From 920b1a01187702887882f39578bf4406e4d2c4c4 Mon Sep 17 00:00:00 2001 From: Pierre-Francois Loos Date: Wed, 4 Dec 2019 22:56:29 +0100 Subject: [PATCH] revision 4 JCTC --- JCTC_revision/GW-srDFT-control.bib | 15 + JCTC_revision/GW-srDFT.bib | 4276 ++++++++++++++++++++++++++++ JCTC_revision/GW-srDFT.tex | 698 +++++ JCTC_revision/TOC.pdf | Bin 0 -> 686716 bytes JCTC_revision/TOC.tiff | Bin 0 -> 1786294 bytes JCTC_revision/fig1a.pdf | Bin 0 -> 29579 bytes JCTC_revision/fig1b.pdf | Bin 0 -> 32153 bytes JCTC_revision/fig2.pdf | Bin 0 -> 432524 bytes 8 files changed, 4989 insertions(+) create mode 100644 JCTC_revision/GW-srDFT-control.bib create mode 100644 JCTC_revision/GW-srDFT.bib create mode 100644 JCTC_revision/GW-srDFT.tex create mode 100644 JCTC_revision/TOC.pdf create mode 100644 JCTC_revision/TOC.tiff create mode 100644 JCTC_revision/fig1a.pdf create mode 100644 JCTC_revision/fig1b.pdf create mode 100644 JCTC_revision/fig2.pdf diff --git a/JCTC_revision/GW-srDFT-control.bib b/JCTC_revision/GW-srDFT-control.bib new file mode 100644 index 0000000..1a5929a --- /dev/null +++ b/JCTC_revision/GW-srDFT-control.bib @@ -0,0 +1,15 @@ +%% This BibTeX bibliography file was created using BibDesk. +%% http://bibdesk.sourceforge.net/ + +%% Created for Pierre-Francois Loos at 2019-05-13 21:13:34 +0200 + + +%% Saved with string encoding Unicode (UTF-8) + + + +@control{achemso-control, + Ctrl-Article-Title = {yes}, + Ctrl-Chapter-Title = {yes}, + Ctrl-Etal-Firstonly = {yes}, + Ctrl-Etal-Number = {30}} diff --git a/JCTC_revision/GW-srDFT.bib b/JCTC_revision/GW-srDFT.bib new file mode 100644 index 0000000..1a8fdde --- /dev/null +++ b/JCTC_revision/GW-srDFT.bib @@ -0,0 +1,4276 @@ +%% This BibTeX bibliography file was created using BibDesk. +%% http://bibdesk.sourceforge.net/ + +%% Created for Pierre-Francois Loos at 2019-11-02 22:34:02 +0100 + + +%% Saved with string encoding Unicode (UTF-8) + + + +@article{Adler_2007, + Author = {T. 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Head-Gordon}, + Date-Added = {2018-09-01 12:02:40 +0200}, + Date-Modified = {2018-09-01 12:03:38 +0200}, + Doi = {10.1021/acs.jctc.8b00731}, + Journal = {J. Chem. Theory Comput.}, + Pages = {ASAP article}, + Title = {Regularized Orbital-Optimized Second-Order M{\o}ller--Plesset Perturbation Theory: A Reliable Fifth-Order-Scaling Electron Correlation Model with Orbital Energy Dependent Regularizers}, + Year = {2018}, + Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.8b00731}} + +@article{Scuseria_1986, + Author = {G. E. Scuseria and T. J. Lee and H. F. {Schaefer III}}, + Date-Added = {2018-09-01 11:53:43 +0200}, + Date-Modified = {2018-09-01 12:03:54 +0200}, + Doi = {10.1016/0009-2614(86)80461-4}, + Journal = {Chem. Phys. Lett.}, + Pages = {236--239}, + Title = {Accelerating the convergence of the coupled-cluster approach: The use of the DIIS method}, + Volume = {130}, + Year = {1986}, + Bdsk-Url-1 = {https://doi.org/10.1016/0009-2614(86)80461-4}} + +@article{Sangalli_2011, + Author = {D. Sangalli and P. Romaniello and G. Onida and A. Marini}, + Date-Added = {2018-08-21 22:20:47 +0200}, + Date-Modified = {2018-08-21 22:21:46 +0200}, + Doi = {10.1063/1.3518705}, + Journal = {J. Chem. Phys.}, + Pages = {034115}, + Title = {Double excitations in correlated systems: A many--body approach}, + Volume = {134}, + Year = {2011}, + Bdsk-Url-1 = {https://doi.org/10.1063/1.3518705}} + +@article{Li_2014, + Author = {Li, Zhendong and Suo, Bingbing and Liu, Wenjian}, + Date-Added = {2018-07-08 13:37:50 +0000}, + Date-Modified = {2018-07-08 13:37:50 +0000}, + Doi = {10.1063/1.4903986}, + File = {/Users/loos/Zotero/storage/48QYYQAM/Li et al. - 2014 - First order nonadiabatic coupling matrix elements .pdf}, + Issn = {0021-9606, 1089-7690}, + Journal = {J. Chem. Phys.}, + Language = {en}, + Month = dec, + Number = {24}, + Pages = {244105}, + Shorttitle = {First Order Nonadiabatic Coupling Matrix Elements between Excited States}, + Title = {First Order Nonadiabatic Coupling Matrix Elements between Excited States: {{Implementation}} and Application at the {{TD}}-{{DFT}} and Pp-{{TDA}} Levels}, + Volume = {141}, + Year = {2014}, + Bdsk-Url-1 = {https://doi.org/10.1063/1.4903986}} + +@article{Ou_2015, + Author = {Ou, Qi and Bellchambers, Gregory D. and Furche, Filipp and Subotnik, Joseph E.}, + Date-Added = {2018-07-08 13:37:50 +0000}, + Date-Modified = {2018-07-08 13:37:50 +0000}, + Doi = {10.1063/1.4906941}, + File = {/Users/loos/Zotero/storage/8YBF69YK/Ou et al. - 2015 - First-order derivative couplings between excited s.pdf}, + Issn = {0021-9606, 1089-7690}, + Journal = {J. Chem. Phys.}, + Language = {en}, + Month = feb, + Number = {6}, + Pages = {064114}, + Title = {First-Order Derivative Couplings between Excited States from Adiabatic {{TDDFT}} Response Theory}, + Volume = {142}, + Year = {2015}, + Bdsk-Url-1 = {https://doi.org/10.1063/1.4906941}} + +@article{Zhang_2015, + Author = {Zhang, Xing and Herbert, John M.}, + Date-Added = {2018-07-08 13:37:50 +0000}, + Date-Modified = {2018-07-08 13:37:50 +0000}, + Doi = {10.1063/1.4907376}, + File = {/Users/loos/Zotero/storage/DHB7LEFQ/Zhang and Herbert - 2015 - Analytic derivative couplings in time-dependent de.pdf}, + Issn = {0021-9606, 1089-7690}, + Journal = {J. Chem. Phys.}, + Language = {en}, + Month = feb, + Number = {6}, + Pages = {064109}, + Shorttitle = {Analytic Derivative Couplings in Time-Dependent Density Functional Theory}, + Title = {Analytic Derivative Couplings in Time-Dependent Density Functional Theory: {{Quadratic}} Response Theory versus Pseudo-Wavefunction Approach}, + Volume = {142}, + Year = {2015}, + Bdsk-Url-1 = {https://doi.org/10.1063/1.4907376}} + +@article{DiSabatino_2016, + Author = {Di Sabatino, Stefano and Berger, J. A. and Reining, Lucia and Romaniello, Pina}, + Date-Added = {2018-07-06 11:15:19 +0000}, + Date-Modified = {2018-07-18 13:09:33 +0000}, + Doi = {10.1103/PhysRevB.94.155141}, + Issn = {2469-9950, 2469-9969}, + Journal = {Physical Review B}, + Language = {en}, + Month = oct, + Number = {15}, + Pages = {155141}, + Shorttitle = {Photoemission Spectra from Reduced Density Matrices}, + Title = {Photoemission Spectra from Reduced Density Matrices: {{The}} Band Gap in Strongly Correlated Systems}, + Volume = {94}, + Year = {2016}, + Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevB.94.155141}} + +@article{DiSabatino_2015, + Author = {Di Sabatino,S. and Berger,J. A. and Reining,L. and Romaniello,P.