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BSEdyn.bib
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BSEdyn.bib
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%% This BibTeX bibliography file was created using BibDesk.
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%% Created for Pierre-Francois Loos at 2020-05-19 17:13:25 +0200
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%% Created for Pierre-Francois Loos at 2020-05-20 22:07:58 +0200
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@article{Baumeier_2012a,
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Author = {Baumeier, Bj\"{o}rn and Andrienko, Denis and Rohlfing, Michael},
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Date-Added = {2020-05-20 22:01:43 +0200},
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Date-Modified = {2020-05-20 22:02:47 +0200},
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Doi = {10.1021/ct300311x},
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Journal = {J. Chem. Theory Comput.},
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Number = {8},
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Pages = {2790-2795},
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Title = {Frenkel and Charge-Transfer Excitations in Donor--Acceptor Complexes From Many-Body Green's Functions Theory},
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Volume = {8},
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Year = {2012},
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Bdsk-Url-1 = {https://doi.org/10.1021/ct300311x}}
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@article{Ma_2009a,
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Author = {Ma, Yuchen and Rohlfing, Michael and Molteni, Carla},
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Date-Added = {2020-05-20 21:59:09 +0200},
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Date-Modified = {2020-05-20 21:59:12 +0200},
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Doi = {10.1103/PhysRevB.80.241405},
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Issue = {24},
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Journal = {Phys. Rev. B},
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Month = {Dec},
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Numpages = {4},
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Pages = {241405},
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Publisher = {American Physical Society},
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Title = {Excited states of biological chromophores studied using many-body perturbation theory: Effects of resonant-antiresonant coupling and dynamical screening},
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Url = {https://link.aps.org/doi/10.1103/PhysRevB.80.241405},
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Volume = {80},
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Year = {2009},
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Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.80.241405},
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Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevB.80.241405}}
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@misc{QuAcK,
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@misc{QuAcK,
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Author = {P. F. Loos},
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Author = {P. F. Loos},
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Date-Added = {2020-05-19 16:22:58 +0200},
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Date-Added = {2020-05-19 16:22:58 +0200},
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@ -1594,20 +1625,15 @@
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Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S002199911730671X},
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Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S002199911730671X},
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Bdsk-Url-2 = {https://doi.org/10.1016/j.jcp.2017.09.012}}
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Bdsk-Url-2 = {https://doi.org/10.1016/j.jcp.2017.09.012}}
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@article{Ma_2009,
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@article{Ma_2009b,
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Author = {Ma, Yuchen and Rohlfing, Michael and Molteni, Carla},
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Author = {Ma, Yuchen and Rohlfing, Michael and Molteni, Carla},
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Date-Added = {2020-05-18 21:40:28 +0200},
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Date-Added = {2020-05-18 21:40:28 +0200},
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Date-Modified = {2020-05-18 21:40:28 +0200},
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Date-Modified = {2020-05-20 22:00:24 +0200},
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Doi = {10.1103/PhysRevB.80.241405},
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Doi = {10.1021/ct900528h},
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Issue = {24},
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Journal = {J. Chem. Theory. Comput.},
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Journal = {Phys. Rev. B},
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Pages = {257--265},
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Month = {Dec},
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Title = {Modeling the Excited States of Biological Chromophores within Many-Body Green's Function Theory},
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Numpages = {4},
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Volume = {6},
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Pages = {241405},
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Publisher = {American Physical Society},
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Title = {Excited states of biological chromophores studied using many-body perturbation theory: Effects of resonant-antiresonant coupling and dynamical screening},
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Url = {https://link.aps.org/doi/10.1103/PhysRevB.80.241405},
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Volume = {80},
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Year = {2009},
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Year = {2009},
