fix refs and comp details
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BSE-PES.bib
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BSE-PES.bib
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%% This BibTeX bibliography file was created using BibDesk.
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%% http://bibdesk.sourceforge.net/
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%% Created for Pierre-Francois Loos at 2020-01-07 18:13:25 +0100
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%% Created for Pierre-Francois Loos at 2020-01-07 22:26:48 +0100
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%% Saved with string encoding Unicode (UTF-8)
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@ -11,14 +11,12 @@
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@article{Ghosh_2018,
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Author = {Ghosh, Soumen and Verma, Pragya and Cramer, Christopher J. and Gagliardi, Laura and Truhlar, Donald G.},
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Date-Added = {2020-01-07 16:02:08 +0100},
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Date-Modified = {2020-01-07 16:02:18 +0100},
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Date-Modified = {2020-01-07 22:18:36 +0100},
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Doi = {10.1021/acs.chemrev.8b00193},
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Eprint = {https://doi.org/10.1021/acs.chemrev.8b00193},
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Journal = {Chem. Rev.},
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Number = {15},
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Pages = {7249--7292},
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Title = {Combining Wave Function Methods with Density Functional Theory for Excited States},
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Url = {https://doi.org/10.1021/acs.chemrev.8b00193},
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Volume = {118},
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Year = {2018},
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Bdsk-Url-1 = {https://doi.org/10.1021/acs.chemrev.8b00193}}
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@ -48,12 +46,14 @@
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@article{Gonzales_2012,
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Author = {Gonz{\'a}lez, Leticia and Escudero, D. and Serrano-Andr\`es, L.},
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Date-Added = {2020-01-07 15:55:40 +0100},
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Date-Modified = {2020-01-07 15:57:20 +0100},
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Date-Modified = {2020-01-07 22:18:05 +0100},
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Doi = {10.1002/cphc.201100200},
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Journal = {ChemPhysChem},
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Title = {Progress and Challenges in the Calculation of Electronic Excited States},
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Volume = {13},
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Year = {2012}}
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Year = {2012},
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Bdsk-Url-1 = {https://doi.org/10.1002/cphc.201100200}}
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@article{Holzer_2018,
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Author = {Christof Holzer and Xin Gui and Michael E. Harding and Georg Kresse and Trygve Helgaker and Wim Klopper},
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@ -126,11 +126,10 @@
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@article{Li_2020,
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Author = {J. Li and I. Duchemin and X. Blase and V. Olevano},
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Date-Added = {2020-01-04 20:06:04 +0100},
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Date-Modified = {2020-01-04 20:10:21 +0100},
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Journal = {arXiv},
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Date-Modified = {2020-01-07 22:26:17 +0100},
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Journal = {arXiv:physics.chem-ph},
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Pages = {1812.00932},
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Title = {Ground-state correlation energy of beryllium dimer by the Bethe-Salpeter equation},
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Volume = {physics.chem-ph},
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Year = {2020}}
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@article{Salpeter_1951,
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@ -197,12 +196,14 @@
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@article{Loos_2019b,
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Author = {Loos, Pierre-Francois and Jacquemin, Denis},
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Date-Added = {2020-01-03 20:54:57 +0100},
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Date-Modified = {2020-01-03 20:55:04 +0100},
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Date-Modified = {2020-01-07 22:19:19 +0100},
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Doi = {10.1002/cptc.201900070},
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Title = {Evaluating 0-0 Energies with Theoretical Tools: a Short Review},
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Volume = {3},
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Year = {2019}}
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Bdsk-Url-1 = {https://doi.org/10.1002/cptc.201900070}}
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@article{Furche_2002,
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Author = {F. Furche and R. Ahlrichs},
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@ -11455,12 +11456,6 @@
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Year = {2016},
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Bdsk-Url-1 = {https://dx.doi.org/10.1002/wcms.1265}}
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@article{Kaplan_,
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Author = {Kaplan, Ferdinand},
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File = {/Users/loos/Zotero/storage/XM6HJ3SR/Kaplan_PhD.pdf},
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Shorttitle = {Quasiparticle {{Self}}-{{Consistent GW}}-{{Approximation}} for {{Molecules}}},
