the complete basis set (CBS) limit, relies on short-range correlation density functionals (with multi-determinant reference) from range-separated density-functional theory (RS-DFT) to estimate the basis set incompleteness error.
 Contrary to conventional RS-DFT schemes which require an \textit{ad hoc} range-separation \textit{parameter} $\mu$, the key ingredient here is a range-separation \textit{function} $\mu(\bf{r})$ which automatically adapts to the spatial non-homogeneity of the basis set incompleteness error.
-As illustrative examples, we show how this density-based correction allows us to obtain coupled-cluster with single and double substitutions and triple CCSD(T) correlation energies near the CBS limit for the G2-1 set of molecules with compact Gaussian basis sets. 
-\titou{For example, while CCSD(T)/cc-pVTZ yields a mean absolute deviation (MAD) of 6.06 kcal/mol compared to CCSD(T)/CBS correlation energies, the CCSD(T)+LDA and CCSD(T)+PBE corrected methods return MAD of 1.19 and 0.85 kcal/mol (respectively) with the same basis.}
+As illustrative examples, we show how this density-based correction allows us to obtain CCSD(T) atomization and correlation energies near the CBS limit for the G2 set of molecules with compact Gaussian basis sets. 
 \end{abstract}
 
 \maketitle
@@ -451,7 +450,7 @@ iii) vanishes in the limit of a complete basis set, hence guaranteeing an unalte
 %%% TABLE II %%%
 \begin{table}
 	\caption{
-	Statistical analysis (in \kcal) of the G2-1 correlation energies depicted in Fig.~\ref{fig:G2_Ec}. 
+	Statistical analysis (in \kcal) of the G2 correlation energies depicted in Fig.~\ref{fig:G2_Ec}. 
 	Mean absolute deviation (MAD), root-mean-square deviation (RMSD), and maximum deviation (MAX) with respect to the CCSD(T)/CBS reference correlation energies.
 	CA corresponds to the number of cases (out of 55) obtained with chemical accuracy.
 	See {\SI} for raw data.
@@ -488,13 +487,11 @@ iii) vanishes in the limit of a complete basis set, hence guaranteeing an unalte
 	\label{fig:G2_Ec}}
 \end{figure*}
 
-%\subsection{Comparison between the CIPSI and CCSD(T) models in the case of C$_2$, N$_2$, O$_2$, F$_2$}
 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).
 \titou{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 G2-1 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 correlation energies of the entire G2-1 set \cite{CurRagTruPop-JCP-91} composed by 55 molecules with the cc-pVXZ family of basis sets.
+\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 correlation energies of the entire G2 set \cite{CurRagTruPop-JCP-91} composed by 55 molecules with the cc-pVXZ family of 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, HauKlo-JCP-12, PetTouUmr-JCP-12, FelPet-JCP-13, KesSylKohTewMar-JCP-18}) \titou{and can be considered as a representative set for typical quantum chemical calculations on small organic molecules}.
-%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 $\modY$ 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.
@@ -529,25 +526,27 @@ Importantly, the sensitivity with respect to the SR-DFT functional is quite larg
 However, from the quadruple-$\zeta$ basis, the LDA and PBE functionals agree within a few tenths of a {\kcal}. 
 Such weak sensitivity when reaching large basis sets shows the robustness of the approach. 
 
