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Manuscript/FarDFT.tex

@@ -572,8 +572,8 @@ Eqs.~\eqref{eq:exp_ens_ener}, \eqref{eq:diff_Ew}, and \eqref{eq:dEdw}]:
 We enforce this type of \textit{exact} constraint (to the maximum possible extent) when optimising the parameters in Eq.~\eqref{eq:Cxw} in order to minimise the curvature of the ensemble energy.
 As readily seen from Eq.~\eqref{eq:Cxw} and graphically illustrated in Fig.~\ref{fig:Cxw} (red curve), the weight-dependent correction does not affect the two ghost-interaction-free limits at $\ew{1} = \ew{2} = 0$ and $\ew{1} = 0 \land \ew{2} = 1$ (\ie, the pure-state limits), as $\Cx{\ew{2}}$ reduces to $\Cx{}$ in these two limits.
 Indeed, it is important to ensure that the weight-dependent functional does not alter these pure-state limits, which are genuine saddle points of the KS equations, as mentioned above.
-Finally, let us mention that, around $\ew{2} = 0$, the behaviour of Eq.~\eqref{eq:Cxw} is linear: this is the main feature that one needs to catch in order to get accurate excitation energies in the zero-weight limit.
-\titou{Nonetheless, the CC-S functional also includes quadratic terms in order to compensate the spurious curvature of the ensemble energy originating, mainly, from the Hartree term [see Eq.~\eqref{eq:Hartree}].}
+Finally, let us mention that, around $\ew{2} = 0$, the behaviour of Eq.~\eqref{eq:Cxw} is linear: this is the main feature that one needs to catch in order to get accurate excitation energies in the zero-weight limit which is ghost-interaction free.
+\titou{Nonetheless, for $\ew{2} > 0$ the CC-S functional also includes quadratic terms in order to compensate the spurious curvature of the ensemble energy originating, mainly, from the Hartree term [see Eq.~\eqref{eq:Hartree}].}
 %We shall come back to this point later on.
 
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