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Title = {Quasiparticle {{Self}}-{{Consistent GW}}-{{Approximation}} for {{Molecules}}: {{Calculation}} of {{Single}}-{{Particle Excitation Energies}} for {{Molecules}}}}
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@article{Ke_2011,
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Author = {Ke, San-Huang},
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Date-Modified = {2018-04-14 07:26:29 +0000},
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@ -12569,19 +12564,19 @@
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@article{Tiago_2008,
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Author = {Tiago, Murilo L. and Kent,P. R. C. and Hood,Randolph Q. and Reboredo,Fernando A.},
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Date-Modified = {2020-01-07 22:20:12 +0100},
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Doi = {10.1063/1.2973627},
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Eprint = {https://doi.org/10.1063/1.2973627},
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Journal = {The Journal of Chemical Physics},
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Journal = {J. Chem. Phys.},
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Number = {8},
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Pages = {084311},
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Title = {Neutral and charged excitations in carbon fullerenes from first-principles many-body theories},
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Url = {https://doi.org/10.1063/1.2973627},
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Volume = {129},
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Year = {2008},
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Bdsk-Url-1 = {https://doi.org/10.1063/1.2973627}}
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@article{Sai_2008,
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Author = {Sai, Na and Tiago, Murilo L. and Chelikowsky, James R. and Reboredo, Fernando A.},
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Date-Modified = {2020-01-07 22:20:02 +0100},
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Doi = {10.1103/PhysRevB.77.161306},
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Issue = {16},
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Journal = {Phys. Rev. B},
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@ -12590,7 +12585,6 @@
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Pages = {161306},
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Publisher = {American Physical Society},
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Title = {Optical spectra and exchange-correlation effects in molecular crystals},
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Url = {https://link.aps.org/doi/10.1103/PhysRevB.77.161306},
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Volume = {77},
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Year = {2008},
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Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.77.161306},
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@ -12598,26 +12592,24 @@
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@article{Palumno_2009,
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Author = {Palummo,Maurizia and Hogan,Conor and Sottile,Francesco and Bagal\'{a},Paolo and Rubio,Angel},
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Date-Modified = {2020-01-07 22:21:10 +0100},
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Doi = {10.1063/1.3204938},
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Eprint = {https://doi.org/10.1063/1.3204938},
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Journal = {The Journal of Chemical Physics},
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Journal = {J. Chem. Phys.},
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Number = {8},
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Pages = {084102},
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Title = {Ab initio electronic and optical spectra of free-base porphyrins: The role of electronic correlation},
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Url = {https://doi.org/10.1063/1.3204938},
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Volume = {131},
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Year = {2009},
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Bdsk-Url-1 = {https://doi.org/10.1063/1.3204938}}
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@article{Rocca_2010,
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Author = {Rocca,Dario and Lu,Deyu and Galli,Giulia},
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Date-Modified = {2020-01-07 22:20:40 +0100},
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Doi = {10.1063/1.3494540},
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Eprint = {https://doi.org/10.1063/1.3494540},
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Journal = {The Journal of Chemical Physics},
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Journal = {J. Chem. Phys.},
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Number = {16},
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Pages = {164109},
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Title = {Ab initio calculations of optical absorption spectra: Solution of the Bethe--Salpeter equation within density matrix perturbation theory},
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Url = {https://doi.org/10.1063/1.3494540},
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Volume = {133},
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Year = {2010},
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Bdsk-Url-1 = {https://doi.org/10.1063/1.3494540}}
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@ -12688,6 +12680,7 @@
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@article{Ziaei_2017,
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Author = {Ziaei, Vafa and Bredow, Thomas},
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Date-Modified = {2020-01-07 22:23:38 +0100},
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Doi = {10.1103/PhysRevB.96.195115},
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Issue = {19},
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Journal = {Phys. Rev. B},
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@ -12696,7 +12689,6 @@
