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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 ``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 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 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 eLDA correlation functional, as readily seen from
Eqs.~\eqref{eq:Taylor_exp_ind_corr_ener_eLDA} and 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 \eqref{eq:Taylor_exp_DDisc_term}. In the biensemble, the weight dependence of the first