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Merge branch 'master' of https://git.irsamc.ups-tlse.fr/loos/eDFT_FUEG

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Pierre-Francois Loos 2020-03-11 23:14:35 +01:00
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Manuscript/eDFT.tex
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@ -1558,7 +1558,7 @@ again that the usage of equal weights has the benefit of significantly reducing
A local and ensemble-weight-dependent correlation density-functional approximation A local and ensemble-weight-dependent correlation density-functional approximation
(eLDA) has been constructed in the context of GOK-DFT for spin-polarized (eLDA) has been constructed in the context of GOK-DFT for spin-polarized
triensembles in triensembles in
1D. The approach is actually general and can be extended to real 1D. The approach is general and can be extended to real
(three-dimensional) (three-dimensional)
systems~\cite{Loos_2009,Loos_2009c,Loos_2010,Loos_2010d,Loos_2017a} systems~\cite{Loos_2009,Loos_2009c,Loos_2010,Loos_2010d,Loos_2017a}
and larger ensembles in order to and larger ensembles in order to
@ -1567,20 +1567,20 @@ progress in this direction.
Unlike any standard functional, eLDA incorporates derivative Unlike any standard functional, eLDA incorporates derivative
discontinuities through its weight dependence. The latter originates discontinuities through its weight dependence. The latter originates
from the finite uniform electron gas \titou{on which} eLDA is from the finite uniform electron gas on which eLDA is
(partially) based on. The KS-eLDA scheme, where exact exchange is (partially) based. The KS-eLDA scheme, where exact \manu{individual
combined with eLDA, delivers accurate excitation energies for both exchange energies are}
combined with \manu{the eLDA correlation functional}, delivers accurate excitation energies for both
single and double excitations, especially when an equiensemble is used. single and double excitations, especially when an equiensemble is used.
In the latter case, the same weights are assigned to each state belonging to the ensemble. In the latter case, the same weights are assigned to each state belonging to the ensemble.
The improvement on the excitation energies brought by the KS-eLDA scheme is particularly impressive in the strong correlation regime where usual methods, such as TDLDA, fail. The improvement on the excitation energies brought by the KS-eLDA scheme is particularly impressive in the strong correlation regime where usual methods, such as TDLDA, fail.
We have observed that, although the ensemble correlation discontinuity has a We have observed that, although the correlation ensemble derivative has a
non-negligible effect on the excitation energies (especially for the non-negligible effect on the excitation energies (especially for the
single excitations), its magnitude can be significantly reduced by single excitations), its magnitude can be significantly reduced by
performing equiweight calculations instead of zero-weight performing equiweight calculations instead of zero-weight
calculations. calculations.
Let us finally stress that the present methodology can be extended Let us finally stress that the present methodology can be extended to other types of ensembles like, for example, the
straightforwardly to other types of ensembles like, for example, the
$\nEl$-centered ones, \cite{Senjean_2018,Senjean_2020} thus allowing for the design of a LDA-type functional for the $\nEl$-centered ones, \cite{Senjean_2018,Senjean_2020} thus allowing for the design of a LDA-type functional for the
calculation of ionization potentials, electron affinities, and calculation of ionization potentials, electron affinities, and
fundamental gaps. fundamental gaps.