}, + Doi = {10.1063/1.4926327}, + Journal = {J. Chem. Phys.}, + Number = {2}, + Pages = {024108}, + Title = {Reduced density-matrix functional theory: Correlation and spectroscopy}, + Volume = {143}, + Year = {2015}, + Bdsk-Url-1 = {https://doi.org/10.1063/1.4926327}} + +@article{Gui_2018, + Abstract = {The performance of the Bethe-Salpeter equation (BSE) approach for the first-principles computation of singlet and triplet excitation energies of small organic, closed-shell molecules has been assessed with respect to the quasiparticle energies used on input, obtained at various levels of GW theory. In the corresponding GW computations, quasiparticle energies have been computed for all orbital levels by means of using full spectral functions. The assessment reveals that, for valence excited states, quasiparticle energies obtained at the levels of eigenvalue-only self-consistent (evGW) or quasiparticle self-consistent theory (qsGW) are required to obtain results of comparable accuracy as in timedependent density-functional theory (TDDFT) using a hybrid functional such as PBE0. In contrast to TDDFT, however, the BSE approach performs well not only for valence excited states but also for excited states with Rydberg or charge-transfer character. To demonstrate the applicability of the BSE approach, computation times are reported for a set of aromatic hydrocarbons. Furthermore, examples of computations of ordinary photoabsorption and electronic circular dichroism spectra are presented for (C60)2 and C84, respectively.}, + Author = {Gui, Xin and Holzer, Christof and Klopper, Wim}, + Date-Added = {2018-07-06 11:01:02 +0000}, + Date-Modified = {2018-07-06 11:04:53 +0000}, + Doi = {10.1021/acs.jctc.8b00014}, + File = {/Users/loos/Zotero/storage/IUX26JSD/Gui et al. - 2018 - Accuracy Assessment of iGWi Starting Points f.pdf}, + Issn = {1549-9618, 1549-9626}, + Journal = {J. Chem. Theory Comput.}, + Language = {en}, + Month = apr, + Number = {4}, + Pages = {2127-2136}, + Title = {Accuracy {{Assessment}} of {{{\emph{GW}}}} {{Starting Points}} for {{Calculating Molecular Excitation Energies Using}} the {{Bethe}}\textendash{{Salpeter Formalism}}}, + Volume = {14}, + Year = {2018}, + Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.8b00014}} + +@article{Langre_2018, + Author = {M. F. Lange and T. C. Berkelbach}, + Date-Added = {2018-07-06 10:58:12 +0000}, + Date-Modified = {2018-07-06 11:05:42 +0000}, + Journal = {arXiv}, + Pages = {1805.00043}, + Title = {On The Relation Between Equation-of-Motion Coupled-Cluster Theory and the GW Approximation}, + Year = {2018}} + +@article{Parker_2016, + Author = {Parker, Shane M. and Roy, Saswata and Furche, Filipp}, + Date-Added = {2018-07-05 14:45:36 +0000}, + Date-Modified = {2018-07-05 14:45:36 +0000}, + Doi = {10.1063/1.4963749}, + File = {/Users/loos/Zotero/storage/GZA8PHWK/Parker et al. - 2016 - Unphysical divergences in response theory.pdf}, + Issn = {0021-9606, 1089-7690}, + Journal = {The Journal of Chemical Physics}, + Language = {en}, + Month = oct, + Number = {13}, + Pages = {134105}, + Title = {Unphysical Divergences in Response Theory}, + Volume = {145}, + Year = {2016}, + Bdsk-Url-1 = {https://doi.org/10.1063/1.4963749}} + +@article{Cave_2004, + Abstract = {The nature and energetics of the low-lying singlet states of polyenes have presented significant challenges for electronic structure methods. This is particularly true for conventional implementations of time-dependent density functional theory (TDDFT), which, because of their use of the adiabatic approximation, have difficulty in describing states of `doubly-excited character'. We show that use of our recently developed `Dressed TDDFT' approach provides a compact and accurate method for treating these doubly excited states, by use of a frequency-dependent exchange-correlation kernel. We present results for the vertical absorption energy for the 21Ag states of butadiene and hexatriene, and the vertical fluorescence and 0\textendash{}0 transitions for the 21Ag state of butadiene.}, + Author = {Cave, Robert J. and Zhang, Fan and Maitra, Neepa T. and Burke, Kieron}, + Date-Added = {2018-07-05 08:28:40 +0000}, + Date-Modified = {2018-07-05 09:24:39 +0000}, + Doi = {10.1016/j.cplett.2004.03.051}, + File = {/Users/loos/Zotero/storage/G6AZSCLV/Cave et al. - 2004 - A dressed TDDFT treatment of the 21Ag states of bu.pdf}, + Issn = {00092614}, + Journal = {Chem. Phys. Lett.}, + Language = {en}, + Month = may, + Number = {1-3}, + Pages = {39--42}, + Title = {A Dressed {{TDDFT}} Treatment of the {{21Ag}} States of Butadiene and Hexatriene}, + Volume = {389}, + Year = {2004}, + Bdsk-Url-1 = {https://doi.org/10.1016/j.cplett.2004.03.051}} + +@article{Becke_1993, + Author = {A. D. Becke}, + Date-Added = {2018-07-04 21:18:18 +0000}, + Date-Modified = {2018-07-18 13:08:55 +0000}, + Doi = {10.1063/1.464913}, + Journal = {J. Chem. Phys.}, + Pages = {5648--5652}, + Title = {Density-Functional Thermochemistry. III. The Role of Exact Exchange}, + Volume = {98}, + Year = {1993}, + Bdsk-Url-1 = {https://doi.org/10.1063/1.464913}} + +@article{Perdew_1996, + Author = {J. P. Perdew and K. Burke and M. Ernzerhof}, + Date-Added = {2018-07-04 21:11:12 +0000}, + Date-Modified = {2018-07-18 13:08:03 +0000}, + Doi = {10.1103/PhysRevLett.77.3865}, + Journal = {Phys. Rev. Lett.}, + Pages = {3865--3868}, + Title = {Generalized Gradient Approximation Made Simple}, + Volume = {77}, + Year = {1996}, + Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevLett.77.3865}} + +@book{ParrBook, + Address = {Clarendon Press}, + Author = {R. G. Parr and W. Yang}, + Date-Added = {2018-07-04 21:10:00 +0000}, + Date-Modified = {2018-07-04 21:10:00 +0000}, + Keywords = {dft; qmech}, + Publisher = {Oxford}, + Title = {Density-functional theory of atoms and molecules}, + Year = {1989}} + +@article{Gill_1994, + Author = {P. M. W. Gill}, + Date-Added = {2018-07-04 20:48:56 +0000}, + Date-Modified = {2018-07-18 13:07:04 +0000}, + Doi = {10.1016/S0065-3276(08)60019-2}, + Journal = {Adv. Quantum Chem.