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Manu: added a sentence after the response of Clotilde to the last comment

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Emmanuel Fromager 2020-06-04 13:06:18 +02:00
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Response_Letter/Response_Letter.tex
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@ -104,7 +104,12 @@ $n^w(r)$ [see Eqs. (5) and (11)] and the notation will be carefully modified acc
The important idea is that the linearity must be in the ensemble energy but the main constraint on the xc-functional should be that it is weight-dependant. The important idea is that the linearity must be in the ensemble energy but the main constraint on the xc-functional should be that it is weight-dependant.
We emphasize that only the exact ensemble-xc-functional would have the ideal weight-dependency that would make the corresponding ensemble energy reproduce perfectly the linear behavior of the exact ensemble energy and lead to weight-independant excitation energies, that is exact excitation energies. We emphasize that only the exact ensemble-xc-functional would have the ideal weight-dependency that would make the corresponding ensemble energy reproduce perfectly the linear behavior of the exact ensemble energy and lead to weight-independant excitation energies, that is exact excitation energies.
The use of an approximate weight-dependant xc-functional could reduce the ensemble energy curvature and give less weight-dependant excitation energies but it is reasonable to admit that it also could make things worse it the weight-dependency of the functional is poorly chosen. The use of an approximate weight-dependant xc-functional could reduce the ensemble energy curvature and give less weight-dependant excitation energies but it is reasonable to admit that it also could make things worse it the weight-dependency of the functional is poorly chosen.
That is why the construction of "good" weight-dependant xc-functionals is a really challenging matter in eDFT.} That is why the construction of "good" weight-dependant
xc-functionals is a really challenging matter in eDFT.\\
As a final comment, we insist after Eq. (28) on the fact that, in the
exact theory, the xc ensemble density functional has no reason to vary (for a fixed density $n$)
linearly with the ensemble weights. We refer to Ref. 92 where exact
expressions for the individual xc energies are derived.}
\end{enumerate} \end{enumerate}