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CO graphs

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Pierre-Francois Loos 2019-06-10 10:28:45 +02:00
parent c94a9082bc
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Manuscript/Ex-srDFT.tex
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@ -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.