}, + Pages = {141--205}, + Title = {Molecular Integrals Over Gaussian Basis Functions}, + Volume = {25}, + Year = {1994}, + Bdsk-Url-1 = {https://doi.org/10.1016/S0065-3276(08)60019-2}} + +@article{Pavlyukh_2017, + Author = {Y. Pavlyukh}, + Date-Added = {2018-07-04 15:36:10 +0000}, + Date-Modified = {2018-07-04 15:38:19 +0000}, + Doi = {10.1038/s41598-017-00355-w}, + Journal = {Nature}, + Pages = {504}, + Title = {Pade resummation of many-body perturbation theory}, + Volume = {7}, + Year = {2017}, + Bdsk-Url-1 = {https://doi.org/10.1038/s41598-017-00355-w}} + +@book{HerzbergBook, + Author = {K. P. Huber and G. Herzberg}, + Date-Added = {2018-07-02 11:52:15 +0000}, + Date-Modified = {2018-07-02 11:52:15 +0000}, + Publisher = {van Nostrand Reinhold Company}, + Title = {Molecular Spectra and Molecular Structure: IV. Constants of diatomic molecules}, + Year = {1979}} + +@article{Maitra_2004, + Author = {N. T. Maitra and F. Zhang, R. J. Cave and K. Burke}, + Date-Added = {2018-06-30 20:21:46 +0000}, + Date-Modified = {2018-06-30 20:23:01 +0000}, + Doi = {10.1063/1.1651060}, + Journal = {J. Chem. Phys.}, + Pages = {5932}, + Title = {Double excitations within time-dependent density functional theory linear response}, + Volume = {120}, + Year = {2004}, + Bdsk-Url-1 = {https://doi.org/10.1063/1.1651060}} + +@article{Caruso_2016, + Author = {F. Caruso and M. Dauth and M. J. {van Setten} and P. Rinke}, + Date-Added = {2018-06-29 11:23:57 +0000}, + Date-Modified = {2018-06-29 11:25:49 +0000}, + Doi = {10.1021/acs.jctc.6b00774}, + Journal = {J. Chem. Theory Comput.}, + Pages = {5076}, + Title = {Benchmark of GW Approaches for the GW100 Test Set}, + Volume = {12}, + Year = {2016}, + Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.6b00774}} + +@article{Loos_2018, + Author = {P. F. Loos and P. Romaniello and J. A. Berger}, + Date-Added = {2018-06-27 18:40:35 +0000}, + Date-Modified = {2018-07-18 13:04:09 +0000}, + Doi = {10.1021/acs.jctc.8b00260}, + Journal = {J. Chem. Theory Comput.}, + Pages = {3071--3082}, + Title = {Green functions and self-consistency: insights from the spherium model}, + Volume = {14}, + Year = {2018}, + Bdsk-Url-1 = {https://dx.doi.org/10.1021/acs.jctc.8b00260}} + +@article{Curtiss_1991, + Author = {Curtiss, Larry A. and Raghavachari, Krishnan and Trucks, Gary W. and Pople, John A.}, + Date-Added = {2018-04-23 07:38:41 +0000}, + Date-Modified = {2018-04-23 07:38:41 +0000}, + Doi = {10.1063/1.460205}, + Issn = {0021-9606, 1089-7690}, + Journal = {J. Chem. Phys.}, + Language = {en}, + Month = jun, + Number = {11}, + Pages = {7221-7230}, + Title = {Gaussian-2 Theory for Molecular Energies of First- and Second-row Compounds}, + Volume = {94}, + 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{Schreiber_2008, + Author = {Schreiber, Marko and Silva-Junior, Mario R. and Sauer, Stephan P. A. and Thiel, Walter}, + Date-Added = {2018-04-23 07:38:41 +0000}, + Date-Modified = {2018-04-23 07:38:41 +0000}, + Doi = {10.1063/1.2889385}, + Issn = {0021-9606, 1089-7690}, + Journal = {J. Chem. Phys.}, + Language = {en}, + Month = apr, + Number = {13}, + Pages = {134110}, + Shorttitle = {Benchmarks for Electronically Excited States}, + Title = {Benchmarks for Electronically Excited States: {{CASPT2}}, {{CC2}}, {{CCSD}}, and {{CC3}}}, + Volume = {128}, + Year = {2008}, + Bdsk-Url-1 = {https://doi.org/10.1063/1.2889385}} + +@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}, + Date-Modified = {2018-04-23 07:38:41 +0000}, + Doi = {10.1063/1.3499598}, + Issn = {0021-9606, 1089-7690}, + Journal = {J. Chem. Phys.}, + Language = {en}, + Month = nov, + Number = {17}, + Pages = {174318}, + Shorttitle = {Benchmarks of Electronically Excited States}, + Title = {Benchmarks of Electronically Excited States: {{Basis}} Set Effects on {{CASPT2}} Results}, + Volume = {133}, + Year = {2010}, + Bdsk-Url-1 = {https://doi.org/10.1063/1.3499598}} + +@article{Silva-Junior_2010b, + Author = {Silva-Junior, Mario R. and Sauer, Stephan P.A. and Schreiber, Marko and Thiel, Walter}, + Date-Added = {2018-04-23 07:38:41 +0000}, + Date-Modified = {2018-04-23 07:38:41 +0000}, + Doi = {10.1080/00268970903549047}, + Issn = {0026-8976, 1362-3028}, + Journal = {Mol. Phys.}, + Language = {en}, + Month = feb, + Number = {3-4}, + Pages = {453-465}, + Shorttitle = {Basis Set Effects on Coupled Cluster Benchmarks of Electronically Excited States}, + Title = {Basis Set Effects on Coupled Cluster Benchmarks of Electronically Excited States: {{CC3}}, {{CCSDR}}(3) and {{CC2}}}, + Volume = {108}, + Year = {2010}, + Bdsk-Url-1 = {https://doi.org/10.1080/00268970903549047}} + +@article{Dolgounitcheva_2016, + Author = {Dolgounitcheva, O. and D{\'\i}az-Tinoco, Manuel and Zakrzewski, V. G. and Richard, Ryan M. and Marom, Noa and Sherrill, C. David and Ortiz, J. V.}, + Date-Added = {2018-04-22 16:22:34 +0000}, + Date-Modified = {2018-04-22 16:22:34 +0000}, + Doi = {10.1021/acs.jctc.5b00872}, + Issn = {1549-9618, 1549-9626}, + Journal = {J. Chem. Theory Comput.}, + Language = {en}, + Month = feb, + Number = {2}, + Pages = {627-637}, + Shorttitle = {Accurate {{Ionization Potentials}} and {{Electron Affinities}} of {{Acceptor Molecules IV}}}, + Title = {Accurate {{Ionization Potentials}} and {{Electron Affinities}} of {{Acceptor Molecules IV}}: {{Electron}}-{{Propagator Methods}}}, + Volume = {12}, + Year = {2016}, + Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.5b00872}} + +@article{Gallandi_2016, + Author = {Gallandi, Lukas and Marom, Noa and Rinke, Patrick and K{\"o}rzd{\"o}rfer, Thomas}, + Date-Added = {2018-04-22 16:22:34 +0000}, + Date-Modified = {2018-04-22 16:22:34 +0000}, + Doi = {10.1021/acs.jctc.5b00873}, + Issn = {1549-9618, 1549-9626}, + Journal = {J. Chem. Theory Comput.}, + Language = {en}, + Month = feb, + Number = {2}, + Pages = {605-614}, + Shorttitle = {Accurate {{Ionization Potentials}} and {{Electron Affinities}} of {{Acceptor Molecules II}}}, + Title = {Accurate {{Ionization Potentials}} and {{Electron Affinities}} of {{Acceptor Molecules II}}: {{Non}}-{{Empirically Tuned Long}}-{{Range Corrected Hybrid Functionals}}}, + Volume = {12}, + Year = {2016}, + Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.5b00873}} + +@article{Knight_2016, + Author = {Knight, Joseph W. and Wang, Xiaopeng and Gallandi, Lukas and Dolgounitcheva, Olga and Ren, Xinguo and Ortiz, J. Vincent and Rinke, Patrick and K{\"o}rzd{\"o}rfer, Thomas and Marom, Noa}, + Date-Added = {2018-04-22 16:22:34 +0000}, + Date-Modified = {2018-04-22 16:22:34 +0000}, + Doi = {10.1021/acs.jctc.5b00871}, + Issn = {1549-9618, 1549-9626}, + Journal = {J. Chem. Theory Comput.