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Manu: done with my revisions

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Emmanuel Fromager 2020-05-08 11:31:35 +02:00
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Revised_Manuscript/eDFT.tex
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@ -610,10 +610,17 @@ energy will be treated at the
DFT level while we rely on HF for the exchange part.
This is different from the usual context where both exchange and
correlation are treated at the LDA level which provides key error compensation features.
Despite the errors
that might be introduced into the ensemble energy within such a scheme,
cancellations may actually occur when computing excitation energies,
which are energy \textit{differences}.}
As shown in Sec.~\ref{sec:res}, moving from the pure
ground-state picture to an equiensemble one can actually improve
the ground-state energy significantly within such a scheme, thus
highlighting a major difference between conventional and GOK DFT
calculations.
\manu{Manu: I changed this last sentence. Do you agree?}
%Despite the errors
%that might be introduced into the ensemble energy within such a scheme,
%cancellations may actually occur when computing excitation energies,
%which are energy \textit{differences}.
}
The resulting KS-eLDA ensemble energy obtained via Eq.~\eqref{eq:min_with_HF_ener_fun}
reads
@ -1087,14 +1094,18 @@ The second excited state is obviously stabilized by the increase of its weight i
\manurev{
These are all very sensible observations.\\
Let us finally stress that the (well-known) poor performance of the
combined full HF-exchange/LDA correlation scheme in
ground-state DFT [$\bw=(0,0)$] is substantially improved for the
ground state within the equiensemble [$\bw=(1/3,1/3)$]} (see the \SI).
combined 100\% HF-exchange/LDA correlation scheme in
ground-state [\ie, $\bw=(0,0)$] DFT, where the correlation energy is
overestimated, is substantially improved for the
ground state within the equiensemble [$\bw=(1/3,1/3)$]} (see the {\SI} for
further details).
This is a
remarkable and promising result. A similar improvement is observed for
the first excited state, at least in the weak correlation regime,
without deteriorating too much the second excited-state energy.
without deteriorating too much the second-excited-state energy.
}
\manu{Manu: do you agree with this final paragraph? I think it is
important.}
%\manu{Finally, we notice that the crossover point of the
%first-excited-state energies based on
%bi- and triensemble calculations, respectively, disappears in the strong correlation