From 18b75cca4878f2c93d383228f2e3c1a47b9c05da Mon Sep 17 00:00:00 2001 From: Pierre-Francois Loos Date: Tue, 7 Jan 2020 22:27:03 +0100 Subject: [PATCH] fix refs and comp details --- BSE-PES.bib | 86 ++++++++++++++++++----------------------------------- BSE-PES.tex | 6 ++-- 2 files changed, 32 insertions(+), 60 deletions(-) diff --git a/BSE-PES.bib b/BSE-PES.bib index c2b8436..7874cd1 100644 --- a/BSE-PES.bib +++ b/BSE-PES.bib @@ -1,7 +1,7 @@ %% This BibTeX bibliography file was created using BibDesk. %% http://bibdesk.sourceforge.net/ -%% Created for Pierre-Francois Loos at 2020-01-07 18:13:25 +0100 +%% Created for Pierre-Francois Loos at 2020-01-07 22:26:48 +0100 %% Saved with string encoding Unicode (UTF-8) @@ -11,14 +11,12 @@ @article{Ghosh_2018, Author = {Ghosh, Soumen and Verma, Pragya and Cramer, Christopher J. and Gagliardi, Laura and Truhlar, Donald G.}, Date-Added = {2020-01-07 16:02:08 +0100}, - Date-Modified = {2020-01-07 16:02:18 +0100}, + Date-Modified = {2020-01-07 22:18:36 +0100}, Doi = {10.1021/acs.chemrev.8b00193}, - Eprint = {https://doi.org/10.1021/acs.chemrev.8b00193}, Journal = {Chem. Rev.}, Number = {15}, Pages = {7249--7292}, Title = {Combining Wave Function Methods with Density Functional Theory for Excited States}, - Url = {https://doi.org/10.1021/acs.chemrev.8b00193}, Volume = {118}, Year = {2018}, Bdsk-Url-1 = {https://doi.org/10.1021/acs.chemrev.8b00193}} @@ -48,12 +46,14 @@ @article{Gonzales_2012, Author = {Gonz{\'a}lez, Leticia and Escudero, D. and Serrano-Andr\`es, L.}, Date-Added = {2020-01-07 15:55:40 +0100}, - Date-Modified = {2020-01-07 15:57:20 +0100}, + Date-Modified = {2020-01-07 22:18:05 +0100}, + Doi = {10.1002/cphc.201100200}, Journal = {ChemPhysChem}, Pages = {28--51}, Title = {Progress and Challenges in the Calculation of Electronic Excited States}, Volume = {13}, - Year = {2012}} + Year = {2012}, + Bdsk-Url-1 = {https://doi.org/10.1002/cphc.201100200}} @article{Holzer_2018, Author = {Christof Holzer and Xin Gui and Michael E. Harding and Georg Kresse and Trygve Helgaker and Wim Klopper}, @@ -126,11 +126,10 @@ @article{Li_2020, Author = {J. Li and I. Duchemin and X. Blase and V. Olevano}, Date-Added = {2020-01-04 20:06:04 +0100}, - Date-Modified = {2020-01-04 20:10:21 +0100}, - Journal = {arXiv}, + Date-Modified = {2020-01-07 22:26:17 +0100}, + Journal = {arXiv:physics.chem-ph}, Pages = {1812.00932}, Title = {Ground-state correlation energy of beryllium dimer by the Bethe-Salpeter equation}, - Volume = {physics.chem-ph}, Year = {2020}} @article{Salpeter_1951, @@ -197,12 +196,14 @@ @article{Loos_2019b, Author = {Loos, Pierre-Francois and Jacquemin, Denis}, Date-Added = {2020-01-03 20:54:57 +0100}, - Date-Modified = {2020-01-03 20:55:04 +0100}, + Date-Modified = {2020-01-07 22:19:19 +0100}, + Doi = {10.1002/cptc.201900070}, Journal = {ChemPhotoChem}, Pages = {684--696}, Title = {Evaluating 0-0 Energies with Theoretical Tools: a Short Review}, Volume = {3}, - Year = {2019}} + Year = {2019}, + Bdsk-Url-1 = {https://doi.org/10.1002/cptc.201900070}} @article{Furche_2002, Author = {F. Furche and R. Ahlrichs}, @@ -11455,12 +11456,6 @@ Year = {2016}, Bdsk-Url-1 = {https://dx.doi.org/10.1002/wcms.1265}} -@article{Kaplan_, - Author = {Kaplan, Ferdinand}, - File = {/Users/loos/Zotero/storage/XM6HJ3SR/Kaplan_PhD.pdf}, - Shorttitle = {Quasiparticle {{Self}}-{{Consistent GW}}-{{Approximation}} for {{Molecules}}}, - Title = {Quasiparticle {{Self}}-{{Consistent GW}}-{{Approximation}} for {{Molecules}}: {{Calculation}} of {{Single}}-{{Particle Excitation Energies}} for {{Molecules}}}} - @article{Ke_2011, Author = {Ke, San-Huang}, Date-Modified = {2018-04-14 07:26:29 +0000}, @@ -12569,19 +12564,19 @@ @article{Tiago_2008, Author = {Tiago, Murilo L. and Kent,P. R. C. and Hood,Randolph Q. and Reboredo,Fernando A.