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Emmanuel Fromager 2020-05-06 17:55:32 +02:00
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Revised_Manuscript/eDFT.tex
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@ -1052,7 +1052,15 @@ case, we
``deteriorate'' these states by optimizing the orbitals for the
ensemble, rather than for each state separately. The reverse actually occurs for the ground state in the triensemble
as $\ew{2}$ increases. The variations in the ensemble
weights are essentially linear or quadratic. They are induced by the
weights are essentially linear or quadratic.
\manurev{This can be rationalized as follows. As readily seen from
Eqs.~(\ref{eq:EI-eLDA}) and (\ref{eq:ind_HF-like_ener}), the individual
HF-like exchange does not depend explicitly on the weights, which means
that the above-mentioned variations originate from the eLDA correlation
functional [second and third terms on the right-hand side of
Eq.~(\ref{eq:EI-eLDA})]. If, for analysis purposes, we consider the
Taylor expansions around the uniform density regime in Eqs.~(\ref{eq:Taylor_exp_ind_corr_ener_eLDA}) and (\ref{eq:Taylor_exp_DDisc_term})
}They are induced by the
eLDA correlation functional, as readily seen from
Eqs.~\eqref{eq:Taylor_exp_ind_corr_ener_eLDA} and
\eqref{eq:Taylor_exp_DDisc_term}. In the biensemble, the weight dependence of the first