update rev

This commit is contained in:
Pierre-Francois Loos 2020-03-20 15:52:15 +01:00
parent 6ff9ad3d11
commit 9aa3b73aa9
32 changed files with 165 additions and 64 deletions

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14
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13
Data/scan_HCl_VQZ_BSE.dat Normal file
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@ -1,11 +1,11 @@
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1.8 -108.9361504777 -0.4460695736 -0.5583975896 -0.0000000000 -0.5583975896 0.0000000000 -0.3988905727 -0.2701218670 -0.4161835292 0.0000000000 -0.5686451959 0.0000000000 -0.4030516358 -0.0860763992 -0.4723666106 0.0000000000 0.457496 0.467925 0.467925 0.474174 0.474174 0.372758 0.388115 0.388115 0.412605 0.412605 0.904711 0.909761 0.909761 0.933848 0.933848 0.865735 0.865735 0.904711 0.904711 0.904711 0.446033 0.461173 0.461173 0.467759 0.467759 0.324910 0.378419 0.378419 0.381357 0.381357 0.463884 0.463884 0.496861 0.516664 0.516664 0.440498 0.440498 0.484042 0.510200 0.510200 0.440498 0.440498 0.484042 0.510200 0.510200 0.440498 0.440498 0.484042 0.510200 0.510200 0.440498 0.440498 0.484042 0.510200 0.510200 0.440498 0.440498 0.484042 0.510200 0.510200
1.9 -108.9801623695 -0.4554641897 -0.5624585195 -0.0000000000 -0.5624585195 0.0000000000 -0.4080100394 -0.2880173704 -0.4203768551 0.0000000000 -0.5717540127 0.0000000000 -0.4097216478 -0.0963493058 -0.4780648997 0.0000000000 0.400389 0.418556 0.418556 0.430136 0.430136 0.315841 0.352013 0.352013 0.355626 0.355626 0.851561 0.882565 0.882565 0.884173 0.884173 0.836750 0.836750 0.851561 0.851561 0.851561 0.386197 0.410768 0.410768 0.422560 0.422560 0.255610 0.317786 0.317786 0.341017 0.341017 0.427872 0.427872 0.442308 0.463787 0.463787 0.406008 0.406008 0.427549 0.454140 0.454140 0.406008 0.406008 0.427549 0.454140 0.454140 0.406008 0.406008 0.427549 0.454140 0.454140 0.406008 0.406008 0.427549 0.454140 0.454140 0.406008 0.406008 0.427549 0.454140 0.454140
2 -108.9946017517 -0.4664403366 -0.5671886068 0.0000000000 -0.5671886068 0.0000000000 -0.4189551669 -0.3123176547 -0.4250927988 0.0000000000 -0.5776787503 0.0000000000 -0.4196950961 -0.1138135037 -0.4874752514 0.0000000000 0.348287 0.367744 0.367744 0.393894 0.393894 0.264202 0.303801 0.303801 0.317965 0.317965 0.801167 0.836791 0.836791 0.854316 0.854316 0.801167 0.801167 0.801167 0.801167 0.807524 0.330715 0.358275 0.358275 0.385378 0.385378 0.185515 0.257284 0.257284 0.305373 0.305373 0.392517 0.393610 0.393610 0.415421 0.415421 0.372696 0.372696 0.374181 0.400172 0.400172 0.372696 0.372696 0.374181 0.400172 0.400172 0.372696 0.372696 0.374181 0.400172 0.400172 0.372696 0.372696 0.374181 0.400172 0.400172 0.372696 0.372696 0.374181 0.400172 0.400172
2.1 -108.9881230895 -0.4791120944 -0.5726225461 0.0000000000 -0.5726225461 0.0000000000 -0.4320345427 -0.3495372446 -0.4302937799 0.0000000000 -0.5836173129 0.0000000000 -0.4300898724 -0.1412806858 -0.4969855383 NaN 0.300807 0.321391 0.321391 0.359371 0.359371 0.217376 0.256692 0.256692 0.285963 0.285963 0.753663 0.791816 0.791816 0.825495 0.825495 0.753663 0.753663 0.753663 0.753663 0.778445 0.278946 0.309832 0.309832 0.349742 0.349742 0.104631 0.197990 0.197990 0.271359 0.271359 0.347348 0.361609 0.361609 0.371469 0.371469 0.322676 0.340352 0.340352 0.347714 0.347714 0.322676 0.340352 0.340352 0.347714 0.347714 0.322676 0.340352 0.340352 0.347714 0.347714 0.322676 0.340352 0.340352 0.347714 0.347714 0.322676 0.340352 0.340352 0.347714 0.347714
2.2 -108.9670794745 -0.4935754689 -0.5787550602 0.0000000000 -0.5787550602 0.0000000000 -0.4476875711 -0.4099821671 -0.4359011308 NaN -0.5898656723 0.0000000000 -0.4410798787 -0.1845550493 -0.5066397194 NaN 0.257570 0.279144 0.279144 0.326594 0.326594 0.174915 0.213878 0.213878 0.255903 0.255903 0.709117 0.749347 0.749347 0.796481 0.796481 0.709117 0.709117 0.709117 0.709117 0.749768 0.230090 0.264943 0.264943 0.315617 0.315617 0.000000 0.135906 0.135906 0.230090 0.238701 0.306551 0.331697 0.331697 0.331931 0.331931 0.270788 0.294624 0.294624 0.308664 0.308664 0.270788 0.294624 0.294624 0.308664 0.308664 0.270788 0.294624 0.294624 0.308664 0.308664 0.270788 0.294624 0.294624 0.308664 0.308664 0.270788 0.294624 0.294624 0.308664 0.308664
2.3 -108.9361377332 -0.5098994345 -0.5855324480 -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

View File

@ -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.

View File

@ -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}

View File

@ -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}