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Pages = {195115},
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Publisher = {American Physical Society},
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Title = {Simple many-body based screening mixing ansatz for improvement of $GW$/Bethe-Salpeter equation excitation energies of molecular systems},
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Url = {https://link.aps.org/doi/10.1103/PhysRevB.96.195115},
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Volume = {96},
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Year = {2017},
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Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.96.195115},
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@ -12752,27 +12744,24 @@
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@article{Blase_2011b,
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Author = {Blase,X. and Attaccalite,C.},
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Date-Modified = {2020-01-07 22:23:09 +0100},
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Doi = {10.1063/1.3655352},
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Eprint = {https://doi.org/10.1063/1.3655352},
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Journal = {Applied Physics Letters},
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Journal = {Appl. Phys. Lett.},
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Number = {17},
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Pages = {171909},
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Title = {Charge-transfer excitations in molecular donor-acceptor complexes within the many-body Bethe-Salpeter approach},
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Url = {https://doi.org/10.1063/1.3655352},
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Volume = {99},
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Year = {2011},
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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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Author = {Baumeier, Bj\"{o}rn and Andrienko, Denis and Rohlfing, Michael},
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Date-Modified = {2020-01-07 22:21:41 +0100},
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Doi = {10.1021/ct300311x},
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Eprint = {https://doi.org/10.1021/ct300311x},
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Journal = {Journal of Chemical Theory and Computation},
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Note = {PMID: 26592120},
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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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Url = {https://doi.org/10.1021/ct300311x},
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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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@ -12811,45 +12800,28 @@
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@article{Ziaei_2016,
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Author = {Ziaei,Vafa and Bredow,Thomas},
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Date-Modified = {2020-01-07 22:23:30 +0100},
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Doi = {10.1063/1.4966920},
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Eprint = {https://doi.org/10.1063/1.4966920},
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Journal = {The Journal of Chemical Physics},
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Journal = {J. Chem. Phys.},
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Number = {17},
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Pages = {174305},
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Title = {GW-BSE approach on S1 vertical transition energy of large charge transfer compounds: A performance assessment},
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Url = {https://doi.org/10.1063/1.4966920},
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Volume = {145},
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Year = {2016},
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Bdsk-Url-1 = {https://doi.org/10.1063/1.4966920}}
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@article{Rangel16,
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@article{Rangel_2016,
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Author = {Rangel, Tonatiuh and Hamed, Samia M. and Bruneval, Fabien and Neaton, Jeffrey B.},
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Date-Modified = {2020-01-07 22:25:49 +0100},
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Doi = {10.1021/acs.jctc.6b00163},
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Eprint = {https://doi.org/10.1021/acs.jctc.6b00163},
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Journal = {Journal of Chemical Theory and Computation},
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Note = {PMID: 27123935},
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Journal = {J. Chem. Theory Comput.},
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Number = {6},
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Pages = {2834-2842},
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Title = {Evaluating the GW Approximation with CCSD(T) for Charged Excitations Across the Oligoacenes},
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Url = {https://doi.org/10.1021/acs.jctc.6b00163},
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Volume = {12},
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Year = {2016},
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Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.6b00163}}
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@article{Kaplan_2018,
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Author = {Kaplan, F. and Harding, M. E. and Seiler, C. and Weigend, F. and Evers, F. and van Setten, M. J.},
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Doi = {10.1021/acs.jctc.5b01238},
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Eprint = {https://doi.org/10.1021/acs.jctc.5b01238},
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Journal = {Journal of Chemical Theory and Computation},
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Note = {PMID: 27168352},
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Number = {6},
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Pages = {2528-2541},