}, + Language = {en}, + Month = feb, + Number = {2}, + Pages = {615-626}, + Shorttitle = {Accurate {{Ionization Potentials}} and {{Electron Affinities}} of {{Acceptor Molecules III}}}, + Title = {Accurate {{Ionization Potentials}} and {{Electron Affinities}} of {{Acceptor Molecules III}}: {{A Benchmark}} of {{{\emph{GW}}}} {{Methods}}}, + Volume = {12}, + Year = {2016}, + Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.5b00871}} + +@article{Maggio_2017, + Author = {Maggio, Emanuele and Liu, Peitao and {van Setten}, Michiel J. and Kresse, Georg}, + Date-Added = {2018-04-22 16:22:34 +0000}, + Date-Modified = {2018-04-22 16:22:34 +0000}, + Doi = {10.1021/acs.jctc.6b01150}, + Issn = {1549-9618, 1549-9626}, + Journal = {J. Chem. Theory Comput.}, + Language = {en}, + Month = feb, + Number = {2}, + Pages = {635-648}, + Shorttitle = {{{{\emph{GW}}}} 100}, + Title = {{{{\emph{GW}}}} 100: {{A Plane Wave Perspective}} for {{Small Molecules}}}, + Volume = {13}, + Year = {2017}, + Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.6b01150}} + +@article{Richard_2016, + Author = {Richard, Ryan M. and Marshall, Michael S. and Dolgounitcheva, O. and Ortiz, J. V. and Br{\'e}das, Jean-Luc and Marom, Noa and Sherrill, C. David}, + Date-Added = {2018-04-22 16:22:34 +0000}, + Date-Modified = {2018-04-22 16:22:34 +0000}, + Doi = {10.1021/acs.jctc.5b00875}, + Issn = {1549-9618, 1549-9626}, + Journal = {J. Chem. Theory Comput.}, + Language = {en}, + Month = feb, + Number = {2}, + Pages = {595-604}, + Title = {Accurate {{Ionization Potentials}} and {{Electron Affinities}} of {{Acceptor Molecules I}}. {{Reference Data}} at the {{CCSD}}({{T}}) {{Complete Basis Set Limit}}}, + Volume = {12}, + Year = {2016}, + Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.5b00875}} + +@article{Rusakov_2014, + Author = {Rusakov, Alexander A. and Phillips, Jordan J. and Zgid, Dominika}, + Date-Added = {2018-04-22 16:22:34 +0000}, + Date-Modified = {2018-04-22 16:22:34 +0000}, + Doi = {10.1063/1.4901432}, + Issn = {0021-9606, 1089-7690}, + Journal = {J. Chem. Phys.}, + Language = {en}, + Month = nov, + Number = {19}, + Pages = {194105}, + Title = {Local {{Hamiltonians}} for Quantitative {{Green}}'s Function Embedding Methods}, + Volume = {141}, + Year = {2014}, + Bdsk-Url-1 = {https://doi.org/10.1063/1.4901432}} + +@article{Baym_1961, + Author = {Baym, Gordon and Kadanoff, Leo P.}, + Date-Added = {2018-04-21 09:30:30 +0000}, + Date-Modified = {2018-04-21 09:30:30 +0000}, + Doi = {10.1103/PhysRev.124.287}, + Issn = {0031-899X}, + Journal = {Phys. Rev.}, + Language = {en}, + Month = oct, + Number = {2}, + Pages = {287--299}, + Title = {Conservation {{Laws}} and {{Correlation Functions}}}, + Volume = {124}, + Year = {1961}, + Bdsk-Url-1 = {https://doi.org/10.1103/PhysRev.124.287}} + +@article{Baym_1962, + Author = {Baym, Gordon}, + Date-Added = {2018-04-21 09:30:30 +0000}, + Date-Modified = {2018-04-21 09:30:44 +0000}, + Doi = {10.1103/PhysRev.127.1391}, + Issn = {0031-899X}, + Journal = {Phys. Rev.}, + Language = {en}, + Month = aug, + Number = {4}, + Pages = {1391--1401}, + Title = {Self-{{Consistent Approximations}} in {{Many}}-{{Body Systems}}}, + Volume = {127}, + Year = {1962}, + Bdsk-Url-1 = {https://doi.org/10.1103/PhysRev.127.1391}} + +@article{Martin_1959, + Author = {Martin, Paul C. and Schwinger, Julian}, + Date-Added = {2018-04-21 09:30:30 +0000}, + Date-Modified = {2018-04-21 09:30:30 +0000}, + Doi = {10.1103/PhysRev.115.1342}, + Issn = {0031-899X}, + Journal = {Phys. Rev.}, + Language = {en}, + Month = sep, + Number = {6}, + Pages = {1342--1373}, + Title = {Theory of {{Many}}-{{Particle Systems}}. {{I}}}, + Volume = {115}, + Year = {1959}, + Bdsk-Url-1 = {https://doi.org/10.1103/PhysRev.115.1342}} + +@book{FetterBook, + Author = {A. L. Fetter and J. D. Waleck}, + Date-Added = {2018-04-21 09:25:00 +0000}, + Date-Modified = {2018-04-21 09:25:48 +0000}, + Publisher = {McGraw Hill, San Francisco}, + Title = {Quantum Theory of Many Particle Systems}, + Year = {1971}} + +@article{Luttinger_1960, + Author = {Luttinger, J. M. and Ward, J. C.}, + Date-Added = {2018-03-12 11:16:46 +0000}, + Date-Modified = {2018-03-12 11:16:46 +0000}, + Doi = {10.1103/PhysRev.118.1417}, + Issn = {0031-899X}, + Journal = {Physical Review}, + Language = {en}, + Month = jun, + Number = {5}, + Pages = {1417--1427}, + Title = {Ground-{State} {Energy} of a {Many}-{Fermion} {System}. {II}}, + Url = {https://link.aps.org/doi/10.1103/PhysRev.118.1417}, + Urldate = {2018-03-12}, + Volume = {118}, + Year = {1960}, + Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRev.118.1417}, + Bdsk-Url-2 = {https://dx.doi.org/10.1103/PhysRev.118.1417}} + +@article{Ren_2012, + Author = {Ren, Xinguo and Rinke, Patrick and Joas, Christian and Scheffler, Matthias}, + Date-Added = {2018-03-08 21:19:25 +0000}, + Date-Modified = {2018-03-08 21:19:25 +0000}, + Doi = {10.1007/s10853-012-6570-4}, + Issn = {0022-2461, 1573-4803}, + Journal = {J. Mater. Sci.}, + Language = {en}, + Month = nov, + Number = {21}, + Pages = {7447--7471}, + Title = {Random-Phase Approximation and Its Applications in Computational Chemistry and Materials Science}, + Volume = {47}, + Year = {2012}, + Bdsk-Url-1 = {https://dx.doi.org/10.1007/s10853-012-6570-4}} + +@article{Wetherell_2018, + Author = {Wetherell, J. and Hodgson, M. J. P. and Godby, R. W.}, + Date-Added = {2018-03-08 21:16:56 +0000}, + Date-Modified = {2018-04-14 07:32:38 +0000}, + Doi = {10.1103/PhysRevB.97.121102}, + Issn = {2469-9950, 2469-9969}, + Journal = {Phys. Rev. B}, + Language = {en}, + Month = mar, + Number = {12}, + Pages = {121102}, + Title = {G {{W}} Self-Screening Error and Its Correction Using a Local Density Functional}, + Volume = {97}, + Year = {2018}, + Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevB.97.121102}} + +@article{Aryasetiawan_2012, + Author = {Aryasetiawan, F. and Sakuma, R. and Karlsson, K.