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%% This BibTeX bibliography file was created using BibDesk.
%% http://bibdesk.sourceforge.net/
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@ -333,14 +333,12 @@
@article{Blase_2011,
Author = {Blase,X. and Attaccalite,C.},
Date-Added = {2020-05-18 21:40:28 +0200},
Date-Modified = {2020-05-18 21:40:28 +0200},
Date-Modified = {2020-05-21 08:47:22 +0200},
Doi = {10.1063/1.3655352},
Eprint = {https://doi.org/10.1063/1.3655352},
Journal = {Appl. Phys. Lett.},
Number = {17},
Pages = {171909},
Title = {Charge-Transfer Excitations in Molecular Donor-Acceptor Complexes within the Many-Body Bethe-Salpeter Approach},
Url = {https://doi.org/10.1063/1.3655352},
Volume = {99},
Year = {2011},
Bdsk-Url-1 = {https://doi.org/10.1063/1.3655352}}
@ -381,11 +379,11 @@
@article{Bredas_2014,
Author = {Bredas, Jean-Luc},
Date-Added = {2020-05-18 21:40:28 +0200},
Date-Modified = {2020-05-18 21:40:28 +0200},
Date-Modified = {2020-05-21 08:48:23 +0200},
Doi = {10.1039/C3MH00098B},
File = {/Users/loos/Zotero/storage/QZ92N6TD/Bredas - 2014 - Mind the gap!.pdf},
Issn = {2051-6347, 2051-6355},
Journal = {Mater Horiz},
Journal = {Mater. Horiz.},
Language = {en},
Number = {1},
Pages = {17-19},
@ -415,14 +413,12 @@
@article{Bruneval_2015,
Author = {Bruneval,Fabien and Hamed,Samia M. and Neaton,Jeffrey B.},
Date-Added = {2020-05-18 21:40:28 +0200},
Date-Modified = {2020-05-18 21:40:28 +0200},
Date-Modified = {2020-05-21 08:42:08 +0200},
Doi = {10.1063/1.4922489},
Eprint = {https://doi.org/10.1063/1.4922489},
Journal = {J. Chem. Phys.},
Number = {24},
Pages = {244101},
Title = {A systematic benchmark of the ab initio Bethe-Salpeter equation approach for low-lying optical excitations of small organic molecules},
Url = {https://doi.org/10.1063/1.4922489},
Volume = {142},
Year = {2015},
Bdsk-Url-1 = {https://doi.org/10.1063/1.4922489}}
@ -712,14 +708,12 @@
@article{Duchemin_2019,
Author = {Duchemin,Ivan and Blase,Xavier},
Date-Added = {2020-05-18 21:40:28 +0200},
Date-Modified = {2020-05-18 21:40:28 +0200},
Date-Modified = {2020-05-21 08:45:34 +0200},
Doi = {10.1063/1.5090605},
Eprint = {https://doi.org/10.1063/1.5090605},
Journal = {J. Chem. Phys.},
Number = {17},
Pages = {174120},
Title = {Separable resolution-of-the-identity with all-electron Gaussian bases: Application to cubic-scaling RPA},
Url = {https://doi.org/10.1063/1.5090605},
Volume = {150},
Year = {2019},
Bdsk-Url-1 = {https://doi.org/10.1063/1.5090605}}
@ -727,9 +721,12 @@
@article{Duchemin_2020,
Author = {Ivan Duchemin and Xavier Blase},
Date-Added = {2020-05-18 21:40:28 +0200},
Date-Modified = {2020-05-18 21:40:28 +0200},
Journal = {J. Chem. Theory Comput (accepted)},
Title = {Robust Analytic Continuation Approach to Many-Body GW Calculations},
Date-Modified = {2020-05-21 08:46:27 +0200},
Doi = {10.1021/acs.jctc.9b01235},
Journal = {J. Chem. Theory Comput.},
Pages = {1742--1756},
Title = {Robust Analytic-Continuation Approach to Many-Body {{GW}} Calculations},
Volume = {16},
Year = {2020},
Bdsk-Url-1 = {}}
@ -980,15 +977,12 @@
@article{Gui_2018,
Author = {Gui, Xin and Holzer, Christof and Klopper, Wim},
Date-Added = {2020-05-18 21:40:28 +0200},
Date-Modified = {2020-05-18 21:40:28 +0200},
Date-Modified = {2020-05-21 08:44:46 +0200},
Doi = {10.1021/acs.jctc.8b00014},
Eprint = {https://doi.org/10.1021/acs.jctc.8b00014},
Journal = {J. Chem. Theory Comput.},
Note = {PMID: 29499116},
Number = {4},
Pages = {2127-2136},
Title = {Accuracy Assessment of GW Starting Points for Calculating Molecular Excitation Energies Using the Bethe--Salpeter Formalism},
Url = {https://doi.org/10.1021/acs.jctc.8b00014},
Volume = {14},
Year = {2018},
Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.8b00014}}
