From 2a3dd5b8ccc9b9c340d788d8d6b66b069f11a117 Mon Sep 17 00:00:00 2001 From: Emmanuel Fromager Date: Tue, 5 May 2020 17:18:19 +0200 Subject: [PATCH] Manu: saving work --- Response_Letter/Response_Letter.tex | 19 +++++++++++++++++-- 1 file changed, 17 insertions(+), 2 deletions(-) diff --git a/Response_Letter/Response_Letter.tex b/Response_Letter/Response_Letter.tex index 7769d21..1f2a85d 100644 --- a/Response_Letter/Response_Letter.tex +++ b/Response_Letter/Response_Letter.tex @@ -62,14 +62,29 @@ refer to Sec. III for further details.} } \\ \alert{The reviewer is right. - We have added a note to clarify this point just after Eq.~(41).} + We have added a note to clarify this point after Eq.~(41).} \item {Page 5: The authors' expansion of the correlation energy around the $I$th state and its resulting neglect of correlation effects between states more remote from one another might affect evaluation and analysis of the approximation and/or the embedding scheme. Could the authors note around eqn 47 somewhere how they decided this expansion was valid and useful, as well as how they anticipate this approximation might affect their later evaluation and analysis of the approximation, and similar for the embedding scheme? This is mentioned elsewhere in the text, but treating it here would bolster the authors' narrative and support their choices more. } \\ - \alert{This part is for you Manu.} + \alert{That is a good point. In order to motivate the derivation +of these Taylor expansions more clearly, we now mention in the revised +manuscript that the individual eLDA correlation energy expressions do +not give much insight as purely individual and mixed terms cannot be +readily distinguished. This is exactly what the Taylor expansions enable +us to do. We also mention that these expansions become useful when +analyzing the performance of eLDA (we refer to the discussion section). +Most importantly, unlike in the original manuscript, we explain the +relevance of these +expansions by considering weak deviations from the uniform density +regime. Indeed, in this case, eLDA is a reasonable approximation and the +difference in density between the ensemble and the individual states is +weak. Let us finally stress that our embedding strategy does not rely on these +Taylor expansions. They are exclusively used for analysis purposes in +this work. As written explicitly in the revised manuscript, it just +gives more insight into eLDA.} \item {Page 5: Though the ringium model is developed elsewhere in the literature in great detail, a diagram for readers not as familiar with it would be a kindness. }