}, + Date-Added = {2018-03-06 20:22:33 +0000}, + Date-Modified = {2018-04-14 07:25:24 +0000}, + Doi = {10.1103/PhysRevB.85.035106}, + Issn = {1098-0121, 1550-235X}, + Journal = {Phys. Rev. B}, + Language = {en}, + Month = jan, + Number = {3}, + Pages = {035106}, + Title = {G {{W}} Approximation with Self-Screening Correction}, + Volume = {85}, + Year = {2012}, + Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevB.85.035106}} + +@article{Phillips_2014, + Author = {Phillips, Jordan J. and Zgid, Dominika}, + Date-Added = {2018-03-06 19:42:15 +0000}, + Date-Modified = {2018-03-06 19:42:15 +0000}, + Doi = {10.1063/1.4884951}, + Issn = {0021-9606, 1089-7690}, + Journal = {J. Chem. Phys.}, + Language = {en}, + Month = jun, + Number = {24}, + Pages = {241101}, + Shorttitle = {Communication}, + Title = {Communication: {{The}} Description of Strong Correlation within Self-Consistent {{Green}}'s Function Second-Order Perturbation Theory}, + Volume = {140}, + Year = {2014}, + Bdsk-Url-1 = {https://dx.doi.org/10.1063/1.4884951}} + +@article{Phillips_2015, + Author = {Phillips, Jordan J. and Kananenka, Alexei A. and Zgid, Dominika}, + Date-Added = {2018-03-06 19:42:15 +0000}, + Date-Modified = {2018-03-06 19:42:15 +0000}, + Doi = {10.1063/1.4921259}, + Issn = {0021-9606, 1089-7690}, + Journal = {J. Chem. Phys.}, + Language = {en}, + Month = may, + Number = {19}, + Pages = {194108}, + Title = {Fractional Charge and Spin Errors in Self-Consistent {{Green}}'s Function Theory}, + Volume = {142}, + Year = {2015}, + Bdsk-Url-1 = {https://dx.doi.org/10.1063/1.4921259}} + +@article{Rusakov_2016, + Author = {Rusakov, Alexander A. and Zgid, Dominika}, + Date-Added = {2018-03-06 19:42:15 +0000}, + Date-Modified = {2018-03-06 19:42:15 +0000}, + Doi = {10.1063/1.4940900}, + Issn = {0021-9606, 1089-7690}, + Journal = {J. Chem. Phys.}, + Language = {en}, + Month = feb, + Number = {5}, + Pages = {054106}, + Title = {Self-Consistent Second-Order {{Green}}'s Function Perturbation Theory for Periodic Systems}, + Volume = {144}, + Year = {2016}, + Bdsk-Url-1 = {https://dx.doi.org/10.1063/1.4940900}} + +@book{Stefanucci_2013, + Abstract = {"The Green's function method is one of the most powerful and versatile formalisms in physics, and its nonequilibrium version has proved invaluable in many research fields. This book provides a unique, self-contained introduction to nonequilibrium many-body theory. Starting with basic quantum mechanics, the authors introduce the equilibrium and nonequilibrium Green's function formalisms within a unified framework called the contour formalism. The physical content of the contour Green's functions and the diagrammatic expansions are explained with a focus on the time-dependent aspect. Every result is derived step-by-step, critically discussed and then applied to different physical systems, ranging from molecules and nanostructures to metals and insulators. With an abundance of illustrative examples, this accessible book is ideal for graduate students and researchers who are interested in excited state properties of matter and nonequilibrium physics"--}, + Address = {Cambridge}, + Author = {Stefanucci, Gianluca and van Leeuwen, Robert}, + Date-Added = {2018-03-06 19:42:15 +0000}, + Date-Modified = {2018-03-06 19:42:15 +0000}, + Isbn = {978-0-521-76617-3}, + Keywords = {Many-body problem,Quantum theory,Green's functions,Mathematics,SCIENCE / Physics}, + Lccn = {QC174.17.G68 S74 2013}, + Publisher = {{Cambridge University Press}}, + Shorttitle = {Nonequilibrium Many-Body Theory of Quantum Systems}, + Title = {Nonequilibrium Many-Body Theory of Quantum Systems: A Modern Introduction}, + Year = {2013}} + +@article{Strinati_1988, + Author = {Strinati, G.}, + Date-Added = {2018-03-06 19:42:15 +0000}, + Date-Modified = {2018-03-06 19:42:15 +0000}, + Doi = {10.1007/BF02725962}, + Issn = {1826-9850}, + Journal = {Riv. Nuovo Cimento}, + Language = {en}, + Month = dec, + Number = {12}, + Pages = {1--86}, + Title = {Application of the {{Green}}'s Functions Method to the Study of the Optical Properties of Semiconductors}, + Volume = {11}, + Year = {1988}, + Bdsk-Url-1 = {https://dx.doi.org/10.1007/BF02725962}} + +@article{vonBarth_1996, + Author = {{von Barth}, Ulf and Holm, Bengt}, + Date-Added = {2018-03-06 19:42:15 +0000}, + Date-Modified = {2018-07-05 09:37:45 +0000}, + Doi = {10.1103/PhysRevB.54.8411}, + File = {/Users/loos/Zotero/storage/QZN2CFQX/vonBarth_1996.pdf}, + Journal = {Phys. Rev. B}, + Number = {12}, + Pages = {8411}, + Shorttitle = {Self-Consistent {{GW}} 0 Results for the Electron Gas}, + Title = {Self-Consistent {{GW}} 0 Results for the Electron Gas: {{Fixed}} Screened Potential {{W}} 0 within the Random-Phase Approximation}, + Volume = {54}, + Year = {1996}, + Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevB.54.8411}} + +@article{Casida_1989, + Author = {Casida, Mark E. and Chong, Delano P.}, + Date-Added = {2018-03-03 16:36:07 +0000}, + Date-Modified = {2018-07-18 13:20:19 +0000}, + Doi = {10.1103/PhysRevA.40.4837}, + File = {/Users/loos/Zotero/storage/Q9SZH8DT/Casida_1989.pdf}, + Journal = {Phys. Rev. A}, + Number = {9}, + Pages = {4837--4848}, + Title = {Physical Interpretation and Assessment of the {{Coulomb}}-Hole and Screened-Exchange Approximation for Molecules}, + Volume = {40}, + Year = {1989}, + Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevA.40.4837}} + +@article{Casida_1991, + Author = {Casida, Mark E. and Chong, Delano P.}, + Date-Added = {2018-03-03 16:36:07 +0000}, + Date-Modified = {2018-07-18 13:19:04 +0000}, + Doi = {10.1103/PhysRevA.44.5773}, + File = {/Users/loos/Zotero/storage/56Z844J7/Casida_1991a.pdf}, + Journal = {Phys. Rev. A}, + Number = {9}, + Pages = {5773--5783}, + Shorttitle = {Simplified {{Green}}-Function Approximations}, + Title = {Simplified {{Green}}-Function Approximations: {{Further}} Assessment of a Polarization Model for Second-Order Calculation of Outer-Valence Ionization Potentials in Molecules}, + Volume = {44}, + Year = {1991}, + Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevA.44.5773}} + +@article{Casida_1991a, + Author = {Casida, Mark E. and Chong, Delano P.}, + Date-Added = {2018-03-03 16:36:07 +0000}, + Date-Modified = {2018-07-18 13:19:44 +0000}, + Doi = {10.1002/qua.560400206}, + File = {/Users/loos/Zotero/storage/XHIUNWXB/Casida_1991b.pdf}, + Journal = {Int. J. Quantum Chem.