From 9aa3b73aa9794a9012225cd5f0e2a40b2f8d06c3 Mon Sep 17 00:00:00 2001 From: Pierre-Francois Loos Date: Fri, 20 Mar 2020 15:52:15 +0100 Subject: [PATCH] update rev --- Data/BF_GS_VQZ.pdf | Bin 42897 -> 42100 bytes Data/BF_GS_VQZ_BSE.pdf | Bin 0 -> 41326 bytes Data/CO_GS_VDZ.pdf | Bin 57732 -> 57702 bytes Data/CO_GS_VQZ.pdf | Bin 37749 -> 37596 bytes Data/CO_GS_VQZ_BSE.pdf | Bin 0 -> 37554 bytes Data/F2_GS_VQZ.pdf | Bin 58427 -> 56362 bytes Data/F2_GS_VQZ_BSE.pdf | Bin 0 -> 56362 bytes Data/H2_GS_VDZ.pdf | Bin 64682 -> 64645 bytes Data/H2_GS_VQZ.pdf | Bin 57151 -> 51358 bytes Data/H2_GS_VQZ_BSE.pdf | Bin 0 -> 51454 bytes Data/H2_GS_VTZ.pdf | Bin 62769 -> 62697 bytes Data/HCl_GS_VQZ.pdf | Bin 40024 -> 39875 bytes Data/HCl_GS_VQZ_BSE.pdf | Bin 0 -> 39944 bytes Data/LiF_GS_VQZ.pdf | Bin 54260 -> 54400 bytes Data/LiF_GS_VQZ_BSE.pdf | Bin 0 -> 54395 bytes Data/LiH_GS_VQZ.pdf | Bin 53762 -> 53684 bytes Data/LiH_GS_VQZ_BSE.pdf | Bin 0 -> 53703 bytes Data/N2_GS_VQZ.pdf | Bin 50527 -> 50689 bytes Data/N2_GS_VQZ_BSE.pdf | Bin 0 -> 49870 bytes Data/scan_BF_VQZ_BSE.dat | 14 +++++++++ Data/scan_CO_VDZ_ppRPA.dat | 12 ++++++++ Data/scan_CO_VQZ_BSE.dat | 12 ++++++++ Data/scan_F2_VQZ_BSE.dat | 14 +++++++++ Data/scan_H2_VQZ_FCI.dat | 43 +++++++++++++++++++--------- Data/scan_HCl_VQZ.dat | 26 ++++++++--------- Data/scan_HCl_VQZ_BSE.dat | 13 +++++++++ Data/scan_LiF_VQZ.dat | 22 +++++++------- Data/scan_LiF_VQZ_BSE.dat | 11 +++++++ Data/scan_N2_VQZ_BSE.dat | 9 ++++++ Response_Letter/Response_Letter.tex | 9 +++--- Revised/BSE-PES.tex | 8 +++--- SI/BSE-PES-SI.tex | 36 +++++++++++------------ 32 files changed, 165 insertions(+), 64 deletions(-) create mode 100644 Data/BF_GS_VQZ_BSE.pdf create mode 100644 Data/CO_GS_VQZ_BSE.pdf create mode 100644 Data/F2_GS_VQZ_BSE.pdf create mode 100644 Data/H2_GS_VQZ_BSE.pdf create mode 100644 Data/HCl_GS_VQZ_BSE.pdf create mode 100644 Data/LiF_GS_VQZ_BSE.pdf create mode 100644 Data/LiH_GS_VQZ_BSE.pdf create mode 100644 Data/N2_GS_VQZ_BSE.pdf create 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-0.0000000000 -0.5855324480 0.0000000000 -0.4666084737 -0.4481938871 -0.4417811570 NaN -0.5965855159 0.0000000000 -0.4530616461 -0.2532874748 -0.5172992703 NaN 0.218210 0.240664 0.240664 0.295514 0.295514 0.136401 0.174968 0.174968 0.218210 0.227636 0.667528 0.709441 0.709441 0.767558 0.767558 0.667528 0.667528 0.667528 0.667528 0.721645 0.183021 0.223046 0.223046 0.282874 0.282874 0.000000 0.052450 0.052450 0.183021 0.206998 0.269820 0.295828 0.295828 0.304556 0.304556 0.214341 0.237024 0.237024 0.260289 0.276649 0.214341 0.237024 0.237024 0.260289 0.276649 0.214341 0.237024 0.237024 0.260289 0.276649 0.214341 0.237024 0.237024 0.260289 0.276649 0.214341 0.237024 0.237024 0.260289 0.276649 +2.4 -108.8987236128 -0.5281313364 -0.5928701090 -0.0000000000 -0.5928701090 0.0000000000 -0.4900986312 -0.4649454329 -0.4477379259 NaN -0.6039509489 0.0000000000 -0.4659418541 -0.3685709573 -0.5282201486 NaN 0.182387 0.205627 0.205627 0.266049 0.266049 0.101452 0.139601 0.139601 0.182387 0.200997 0.628835 