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new fig 6

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Pierre-Francois Loos 2020-03-09 09:25:11 +01:00
parent 63872b3fc0
commit 4f1d980dae
4 changed files with 30 additions and 10 deletions
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21
Data/DD_8pi.dat Normal file
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@ -0,0 +1,21 @@
0.4721 1.0633 1.9492 3.1633 4.7359
0.5606 1.1764 2.0855 3.3217 4.9156
0.7990 1.4749 2.4547 3.7572 5.4146
0.0885 0.1131 0.1363 0.1583 0.1797
0.3269 0.4116 0.5055 0.5938 0.6787
-0.0257 -0.0386 -0.0506 -0.0612 -0.0702
0.0008 0.0008 0.0033 0.0078 0.0131
0.0209 0.0149 0.0196 0.0271 0.0360
0.0266 0.0394 0.0540 0.0690 0.0834
0.0467 0.0534 0.0703 0.0884 0.1063
0.0000 0.0000 0.0000 0.0000 0.0000
-0.0072 -0.0080 -0.0080 -0.0075 -0.0065
-0.0050 -0.0028 0.0005 0.0046 0.0095
-0.0022 -0.0015 -0.0049 -0.0067 -0.0079
0.0004 -0.0044 -0.0095 -0.0160 -0.0209
0.0300 0.0300 0.0325 0.0355 0.0389
0.0026 -0.0029 -0.0047 -0.0093 -0.0130
0.0323 0.0315 0.0373 0.0423 0.0469
0.0045 0.0040 0.0029 0.0013 -0.0007
-0.0032 -0.0044 -0.0056 -0.0066 -0.0076
-0.0013 0.0004 0.0027 0.0053 0.0083

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Manuscript/EvsN_DD.pdf Normal file
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Manuscript/EvsN_HF.pdf
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Manuscript/eDFT.tex
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@ -1307,15 +1307,15 @@ electrons.
\begin{figure}
\includegraphics[width=\linewidth]{EvsL_3_DD}
\caption{
\label{fig:EvsLHF}
Error with respect to FCI (in \%) associated with the single excitation $\Ex{}{(1)}$ (bottom) and double excitation $\Ex{}{(2)}$ (top) as a function of the box length $L$ for 3-boxium at the KS-eLDA level.
\label{fig:EvsL_DD}
Error with respect to FCI (in \%) associated with the single excitation $\Ex{}{(1)}$ (bottom) and double excitation $\Ex{}{(2)}$ (top) as a function of the box length $L$ for 3-boxium at the KS-eLDA level with and without the contribution of the ensemble correlation derivative $\DD{c}{(I)}$.
Zero-weight (\ie, $\ew{1} = \ew{2} = 0$, red lines) and equiweight (\ie, $\ew{1} = \ew{2} = 1/3$, blue lines) calculations are reported.
}
\end{figure}
%%% %%% %%%
It is also interesting to investigate the influence of the ensemble correlation derivative $\DD{c}{I}$ [defined in Eq.~\eqref{eq:DD-eLDA}] on both the single and double excitations.
To do so, we have reported in Fig.~\ref{fig:EvsLHF}, in the case of 3-boxium, the error percentage (with respect to FCI) as a function of the box length $L$
To do so, we have reported in Fig.~\ref{fig:EvsL_DD}, in the case of 3-boxium, the error percentage (with respect to FCI) as a function of the box length $L$
on the excitation energies obtained at the KS-eLDA with and without $\DD{c}{I}$ [\ie, the last term in Eq.~\eqref{eq:Om-eLDA}].
%\manu{Manu: there is something I do not understand. If you want to
%evaluate the importance of the ensemble correlation derivatives you
@ -1344,18 +1344,17 @@ of modeling properly the ensemble correlation derivative.
%%% FIG 6 %%%
\begin{figure}
\includegraphics[width=\linewidth]{EvsN_HF}
\includegraphics[width=\linewidth]{EvsN_DD}
\caption{
\label{fig:EvsN_HF}
Error with respect to FCI in single and double excitation energies for $\nEl$-boxium (with a box length of $L=8\pi$) as a function of the number of electrons $\nEl$ at the KS-eLDA (solid lines) and eHF (dashed lines) levels.
Zero-weight (\ie, $\ew{1} = \ew{2} = 0$, black and red lines) and
equiweight (\ie, $\ew{1} = \ew{2} = 1/3$, blue and green lines) calculations are reported.
\label{fig:EvsN_DD}
Error with respect to FCI in single and double excitation energies for $\nEl$-boxium (with a box length of $L=8\pi$) as a function of the number of electrons $\nEl$ at the KS-eLDA level with and without the contribution of the ensemble correlation derivative $\DD{c}{(I)}$.
Zero-weight (\ie, $\ew{1} = \ew{2} = 0$, red lines) and equiweight (\ie, $\ew{1} = \ew{2} = 1/3$, blue lines) calculations are reported.
}
\end{figure}
%%% %%% %%%
Finally, in Fig.~\ref{fig:EvsN_HF}, we report the same quantities as a function of the electron number for a box of length $8\pi$ (\ie, in the strong correlation regime).
The difference between the eHF and KS-eLDA excitation energies
Finally, in Fig.~\ref{fig:EvsN_DD}, we report the same quantities as a function of the electron number for a box of length $8\pi$ (\ie, in the strong correlation regime).
The difference between the solid and dashed lines and KS-eLDA excitation energies
undoubtedly show that, even in the strong correlation regime, the
ensemble correlation derivative has a small impact on the double
excitations with a slight tendency of worsening the excitation energies