@ -1257,11 +1251,9 @@
@article{Jacquemin_2015a,
Author = {Jacquemin, Denis and Duchemin, Ivan and Blase, Xavier},
Date-Added = {2020-05-18 21:40:28 +0200},
Date-Modified = {2020-05-18 21:40:28 +0200},
Date-Modified = {2020-05-21 08:42:32 +0200},
Doi = {10.1021/acs.jctc.5b00304},
Issn = {1549-9618, 1549-9626},
Journal = {J. Chem. Theory Comput.},
Language = {en},
Month = jul,
Number = {7},
Pages = {3290-3304},
@ -1273,31 +1265,25 @@
@article{Jacquemin_2015b,
Author = {Jacquemin, Denis and Duchemin, Ivan and Blase, Xavier},
Date-Added = {2020-05-18 21:40:28 +0200},
Date-Modified = {2020-05-18 21:40:28 +0200},
Date-Modified = {2020-05-21 08:42:59 +0200},
Doi = {10.1021/acs.jctc.5b00619},
Eprint = {https://doi.org/10.1021/acs.jctc.5b00619},
Journal = {J. Chem. Theory Comput.},
Note = {PMID: 26574326},
Number = {11},
Pages = {5340-5359},
Title = {0--0 Energies Using Hybrid Schemes: Benchmarks of TD-DFT, CIS(D), ADC(2), CC2, and BSE/GW formalisms for 80 Real-Life Compounds},
Url = {https://doi.org/10.1021/acs.jctc.5b00619},
Volume = {11},
Year = {2015},
Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.5b00619}}
@article{Jacquemin_2017,
@article{Jacquemin_2017a,
Author = {Jacquemin, Denis and Duchemin, Ivan and Blase, Xavier},
Date-Added = {2020-05-18 21:40:28 +0200},
Date-Modified = {2020-05-18 21:40:28 +0200},
Date-Modified = {2020-05-21 08:44:05 +0200},
Doi = {10.1021/acs.jpclett.7b00381},
Eprint = {https://doi.org/10.1021/acs.jpclett.7b00381},
Journal = {J. Phys. Chem. Lett.},
Note = {PMID: 28301726},
Number = {7},
Pages = {1524-1529},
Title = {Is the Bethe--Salpeter Formalism Accurate for Excitation Energies? Comparisons with TD-DFT, CASPT2, and EOM-CCSD},
Url = {https://doi.org/10.1021/acs.jpclett.7b00381},
Volume = {8},
Year = {2017},
Bdsk-Url-1 = {https://doi.org/10.1021/acs.jpclett.7b00381}}
@ -1305,15 +1291,12 @@
@article{Jacquemin_2017b,
Author = {Jacquemin, Denis and Duchemin, Ivan and Blondel, Aymeric and Blase, Xavier},
Date-Added = {2020-05-18 21:40:28 +0200},
Date-Modified = {2020-05-18 21:40:28 +0200},
Date-Modified = {2020-05-21 08:43:58 +0200},
Doi = {10.1021/acs.jctc.6b01169},
Eprint = {https://doi.org/10.1021/acs.jctc.6b01169},
Journal = {J. Chem. Theory Comput.},
Note = {PMID: 28107000},
Number = {2},
Pages = {767-783},
Title = {Benchmark of Bethe-Salpeter for Triplet Excited-States},
Url = {https://doi.org/10.1021/acs.jctc.6b01169},
Volume = {13},
Year = {2017},
Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.6b01169}}
@ -1355,15 +1338,12 @@
@article{Korbel_2014,
Author = {K{\"{o}}rbel, Sabine and Boulanger, Paul and Duchemin, Ivan and Blase, Xavier and Marques, Miguel A. L. and Botti, Silvana},
Date-Added = {2020-05-18 21:40:28 +0200},
Date-Modified = {2020-05-18 21:40:28 +0200},
Date-Modified = {2020-05-21 08:41:51 +0200},
Doi = {10.1021/ct5003658},
Eprint = {https://doi.org/10.1021/ct5003658},
Journal = {J. Chem. Theory Comput.},
Note = {PMID: 26588537},
Number = {9},
Pages = {3934-3943},
Title = {Benchmark Many-Body GW and Bethe--Salpeter Calculations for Small Transition Metal Molecules},
Url = {https://doi.org/10.1021/ct5003658},
Volume = {10},
Year = {2014},
Bdsk-Url-1 = {https://doi.org/10.1021/ct5003658}}
@ -1408,15 +1388,12 @@
Abstract = {A software update solving the BetheSalpeter equation ...},
Author = {Krause, Katharina and Klopper, Wim},
Date-Added = {2020-05-18 21:40:28 +0200},
Date-Modified = {2020-05-18 21:40:28 +0200},
Date-Modified = {2020-05-21 08:44:35 +0200},
Doi = {10.1002/jcc.24688},
Eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/jcc.24688},
Journal = {J. Comp. Chem.},
Keywords = {electronic excitation energy, time-dependent density-functional theory, BetheSalpeter equation, resolution-of-the-identity approximation, exchange interaction},
