diff --git a/Response_Letter/Response_Letter.tex b/Response_Letter/Response_Letter.tex index b04c18d..78e914d 100644 --- a/Response_Letter/Response_Letter.tex +++ b/Response_Letter/Response_Letter.tex @@ -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. 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. - 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}