diff --git a/Manuscript/C2H4.pdf b/Manuscript/C2H4.pdf index 81271f1..d4366ef 100644 Binary files a/Manuscript/C2H4.pdf and b/Manuscript/C2H4.pdf differ diff --git a/Manuscript/CO.pdf b/Manuscript/CO.pdf new file mode 100644 index 0000000..49c1756 Binary files /dev/null and b/Manuscript/CO.pdf differ diff --git a/Manuscript/Ex-srDFT.tex b/Manuscript/Ex-srDFT.tex index 24c5c84..d724d85 100644 --- a/Manuscript/Ex-srDFT.tex +++ b/Manuscript/Ex-srDFT.tex @@ -573,9 +573,9 @@ However, these results also clearly evidence that special care has to be taken f \\ \\ Carbon monoxide & $1\,^{1}\Sigma^+ \ra 1\,^{1}\Pi$ & Val. & 8.48\fnm[1] & 0.09 & 0.01 & 0.02 - & 0.05 & 0.00 & - & 0.07 & 0.01 & - & 0.07 & 0.00 & + & 0.05 & 0.00 & 0.00 + & 0.07 & 0.01 & 0.02 + & 0.07 & 0.00 & 0.02 \\ \\ Ethylene & $1\,^{1}A_{1g} \ra 1\,^{1}B_{3u}$ & Ryd. & 7.43\fnm[3] & -0.12 & -0.04 & @@ -594,17 +594,17 @@ However, these results also clearly evidence that special care has to be taken f & 0.00 & 0.01 & \\ & $1\,^{1}A_{1g} \ra 1\,^{3}B_{1u}$ & Val. & 4.54\fnm[3] & 0.01 & 0.00 & - & 0.07 & 0.03 & - & 0.10 & 0.04 & + & 0.05 & 0.03 & & 0.08 & 0.04 & + & 0.07 & 0.04 & \\ & $1\,^{1}A_{1g} \ra 1\,^{3}B_{3u}$ & Val. & 7.28\fnm[4] & -0.12 & -0.04 & - & -0.03 & 0.00 & + & -0.04 & 0.00 & & 0.00 & 0.00 & & 0.00 & 0.02 & \\ & $1\,^{1}A_{1g} \ra 1\,^{3}B_{1g}$ & Val. & 8.00\fnm[4] & -0.07 & -0.01 & - & 0.01 & 0.03 & + & 0.00 & 0.03 & & 0.04 & 0.03 & & 0.05 & 0.04 & \\ @@ -680,11 +680,11 @@ To do so, we consider the ground state (${}^{1}\Sigma^+$) of carbon monoxide as 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 %%% +%%% FIG 4 %%% \begin{figure} \includegraphics[width=\linewidth]{CO} - \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.} + \caption{$\rsmu{}{\Bas}(z)$ along the molecular axis ($z$) for the ground state ${}^{1}\Sigma^+$ (black curve) and first singlet excited state ${}^{1}\Pi$ (red curve) 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, and are represented by the thin black lines.} \label{fig:CO} \end{figure} %%% %%% %%% @@ -701,7 +701,7 @@ An interesting point here is that one really needs the PBEot to get chemically-a 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. -%%% FIG 4 %%% +%%% FIG 5 %%% \begin{figure} \includegraphics[width=\linewidth]{C2} \caption{Error in vertical excitation energies $\Eabs$ (in eV) for two doubly-excited states of the carbon dimer for various basis sets and methods. @@ -721,9 +721,10 @@ We refer the interested reader to the work of Feller et al.\cite{FelPetDav-JCP-1 In the present context, ethylene is a particularly interesting system as it contains a mixture of valence and Rydberg excited states. Our basis set corrected vertical excitation energies are gathered in Table \ref{tab:Mol} and depicted in Fig.~\ref{fig:C2H4}. Except for one particular excitation (the lowest singlet-triplet excitation $1\,^{1}A_{1g} \ra 1\,^{3}B_{1u}$), the exFCI+PBEot/AVDZ excitation energies are chemically accurate and the errors drop further when one goes to the triple-$\zeta$ basis. +%(Note that one cannot afford exFCI/AVQZ calculations for ethylene.) Consistently with the previous examples, the LDA and PBE functionals are slightly less accurate, although they still correct the excitation energies in the right direction. -%%% FIG 5 %%% +%%% FIG 6 %%% \begin{figure} \includegraphics[width=\linewidth]{C2H4} \caption{Error in vertical excitation energies $\Eabs$ (in eV) of ethylene for various basis sets and methods.