Manu: minor changes in II A

Manuscript/eDFT.tex

@@ -353,7 +353,8 @@ auxiliary double-weight ensemble density reads
 \beq
 	\n{}{\bw,\bxi}(\br{}) = \sum_{K\geq 0} \ew{K} \n{\Det{(K),\bxi}}{}(\br{}).
 \eeq 
-Since, for given ensemble weights $\bw$ and $\bxi$, the ensemble densities $\n{}{\bxi,\bxi}$ and $\n{}{\bw,\bxi}$ are generated from the \textit{same} KS potential (which is unique up to a constant), it comes
+Since, for given ensemble weights $\bw$ and $\bxi$, the ensemble
+densities $\n{}{\bxi,\bxi}$ and $\n{}{\bw,\bxi}$ are obtained from the \textit{same} KS potential (which is unique up to a constant), it comes
 from the exact expression in Eq.~\eqref{eq:exact_ens_Hx} that 
 \beq
 	\E{Hx}{\bxi}[\n{}{\bxi,\bxi}] = \sum_{K \geq 0} \xi_K \mel*{\Det{(K),\bxi}}{\hWee}{\Det{(K),\bxi}},
@@ -402,7 +403,7 @@ we finally recover from Eqs.~\eqref{eq:KS_ens_density} and
 Note that, when $\bw=0$, the ensemble correlation functional reduces to the
 conventional (ground-state) correlation functional $E_{\rm c}[n]$. As a
 result, the regular KS-DFT expression is recovered from
-Eq.~\eqref{eq:exact_ener_level_dets} for the ground-state energy
+Eq.~\eqref{eq:exact_ener_level_dets} for the ground-state energy:
 \beq
 \E{}{(0)}=\mel*{\Det{(0)}}{\hH}{\Det{(0)}} +
 \E{c}{}[\n{\Det{(0)}}{}],
@@ -445,8 +446,8 @@ potential leaves the density-functional Hamiltonian $\hat{H}[n]$ (and
 therefore the individual energy levels) unchanged. As a result, in
 this context,
 the correlation derivative discontinuities induced by the 
-excitation process~\cite{Levy_1995} will be fully described by the ensemble
-correlation derivatives [second term on the right-hand side of
+excitation process~\cite{Levy_1995} will be fully described by the 
+correlation ensemble derivatives [second term on the right-hand side of
 Eq.~\eqref{eq:excited_ener_level_gs_lim}].    
 
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