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HCl done

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Pierre-Francois Loos 2020-02-10 20:42:34 +01:00
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12
BSE-PES.tex
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@ -534,11 +534,10 @@ The error (in \%) compared to the reference CC3 values are reported in square br
CCSD & 1.402[$+0.00\%$] & 3.020[$+0.03\%$] & 2.953[$-0.34\%$] & 2.398[$-0.21\%$] & 2.059[$-0.77\%$] & 2.118[$-0.84\%$] & 2.380[$-0.42\%$] & 2.621[$-1.58\%$] \\
CC2 & 1.391[$-0.78\%$] & 2.989[$-0.99\%$] & 2.982[$+0.64\%$] & 2.396[$-0.29\%$] & 2.106[$+1.49\%$] & 2.156[$+0.94\%$] & 2.393[$+0.13\%$] & 2.665[$+0.08\%$] \\
MP2 & 1.391[$-0.78\%$] & 3.008[$-0.36\%$] & 2.970[$+0.24\%$] & 2.395[$-0.33\%$] & 2.091[$+0.77\%$] & 2.137[$+0.05\%$] & 2.382[$-0.33\%$] & 2.634[$-1.09\%$] \\
BSE@{\GOWO}@HF & 1.399[$-0.21\%$] & 3.017[$-0.07\%$] & (2.974)[$+0.37\%$] & \gb{(2.408)} & 2.065[$-0.48\%$] & 2.134[$-0.09\%$] & 2.385[$-0.21\%$] & (2.640)[$-0.86\%$] \\
RPA@{\GOWO}@HF & 1.382[$-1.43\%$] & 2.997[$-0.73\%$] & (2.965)[$+0.07\%$] & \gb{(2.389)} & 2.043[$-1.54\%$] & 2.132[$-0.19\%$] & 2.365[$-1.05\%$] & (2.571)[$-3.45\%$] \\
BSE@{\GOWO}@HF & 1.399[$-0.21\%$] & 3.017[$-0.07\%$] & (2.974)[$+0.37\%$] & 2.400[$-0.12\%$] & 2.065[$-0.48\%$] & 2.134[$-0.09\%$] & 2.385[$-0.21\%$] & (2.640)[$-0.86\%$] \\
RPA@{\GOWO}@HF & 1.382[$-1.43\%$] & 2.997[$-0.73\%$] & (2.965)[$+0.07\%$] & 2.370[$-1.50\%$] & 2.043[$-1.54\%$] & 2.132[$-0.19\%$] & 2.365[$-1.05\%$] & (2.571)[$-3.45\%$] \\
RPAx@HF & 1.394[$-0.57\%$] & 3.011[$-0.26\%$] & 2.944[$-0.64\%$] & 2.391[$-0.50\%$] & 2.041[$-1.64\%$] & 2.104[$-1.50\%$] & 2.366[$-1.00\%$] & 2.565[$-3.68\%$] \\
RPA@HF & 1.386[$-1.14\%$] & 2.994[$-0.83\%$] & 2.946[$-0.57\%$] & 2.382[$-0.87\%$] & 2.042[$-1.59\%$] & 2.103[$-1.54\%$] & 2.364[$-1.09\%$] & 2.573[$-3.38\%$] \\
\\
\hline
& \mc{8}{c}{Correlation energy $-\Ec$ (millihartree)} \\
\cline{2-9}
@ -548,8 +547,8 @@ The error (in \%) compared to the reference CC3 values are reported in square br
CCSD & 40.382[$+0.00\%$] & 69.845[$-0.18\%$] & 372.580[$-2.89\%$] & 370.764[$-2.99\%$] & 470.627[$-4.81\%$] & 455.214[$-4.68\%$] & 432.856[$-3.27\%$] & 644.001[$-3.72\%$] \\
CC2 & 33.259[$-17.64\%$] & 57.289[$-18.13\%$] & 376.712[$-1.82\%$] & 356.909[$-6.61\%$] & 488.017[$-1.29\%$] & 465.492[$-2.53\%$] & 427.285[$-4.51\%$] & 654.878[$-2.09\%$] \\
MP2 & 33.164[$-17.87\%$] & 57.930[$-17.21\%$] & 372.997[$-2.79\%$] & 355.652[$-6.94\%$] & 477.951[$-3.33\%$] & 455.020[$-4.72\%$] & 421.600[$-5.78\%$] & 644.349[$-3.67\%$] \\
BSE@{\GOWO}@HF & 46.498[$+15.15\%$] & 78.075[$+11.58\%$] & 388.907[$+1.36\%$] & xxx.xxx[$+0.00\%$] & 499.145[$+0.96\%$] & 481.151[$+0.75\%$] & 453.137[$+1.27\%$] & 675.701[$+1.02\%$] \\
RPA@{\GOWO}@HF & 57.567[$+42.56\%$] & 101.092[$+44.47\%$] & 473.053[$+23.29\%$] & xxx.xxx[$+0.00\%$] & 580.318[$+17.38\%$] & 566.536[$+18.63\%$] & 545.546[$+21.92\%$] & 794.324[$+18.76\%$] \\