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Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.80.241405},
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Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.80.241405},
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Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevB.80.241405}}
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Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevB.80.241405}}
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@ -14319,14 +14345,13 @@
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Year = {2011},
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Year = {2011},
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Bdsk-Url-1 = {https://doi.org/10.1063/1.3655352}}
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Bdsk-Url-1 = {https://doi.org/10.1063/1.3655352}}
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@article{Baumeier_2012,
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@article{Baumeier_2012b,
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Author = {Baumeier, Bj\"{o}rn and Andrienko, Denis and Rohlfing, Michael},
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Author = {Baumeier, Bj\"{o}rn and Andrienko, Denis and Ma, Yuchen and Rohlfing, Michael},
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Date-Modified = {2020-02-05 20:52:41 +0100},
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Date-Modified = {2020-05-20 22:02:44 +0200},
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Doi = {10.1021/ct300311x},
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Doi = {10.1021/ct2008999},
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Journal = {J. Chem. Theory Comput.},
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Journal = {J. Chem. Theory Comput.},
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Number = {8},
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Pages = {997--1002},
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Pages = {2790-2795},
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Title = {Excited States of Dicyanovinyl-Substituted Oligothiophenes from Many-Body Green's Functions Theory},
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Title = {Frenkel and Charge-Transfer Excitations in Donor--Acceptor Complexes From Many-Body Green's Functions Theory},
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Volume = {8},
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Volume = {8},
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Year = {2012},
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Year = {2012},
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Bdsk-Url-1 = {https://doi.org/10.1021/ct300311x}}
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Bdsk-Url-1 = {https://doi.org/10.1021/ct300311x}}
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18
BSEdyn.tex
18
BSEdyn.tex
@ -246,11 +246,13 @@ One key consequence of this approximation is that double (and higher) excitation
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Although these double excitations are usually experimentally dark (which means that they usually cannot be observed in photo-absorption spectroscopy), these states play, indirectly, a key role in many photochemistry mechanisms. \cite{Boggio-Pasqua_2007}
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Although these double excitations are usually experimentally dark (which means that they usually cannot be observed in photo-absorption spectroscopy), these states play, indirectly, a key role in many photochemistry mechanisms. \cite{Boggio-Pasqua_2007}
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They are, moreover, a real challenge for high-level computational methods. \cite{Loos_2018a,Loos_2019,Loos_2020b}
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They are, moreover, a real challenge for high-level computational methods. \cite{Loos_2018a,Loos_2019,Loos_2020b}
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Going beyond the static approximation is tricky and very few groups have dared to take the plunge. \cite{Strinati_1988,Rohlfing_2000,Sottile_2003,Ma_2009,Romaniello_2009b,Sangalli_2011,Huix-Rotllant_2011,Zhang_2013,Rebolini_2016,Olevano_2019,Lettmann_2019}
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Going beyond the static approximation is tricky and very few groups have dared to take the plunge. \cite{Strinati_1988,Rohlfing_2000,Sottile_2003,Ma_2009a,Ma_2009b,Romaniello_2009b,Sangalli_2011,Huix-Rotllant_2011,Zhang_2013,Rebolini_2016,Olevano_2019,Lettmann_2019}
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Nonetheless, it is worth mentioning the seminal work of Strinati, \cite{Strinati_1988} who \titou{bla bla bla.}
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Nonetheless, it is worth mentioning the seminal work of Strinati, \cite{Strinati_1988} who \titou{bla bla bla.}
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Following Strinati's footsteps, Rohlfing and coworkers have developed an efficient way of taking into account, thanks to first-order perturbation theory, the dynamical effects via a plasmon-pole approximation combined with the Tamm-Dancoff approximation (TDA). \cite{Rohlfing_2000,Ma_2009}
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Following Strinati's footsteps, Rohlfing and coworkers have developed an efficient way of taking into account, thanks to first-order perturbation theory, the dynamical effects via a plasmon-pole approximation combined with the Tamm-Dancoff approximation (TDA). \cite{Rohlfing_2000,Ma_2009a,Ma_2009b,Baumeier_2012b}
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With such as scheme, they have been able to compute the excited state of biological chromophores, showing that taking into account the electron-hole screening is important for an accurate description of the lowest $n \rightarrow \pi^*$ excitations. \cite{Ma_2009}
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With such as scheme, they have been able to compute the excited state of biological chromophores, showing that taking into account the electron-hole screening is important for an accurate description of the lowest $n \ra \pi^*$ excitations. \cite{Ma_2009a,Ma_2009b,Baumeier_2012b}
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Zhang \text{et al.} \cite{Zhang_2013}, as well as Rebolini and Toulouse \cite{Rebolini_2016} (in a range-separated context) have separately studied the frequency-dependent second-order Bethe-Salpeter kernel showing a modest improvement over its static counterpart.