}, + Date-Modified = {2020-01-07 22:20:12 +0100}, Doi = {10.1063/1.2973627}, - Eprint = {https://doi.org/10.1063/1.2973627}, - Journal = {The Journal of Chemical Physics}, + Journal = {J. Chem. Phys.}, Number = {8}, Pages = {084311}, Title = {Neutral and charged excitations in carbon fullerenes from first-principles many-body theories}, - Url = {https://doi.org/10.1063/1.2973627}, Volume = {129}, Year = {2008}, Bdsk-Url-1 = {https://doi.org/10.1063/1.2973627}} @article{Sai_2008, Author = {Sai, Na and Tiago, Murilo L. and Chelikowsky, James R. and Reboredo, Fernando A.}, + Date-Modified = {2020-01-07 22:20:02 +0100}, Doi = {10.1103/PhysRevB.77.161306}, Issue = {16}, Journal = {Phys. Rev. B}, @@ -12590,7 +12585,6 @@ Pages = {161306}, Publisher = {American Physical Society}, Title = {Optical spectra and exchange-correlation effects in molecular crystals}, - Url = {https://link.aps.org/doi/10.1103/PhysRevB.77.161306}, Volume = {77}, Year = {2008}, Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.77.161306}, @@ -12598,26 +12592,24 @@ @article{Palumno_2009, Author = {Palummo,Maurizia and Hogan,Conor and Sottile,Francesco and Bagal\'{a},Paolo and Rubio,Angel}, + Date-Modified = {2020-01-07 22:21:10 +0100}, Doi = {10.1063/1.3204938}, - Eprint = {https://doi.org/10.1063/1.3204938}, - Journal = {The Journal of Chemical Physics}, + Journal = {J. Chem. Phys.}, Number = {8}, Pages = {084102}, Title = {Ab initio electronic and optical spectra of free-base porphyrins: The role of electronic correlation}, - Url = {https://doi.org/10.1063/1.3204938}, Volume = {131}, Year = {2009}, Bdsk-Url-1 = {https://doi.org/10.1063/1.3204938}} @article{Rocca_2010, Author = {Rocca,Dario and Lu,Deyu and Galli,Giulia}, + Date-Modified = {2020-01-07 22:20:40 +0100}, Doi = {10.1063/1.3494540}, - Eprint = {https://doi.org/10.1063/1.3494540}, - Journal = {The Journal of Chemical Physics}, + Journal = {J. Chem. Phys.}, Number = {16}, Pages = {164109}, Title = {Ab initio calculations of optical absorption spectra: Solution of the Bethe--Salpeter equation within density matrix perturbation theory}, - Url = {https://doi.org/10.1063/1.3494540}, Volume = {133}, Year = {2010}, Bdsk-Url-1 = {https://doi.org/10.1063/1.3494540}} @@ -12688,6 +12680,7 @@ @article{Ziaei_2017, Author = {Ziaei, Vafa and Bredow, Thomas}, + Date-Modified = {2020-01-07 22:23:38 +0100}, Doi = {10.1103/PhysRevB.96.195115}, Issue = {19}, Journal = {Phys. Rev. B}, @@ -12696,7 +12689,6 @@ Pages = {195115}, Publisher = {American Physical Society}, Title = {Simple many-body based screening mixing ansatz for improvement of $GW$/Bethe-Salpeter equation excitation energies of molecular systems}, - Url = {https://link.aps.org/doi/10.1103/PhysRevB.96.195115}, Volume = {96}, Year = {2017}, Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.96.195115}, @@ -12752,27 +12744,24 @@ @article{Blase_2011b, Author = {Blase,X. and Attaccalite,C.}, + Date-Modified = {2020-01-07 22:23:09 +0100}, Doi = {10.1063/1.3655352}, - Eprint = {https://doi.org/10.1063/1.3655352}, - Journal = {Applied Physics Letters}, + 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}} @article{Baumeier_2012, Author = {Baumeier, Bj\"{o}rn and Andrienko, Denis and Rohlfing, Michael}, + Date-Modified = {2020-01-07 22:21:41 +0100}, Doi = {10.1021/ct300311x}, - Eprint = {https://doi.org/10.1021/ct300311x}, - Journal = {Journal of Chemical Theory and Computation}, - Note = {PMID: 26592120}, + Journal = {J. Chem. Theory Comput.