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BSE-PES.tex
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BSE-PES.tex
@ -182,15 +182,14 @@
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\affiliation{\NEEL}
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\begin{abstract}
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%\begin{wrapfigure}[12]{o}[-1.25cm]{0.4\linewidth}
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% \centering
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% \includegraphics[width=\linewidth]{TOC}
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%\end{wrapfigure}
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The combination of the many-body Green's function $GW$ and the Bethe-Salpeter equation (BSE) formalisms has shown to be a promising alternative to time-dependent density-functional theory (TD-DFT) for computing vertical transition energies and oscillator strengths in molecular systems.
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The BSE formalism can also be employed to compute ground-state correlation energies thanks to the adiabatic-connection fluctuation-dissipation theorem (ACFDT).
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Here, we study the topology of the ground-state potential energy surfaces (PES) of several diatomic molecules near their equilibrium bond length.
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Thanks to comparisons with state-of-art computational approaches, we show that ACFDT@BSE is surprisingly accurate, and can even compete with coupled cluster methods in terms of total energies and equilibrium bond distances for the systems considered here.
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However, we sometimes observe unphysical irregularities on the ground-state PES in relation with the appearance of satellite resonances with a weight similar to that of the $GW$ quasiparticle peak.
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\begin{center}
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\boxed{\includegraphics[width=0.5\linewidth]{TOC}}
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\end{center}
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\end{abstract}
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\maketitle
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@ -523,27 +522,33 @@ The error (in \%) compared to the reference CC3 values are reported in square br
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}
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\label{tab:Req}
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\begin{ruledtabular}
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\begin{tabular}{llrrrrrrrr}
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& & \mc{8}{c}{Molecules} \\
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\cline{3-10}
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Method & & \ce{H2} & \ce{LiH} & \ce{LiF} & \ce{HCl} & \ce{N2} & \ce{CO} & \ce{BF} & \ce{F2} \\
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\begin{tabular}{lrrrrrrrr}
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& \mc{8}{c}{Equilibrium bond length $\Req$ (bohr) } \\
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\cline{2-9}
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Method & \tabc{\ce{H2}} & \tabc{\ce{LiH}} & \tabc{\ce{LiF}} & \tabc{\ce{HCl}} & \tabc{\ce{N2}} & \tabc{\ce{CO}} & \tabc{\ce{BF}} & \tabc{\ce{F2}} \\
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\hline
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CC3 & $\Req$ & 1.402 & 3.019 & 2.963 & 2.403 & 2.075 & 2.136 & 2.390 & 2.663 \\
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& $\Ec$ & 40.382 & 69.974 & 383.686 & 382.188 & 494.393 & 477.580 & 447.472 & 668.875 \\
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CCSD & $\Req$ & 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[$-1.58\%$] \\
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& $\Ec$ & 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[$-3.72\%$] \\
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CC2 & $\Req$ & 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[$+0.08\%$] \\
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& $\Ec$ & 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[$-2.09\%$] \\
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MP2 & $\Req$ & 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[$-1.09\%$] \\
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& $\Ec$ & 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[$-3.67\%$] \\
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BSE@{\GOWO}@HF & $\Req$ & 1.399[$-0.21\%$] & 3.017[$-0.07\%$] & (2.974)[$+0.37\%$] & \gb{(2.408)} & \gb{(2.070)} & \gb{(2.130)} & \gb{(2.383)} & (2.640)[$-0.86\%$] \\
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& $\Ec$ & 46.498[$+15.15\%$] & 78.075[$+11.58\%$] & 388.907[$+1.36\%$] & xxx.xxx[$+0.00\%$] & xxx.xxx[$+0.00\%$] & xxx.xxx[$+0.00\%$] & xxx.xxx[$+0.00\%$] & xxx.xxx[$+0.00\%$] \\
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RPA@{\GOWO}@HF & $\Req$ & 1.382[$-1.43\%$] & 2.997[$-0.73\%$] & (2.965)[$+0.07\%$] & \gb{(2.389)} & \gb{(2.043)} & \gb{(2.110)} & \gb{(2.367)} & (2.571)[$-3.45\%$] \\
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& $\Ec$ & 57.567[$+42.56\%$] & 101.092[$+44.47\%$] & 473.053[$+23.29\%$] & xxx.xxx[$+0.00\%$] & xxx.xxx[$+0.00\%$] & xxx.xxx[$+0.00\%$] & xxx.xxx[$+0.00\%$] & xxx.xxx[$+0.00\%$] \\
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RPAx@HF & $\Req$ & 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[$-3.68\%$] \\
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& $\Ec$ & 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[$-12.38\%$] \\
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RPA@HF & $\Req$ & 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[$-3.38\%$] \\
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& $\Ec$ & 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[$+16.81\%$] \\
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CC3 & 1.402 & 3.019 & 2.963 & 2.403 & 2.075 & 2.136 & 2.390 & 2.663 \\
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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[$-1.58\%$] \\
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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[$+0.08\%$] \\
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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[$-1.09\%$] \\
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BSE@{\GOWO}@HF & 1.399[$-0.21\%$] & 3.017[$-0.07\%$] & (2.974)[$+0.37\%$] & \gb{(2.408)} & \gb{(2.070)} & \gb{(2.130)} & \gb{(2.383)} & (2.640)[$-0.86\%$] \\
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RPA@{\GOWO}@HF & 1.382[$-1.43\%$] & 2.997[$-0.73\%$] & (2.965)[$+0.07\%$] & \gb{(2.389)} & \gb{(2.043)} & \gb{(2.110)} & \gb{(2.367)} & (2.571)[$-3.45\%$] \\
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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[$-3.68\%$] \\
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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[$-3.38\%$] \\
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\\
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\hline
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& \mc{8}{c}{Correlation energy $-\Ec$ (millihartree)} \\
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\cline{2-9}
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Method & \tabc{\ce{H2}} & \tabc{\ce{LiH}} & \tabc{\ce{LiF}} & \tabc{\ce{HCl}} & \tabc{\ce{N2}} & \tabc{\ce{CO}} & \tabc{\ce{BF}} & \tabc{\ce{F2}} \\
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\hline
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CC3 & 40.382 & 69.974 & 383.686 & 382.188 & 494.393 & 477.580 & 447.472 & 668.875 \\
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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[$-3.72\%$] \\
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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[$-2.09\%$] \\
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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[$-3.67\%$] \\
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BSE@{\GOWO}@HF & 46.498[$+15.15\%$] & 78.075[$+11.58\%$] & 388.907[$+1.36\%$] & xxx.xxx[$+0.00\%$] & xxx.xxx[$+0.00\%$] & xxx.xxx[$+0.00\%$] & xxx.xxx[$+0.00\%$] & xxx.xxx[$+0.00\%$] \\
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RPA@{\GOWO}@HF & 57.567[$+42.56\%$] & 101.092[$+44.47\%$] & 473.053[$+23.29\%$] & xxx.xxx[$+0.00\%$] & xxx.xxx[$+0.00\%$] & xxx.xxx[$+0.00\%$] & xxx.xxx[$+0.00\%$] & 794.324[$+18.76\%$] \\
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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[$-12.38\%$] \\
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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[$+16.81\%$] \\
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\end{tabular}
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\end{ruledtabular}
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\end{table*}
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