}, + Number = {2}, + Pages = {225--242}, + Title = {Quasi-Particle Equation from the Configuration-Interaction ({{CI}}) Wave-Function Method}, + Volume = {40}, + Year = {1991}, + Bdsk-Url-1 = {https://doi.org/10.1002/qua.560400206}} + +@article{Friedrich_2006a, + Author = {Friedrich, Christoph and Schindlmayr, Arno and Bl{\"u}gel, Stefan and Kotani, Takao}, + Date-Added = {2018-03-03 16:36:07 +0000}, + Date-Modified = {2018-04-14 07:26:06 +0000}, + Doi = {10.1103/PhysRevB.74.045104}, + File = {/Users/loos/Zotero/storage/E7JYZIM2/Friedrich_2006.pdf}, + Issn = {1098-0121, 1550-235X}, + Journal = {Phys. Rev. B}, + Language = {en}, + Month = jul, + Number = {4}, + Pages = {045104}, + Title = {Elimination of the Linearization Error in {{{\emph{GW}}}} Calculations Based on the Linearized Augmented-Plane-Wave Method}, + Volume = {74}, + Year = {2006}, + Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevB.74.045104}} + +@article{Hernandez_1977, + Author = {Hern{\'a}ndez, A. J. and Langhoff, P. W.}, + Date-Added = {2018-03-03 16:36:07 +0000}, + Date-Modified = {2018-03-03 16:36:07 +0000}, + File = {/Users/loos/Zotero/storage/XEF84BE7/Hernandez_1977.pdf}, + Journal = {Chem. Phys. Lett.}, + Number = {3}, + Pages = {421--426}, + Title = {On {{Rayleigh}}-{{Schr{\"o}dinger}} and Green's-Function Calculations of Ionization Potentials and Electron Affinities}, + Volume = {49}, + Year = {1977}} + +@article{Schone_1998a, + Author = {Sch{\"o}ne, Wolf-Dieter and Eguiluz, Adolfo G.}, + Date-Added = {2018-03-03 16:36:07 +0000}, + Date-Modified = {2018-03-03 16:36:07 +0000}, + File = {/Users/loos/Zotero/storage/J4XS8Z9Q/Schone_1998.pdf}, + Journal = {Phys. Rev. Lett.}, + Number = {8}, + Pages = {1662}, + Title = {Self-Consistent Calculations of Quasiparticle States in Metals and Semiconductors}, + Volume = {81}, + Year = {1998}} + +@article{Pulay_1980, + Author = {Pulay, P{\'e}ter}, + Date-Added = {2018-02-25 19:37:56 +0000}, + Date-Modified = {2018-02-25 19:37:56 +0000}, + Doi = {10.1016/0009-2614(80)80396-4}, + Issn = {00092614}, + Journal = {Chem. Phys. Lett.}, + Language = {en}, + Month = jul, + Number = {2}, + Pages = {393--398}, + Title = {Convergence Acceleration of Iterative Sequences. the Case of Scf Iteration}, + Volume = {73}, + Year = {1980}, + Bdsk-Url-1 = {https://dx.doi.org/10.1016/0009-2614(80)80396-4}} + +@article{Pulay_1982, + Author = {Pulay, P.}, + Date-Added = {2018-02-25 19:37:56 +0000}, + Date-Modified = {2018-02-25 19:37:56 +0000}, + Doi = {10.1002/jcc.540030413}, + Issn = {0192-8651, 1096-987X}, + Journal = {J. Comput. Chem.}, + Language = {en}, + Number = {4}, + Pages = {556--560}, + Title = {{{ImprovedSCF}} Convergence Acceleration}, + Volume = {3}, + Year = {1982}, + Bdsk-Url-1 = {https://dx.doi.org/10.1002/jcc.540030413}} + +@article{Berger_2014a, + Author = {Berger, J A and Romaniello, Pina and Tandetzky, Falk and Mendoza, Bernardo S and Brouder, Christian and Reining, Lucia}, + Date-Added = {2018-02-25 15:53:21 +0000}, + Date-Modified = {2018-02-25 15:53:21 +0000}, + Doi = {10.1088/1367-2630/16/11/113025}, + Issn = {1367-2630}, + Journal = {New J. Phys.}, + Month = nov, + Number = {11}, + Pages = {113025}, + Title = {Solution to the Many-Body Problem in One Point}, + Volume = {16}, + Year = {2014}, + Bdsk-Url-1 = {https://dx.doi.org/10.1088/1367-2630/16/11/113025}} + +@article{Casida_1995, + Author = {Casida, Mark E.}, + Date-Added = {2018-02-24 22:54:58 +0000}, + Date-Modified = {2018-02-24 22:54:58 +0000}, + Doi = {10.1103/PhysRevA.51.2005}, + Issn = {1050-2947, 1094-1622}, + Journal = {Phys. Rev. A}, + Language = {en}, + Month = mar, + Number = {3}, + Pages = {2005--2013}, + Shorttitle = {Generalization of the Optimized-Effective-Potential Model to Include Electron Correlation}, + Title = {Generalization of the Optimized-Effective-Potential Model to Include Electron Correlation: {{A}} Variational Derivation of the {{Sham}}-{{Schl{\"u}ter}} Equation for the Exact Exchange-Correlation Potential}, + Volume = {51}, + Year = {1995}, + Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevA.51.2005}} + +@article{Holm_1999, + Author = {Holm, Bengt}, + Date-Added = {2018-02-24 22:54:58 +0000}, + Date-Modified = {2018-02-24 22:54:58 +0000}, + Doi = {10.1103/PhysRevLett.83.788}, + Issn = {0031-9007, 1079-7114}, + Journal = {Phys. Rev. Lett.}, + Language = {en}, + Month = jul, + Number = {4}, + Pages = {788--791}, + Title = {Total {{Energies}} from {{GW Calculations}}}, + Volume = {83}, + Year = {1999}, + Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevLett.83.788}} + +@book{SzaboBook, + Address = {New York}, + Author = {A. Szabo and N. S. Ostlund}, + Date-Added = {2018-02-24 21:04:21 +0000}, + Date-Modified = {2018-02-24 21:04:21 +0000}, + Keywords = {qmech}, + Publisher = {McGraw-Hill}, + Title = {Modern quantum chemistry}, + Year = {1989}} + +@article{Faber_2011, + Author = {Faber, Carina and Attaccalite, Claudio and Olevano, V. and Runge, E. and Blase, X.}, + Date-Added = {2018-02-24 20:47:47 +0000}, + Date-Modified = {2018-04-14 07:19:37 +0000}, + Doi = {10.1103/PhysRevB.83.115123}, + Issn = {1098-0121, 1550-235X}, + Journal = {Phys. Rev. B}, + Language = {en}, + Month = mar, + Number = {11}, + Pages = {115123}, + Title = {First-Principles {{GW}} Calculations for {{DNA}} and {{RNA}} Nucleobases}, + Volume = {83}, + Year = {2011}, + Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevB.83.115123}} + +@incollection{Hedin_1970, + Author = {Hedin, Lars and Lundqvist, Stig}, + Booktitle = {Solid State Physics}, + Date-Added = {2018-02-24 19:55:02 +0000}, + Date-Modified = {2018-02-24 19:57:12 +0000}, + Doi = {10.1016/S0081-1947(08)60615-3}, + Isbn = {978-0-12-607723-0}, + Language = {en}, + Pages = {1--181}, + Publisher = {Elsevier}, + Title = {Effects of Electron-Electron and Electron-Phonon Interactions on the One-Electron States of Solids}, + Volume = {23}, + Year = {1970}, + Bdsk-Url-1 = {https://dx.doi.org/10.1016/S0081-1947(08)60615-3}} + +@article{Hybertsen_1986, + Author = {Hybertsen, Mark S. and Louie, Steven G.