clean up Bruno

Manuscript/FarDFT.tex

@@ -17,6 +17,7 @@
 \usepackage[normalem]{ulem}
 \newcommand{\titou}[1]{\textcolor{red}{#1}}
 \newcommand{\cloclo}[1]{\textcolor{purple}{#1}}
+\newcommand{\bruno}[1]{\textcolor{blue}{Bruno: #1}}
 \newcommand{\trashPFL}[1]{\textcolor{red}{\sout{#1}}}
 \newcommand{\trashCM}[1]{\textcolor{purple}{\sout{#1}}}
 
@@ -117,7 +118,7 @@
 \newcommand{\LCQ}{Laboratoire de Chimie Quantique, Institut de Chimie, CNRS, Universit\'e de Strasbourg, Strasbourg, France}
 \newcommand{\UL}{Instituut-Lorentz, Universiteit Leiden, P.O.~Box 9506, 2300 RA Leiden, The Netherlands}
 \newcommand{\VU}{Division of Theoretical Chemistry, Vrije Universiteit Amsterdam, De Boelelaan 1083, 1081 HV Amsterdam, The Netherlands}
-\newcommand{\bruno}[1]{\textcolor{blue}{Bruno: #1}}
+
 \begin{document}	
 
 \title{Weight Dependence of Local Exchange-Correlation Functionals: Double Excitations in Two-Electron Systems}
@@ -639,16 +640,16 @@ The weight dependence of $\Cx{\ew{}}$ is illustrated in Fig.~\ref{fig:Cxw} (gree
 
 One clearly sees that the correction brought by GIC-S is much more gentle than at $\RHH = 1.4$ bohr, which means that the ensemble energy obtained with the LDA exchange functional is much more linear at $\RHH = 3.7$ bohr.
 In other words, the ghost-interaction ``hole'' depicted in Fig.~\ref{fig:Cxw} is thus much more shallow at stretched geometry.
-Note that this linearity at $\RHH = 3.7$ bohr was
+Note that this linearity at $\RHH = 3.7$ bohr was also observed using weight-independent xc functionals in Ref.~\onlinecite{Senjean_2015}.
-also observed using weight-independent xc-functionals in Ref.~\cite{Senjean_2015}.
 Table \ref{tab:BigTab_H2st} reports, for the aug-cc-pVTZ basis set (which delivers basis set converged results), the same set of calculations as in Table \ref{tab:BigTab_H2}.
 As a reference value, we computed a FCI/aug-cc-pV5Z excitation energy of $8.69$ eV, which compares well with previous studies. \cite{Senjean_2015}
-For $\RHH = 3.7$ bohr, it is much harder to get an accurate estimate of the excitation energy, the best match being reached with HF exchange \bruno{? I don't see it, for me HF is really bad here, especially due to its very hight dependence on the weight ! Maybe you are just referring to MOM ?}. 
+For $\RHH = 3.7$ bohr, it is much harder to get an accurate estimate of the excitation energy, the closest match being reached with HF exchange and eVWN5 correlation at equi-ensemble.
+%\bruno{? I don't see it, for me HF is really bad here, especially due to its very hight dependence on the weight ! Maybe you are just referring to MOM ?}. 
 As expected from the linearity of the ensemble energy, the GIC-S functional coupled or not with a correlation functional yield extremely stable excitation energies as a function of the weight, with only a few tenths of eV difference between the zero- and equi-weights limits.
-Nonetheless, the excitation energy is still off by 3 eV.
+Nonetheless, the excitation energy is still off by $3$ eV.
 The fundamental theoretical reason of such a poor agreement is not clear.
 The fact that HF exchange yields better excitation energies hints at the effect of self-interaction error.
-\bruno{I'm a bit surprise that the ensemble correction to the correlation functional does not improve things at all... Is the derivative discontinuity, computed with this functional, almost 0 here ?}
+%\bruno{I'm a bit surprise that the ensemble correction to the correlation functional does not improve things at all... Is the derivative discontinuity, computed with this functional, almost 0 here ?}
 
 %%% TABLE IV %%%
 \begin{table}
@@ -700,11 +701,10 @@ The parameters of the GIC-S weight-dependent exchange functional (computed with
 In other words, the ghost-interaction hole is deeper.
 The results reported in Table \ref{tab:BigTab_He} evidence this strong weight dependence of the excitation energies for HF or LDA exchange.
 
-The GIC-S exchange functional attenuates significantly this dependence, and when coupled with the eVWN5 weight-dependent correlation functional, the GIC-SeVWN5 excitation energy for $\ew{} = 0$ is only $8$ millihartree (or $0.22$ eV) off the reference value.\bruno{But also with GIC-SVWN5, as in the rest of this article, so one could wonder about the usefulness of the eVWN5 functional...}
+The GIC-S exchange functional attenuates significantly this dependence, and when coupled with the eVWN5 weight-dependent correlation functional, the GIC-SeVWN5 excitation energy for $\ew{} = 0$ is only $8$ millihartree (or $0.22$ eV) off the reference value.
-As in the case of \ce{H2}, the excitation energies obtained at zero-weight are more accurate than at equi-weight, while the opposite conclusion were
+%\bruno{But also with GIC-SVWN5, as in the rest of this article, so one could wonder about the usefulness of the eVWN5 functional...}
-made in Ref.~\cite{Loos_2020} thus strengthening the importance of
+As in the case of \ce{H2}, the excitation energies obtained at zero-weight are more accurate than at equi-weight, while the opposite conclusion were made in Ref.~\onlinecite{Loos_2020}. 
-developing weight-dependent functionals that gives linear ensemble
+This motivates further the importance of developing weight-dependent functionals that yields linear ensemble energies in order to get rid of the weight-dependency of the excitation energy.
-energies, \ie, to get rid of the weight-dependency of the excitation energy.
 As a final comment, let us stress again that the present protocol does not rely on high-level calculations as the sole requirement for constructing the GIC-S functional is the linearity of the ensemble energy with respect to the weight of the double excitation.