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a/Manuscript/Ex-srDFT.tex +++ b/Manuscript/Ex-srDFT.tex @@ -678,7 +678,8 @@ However, these results also clearly evidence that special care has to be taken f 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. +Figure \ref{fig:CO} represents $\rsmu{}{}(z)$ along the nuclear axis ($z$) for these two electronic states computed with the AVDZ, AVTZ and AVQZ basis sets. +\titou{Add description about the graphs here.} %%% FIG 4 %%% \begin{figure} @@ -693,13 +694,13 @@ Figure \ref{fig:CO} represents $\rsmu{}{}(\br{})$ for these two electronic state \subsection{Doubly-Excited States of the Carbon Dimer} \label{sec:C2} %======================= -In order to have a miscellaneous test set of excitations, in a third time, we propose to study some doubly-excited states of the carbon dimer \ce{C2}, a prototype system for strongly correlated and multireference systems. \cite{AbrShe-JCP-04, AbrShe-CPL-05, Var-JCP-08, PurZhaKra-JCP-09, AngCimPas-MP-12, BooCleThoAla-JCP-11, Sha-JCP-15, SokCha-JCP-16, HolUmrSha-JCP-17, VarRoc-PTRSMPES-18} +In order to have a miscellaneous test set of excitations, in a fourth time, we propose to study some doubly-excited states of the carbon dimer \ce{C2}, a prototype system for strongly correlated and multireference systems. \cite{AbrShe-JCP-04, AbrShe-CPL-05, Var-JCP-08, PurZhaKra-JCP-09, AngCimPas-MP-12, BooCleThoAla-JCP-11, Sha-JCP-15, SokCha-JCP-16, HolUmrSha-JCP-17, VarRoc-PTRSMPES-18} These two valence excitations --- $1\,^{1}\Sigma_g^+ \ra 1\,^{1}\Delta_g$ and $1\,^{1}\Sigma_g^+ \ra 2\,^{1}\Sigma_g^+$ --- are both of $(\pi,\pi) \ra (\si,\si)$ character. They have been recently studied with state-of-the-art methods, and have been shown to be ``pure'' doubly-excited states as they do not involve single excitations. \cite{LooBogSceCafJac-JCTC-19} The vertical excitation energies associated with these transitions are reported in Table \ref{tab:Mol} and represented in Fig.~\ref{fig:C2}. -An interesting point here is that one really needs the PBEot to get chemically-accurate absorption energies with the AVDZ atomic basis set. +An interesting point here is that one really needs to consider the PBEot functional to get chemically-accurate absorption energies with the AVDZ atomic basis set. We believe that the present result is a direct consequence of the multireference character of the \ce{C2} molecule. -In other words, the UEG on-top density used in the LDA and PBE functionals (see Sec.~\ref{sec:func}) is a particularly bad approximation of the true on-top density. +In other words, the UEG on-top density used in the LDA and PBE functionals (see Sec.~\ref{sec:func}) is a particularly bad approximation of the true on-top density for the present system. %%% FIG 5 %%% \begin{figure} diff --git a/Manuscript/SI/Ex-srDFT-SI.tex b/Manuscript/SI/Ex-srDFT-SI.tex index aba399d..34c21b8 100644 --- a/Manuscript/SI/Ex-srDFT-SI.tex +++ b/Manuscript/SI/Ex-srDFT-SI.tex @@ -450,14 +450,14 @@ Here, we report the absolute energetic corrections for each state of each molecu \\ \\ Carbon monoxyde & $1\,^{1}\Sigma^+$ - & & & - & & & - & & & + & -0.074\,328 & -0.031\,117 & -0.015\,510 + & -0.084\,655 & -0.035\,318 & -0.017\,142 + & -0.076\,668 & -0.077\,437 & -0.018\,768 \\ & $1\,^{1}\Pi$ - & & & - & & & - & & & + & -0.075\,790 & -0.031\,456 & -0.016\,083 + & -0.085\,494 & -0.035\,255 & -0.017\,182 + & -0.036\,301 & -0.036\,359 & -0.018\,855 \\ \\ Water & $1\,^{1}A_1$