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Indeed, studying PYP, retinal and GFP chromophore models, Ma \textit{et al.}~found that \textit{``the influence of dynamical screening on the excitation energies is about $0.1$ eV for the lowest $\pi \ra \pis$ transitions, but for the lowest $n \ra \pis$ transitions the influence is larger, up to $0.25$ eV.''} \cite{Ma_2009b}
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A similar conclusion was reached in Ref.~\onlinecite{Ma_2009a}.
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Zhang \textit{et al.} \cite{Zhang_2013}, as well as Rebolini and Toulouse \cite{Rebolini_2016} (in a range-separated context) have separately studied the frequency-dependent second-order Bethe-Salpeter kernel showing a modest improvement over its static counterpart.
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In the two latter studies, they also followed a perturbative approach within the TDA with a renormalization of the first-order perturbative correction.
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In the two latter studies, they also followed a perturbative approach within the TDA with a renormalization of the first-order perturbative correction.
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It is important to note that, although these studies are clearly going beyond the static approximation of BSE, they are not able to recover double excitations as the perturbative treatment makes ultimately the BSE kernel static.
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It is important to note that, although these studies are clearly going beyond the static approximation of BSE, they are not able to recover double excitations as the perturbative treatment makes ultimately the BSE kernel static.
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@ -258,7 +260,7 @@ However, it does permit to recover additional relaxation effects coming from the
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Finally, let us also mentioned the work of Romaniello and coworkers, \cite{Romaniello_2009b,Sangalli_2011} in which the authors genuinely accessed additional excitations by solving the non-linear, frequency-dependent eigenvalue problem.
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Finally, let us also mentioned the work of Romaniello and coworkers, \cite{Romaniello_2009b,Sangalli_2011} in which the authors genuinely accessed additional excitations by solving the non-linear, frequency-dependent eigenvalue problem.
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However, it is based on a rather simple model (the Hubbard dimer) which permits to analytically solve the dynamical equations.
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However, it is based on a rather simple model (the Hubbard dimer) which permits to analytically solve the dynamical equations.
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In the present study, we extend the work of Rohlfing and coworkers \cite{Rohlfing_2000,Ma_2009} by proposing a renormalized first-order perturbative correction to the static neutral excitation energy.
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In the present study, we extend the work of Rohlfing and coworkers \cite{Rohlfing_2000,Ma_2009a,Ma_2009b,Baumeier_2012b} by proposing a renormalized first-order perturbative correction to the static neutral excitation energy.
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Importantly, our correction goes beyond the plasmon-pole approximation as the dynamical screening of the Coulomb interaction is computed exactly.
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Importantly, our correction goes beyond the plasmon-pole approximation as the dynamical screening of the Coulomb interaction is computed exactly.
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Moreover, we investigate quantitatively the effect of the TDA by computing both the resonant and anti-resonant dynamical corrections to the BSE excitation energies.
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Moreover, we investigate quantitatively the effect of the TDA by computing both the resonant and anti-resonant dynamical corrections to the BSE excitation energies.
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Unless otherwise stated, atomic units are used.
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Unless otherwise stated, atomic units are used.
