Manu: saving corrections

Manuscript/FarDFT.bib

@@ -15,7 +15,8 @@
 	Date-Modified = {2020-05-13 07:41:14 +0200},
 	Eprint = {2001.08605},
 	Primaryclass = {physics.chem-ph},
-	Title = {Individual correlations in ensemble density-functional theory: State-driven/density-driven decomposition without additional Kohn-Sham systems},
+	Title = {Individual correlations in ensemble density-functional
+theory: State-driven/density-driven decompositions without additional Kohn-Sham systems},
 	Year = {2020}}
 
 @article{Refaely-Abramson_2012,
@@ -4026,6 +4027,10 @@
 	Title = {Density driven correlations in ensemble density functional theory: insights from simple excitations in atoms},
 	Year = {2020}}
 
+@misc{gould_2020, title={Approximately Self-Consistent Ensemble Density Functional Theory With All Correlations}, url={https://chemrxiv.org/articles/Approximately_Self-Consistent_Ensemble_Density_Functional_Theory_With_All_Correlations/12382595/1}, DOI={10.26434/chemrxiv.12382595.v1}, abstractNote={The ability to predict low-lying excited states with the same ease as ground-states would represent a major advance in understanding interactions between light and chemistry, e.g. for solar cells or photocatalysis. Recent theory developments in ensemble density functional theory (EDFT) promise to bring decades of work for ground-states to the practical resolution of excited-state problem - provided newly-discovered "density-driven correlations" can be dealt with and adequate effective potentials can be found. This Letter introduces simple approximations to both the density-driven correlations and the potential; and shows that EDFT with the ωB97X density functional approximation outperforms ΔSCF DFT for singlet-triplet gaps in small atoms and molecules. It thus establishes EDFT as a vitally promising tool for low-cost but high-accuracy studies of excited states; and provides a clear route to practical EDFT implementation of arbitrary functional approximations.
+
+}, publisher={ChemRxiv}, author={Gould, Tim}, year={2020}, month={May} }
+
 @article{Gould_2013,
 	Author = {Gould, Tim and Dobson, John F.},
 	Date-Added = {2018-10-24 22:38:52 +0200},

Manuscript/FarDFT.tex

@@ -390,6 +390,30 @@ We will also adopt the usual decomposition, and write down the weight-dependent
 where $\e{\ex}{\bw{}}(\n{}{})$ and $\e{\co}{\bw{}}(\n{}{})$ are the
 weight-dependent density-functional exchange and correlation energies
 per particle, respectively.
+\manu{As shown in Sec.~\ref{subsubsec:weight-dep_corr_func}, the weight
+dependence of the correlation energy can be extracted from a FUEG model. In order to make the resulting weight-dependent
+correlation functional truly universal, \ie~
+independent on the number of electrons in the FUEG, one could use the
+curvature of the Fermi hole~\cite{Loos_2017a} as an additional variable in the
+density-functional approximation. The development of such a 
+generalized correlation eLDA is left for future work. Even though a similar strategy could be applied
+to the weight-dependent exchange part, we
+explore in the present work a different path where the
+(system-dependent) exchange functional
+parameterization relies on the ensemble energy linearity
+constraint (see Sec.~\ref{subsubsec:weight-dep_x_fun}). Finally, let us
+stress that, in order to further
+improve the description of the ensemble correlation energy, a
+post-treatment of the recently
+revealed density-driven
+correlations~\cite{Gould_2019,Gould_2019_insights,gould_2020,Fromager_2020} [which, by construction, are absent
+from FUEGs] might be necessary. An orbital-dependent correction derived
+in Ref.~\onlinecite{Fromager_2020} might be
+used for that purpose. Work is currently in progress in this 
+direction.\\ 
+ }
+
+
 The explicit construction of these functionals is discussed at length in Sec.~\ref{sec:res}.
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -501,7 +525,8 @@ linear ensemble energy and, hence, the same value of the excitation energy indep
 %%% %%% %%%
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\subsubsection{Weight-dependent exchange functional}
+\subsubsection{Weight-dependent exchange
+functional}\label{subsubsec:weight-dep_x_fun}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 Second, in order to remove some of this spurious curvature of the ensemble
@@ -590,7 +615,8 @@ For the sake of clarity, the explicit expression of the VWN5 functional is not r
 The combination of the (weight-independent) Slater and VWN5 functionals (SVWN5) yield a highly convex ensemble energy (green curve in Fig.~\ref{fig:Ew_H2}), while the combination of CC-S and VWN5 (CC-SVWN5) exhibit a smaller curvature and improved excitation energies (red curve in Figs.~\ref{fig:Ew_H2} and \ref{fig:Om_H2}), especially at small weights, where the CC-SVWN5 excitation energy is almost spot on. 
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\subsubsection{Weight-dependent correlation functional}
+\subsubsection{Weight-dependent correlation
+functional}\label{subsubsec:weight-dep_corr_func}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 Fourth, in the spirit of our recent work, \cite{Loos_2020} we design a universal, weight-dependent correlation functional.