mu

Manuscript/Ex-srDFT.tex

@@ -344,7 +344,7 @@ Except for methylene for which FCI/TZVP geometries have been taken from Ref.~\on
 For the sake of completeness, they are also reported in the {\SI}.
 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}.
 The frozen-core density-based correction is used consistently with the frozen-core approximation in WFT methods.
-We refer the interested reader to Ref.~\onlinecite{LooPraSceTouGin-JPCL-19} for an explicit derivation of the equations associated with the frozen-core version of the present density-based basis set correction.
+We refer the reader to Ref.~\onlinecite{LooPraSceTouGin-JPCL-19} for an explicit derivation of the equations associated with the frozen-core version of the present density-based basis set correction.
 Compared to the exFCI calculations performed to compute energies and densities, the basis set correction represents, in any case, a marginal computational cost.
 In the following, we employ the AVXZ shorthand notations for Dunning's aug-cc-pVXZ basis sets.
 
@@ -675,14 +675,15 @@ However, these results also clearly evidence that special care has to be taken f
 \label{sec:CO}
 %=======================
 
-\titou{It is interesting to have a look at $\rsmu{}{}(\br{})$ for the ground and excited states.
-To do so, we consider the first singlet excited state of carbon monoxide (vertical excitation energies are reported in Table \ref{tab:Mol}).
-Figure \ref{fig:mu} represent $\rsmu{}{}(\br{})$ for the ground and excited states for the AVDZ, AVTZ and AVQZ basis sets.}
+It is interesting to study the behavior of $\rsmu{}{\Bas}(\br{})$ for different states as the basis set incompleteness error is obviously state specific.
+To do so, we consider the ground state (${}^{1}\Sigma^+$) of carbon monoxide as well as its lowest singlet excited state (${}^{1}\Pi$). 
+The values of the vertical excitation energies obtained for various methods and basis sets are reported in Table \ref{tab:Mol}.
+Figure \ref{fig:CO} represents $\rsmu{}{}(\br{})$ for these two electronic states computed with the AVDZ, AVTZ and AVQZ basis sets.
 
 %%% FIG 3 %%%
 \begin{figure}
 	\includegraphics[width=\linewidth]{CO}
-	\caption{$\rsmu{}{\Bas}(z)$ along the molecular axis ($z$) for the ground state and first singlet excited state of \ce{CO} for various basis sets $\Bas$.
+	\caption{$\rsmu{}{\Bas}(z)$ along the molecular axis ($z$) for the ground state ${}^{1}\Sigma^+$ and first singlet excited state ${}^{1}\Pi$ of \ce{CO} for various basis sets $\Bas$.
 	The carbon and oxygen nuclei are located at $z=-1.249$ and $z=0.893$ bohr, respectively.}
 	\label{fig:CO}
 \end{figure}
@@ -736,7 +737,7 @@ Consistently with the previous examples, the LDA and PBE functionals are slightl
 \section{Conclusion}
 \label{sec:ccl}
 %%%%%%%%%%%%%%%%%%%%%%%%
-We have shown that, by employing the recently proposed density-based basis set correction developed by some of the authors, \cite{GinPraFerAssSavTou-JCP-18} one can obtain chemically-accurate excitation energies with typically augmented double-$\zeta$ basis sets.
+We have shown that, by employing the recently proposed density-based basis set correction developed by some of the authors, \cite{GinPraFerAssSavTou-JCP-18} one can obtain, using sCI methods, chemically-accurate excitation energies with typically augmented double-$\zeta$ basis sets.
 This nicely complements our recent investigation on ground-state properties, \cite{LooPraSceTouGin-JPCL-19} which has evidenced that one recovers quintuple-$\zeta$ quality atomization and correlation energies with triple-$\zeta$ basis sets.
 The present study clearly shows that, for very diffuse excited states, the present correction relying on short-range correlation functionals from RS-DFT might not be enough to catch the radial incompleteness of the one-electron basis set.
 Also, in the case of multireference systems, we have evidenced that the PBEot functional is more appropriate than the LDA and PBE functionals relying on the UEG on-top density.