}, Number = {8}, Pages = {2790-2795}, Title = {Frenkel and Charge-Transfer Excitations in Donor--acceptor Complexes from Many-Body Green's Functions Theory}, - Url = {https://doi.org/10.1021/ct300311x}, Volume = {8}, Year = {2012}, Bdsk-Url-1 = {https://doi.org/10.1021/ct300311x}} @@ -12811,45 +12800,28 @@ @article{Ziaei_2016, Author = {Ziaei,Vafa and Bredow,Thomas}, + Date-Modified = {2020-01-07 22:23:30 +0100}, Doi = {10.1063/1.4966920}, - Eprint = {https://doi.org/10.1063/1.4966920}, - Journal = {The Journal of Chemical Physics}, + Journal = {J. Chem. Phys.}, Number = {17}, Pages = {174305}, Title = {GW-BSE approach on S1 vertical transition energy of large charge transfer compounds: A performance assessment}, - Url = {https://doi.org/10.1063/1.4966920}, Volume = {145}, Year = {2016}, Bdsk-Url-1 = {https://doi.org/10.1063/1.4966920}} -@article{Rangel16, +@article{Rangel_2016, Author = {Rangel, Tonatiuh and Hamed, Samia M. and Bruneval, Fabien and Neaton, Jeffrey B.}, + Date-Modified = {2020-01-07 22:25:49 +0100}, Doi = {10.1021/acs.jctc.6b00163}, - Eprint = {https://doi.org/10.1021/acs.jctc.6b00163}, - Journal = {Journal of Chemical Theory and Computation}, - Note = {PMID: 27123935}, + Journal = {J. Chem. Theory Comput.}, Number = {6}, Pages = {2834-2842}, Title = {Evaluating the GW Approximation with CCSD(T) for Charged Excitations Across the Oligoacenes}, - Url = {https://doi.org/10.1021/acs.jctc.6b00163}, Volume = {12}, Year = {2016}, Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.6b00163}} -@article{Kaplan_2018, - Author = {Kaplan, F. and Harding, M. E. and Seiler, C. and Weigend, F. and Evers, F. and van Setten, M. J.}, - Doi = {10.1021/acs.jctc.5b01238}, - Eprint = {https://doi.org/10.1021/acs.jctc.5b01238}, - Journal = {Journal of Chemical Theory and Computation}, - Note = {PMID: 27168352}, - Number = {6}, - Pages = {2528-2541}, - Title = {Quasi-Particle Self-Consistent GW for Molecules}, - Url = {https://doi.org/10.1021/acs.jctc.5b01238}, - Volume = {12}, - Year = {2016}, - Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.5b01238}} - @article{Beigi_2003, Author = {Ismail-Beigi, Sohrab and Louie, Steven G.}, Doi = {10.1103/PhysRevLett.90.076401}, diff --git a/BSE-PES.tex b/BSE-PES.tex index d21bc38..bfb667f 100644 --- a/BSE-PES.tex +++ b/BSE-PES.tex @@ -214,7 +214,7 @@ Yet another problem is the choice of the xc functionals as the quality of excita 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} 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} 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} -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} +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} However, similar to TD-DFT, the static version of BSE cannot describe multiple excitations. \cite{Romaniello_2009a,Sangalli_2011} 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, @@ -383,14 +383,14 @@ As a final remark, we point out that Eq.~\eqref{eq:EtotBSE} can be easily genera \label{sec:comp_details} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 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. -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. +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. These will be labeled as BSE@{\GOWO} and BSE@{\evGW}, respectively. In the case of {\GOWO}, the quasiparticle energies have been obtained by linearizing the non-linear, frequency-dependent quasiparticle equation. 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. Further details about our implementation of {\GOWO} and {\evGW} can be found in Refs.~\onlinecite{Loos_2018,Veril_2018}. Finally, the infinitesimal $\eta$ has been set to $10^{-3}$ for all calculations. -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. +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. This step is, by far, the computational bottleneck in our current implementation. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%