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Title = {Quasi-Particle Self-Consistent GW for Molecules},
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Url = {https://doi.org/10.1021/acs.jctc.5b01238},
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Volume = {12},
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Year = {2016},
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Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.5b01238}}
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@article{Beigi_2003,
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Author = {Ismail-Beigi, Sohrab and Louie, Steven G.},
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Doi = {10.1103/PhysRevLett.90.076401},
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@ -214,7 +214,7 @@ Yet another problem is the choice of the xc functionals as the quality of excita
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With a similar computational cost, the many-body Green's function Bethe-Salpeter equation (BSE) formalism \cite{Salpeter_1951,Strinati_1988} is a very valuable alternative to TD-DFT with early \textit{ab initio} calculations in condensed matter physics appearing at the end of the 90's. \cite{Albrecht_1998,Rohlfing_1998,Benedict_1998,vanderHorst_1999}
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In the past few years, BSE has gained momentum for the study of molecular systems \cite{Ma_2009,Pushchnig_2002,Tiago_2003,Tiago_2008,Sai_2008,Palumno_2009,Rocca_2010,Sharifzadeh_2012,Cudazzo_2012,Boulanger_2014,Ljungberg_2015,Hirose_2015,Cocchi_2015,Ziaei_2017,Abramson_2017} and is now a serious candidate as a computationally inexpensive method that can effectively model excited states with a typical error of $0.1$--$0.3$ eV according to large and systematic benchmark calculations. \cite{Jacquemin_2015,Bruneval_2015,Blase_2016,Jacquemin_2016,Hung_2016,Hung_2017,Krause_2017,Jacquemin_2017,Blase_2018}
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One of the main advantage of BSE compared to TD-DFT is that it allows a faithful description of charge-transfer states. \cite{Lastra_2011,Blase_2011b,Baumeier_2012,Duchemin_2012,Cudazzo_2013,Ziaei_2016}
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Moreover, when performed on top of a (partially) self-consistently {\evGW} calculation, \cite{Hybertsen_1986, Shishkin_2007, Blase_2011, Faber_2011,Rangel16,Kaplan_2018,Gui_2018} BSE@{\evGW} has been shown to be weakly dependent on its starting point (\ie, on the xc functional selected for the underlying DFT calculation). \cite{Jacquemin_2016,Gui_2018}
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Moreover, when performed on top of a (partially) self-consistently {\evGW} calculation, \cite{Hybertsen_1986, Shishkin_2007, Blase_2011, Faber_2011,Rangel_2016,Kaplan_2016,Gui_2018} BSE@{\evGW} has been shown to be weakly dependent on its starting point (\ie, on the xc functional selected for the underlying DFT calculation). \cite{Jacquemin_2016,Gui_2018}
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However, similar to TD-DFT, the static version of BSE cannot describe multiple excitations. \cite{Romaniello_2009a,Sangalli_2011}
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A significant limitation of the BSE formalism as compared to TD-DFT lies in the lack of analytic forces for the excited states, preventing efficient applications to the study of photoluminescence, photocatalysis, etc. While calculations of the {\GW} quasiparticle energies ionic gradients is becoming very popular,
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@ -383,14 +383,14 @@ As a final remark, we point out that Eq.~\eqref{eq:EtotBSE} can be easily genera
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\label{sec:comp_details}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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All the preliminary {\GW} calculations performed to obtain the screened Coulomb operator and the quasiparticle energies have been done using a Hartree-Fock (HF) starting point, which is a very adequate choice in the case of the (small) systems that we consider here.
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Both perturbative {\GW} (or {\GOWO}) \cite{Hybertsen_1985a, Hybertsen_1986} and partially self-consistent {\evGW} \cite{Hybertsen_1986, Shishkin_2007, Blase_2011, Faber_2011} calculations are performed here.
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Both perturbative {\GW} (or {\GOWO}) \cite{Hybertsen_1985a, Hybertsen_1986} and partially self-consistent {\evGW} \cite{Hybertsen_1986, Shishkin_2007, Blase_2011, Faber_2011} calculations are employed as starting point to compute the BSE neutral excitations.
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These will be labeled as BSE@{\GOWO} and BSE@{\evGW}, respectively.
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In the case of {\GOWO}, the quasiparticle energies have been obtained by linearizing the non-linear, frequency-dependent quasiparticle equation.
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For {\evGW}, the quasiparticle energies are obtained self-consistently and we have used the DIIS convergence accelerator technique proposed by Pulay \cite{Pulay_1980,Pulay_1982} to avoid convergence issues.
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Further details about our implementation of {\GOWO} and {\evGW} can be found in Refs.~\onlinecite{Loos_2018,Veril_2018}.
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Finally, the infinitesimal $\eta$ has been set to $10^{-3}$ for all calculations.
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Because Eq.~\eqref{eq:EcBSE} requires the entire BSE excitation spectrum (both singlet and triplet), we perform a complete diagonalization of the $OV \times OV$ BSE linear response matrix [see Eq.~\eqref{eq:small-LR}], which corresponds to a $\order{O^3V^3}$ computational cost.
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Because Eq.~\eqref{eq:EcBSE} requires the entire BSE excitation spectrum (both singlet and triplet), we perform a complete diagonalization of the $\Nocc \Nvir \times \Nocc \Nvir$ BSE linear response matrix [see Eq.~\eqref{eq:small-LR}], which corresponds to a $\order{\Nocc^3 \Nvir^3}$ computational cost.
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This step is, by far, the computational bottleneck in our current implementation.
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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