0.672102 0.672102 0.738925 0.738925 0.628835 0.628835 0.628835 0.628835 0.694159 0.135758 0.183455 0.183455 0.251330 0.251330 0.000000 0.000000 0.000000 0.135758 0.175694 0.236822 0.263543 0.263543 0.279353 0.279353 0.142741 0.165690 0.165690 0.188919 0.242887 0.142741 0.165690 0.165690 0.188919 0.242887 0.142741 0.165690 0.165690 0.188919 0.242887 0.142741 0.165690 0.165690 0.188919 0.242887 0.142741 0.165690 0.165690 0.188919 0.242887 +2.5 -108.8573423789 -0.5483083335 -0.6006808993 -0.0000000000 -0.6006808993 0.0000000000 -0.5215111580 -0.4417493640 -0.4534886684 NaN -0.6109258311 0.0000000000 -0.4787560546 -0.6637564240 -0.5407665357 NaN 0.149785 0.173733 0.173733 0.238115 0.238115 0.069722 0.107445 0.107445 0.149785 0.175833 0.592937 0.637291 0.637291 0.710727 0.710727 0.592937 0.592937 0.592937 0.592937 0.667355 0.082966 0.145204 0.145204 0.220763 0.220763 0.000000 0.000000 0.000000 0.082966 0.143949 0.207232 0.234536 0.234536 0.256189 0.256189 0.000000 0.000000 0.000000 0.064094 0.205369 0.000000 0.000000 0.000000 0.064094 0.205369 0.000000 0.000000 0.000000 0.064094 0.205369 0.000000 0.000000 0.000000 0.064094 0.205369 0.000000 0.000000 0.000000 0.064094 0.205369 diff --git a/Response_Letter/Response_Letter.tex b/Response_Letter/Response_Letter.tex index d0aa19e..066e585 100644 --- a/Response_Letter/Response_Letter.tex +++ b/Response_Letter/Response_Letter.tex @@ -160,15 +160,16 @@ We look forward to hearing from you. \\ \alert{We thank the reviewer for spotting this unfortunate typo. We have indeed forgotten a factor 2 in the definition of $\Tilde{A}$. - This has been corrected.} + This has been corrected. + Note that this factor 2 was present in our code.} \item {The authors point out that the approach that they denote as ``BSE'' had been named ``XBS'' by the authors of Ref.~67. It would be very helpful if results could be presented not only for this ``XBS'' approach but also for what the authors of Ref.~67 denote as ``BSE''.} \\ - \alert{We have added in the supplementary information the ``BSE'' numbers, as described in Ref.~67. - The various PES obtained at this level of theory have been also reported in the supplementary information, and compared to the ``XBS'' scheme.} -% As one can see, we found the ``XBS'' scheme significantly superior to the ``BSE'' scheme.} + \alert{We have added in the supplementary information the ``BSE'' correlation energies (as described in Ref.~67) computed at the XBS equilibrium geometries. + The various PES obtained at this level of theory are not reported as they are very similar to the XBS ones. + As one can see from these new values, we found the ``BSE'' and ``XBS'' schemes yield very similar results, and that the ``BSE'' scheme seems to provide slightly more accurate results due to compensation of errors.