Journal = {J. Comput. Chem.},
Number = {6},
Pages = {383-388},
Title = {Implementation of the Bethe-Salpeter equation in the TURBOMOLE program},
Url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/jcc.24688},
Volume = {38},
Year = {2017},
Bdsk-Url-1 = {https://onlinelibrary.wiley.com/doi/abs/10.1002/jcc.24688},
@ -1684,14 +1661,12 @@
@article{Olevano_2019,
Author = {Olevano,Valerio and Toulouse,Julien and Schuck,Peter},
Date-Added = {2020-05-18 21:40:28 +0200},
Date-Modified = {2020-05-18 21:40:28 +0200},
Date-Modified = {2020-05-21 08:41:29 +0200},
Doi = {10.1063/1.5080330},
Eprint = {https://doi.org/10.1063/1.5080330},
Journal = {J. Chem. Phys.},
Number = {8},
Pages = {084112},
Title = {A formally exact one-frequency-only Bethe-Salpeter-like equation. Similarities and differences between GW+BSE and self-consistent RPA},
Url = {https://doi.org/10.1063/1.5080330},
Volume = {150},
Year = {2019},
Bdsk-Url-1 = {https://doi.org/10.1063/1.5080330}}
@ -1799,14 +1774,12 @@
@article{Rebolini_2016,
Author = {Rebolini,Elisa and Toulouse,Julien},
Date-Added = {2020-05-18 21:40:28 +0200},
Date-Modified = {2020-05-18 21:40:28 +0200},
Date-Modified = {2020-05-21 08:41:16 +0200},
Doi = {10.1063/1.4943003},
Eprint = {https://doi.org/10.1063/1.4943003},
Journal = {J. Chem. Phys.},
Number = {9},
Pages = {094107},
Title = {Range-separated time-dependent density-functional theory with a frequency-dependent second-order Bethe-Salpeter correlation kernel},
Url = {https://doi.org/10.1063/1.4943003},
Volume = {144},
Year = {2016},
Bdsk-Url-1 = {https://doi.org/10.1063/1.4943003}}
@ -1938,14 +1911,12 @@
@article{Romaniello_2009b,
Author = {Romaniello,P. and Sangalli,D. and Berger,J. A. and Sottile,F. and Molinari,L. G. and Reining,L. and Onida,G.},
Date-Added = {2020-05-18 21:40:28 +0200},
Date-Modified = {2020-05-18 21:40:28 +0200},
Date-Modified = {2020-05-21 08:45:19 +0200},
Doi = {10.1063/1.3065669},
Eprint = {https://doi.org/10.1063/1.3065669},
Journal = {J. Chem. Phys.},
Number = {4},
Pages = {044108},
Title = {Double excitations in finite systems},
Url = {https://doi.org/10.1063/1.3065669},
Volume = {130},
Year = {2009},
Bdsk-Url-1 = {https://doi.org/10.1063/1.3065669}}
@ -2455,14 +2426,12 @@
@article{Zhang_2013,
Author = {Zhang,Du and Steinmann,Stephan N. and Yang,Weitao},
Date-Added = {2020-05-18 21:40:28 +0200},
Date-Modified = {2020-05-18 21:40:28 +0200},
Date-Modified = {2020-05-21 08:40:56 +0200},
Doi = {10.1063/1.4824907},
Eprint = {https://doi.org/10.1063/1.4824907},
Journal = {J. Chem. Phys.},
Number = {15},
Pages = {154109},
Title = {Dynamical second-order Bethe-Salpeter equation kernel: A method for electronic excitation beyond the adiabatic approximation},
Url = {https://doi.org/10.1063/1.4824907},
Volume = {139},
Year = {2013},
Bdsk-Url-1 = {https://doi.org/10.1063/1.4824907}}
@ -11990,22 +11959,6 @@
Year = {1991},
Bdsk-Url-1 = {https://doi.org/10.1063/1.460205}}
@article{Jacquemin_2015,
Author = {Jacquemin, Denis and Duchemin, Ivan and Blase, Xavier},
Date-Added = {2018-04-23 07:38:41 +0000},
Date-Modified = {2018-04-23 07:38:41 +0000},
Doi = {10.1021/acs.jctc.5b00304},
Issn = {1549-9618, 1549-9626},
Journal = {J. Chem. Theory Comput.},
Language = {en},
Month = jul,
Number = {7},
Pages = {3290-3304},
Title = {Benchmarking the {{Bethe}}\textendash{}{{Salpeter Formalism}} on a {{Standard Organic Molecular Set}}},
Volume = {11},
Year = {2015},
Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.5b00304}}
@article{Silva-Junior_2010,
Author = {Silva-Junior, Mario R. and Schreiber, Marko and Sauer, Stephan P. A. and Thiel, Walter},
Date-Added = {2018-04-23 07:38:41 +0000},
@ -13999,17 +13952,6 @@
Volume = {30},
Year = {2018}}
@article{Romaniello_2009_JCP,
