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Pierre-Francois Loos 2020-05-04 00:27:50 +02:00
parent 2f69590324
commit a4cba166c0
9 changed files with 2184 additions and 2181 deletions
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46
Data/w/H2_aug-cc-pvtz_RCC_H.dat
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FarDFT.nb
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Manuscript/Ew_H2.pdf
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Manuscript/FarDFT.tex
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@ -624,7 +624,7 @@ In the case of \ce{H2}, the ensemble is composed by the $\Sigma_g^+$ ground stat
The ensemble energy $\E{}{\ew{}}$ is depicted in Fig.~\ref{fig:Ew_H2} as a function of weight $0 \le \ew{} \le 1/3$ (blue curve).
Because the Slater exchange functional defined in Eq.~\eqref{eq:Slater} does not depend on the ensemble weight, there is no contribution from the ensemble derivative term [last term in Eq.~\eqref{eq:dEdw}].
As anticipated, $\E{}{\ew{}}$ is far from being linear, which means that the excitation energy associated with the doubly-excited state obtained via the derivative of the ensemble energy varies significantly with $\ew{}$ (see blue curve in Fig.~\ref{fig:Om_H2}).
Taking as a reference the full configuration interaction (FCI) value of $28.75$ eV obtained with the aug-mcc-pV8Z basis set, \cite{Barca_2018a} one can see that the excitation energy varies by more than $7$ eV from $\ew{} = 0$ to $1/3$.
Taking as a reference the full configuration interaction (FCI) value of $28.75$ eV obtained with the aug-mcc-pV8Z basis set, \cite{Barca_2018a} one can see that the excitation energy varies by more than $8$ eV from $\ew{} = 0$ to $1/3$.
Note that the exact xc ensemble functional would yield a perfectly linear energy and, hence, the same value of the excitation energy independently of the ensemble weights.
\begin{figure}

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Manuscript/Om_H2.pdf
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