} \item {I have tried to reproduce the results presented in Table 1 by computing the correlation energy for the given bond length using the TURBOMOLE package of programs. diff --git a/Revised/BSE-PES.tex b/Revised/BSE-PES.tex index ec2d092..7cac43b 100644 --- a/Revised/BSE-PES.tex +++ b/Revised/BSE-PES.tex @@ -421,7 +421,7 @@ is the interaction kernel \cite{Angyan_2011, Holzer_2018} [with $\tA{ia,jb}{\IS} \end{equation} is the correlation part of the two-electron density matrix at interaction strength $\IS$, and $\Tr$ denotes the matrix trace. Note that the present definition of the BSE correlation energy [see Eq.~\eqref{eq:EcBSE}], which we refer to as BSE@$GW$@HF in the following, has been named ``XBS'' for ``extended Bethe Salpeter'' by Holzer \textit{et al.} \cite{Holzer_2018} -\titou{Comparison between the extended and regular BSE schemes can be found in the {\SI}.} +\titou{For the sake of completeness, comparisons between the extended and regular BSE schemes can be found in the {\SI}.} In contrast to DFT where the electron density is fixed along the adiabatic path, in the present formalism, the density is not maintained as $\IS$ varies. Therefore, an additional contribution to Eq.~\eqref{eq:EcBSE} originating from the variation of the Green's function along the adiabatic connection should be, in principle, added. However, as commonly done within RPA and RPAx, \cite{Toulouse_2009, Toulouse_2010, Colonna_2014, Holzer_2018} we shall neglect it in the present study. @@ -538,9 +538,9 @@ The error (in \%) compared to the reference CC3 values are reported in square br \hline CC3 & 1.402 & 3.019 & 2.963 & 2.403 & 2.075 & 2.136 & 2.390 & 2.663 \\ CCSD & 1.402[$+0.0\%$] & 3.020[$+0.0\%$] & 2.953[$-0.3\%$] & 2.398[$-0.2\%$] & 2.059[$-0.8\%$] & 2.118[$-0.8\%$] & 2.380[$-0.4\%$] & 2.621[$-1.6\%$] \\ - CC2 & 1.391[$-0.8\%$] & \titou{3.010}[$-1.0\%$] & 2.982[$+0.6\%$] & 2.396[$-0.3\%$] & 2.106[$+1.5\%$] & 2.156[$+0.9\%$] & 2.393[$+0.1\%$] & 2.665[$+0.1\%$] \\ + CC2 & 1.391[$-0.8\%$] & \titou{3.010[$-0.3\%$]} & 2.982[$+0.6\%$] & 2.396[$-0.3\%$] & 2.106[$+1.5\%$] & 2.156[$+0.9\%$] & 2.393[$+0.1\%$] & 2.665[$+0.1\%$] \\ MP2 & 1.391[$-0.8\%$] & 3.008[$-0.4\%$] & 2.970[$+0.2\%$] & 2.395[$-0.3\%$] & 2.091[$+0.8\%$] & 2.137[$+0.1\%$] & 2.382[$-0.3\%$] & 2.634[$-1.1\%$] \\ - BSE@{\GOWO}@HF & 1.399[$-0.2\%$] & 3.017[$-0.1\%$] & (2.974)[$+0.4\%$] & 2.400[$-0.1\%$] & 2.065[$-0.5\%$] & 2.134[$-0.1\%$] & 2.385[$-0.2\%$] & (2.640)[$-0.9\%$] \\ + BSE@{\GOWO}@HF & 1.399[$-0.2\%$] & 3.017[$-0.1\%$] & (2.973)[$+0.3\%$] & 2.400[$-0.1\%$] & 2.065[$-0.5\%$] & 2.134[$-0.1\%$] & 2.385[$-0.2\%$] & (2.638)[$-0.9\%$] \\ RPA@{\GOWO}@HF & 1.382[$-1.4\%$] & 2.997[$-0.7\%$] & (2.965)[$+0.1\%$] & 2.370[$-1.5\%$] & 2.043[$-1.5\%$] & 2.132[$-0.2\%$] & 2.365[$-1.1\%$] & (2.571)[$-3.5\%$] \\ RPAx@HF & 1.394[$-0.6\%$] & 3.011[$-0.3\%$] & 2.944[$-0.6\%$] & 2.391[$-0.5\%$] & 2.041[$-1.6\%$] & 2.104[$-1.5\%$] & 2.366[$-1.0\%$] & 2.565[$-3.7\%$] \\ RPA@HF & 1.386[$-1.1\%$] & 2.994[$-0.8\%$] & 2.946[$-0.6\%$] & 2.382[$-0.9\%$] & 2.042[$-1.6\%$] & 2.103[$-1.5\%$] & 2.364[$-1.1\%$] & 2.573[$-3.4\%$] \\ @@ -645,7 +645,7 @@ This work has also been supported through the EUR grant NanoX ANR-17-EURE-0009 i \section*{Supporting Information} %%%%%%%%%%%%%%%%%%%%%%%% See {\SI} for additional potential energy curves computed with other basis sets and within the frozen-core approximation, as well as tables gathering equilibrium distances for smaller basis sets (cc-pVDZ and cc-pVTZ). -\titou{Comparisons between the extended and regular BSE schemes (correlation energies at equilibrium geometries and potential energy surfaces).