done with discussion

Manuscript/eDFT.tex

@@ -1273,15 +1273,15 @@ drastically.
 %correlation is strong. It is not clear to me which integral ($W_{01}?$)
 %drives the all thing.\\} 
 It is important to note that, even though the GIC removes the explicit
-quadratic \manu{Hx} terms from the ensemble energy, a non-negligible curvature
+quadratic Hx terms from the ensemble energy, a non-negligible curvature
-remains in the GIC-eLDA ensemble energy \manu{when the electron
+remains in the GIC-eLDA ensemble energy when the electron
-correlation is strong}. \manu{This is due to
+correlation is strong. This is due to
-\textit{(i)} the correlation eLDA
+(i) the correlation eLDA
 functional, which contributes linearly (or even quadratically) to the individual
 energies [see Eqs.~\eqref{eq:Taylor_exp_ind_corr_ener_eLDA} and
-\eqref{eq:Taylor_exp_DDisc_term}], and \textit{(ii)} the optimization of the
+\eqref{eq:Taylor_exp_DDisc_term}], and (ii) the optimization of the
-ensemble KS orbitals in the presence of ghost-interaction errors {[see
+ensemble KS orbitals in the presence of ghost-interaction errors [see
-Eqs.~\eqref{eq:min_with_HF_ener_fun} and \eqref{eq:WHF}]}}.
+Eqs.~\eqref{eq:min_with_HF_ener_fun} and \eqref{eq:WHF}].
 %However, this orbital-driven error is small (in our case at
 %least) \trashEF{as the correlation part of the ensemble KS potential $\delta
 %\E{c}{\bw}[\n{}{}] /\delta \n{}{}(\br{})$ is relatively small compared
@@ -1335,13 +1335,13 @@ The reverse is observed for the second excited state.
 	\includegraphics[width=\linewidth]{EvsL_5}
 	\caption{
 	\label{fig:EvsL}
-	Excitation energies (multiplied by $L^2$) associated with the single excitation $\Ex{}{(1)}$ (bottom) and double excitation $\Ex{}{(2)}$ (top) of 5-boxium for various methods and box length $L$.
+	Excitation energies (multiplied by $L^2$) associated with the single excitation $\Ex{}{(1)}$ (bottom) and double excitation $\Ex{}{(2)}$ (top) of 5-boxium for various methods and box lengths $L$.
 	Graphs for additional values of $\nEl$ can be found as {\SI}.
 	}
 \end{figure}
 %%% %%% %%%
 
-Figure \ref{fig:EvsL} reports the excitation energies (multiplied by $L^2$) for various methods and box sizes in the case of 5-boxium (\ie, $\nEl = 5$).
+Figure \ref{fig:EvsL} reports the excitation energies (multiplied by $L^2$) for various methods and box lengths in the case of 5-boxium (\ie, $\nEl = 5$).
 Similar graphs are obtained for the other $\nEl$ values and they can be found in the {\SI} alongside the numerical data associated with each method.
 For small $L$, the single and double excitations can be labeled as
 ``pure'', as revealed by a thorough analysis of the FCI wavefunctions.
@@ -1541,15 +1541,12 @@ shown).\\
 
 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 curves
-undoubtedly show that \trashEF{, even in the strong correlation regime,}
+undoubtedly show that the
-\manu{Manu: in the light of what we already discussed, we expect the
-derivative to be important in the strongly correlated regime so the
-sentence "even in ..." is useless (that's why I would remove it)} the
 correlation ensemble derivative has a rather significant impact on the double
 excitation (around $10\%$) with a slight tendency of worsening the excitation energies
 in the case of equal weights, as the number of electrons
-increases. It has a rather large influence \manu{(which decreases with the
+increases. It has a rather large influence (which decreases with the
-number of electrons)} on the single
+number of electrons) on the single
 excitation energies obtained in the zero-weight limit, showing once
 again that the usage of equal weights has the benefit of significantly reducing the magnitude of the correlation ensemble derivative.