BSE@{\GOWO}@HF & 46.498[$+15.15\%$] & 78.075[$+11.58\%$] & 388.907[$+1.36\%$] & 385.864[$+0.96\%$] & 499.145[$+0.96\%$] & 481.151[$+0.75\%$] & 453.137[$+1.27\%$] & 675.701[$+1.02\%$] \\
RPA@{\GOWO}@HF & 57.567[$+42.56\%$] & 101.092[$+44.47\%$] & 473.053[$+23.29\%$] & 451.232[$+18.07\%$] & 580.318[$+17.38\%$] & 566.536[$+18.63\%$] & 545.546[$+21.92\%$] & 794.324[$+18.76\%$] \\
RPAx@HF & 37.886[$-6.18\%$] & 65.203[$-6.82\%$] & 343.604[$-10.45\%$] & 344.249[$-9.93\%$] & 427.170[$-13.60\%$] & 416.315[$-12.83\%$] & 399.060[$-10.82\%$] & 586.090[$-12.38\%$] \\
RPA@HF & 57.332[$+41.98\%$] & 100.164[$+43.15\%$] & 465.905[$+21.43\%$] & 442.675[$+15.83\%$] & 569.384[$+15.17\%$] & 555.857[$+16.39\%$] & 537.685[$+20.16\%$] & 781.323[$+16.81\%$] \\
\end{tabular}
@ -579,8 +578,7 @@ Moreover, this is consistent with the study by Maggio and Kresse on the HEG show
Similarly, the much larger overestimation of the correlation energy that we observe at the RPA@$GW$ level was also observed for the HEG.
Care must be taken however in drawing comparisons since the HEG study of Ref.~\onlinecite{Maggio_2016} was performed starting with LDA eigenstates.
For \ce{HCl}, the data reported in Table \ref{tab:Req} show that the BSE@{\GOWO}@HF equilibrium bond length is again in very good agreement with its CC3 counterpart.
In contrast to CCSD which is known to provide slightly shorter bond lengths, ACFDT@BSE underestimates the bond lengths by a few hundredths of bohr.
For \ce{HCl}, the data reported in Table \ref{tab:Req} show that the BSE@{\GOWO}@HF equilibrium bond length is again in very good agreement with its CC3 counterpart as it underestimates the bond lengths by a few hundredths of bohr only.
However, in the case of \ce{LiF}, the attentive reader can observe a small ``glitch'' in the $GW$-based curves very close to their minimum.
As observed in Refs.~\onlinecite{vanSetten_2015,Maggio_2017,Loos_2018} and explained in details in Refs.~\onlinecite{Veril_2018,Duchemin_2020}, these irregularities, which makes particularly tricky the location of the minima, are due to ``jumps'' between distinct solutions of the $GW$ quasiparticle equation.
Including a broadening via an increase of the $\eta$ value entering in the expression of the $GW$ self-energy and the screened Coulomb operator softens the problem, but does not remove it completely.

4
SI/BSE-PES-SI.tex
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@ -208,10 +208,10 @@ 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)} &\gb{2.408} &\rb{2.065} &\rb{2.134} &\rb{2.383} &\rb{(2.640)}\\
& 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)}\\
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) &\gb{2.389} & 2.043 & 2.132 & 2.367 & (2.571) \\
& cc-pVQZ & 1.382 & 2.997 & (2.965) & 2.370 & 2.043 & 2.132 & 2.367 & (2.571) \\
RPAx@HF & cc-pVDZ & 1.428 & 3.040 & 2.998 & 2.424 & 2.077 & 2.130 & 2.417 & 2.611 \\
& cc-pVTZ & 1.395 & 3.003 & 2.943 & 2.400 & 2.046 & 2.110 & 2.368 & 2.568 \\
& cc-pVQZ & 1.394 & 3.011 & 2.944 & 2.391 & 2.041 & 2.104 & 2.366 & 2.565 \\