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@ -686,9 +688,9 @@ All the BSE calculations have been performed with our locally developed $GW$ sof
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& \tabc{$\Eg^{\GW}$} & \tabc{$\Om{m}{\stat}$} & \tabc{$\Om{m}{\dyn}$} & \tabc{$\Delta\Om{m}{\dyn}$} & \tabc{$Z_{m}$}
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& \tabc{$\Eg^{\GW}$} & \tabc{$\Om{m}{\stat}$} & \tabc{$\Om{m}{\dyn}$} & \tabc{$\Delta\Om{m}{\dyn}$} & \tabc{$Z_{m}$}
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& \tabc{CIS(D)} & \tabc{ADC(2)} & \tabc{CCSD} & \tabc{CC2} & \tabc{CC3} \\
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& \tabc{CIS(D)} & \tabc{ADC(2)} & \tabc{CCSD} & \tabc{CC2} & \tabc{CC3} \\
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\hline
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\hline
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\ce{HCl} & $^1\Pi$(CT) & 13.43 & 8.30 & 8.19 & -0.11 & 1.009 & & & & & & 6.07 & 7.97 & 7.91 & 7.96 & 7.84 \\
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\ce{HCl} & $^1\Pi$(CT) & 13.43 & 8.30 & 8.19 & -0.11 & 1.009 & 13.42 & 8.29 & 8.18 & -0.11 & 1.010 & 6.07 & 7.97 & 7.91 & 7.96 & 7.84 \\
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\\
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\\
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\ce{H2O} & $^1B_1(n \ra 3s)$ & 13.58 & 8.09 & 8.00 & -0.09 & 1.007 & & & & & & 7.62 & 7.18 & 7.60 & 7.23 & 7.65 \\
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\ce{H2O} & $^1B_1(n \ra 3s)$ & 13.58 & 8.09 & 8.00 & -0.09 & 1.007 & & & & & & 7.62 & 7.18 & 7.60 & 7.23 & 7.65 \\
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& $^1A_2(n \ra 3p)$ & & 9.79 & 9.72 & -0.07 & 1.005 & & & & & & 9.41 & 8.84 & 9.36 & 8.89 & 9.43 \\
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& $^1A_2(n \ra 3p)$ & & 9.79 & 9.72 & -0.07 & 1.005 & & & & & & 9.41 & 8.84 & 9.36 & 8.89 & 9.43 \\
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& $^1A_1(n \ra 3s)$ & & 10.42 & 10.35 & -0.07 & 1.006 & & & & & & 9.99 & 9.52 & 9.96 & 9.58 & 10.00 \\
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& $^1A_1(n \ra 3s)$ & & 10.42 & 10.35 & -0.07 & 1.006 & & & & & & 9.99 & 9.52 & 9.96 & 9.58 & 10.00 \\
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\\
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\\
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@ -737,7 +739,7 @@ All the BSE calculations have been performed with our locally developed $GW$ sof
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& \tabc{$\Eg^{\GW}$} & \tabc{$\Om{m}{\stat}$} & \tabc{$\Om{m}{\dyn}$} & \tabc{$\Delta\Om{m}{\dyn}$} & \tabc{$Z_{m}$}
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& \tabc{$\Eg^{\GW}$} & \tabc{$\Om{m}{\stat}$} & \tabc{$\Om{m}{\dyn}$} & \tabc{$\Delta\Om{m}{\dyn}$} & \tabc{$Z_{m}$}
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& \tabc{CIS(D)} & \tabc{ADC(2)} & \tabc{CCSD} & \tabc{CC2} & \tabc{CC3} \\
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& \tabc{CIS(D)} & \tabc{ADC(2)} & \tabc{CCSD} & \tabc{CC2} & \tabc{CC3} \\
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\hline
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\hline
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\ce{H2O} & $^3B_1(n \ra 3s)$ & 13.58 & 8.14 & 7.98 & -0.15 & 1.014 & & & & & & 7.25 & 6.86 & 7.20 & 6.91 & 7.28 \\
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\ce{H2O} & $^3B_1(n \ra 3s)$ & 13.58 & 8.14 & 7.98 & -0.15 & 1.014 & & & & & & 7.25 & 6.86 & 7.20 & 6.91 & 7.28 \\
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& $^3A_2(n \ra 3p)$ & & 9.97 & 9.89 & -0.07 & 1.008 & & & & & & 9.24 & 8.72 & 9.20 & 8.77 & 9.26 \\
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& $^3A_2(n \ra 3p)$ & & 9.97 & 9.89 & -0.07 & 1.008 & & & & & & 9.24 & 8.72 & 9.20 & 8.77 & 9.26 \\
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& $^3A_1(n \ra 3s)$ & & 10.28 & 10.13 & -0.15 & 1.012 & & & & & & 9.54 & 9.15 & 9.49 & 9.20 & 9.56 \\
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& $^3A_1(n \ra 3s)$ & & 10.28 & 10.13 & -0.15 & 1.012 & & & & & & 9.54 & 9.15 & 9.49 & 9.20 & 9.56 \\
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\\
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\\
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