} +\titou{Comparisons between the extended and regular BSE schemes (correlation energies at equilibrium geometries).} \bibliography{BSE-PES,BSE-PES-control} diff --git a/SI/BSE-PES-SI.tex b/SI/BSE-PES-SI.tex index 3e4ac92..d9f7c02 100644 --- a/SI/BSE-PES-SI.tex +++ b/SI/BSE-PES-SI.tex @@ -208,7 +208,7 @@ When irregularities appear in the PES, the values are reported in parenthesis an & cc-pVQZ & 1.391 & 3.008 & 2.970 & 2.395 & 2.091 & 2.137 & 2.382 & 2.634 \\ BSE@{\GOWO}@HF & cc-pVDZ & 1.437 & 3.042 & 3.000 & 2.454 & 2.107 & 2.153 & 2.407 & (2.698) \\ & cc-pVTZ & 1.404 & 3.023 & (2.982) & 2.410 & 2.068 & 2.116 & (2.389) & (2.647) \\ - & cc-pVQZ &\rb{1.399} &\rb{3.017} &\rb{(2.974)} &\rb{2.400} &\rb{2.065} &\rb{2.134} &\rb{2.383} &\rb{(2.640)}\\ + & cc-pVQZ &\rb{1.399} &\rb{3.017} &\rb{(2.973)} &\rb{2.400} &\rb{2.065} &\rb{2.134} &\rb{2.383} &\rb{(2.638)}\\ RPA@{\GOWO}@HF & cc-pVDZ & 1.426 & 3.019 & 2.994 & 2.436 & 2.083 & 2.144 & 2.403 & (2.629) \\ & cc-pVTZ & 1.388 & 2.988 & (2.965) & 2.408 & 2.055 & 2.114 & (2.370) & (2.584) \\ & cc-pVQZ & 1.382 & 2.997 & (2.965) & 2.370 & 2.043 & 2.132 & 2.367 & (2.571) \\ @@ -416,31 +416,31 @@ All the calculations have been performed without frozen-core approximation with \label{fig:XBS} } \begin{ruledtabular} -\begin{tabular}{lllcc} +\begin{tabular}{lllrr} System & Geometry & Method & $-\Ec$ (mHa) & Error wrt CC3 (\%) \\ \hline \ce{H2} & $R_{\ce{H-H}} = 1.399$ -& BSE & $46.480$ & $+15.10\%$ \\ -& & XBS & $47.209$ & $+16.91\%$ \\ +& BSE & $46.5$ & $+15.1\%$ \\ +& & XBS & $47.2$ & $+16.9\%$ \\ \ce{LiH} & $R_{\ce{Li-H}} = 3.017$ -& BSE & $77.973$ & $+11.43\%$ \\ -& & XBS & $78.110$ & $+11.63\%$ \\ -\ce{LiF} & $R_{\ce{Li-F}} = 2.974$ -& BSE & $388.307$ & $+1.20\%$ \\ -& & XBS & $385.041$ & $+0.35\%$ \\ +& BSE & $78.0$ & $+11.4\%$ \\ +& & XBS & $78.1$ & $+11.6\%$ \\ +\ce{LiF} & $R_{\ce{Li-F}} = 2.973$ +& BSE & $388.3$ & $+1.2\%$ \\ +& & XBS & $385.0$ & $+0.4\%$ \\ \ce{HCl} & $R_{\ce{H-Cl}} = 2.400$ -& BSE & $385.147$ & $+0.77\%$ \\ -& & XBS & $384.544$ & $+0.62\%$ \\ +& BSE & $385.1$ & $+0.8\%$ \\ +& & XBS & $384.5$ & $+0.6\%$ \\ \ce{N2} & $R_{\ce{N-N}} = 2.065$ -& BSE & $493.742$ & $-0.13\%$ \\ -& & XBS & $497.856$ & $+0.70\%$ \\ +& BSE & $493.7$ & $-0.1\%$ \\ +& & XBS & $497.9$ & $+0.7\%$ \\ \ce{CO} & $R_{\ce{C-O}} = 2.134$ -& BSE & $476.210$ & $-0.29\%$ \\ -& & XBS & $480.023$ & $+0.51\%$ \\ +& BSE & $476.2$ & $-0.3\%$ \\ +& & XBS & $480.0$ & $+0.5\%$ \\ \ce{BF} & $R_{\ce{B-F}} = 2.385$ -& BSE & $x$ & $x\%$ \\ -& & XBS & $452.337$ & $1.09\%$ \\ -\ce{F2} & $R_{\ce{F-F}} = 2.640$ +& BSE & $450.0$ & $+0.6\%$ \\ +& & XBS & $452.3$ & $+1.1\%$ \\ +\ce{F2} & $R_{\ce{F-F}} = 2.638$ & BSE & $x$ & $x\%$ \\ & & XBS & $x$ & $x\%$ \\ \end{tabular}