}, + Date-Added = {2018-02-24 19:55:02 +0000}, + Date-Modified = {2018-02-24 19:55:02 +0000}, + Doi = {10.1103/PhysRevB.34.5390}, + Issn = {0163-1829}, + Journal = {Phys. Rev. B}, + Language = {en}, + Month = oct, + Number = {8}, + Pages = {5390--5413}, + Shorttitle = {Electron Correlation in Semiconductors and Insulators}, + Title = {Electron Correlation in Semiconductors and Insulators: {{Band}} Gaps and Quasiparticle Energies}, + Volume = {34}, + Year = {1986}, + Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevB.34.5390}} + +@article{Hybertsen_1985a, + Author = {Hybertsen, Mark S. and Louie, Steven G.}, + Date-Added = {2018-02-24 19:55:02 +0000}, + Date-Modified = {2018-02-24 19:55:02 +0000}, + Doi = {10.1103/PhysRevLett.55.1418}, + Issn = {0031-9007}, + Journal = {Phys. Rev. Lett.}, + Language = {en}, + Month = sep, + Number = {13}, + Pages = {1418--1421}, + Shorttitle = {First-{{Principles Theory}} of {{Quasiparticles}}}, + Title = {First-{{Principles Theory}} of {{Quasiparticles}}: {{Calculation}} of {{Band Gaps}} in {{Semiconductors}} and {{Insulators}}}, + Volume = {55}, + Year = {1985}, + Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevLett.55.1418}} + +@article{Friedrich_2006, + Author = {Friedrich, Christoph and Schindlmayr, Arno and Bl{\"u}gel, Stefan and Kotani, Takao}, + Date-Added = {2018-02-24 19:51:02 +0000}, + Date-Modified = {2018-04-14 07:25:57 +0000}, + Doi = {10.1103/PhysRevB.74.045104}, + Issn = {1098-0121, 1550-235X}, + Journal = {Phys. Rev. B}, + Language = {en}, + Month = jul, + Number = {4}, + Pages = {045104}, + Title = {Elimination of the Linearization Error in {{{\emph{GW}}}} Calculations Based on the Linearized Augmented-Plane-Wave Method}, + Volume = {74}, + Year = {2006}, + Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevB.74.045104}} + +@article{Klein_1961, + Author = {Klein, Abraham}, + Date-Added = {2018-02-24 19:51:02 +0000}, + Date-Modified = {2018-02-24 19:51:02 +0000}, + Doi = {10.1103/PhysRev.121.950}, + Issn = {0031-899X}, + Journal = {Phys. Rev.}, + Language = {en}, + Month = feb, + Number = {4}, + Pages = {950--956}, + Title = {Perturbation {{Theory}} for an {{Infinite Medium}} of {{Fermions}}. {{II}}}, + Volume = {121}, + Year = {1961}, + Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRev.121.950}} + +@article{Schone_1998, + Author = {Sch{\"o}ne, Wolf-Dieter and Eguiluz, Adolfo G.}, + Date-Added = {2018-02-24 19:51:02 +0000}, + Date-Modified = {2018-02-24 19:51:02 +0000}, + Doi = {10.1103/PhysRevLett.81.1662}, + Issn = {0031-9007, 1079-7114}, + Journal = {Phys. Rev. Lett.}, + Language = {en}, + Month = aug, + Number = {8}, + Pages = {1662--1665}, + Title = {Self-{{Consistent Calculations}} of {{Quasiparticle States}} in {{Metals}} and {{Semiconductors}}}, + Volume = {81}, + Year = {1998}, + Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevLett.81.1662}} + +@article{deGroot_1995, + Author = {{de Groot}, H. J. and Bobbert, P. A. and {van Haeringen}, W.}, + Date-Added = {2018-02-24 19:51:02 +0000}, + Date-Modified = {2018-02-24 19:51:02 +0000}, + Doi = {10.1103/PhysRevB.52.11000}, + Issn = {0163-1829, 1095-3795}, + Journal = {Phys. Rev. B}, + Language = {en}, + Month = oct, + Number = {15}, + Pages = {11000--11007}, + Title = {Self-Consistent {{{\emph{GW}}}} for a Quasi-One-Dimensional Semiconductor}, + Volume = {52}, + Year = {1995}, + Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevB.52.11000}} + +@article{Galitskii_1958, + Author = {V. Galitskii and A. Migdal}, + Date-Added = {2018-02-24 19:47:40 +0000}, + Date-Modified = {2018-02-24 19:48:36 +0000}, + Journal = {Sov. Phys. JETP}, + Pages = {96}, + Volume = {7}, + Year = {1958}} + +@book{NISTbook, + Address = {New York}, + Date-Added = {2018-02-24 19:02:50 +0000}, + Date-Modified = {2018-02-24 19:02:50 +0000}, + Editor = {F. W. J. Olver and D. W. Lozier and R. F. Boisvert and C. W. Clark}, + Keywords = {maths}, + Publisher = {Cambridge University Press}, + Title = {NIST Handbook of Mathematical Functions}, + Year = {2010}} + +@article{Seidl_2007, + Author = {Seidl, Michael}, + Date-Added = {2018-02-24 13:48:36 +0000}, + Date-Modified = {2018-04-14 07:29:55 +0000}, + Doi = {10.1103/PhysRevA.75.062506}, + Issn = {1050-2947, 1094-1622}, + Journal = {Phys. Rev. A}, + Language = {en}, + Month = jun, + Number = {6}, + Pages = {062506}, + Shorttitle = {Adiabatic Connection in Density-Functional Theory}, + Title = {Adiabatic Connection in Density-Functional Theory: {{Two}} Electrons on the Surface of a Sphere}, + Volume = {75}, + Year = {2007}, + Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevA.75.062506}} + +@article{Loos_2010e, + Author = {Loos, Pierre-Fran{\c c}ois and Gill, Peter M.W.}, + Date-Added = {2018-02-24 13:46:12 +0000}, + Date-Modified = {2018-02-24 13:46:12 +0000}, + Doi = {10.1080/00268976.2010.508472}, + File = {/Users/loos/Zotero/storage/TLWJZ3HQ/25.pdf}, + Issn = {0026-8976, 1362-3028}, + Journal = {Mol. Phys.}, + Language = {en}, + Month = oct, + Number = {19-20}, + Pages = {2527--2532}, + Title = {Excited States of Spherium}, + Volume = {108}, + Year = {2010}, + Bdsk-Url-1 = {https://dx.doi.org/10.1080/00268976.2010.508472}} + +@article{Loos_2017a, + Author = {Loos, Pierre-Fran{\c c}ois}, + Date-Added = {2018-02-24 13:46:12 +0000}, + Date-Modified = {2018-02-24 13:46:12 +0000}, + Doi = {10.1063/1.4978409}, + File = {/Users/loos/Zotero/storage/NJ3WTVZZ/54.pdf}, + Issn = {0021-9606, 1089-7690}, + Journal = {J. Chem. Phys.}, + Language = {en}, + Month = mar, + Number = {11}, + Pages = {114108}, + Title = {Exchange Functionals Based on Finite Uniform Electron Gases}, + Volume = {146}, + Year = {2017}, + Bdsk-Url-1 = {https://dx.doi.org/10.1063/1.4978409}} + +@article{Onida_2002, + Author = {G. Onida and L. Reining and A. Rubio and}, + Date-Added = {2018-02-24 13:00:32 +0000}, + Date-Modified = {2018-07-05 09:48:14 +0000}, + Doi = {10.1103/RevModPhys.74.601}, + Journal = {Rev. Mod. Phys.}, + Pages = {601--659}, + Title = {Electronic excitations: density-functional versus many-body Green's-function approaches}, + Volume = {74}, + Year = {2002}, + Bdsk-Url-1 = {https://doi.org/10.1103/RevModPhys.74.601}} + +@article{Aryasetiawan_1998, + Author = {F. Aryasetiawan and O. Gunnarsson}, + Date-Added = {2018-02-24 12:59:01 +0000}, + Date-Modified = {2018-07-05 09:40:02 +0000}, + Doi = {10.1088/0034-4885/61/3/002}, + Journal = {Rep. Prog. Phys.