diff --git a/Response_Letter/Response_Letter.tex b/Response_Letter/Response_Letter.tex index 3a62773..cb0064f 100644 --- a/Response_Letter/Response_Letter.tex +++ b/Response_Letter/Response_Letter.tex @@ -219,10 +219,7 @@ manuscrit before commenting on the plots.} {Are there similar issues with combining HF exchange with LDA C as seen in the ground-state? If not, why not? } \\ - \alert{Yes, as readily seen from the data provided in the -supplemental material, similar issues appear for excited states.\manu{I -would remove your sentence and be more optimistic (see what follows). Do -you agree?}\\ + \alert{ Interestingly, increasing the ensemble weights (which of course cannot be done in conventional ground-state DFT calculations) leads to a significant improvement of the ground-state energy while either diff --git a/Revised_Manuscript/eDFT.tex b/Revised_Manuscript/eDFT.tex index 24a128e..757bdee 100644 --- a/Revised_Manuscript/eDFT.tex +++ b/Revised_Manuscript/eDFT.tex @@ -15,9 +15,9 @@ \newcommand{\alert}[1]{\textcolor{red}{#1}} \usepackage[normalem]{ulem} -\newcommand{\titou}[1]{\textcolor{red}{#1}} +\newcommand{\titou}[1]{\textcolor{black}{#1}} \newcommand{\manu}[1]{\textcolor{blue}{#1}} -\newcommand{\manurev}[1]{\textcolor{red}{#1}} +\newcommand{\manurev}[1]{\textcolor{black}{#1}} \newcommand{\trashPFL}[1]{\textcolor{red}{\sout{#1}}} \newcommand{\trashEF}[1]{\textcolor{blue}{\sout{#1}}} @@ -614,13 +614,7 @@ As shown in Sec.~\ref{sec:res}, moving from the pure ground-state picture to an equiensemble one can actually improve the ground-state energy significantly within such a scheme, thus highlighting a major difference between conventional and GOK DFT -calculations. -\manu{Manu: I changed this last sentence. Do you agree?} -%Despite the errors -%that might be introduced into the ensemble energy within such a scheme, -%cancellations may actually occur when computing excitation energies, -%which are energy \textit{differences}. -} +calculations.} The resulting KS-eLDA ensemble energy obtained via Eq.~\eqref{eq:min_with_HF_ener_fun} reads @@ -1102,19 +1096,8 @@ further details). This is a remarkable and promising result. A similar improvement is observed for the first excited state, at least in the weak correlation regime, -without deteriorating too much the second-excited-state energy. -} -\manu{Manu: do you agree with this final paragraph? I think it is -important.} -%\manu{Finally, we notice that the crossover point of the -%first-excited-state energies based on -%bi- and triensemble calculations, respectively, disappears in the strong correlation -%regime [see the right panel of Fig.~\ref{fig:EIvsW}], thus illustrating -%the importance of (individual and ensemble) densities, in -%addition to the -%weights, in the evaluation of individual energies within -%an ensemble. -%} +without deteriorating too much the second-excited-state energy.} + %%% FIG 3 %%% \begin{figure} \includegraphics[width=\linewidth]{fig5} @@ -1323,6 +1306,1169 @@ This work has been supported through the EUR grant NanoX ANR-17-EURE-0009 in the \end{acknowledgements} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\bibliography{eDFT} - +%merlin.mbs aipnum4-1.bst 2010-07-25 4.21a (PWD, AO, DPC) hacked +%Control: key (0) +%Control: author (8) initials jnrlst +%Control: editor formatted (1) identically to author +%Control: production of article title (-1) disabled +%Control: page (0) single +%Control: year (1) truncated +%Control: production of eprint (0) enabled +\begin{thebibliography}{118}% +\makeatletter +\providecommand \@ifxundefined [1]{% + \@ifx{#1\undefined} +}% +\providecommand \@ifnum [1]{% + \ifnum #1\expandafter \@firstoftwo + \else \expandafter \@secondoftwo + \fi +}% +\providecommand \@ifx [1]{% + \ifx #1\expandafter \@firstoftwo + \else \expandafter \@secondoftwo + \fi +}% +\providecommand \natexlab [1]{#1}% +\providecommand \enquote [1]{``#1''}% +\providecommand \bibnamefont [1]{#1}% +\providecommand \bibfnamefont [1]{#1}% +\providecommand \citenamefont [1]{#1}% +\providecommand \href@noop [0]{\@secondoftwo}% +\providecommand \href [0]{\begingroup \@sanitize@url \@href}% +\providecommand \@href[1]{\@@startlink{#1}\@@href}% +\providecommand \@@href[1]{\endgroup#1\@@endlink}% +\providecommand \@sanitize@url [0]{\catcode `\\12\catcode `\$12\catcode + `\&12\catcode `\#12\catcode `\^12\catcode `\_12\catcode `\%12\relax}% +\providecommand \@@startlink[1]{}% +\providecommand \@@endlink[0]{}% +\providecommand \url [0]{\begingroup\@sanitize@url \@url }% +\providecommand \@url [1]{\endgroup\@href {#1}{\urlprefix }}% +\providecommand \urlprefix [0]{URL }% +\providecommand \Eprint [0]{\href }% +\providecommand \doibase [0]{http://dx.doi.org/}% +\providecommand \selectlanguage [0]{\@gobble}% +\providecommand \bibinfo [0]{\@secondoftwo}% +\providecommand \bibfield [0]{\@secondoftwo}% +\providecommand \translation [1]{[#1]}% +\providecommand \BibitemOpen [0]{}% +\providecommand \bibitemStop [0]{}% +\providecommand \bibitemNoStop [0]{.\EOS\space}% +\providecommand \EOS [0]{\spacefactor3000\relax}% +\providecommand \BibitemShut [1]{\csname bibitem#1\endcsname}% +\let\auto@bib@innerbib\@empty +% +\bibitem [{\citenamefont {Hohenberg}\ and\ \citenamefont + {Kohn}(1964)}]{Hohenberg_1964}% + \BibitemOpen + \bibfield {author} {\bibinfo {author} {\bibfnamefont {P.}~\bibnamefont + {Hohenberg}}\ and\ \bibinfo {author} {\bibfnamefont {W.}~\bibnamefont + {Kohn}},\ }\href {\doibase 10.1103/PhysRev.136.B864} {\bibfield {journal} + {\bibinfo {journal} {Phys. 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