diff --git a/Manuscript/FarDFT.tex b/Manuscript/FarDFT.tex index 937efd7..7fbcae7 100644 --- a/Manuscript/FarDFT.tex +++ b/Manuscript/FarDFT.tex @@ -573,7 +573,7 @@ We enforce this type of \textit{exact} constraint (to the maximum possible exten 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 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}].} +\titou{Nonetheless, beyond the $\ew{2} = 0$ limit, 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. %%% FIG 3 %%%