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CO added to SI

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Pierre-Francois Loos 2019-06-10 14:35:17 +02:00
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Manuscript/C2.pdf
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Manuscript/Ex-srDFT.tex
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@ -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. 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 (${}^{1}\Pi$). 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}. 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 %%% %%% FIG 4 %%%
\begin{figure} \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} \subsection{Doubly-Excited States of the Carbon Dimer}
\label{sec:C2} \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. 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} 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}. 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. 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 %%% %%% FIG 5 %%%
\begin{figure} \begin{figure}

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Manuscript/SI/Ex-srDFT-SI.tex
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@ -450,14 +450,14 @@ Here, we report the absolute energetic corrections for each state of each molecu
\\ \\
\\ \\
Carbon monoxyde & $1\,^{1}\Sigma^+$ 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
\\ \\
& $1\,^{1}\Pi$ & $1\,^{1}\Pi$
& & & & -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 & $1\,^{1}A_1$ Water & $1\,^{1}A_1$