Manu: III A

Manuscript/eDFT.tex

@@ -1023,22 +1023,23 @@ is the eLDA correlation ensemble derivative contribution to the $I$th excitation
 Most of the standard local and semi-local density-functional approximations rely on the infinite uniform electron gas model (also known as jellium). \cite{ParrBook, Loos_2016}
 One major drawback of the jellium paradigm, when it comes to develop density-functional approximations for ensembles, is that the ground and excited states are not easily accessible like in a molecule. \cite{Gill_2012, Loos_2012, Loos_2014a, Loos_2014b, Agboola_2015, Loos_2017a}
 Moreover, because the infinite uniform electron gas model is a metal, it is gapless, which means that both the fundamental and optical gaps are zero.
-From this point of view, using finite finite uniform electron gases, \cite{Loos_2011b,
+From this point of view, using finite uniform electron gases, \cite{Loos_2011b,
 Gill_2012} which have, like an atom, discrete energy levels and non-zero
 gaps, can be seen as more relevant in this context. \cite{Loos_2014a, Loos_2014b, Loos_2017a}
-However, an obvious drawback of using finite uniform electron gases is that the resulting density-functional approximation for ensemble
+However, an obvious drawback of using finite uniform electron gases is
+that the resulting density-functional approximation for ensembles
 will inexorably depend on the number of electrons in the finite uniform electron gas (see below).
 Here, we propose to construct a weight-dependent eLDA for the
-calculations of excited states in 1D systems by combining finite uniform electron gases with the
+calculation of excited states in 1D systems by combining finite uniform electron gases with the
 usual infinite uniform electron gas. 
 
 As a finite uniform electron gas, we consider the ringium model in which electrons move on a perfect ring (\ie, a circle) but interact \textit{through} the ring. \cite{Loos_2012, Loos_2013a, Loos_2014b}
 The most appealing feature of ringium regarding the development of
-functionals in the context of eDFT is the fact that both ground- and
+functionals in the context of GOK-DFT is the fact that both ground- and
 excited-state densities are uniform, and therefore {\it equal}. 
 As a result, the ensemble density will remain constant (and uniform) as the ensemble weights vary. 
-This is a necessary condition for being able to model the ensemble
+This is a necessary condition for being able to model the 
-correlation derivatives with respect to the weights [last term
+correlation ensemble derivatives [last term
 on the right-hand side of Eq.~\eqref{eq:exact_ener_level_dets}].
 Moreover, it has been shown that, in the thermodynamic limit, the ringium model is equivalent to the ubiquitous infinite uniform electron gas paradigm. \cite{Loos_2013,Loos_2013a}
 Let us stress that, in a finite uniform electron gas like ringium, the interacting and