-As a second set of numerical examples, we compute the \manu{error with respect to the CBS values} of the correlation energy contribution to the atomization energies of the G2-1 test sets with $\modY=\CCSDT$, $\modZ=\HF$ and the cc-pVXZ basis sets.
-\manu{Investigating the convergence of correlation energies or difference of such quantities is usually done to appreciate the performance of basis set corrections aiming at correcting two-electron effects\cite{Tenno-CPL-04,TewKloNeiHat-PCCP-07,IrmGru-arXiv-2019}, as these quantities do not contain the HF energy component whose rate of convergence is very different depending on the molecular system. }
-The ``plain'' CCSD(T) correlation energies as well as the corrected CCSD(T)+LDA and CCSD(T)+PBE values are depicted in Fig.~\ref{fig:G2_Ec}.
+As a second set of numerical examples, we compute the error with respect to the CBS values of the atomization energies of the G2 test sets with $\modY=\CCSDT$, $\modZ=\HF$ and the cc-pVXZ basis sets.
+\titou{Here we use HF/CBS values to compute the atomization energies which is equivalent to looking at the correlation energy contribution to the atomization energies.
+Investigating the convergence of correlation energies or difference of such quantities is usually done to appreciate the performance of basis set corrections aiming at correcting two-electron effects\cite{Tenno-CPL-04,TewKloNeiHat-PCCP-07,IrmGru-arXiv-2019}, as these quantities do not contain the HF energy component whose rate of convergence is very different depending on the molecular system.}
+The ``plain'' CCSD(T) atomization energies as well as the corrected CCSD(T)+LDA and CCSD(T)+PBE values are depicted in Fig.~\ref{fig:G2_Ec}.
 The raw data can be found in the {\SI}.
-A statistical analysis of these data is also provided in Table \ref{tab:stats}, where we report the mean absolute deviation (MAD), root-mean-square deviation (RMSD), and maximum deviation (MAX) with respect to the CCSD(T)/CBS correlation energies.
-From double-$\zeta$ to quintuple-$\zeta$ basis, the MAD associated with the CCSD(T) correlation energy contribution to the atomization energies goes down slowly from 14.29 to 1.28 {\kcal}.
+A statistical analysis of these data is also provided in Table \ref{tab:stats}, where we report the mean absolute deviation (MAD), root-mean-square deviation (RMSD), and maximum deviation (MAX) with respect to the CCSD(T)/CBS atomization energies.
+\titou{Compared to the reference values extracted from Ref.~\onlinecite{HauKlo-JCP-12} which 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 ($E_\text{CCSDT(Q)/cc-pV(D+d)Z} - E_\text{CCSD(T)/cc-pV(D+d)Z})$, our CCSD(T)/CBS atomization energies differ by MAD = 0.37 {\kcal}.}
+From double-$\zeta$ to quintuple-$\zeta$ basis, the MAD associated with the CCSD(T) atomization energies goes down slowly from 14.29 to 1.28 {\kcal}.
 For a commonly-used basis like cc-pVTZ, the MAD of CCSD(T) is still 6.06 {\kcal}.
 Applying the basis set correction drastically reduces the basis set incompleteness error.
 Already at the CCSD(T)+LDA/cc-pVDZ and CCSD(T)+PBE/cc-pVDZ levels, the MAD is reduced to 3.24 and 1.96 {\kcal}.
 With the triple-$\zeta$ basis, the MAD of CCSD(T)+PBE/cc-pVTZ is already below 1 {\kcal} with 36 cases (out of 55) where we achieve chemical accuracy.
 CCSD(T)+LDA/cc-pVQZ and CCSD(T)+PBE/cc-pVQZ return MAD of 0.33 and 0.31 kcal/mol (respectively) while CCSD(T)/cc-pVQZ still yields a fairly large MAD of 2.50 {\kcal}.
 
-\titou{Therefore, similar to F12 methods, \cite{TewKloNeiHat-PCCP-07} we can safely claim that the present basis set correction recovers quintuple-$\zeta$ quality correlation energies with triple-$\zeta$ basis sets for a much cheaper computational cost.
-Encouraged by these results for weakly correlated ground states molecules, we are developing this theory towards the treatment of the basis set error for strongly correlated systems, excited states and the treatment of the one-electron error in the basis set incompleteness.}
+\titou{Therefore, similar to F12 methods, \cite{TewKloNeiHat-PCCP-07} we can safely claim that the present basis set correction recovers quintuple-$\zeta$ quality atomization and correlation energies with triple-$\zeta$ basis sets for a much cheaper computational cost.
+Encouraged by these results obtained for weakly correlated systems, we are currently developing this theory towards the treatment of the basis set error for strongly correlated systems, excited states and the treatment of the one-electron error in the basis set incompleteness.}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \section*{Supporting information}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-See {\SI} for raw data associated with the atomization energies of the four diatomics and the G2-1 correlation energies.
+See {\SI} for raw data associated with the atomization energies of the four diatomics and the G2 correlation energies.
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{acknowledgements}