Author = {Romaniello,P. and Sangalli,D. and Berger,J. A. and Sottile,F. and Molinari,L. G. and Reining,L. and Onida,G.},
Doi = {10.1063/1.3065669},
Journal = {J. Chem. Phys.},
Number = {4},
Pages = {044108},
Title = {Double excitations in finite systems},
Volume = {130},
Year = {2009},
Bdsk-Url-1 = {https://doi.org/10.1063/1.3065669}}
@article{Kozik_2014,
Author = {Kozik, Evgeny and Ferrero, Michel and Georges, Antoine},
Doi = {10.1103/PhysRevLett.114.156402},
@ -14333,18 +14275,6 @@
Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.106.187402},
Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevLett.106.187402}}
@article{Blase_2011b,
Author = {Blase,X. and Attaccalite,C.},
Date-Modified = {2020-02-05 20:52:19 +0100},
Doi = {10.1063/1.3655352},
Journal = {Appl. Phys. Lett.},
Number = {17},
Pages = {171909},
Title = {Charge-Transfer Excitations in Molecular Donor-Acceptor Complexes Within the Many-Body Bethe-Salpeter Approach},
Volume = {99},
Year = {2011},
Bdsk-Url-1 = {https://doi.org/10.1063/1.3655352}}
@article{Baumeier_2012b,
Author = {Baumeier, Bj\"{o}rn and Andrienko, Denis and Ma, Yuchen and Rohlfing, Michael},
Date-Modified = {2020-05-20 22:02:44 +0200},

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@ -223,7 +223,7 @@ Moreover, we investigate quantitatively the effect of the Tamm-Dancoff approxima
\label{sec:intro}
%%%%%%%%%%%%%%%%%%%%%%%%
The Bethe-Salpeter equation (BSE) formalism \cite{Salpeter_1951,Strinati_1988} is to the $GW$ approximation \cite{Hedin_1965,Golze_2019} of many-body perturbation theory (MBPT) \cite{Martin_2016} what time-dependent density-functional theory (TD-DFT) \cite{Runge_1984,Casida_1995} is to Kohn-Sham density-functional theory (KS-DFT), \cite{Hohenberg_1964,Kohn_1965} an affordable way of computing the neutral excitations of a given electronic system.
In recent years, it has shown to be useful for molecular systems with a large number of systematic benchmark studies appearing in the scientific literature \cite{Korbel_2014,Jacquemin_2015a,Bruneval_2015,Jacquemin_2015b,Hirose_2015,Jacquemin_2017,Krause_2017,Gui_2018} (see Ref.~\onlinecite{Blase_2018} for a recent review).
In recent years, it has shown to be useful for molecular systems with a large number of systematic benchmark studies appearing in the scientific literature \cite{Korbel_2014,Jacquemin_2015a,Bruneval_2015,Jacquemin_2015b,Hirose_2015,Jacquemin_2017a,Jacquemin_2017b,Krause_2017,Gui_2018} (see Ref.~\onlinecite{Blase_2018} for a recent review).
Taking the optical gap (\ie, the lowest optical excitation energy) as an example, BSE builds on top of a $GW$ calculation by adding up excitonic effects $\EB$ to the $GW$ HOMO-LUMO gap
\begin{equation}
@ -623,7 +623,9 @@ Although it might be reduced to $\order*{\Norb^4}$ operations with standard reso
\section{Computational details}
\label{sec:compdet}
%%%%%%%%%%%%%%%%%%%%%%%%
All the $GW$ calculations performed to obtain the screened Coulomb operator and the quasiparticle energies are done using a (restricted) HF starting point.
All systems under investigation have close-shell singlet ground states.
We then adopt a restricted formalism throughout this work.
The $GW$ calculations performed to obtain the screened Coulomb operator and the quasiparticle energies are done using a (restricted) HF starting point.
Perturbative $GW$ (or {\GOWO}) \cite{Hybertsen_1985a, Hybertsen_1986} and partially self-consistent ev$GW$ \cite{Hybertsen_1986,Shishkin_2007,Blase_2011,Faber_2011}calculations are employed as starting points to compute the BSE neutral excitations.
For both {\GOWO} and {\evGW}, the entire set of orbitals are corrected.
In the case of {\GOWO}, the quasiparticle energies are obtained by linearizing the frequency-dependent quasiparticle equation.