}, + Pages = {237--312}, + Title = {The GW method}, + Volume = {61}, + Year = {1998}, + Bdsk-Url-1 = {https://doi.org/10.1088/0034-4885/61/3/002}} + +@article{Agboola_2015, + Author = {Agboola, Davids and Knol, Anneke L. and Gill, Peter M. W. and Loos, Pierre-Fran{\c c}ois}, + Date-Added = {2018-02-24 12:51:10 +0000}, + Date-Modified = {2018-02-24 12:51:10 +0000}, + Doi = {10.1063/1.4929353}, + File = {/Users/loos/Zotero/storage/YFD785CA/46.pdf}, + Issn = {0021-9606, 1089-7690}, + Journal = {J. Chem. Phys.}, + Language = {en}, + Month = aug, + Number = {8}, + Pages = {084114}, + Title = {Uniform Electron Gases. {{III}}. {{Low}}-Density Gases on Three-Dimensional Spheres}, + Volume = {143}, + Year = {2015}, + Bdsk-Url-1 = {https://dx.doi.org/10.1063/1.4929353}} + +@article{Ambrosek_2010, + Author = {Ambrosek, David and Loos, Pierre-Fran{\c c}ois and Assfeld, Xavier and Daniel, Chantal}, + Date-Added = {2018-02-24 12:51:10 +0000}, + Date-Modified = {2018-02-24 12:51:10 +0000}, + Doi = {10.1016/j.jinorgbio.2010.04.002}, + File = {/Users/loos/Zotero/storage/WA85FMNN/22.pdf}, + Issn = {01620134}, + Journal = {Journal of Inorganic Biochemistry}, + Language = {en}, + Month = sep, + Number = {9}, + Pages = {893--901}, + Title = {A Theoretical Study of {{Ru}}({{II}}) Polypyridyl {{DNA intercalatorsStructure}} and Electronic Absorption Spectroscopy of [{{Ru}}(Phen)2(Dppz)]2+ and [{{Ru}}(Tap)2(Dppz)]2+ Complexes Intercalated in Guanine\textendash{}cytosine Base Pairs}, + Volume = {104}, + Year = {2010}, + Bdsk-Url-1 = {https://dx.doi.org/10.1016/j.jinorgbio.2010.04.002}} + +@article{Ball_2017, + Author = {Ball, Caleb J. and Loos, Pierre-Fran{\c c}ois and Gill, Peter M. W.}, + Date-Added = {2018-02-24 12:51:10 +0000}, + Date-Modified = {2018-02-24 12:51:10 +0000}, + Doi = {10.1039/C6CP06801D}, + File = {/Users/loos/Zotero/storage/7X5YE6WH/52.pdf}, + Issn = {1463-9076, 1463-9084}, + Journal = {Physical Chemistry Chemical Physics}, + Language = {en}, + Number = {5}, + Pages = {3987--3998}, + Title = {Molecular Electronic Structure in One-Dimensional {{Coulomb}} Systems}, + Volume = {19}, + Year = {2017}, + Bdsk-Url-1 = {https://dx.doi.org/10.1039/C6CP06801D}} + +@article{Barca_2016, + Author = {Barca, Giuseppe M. J. and Loos, Pierre-Fran{\c c}ois and Gill, Peter M. W.}, + Date-Added = {2018-02-24 12:51:10 +0000}, + Date-Modified = {2018-02-24 12:51:10 +0000}, + Doi = {10.1021/acs.jctc.6b00130}, + File = {/Users/loos/Zotero/storage/JS793AVF/49.pdf}, + Issn = {1549-9618, 1549-9626}, + Journal = {Journal of Chemical Theory and Computation}, + Language = {en}, + Month = apr, + Number = {4}, + Pages = {1735--1740}, + Title = {Many-{{Electron Integrals}} over {{Gaussian Basis Functions}}. {{I}}. {{Recurrence Relations}} for {{Three}}-{{Electron Integrals}}}, + Volume = {12}, + Year = {2016}, + Bdsk-Url-1 = {https://dx.doi.org/10.1021/acs.jctc.6b00130}} + +@article{Barca_2017, + Author = {Barca, Giuseppe MJ and Loos, Pierre-Fran{\c c}ois}, + Date-Added = {2018-02-24 12:51:10 +0000}, + Date-Modified = {2018-02-24 12:51:10 +0000}, + File = {/Users/loos/Zotero/storage/DCFUMHWZ/56.pdf}, + Journal = {The Journal of chemical physics}, + Number = {2}, + Pages = {024103}, + Shorttitle = {Three-and Four-Electron Integrals Involving {{Gaussian}} Geminals}, + Title = {Three-and Four-Electron Integrals Involving {{Gaussian}} Geminals: {{Fundamental}} Integrals, Upper Bounds, and Recurrence Relations}, + Volume = {147}, + Year = {2017}} + +@incollection{Barca_2018, + Author = {Barca, Giuseppe M.J. and Loos, Pierre-Fran{\c c}ois}, + Booktitle = {Advances in {{Quantum Chemistry}}}, + Date-Added = {2018-02-24 12:51:10 +0000}, + Date-Modified = {2018-02-24 12:51:10 +0000}, + Doi = {10.1016/bs.aiq.2017.03.004}, + File = {/Users/loos/Zotero/storage/JQKXB9RU/58.pdf}, + Isbn = {978-0-12-813002-5}, + Language = {en}, + Pages = {147--165}, + Publisher = {{Elsevier}}, + Title = {Recurrence {{Relations}} for {{Four}}-{{Electron Integrals Over Gaussian Basis Functions}}}, + Volume = {76}, + Year = {2018}, + Bdsk-Url-1 = {https://dx.doi.org/10.1016/bs.aiq.2017.03.004}} + +@article{Bernard_2013, + Author = {Bernard, Yves A. and Loos, Pierre-Fran{\c c}ois and Gill, Peter M.W.}, + Date-Added = {2018-02-24 12:51:10 +0000}, + Date-Modified = {2018-02-24 12:51:10 +0000}, + Doi = {10.1080/00268976.2013.811302}, + File = {/Users/loos/Zotero/storage/8XRA54GV/39.pdf}, + Issn = {0026-8976, 1362-3028}, + Journal = {Mol. Phys.}, + Language = {en}, + Month = sep, + Number = {16-17}, + Pages = {2414--2426}, + Title = {Distribution of r {\textsubscript{12}} $\cdot$ p {\textsubscript{12}} in Quantum Systems}, + Volume = {111}, + Year = {2013}, + Bdsk-Url-1 = {https://dx.doi.org/10.1080/00268976.2013.811302}} + +@article{Dumont_2008, + Author = {Dumont, {\'E}lise and Loos, Pierre-Fran{\c c}ois and Assfeld, Xavier}, + Date-Added = {2018-02-24 12:51:10 +0000}, + Date-Modified = {2018-02-24 12:51:10 +0000}, + Doi = {10.1016/j.cplett.2008.05.010}, + File = {/Users/loos/Zotero/storage/5Q5WP253/12.pdf}, + Issn = {00092614}, + Journal = {Chem. Phys. Lett.}, + Language = {en}, + Month = jun, + Number = {4-6}, + Pages = {276--280}, + Title = {Effect of Ring Strain on Disulfide Electron Attachment}, + Volume = {458}, + Year = {2008}, + Bdsk-Url-1 = {https://dx.doi.org/10.1016/j.cplett.2008.05.010}} + +@article{Dumont_2008a, + Author = {Dumont, {\'E}lise and Loos, Pierre-Fran{\c c}ois and Assfeld, Xavier}, + Date-Added = {2018-02-24 12:51:10 +0000}, + Date-Modified = {2018-02-24 12:51:10 +0000}, + Doi = {10.1021/jp806465e}, + File = {/Users/loos/Zotero/storage/5FHSI4FF/14.pdf}, + Issn = {1520-6106, 1520-5207}, + Journal = {The Journal of Physical Chemistry B}, + Language = {en}, + Month = oct, + Number = {43}, + Pages = {13661--13669}, + Title = {Factors {{Governing Electron Capture}} by {{Small Disulfide Loops}} in {{Two}}-{{Cysteine Peptides}}}, + Volume = {112}, + Year = {2008}, + Bdsk-Url-1 = {https://dx.doi.org/10.1021/jp806465e}} + +@article{Dumont_2008b, + Author = {Dumont, Elise and Loos, Pierre-Fran{\c c}ois and Laurent, Ad{\`e}le D. and Assfeld, Xavier}, + Date-Added = {2018-02-24 12:51:10 +0000}, + Date-Modified = {2018-02-24 12:51:10 +0000}, + Doi = {10.1021/ct800161m}, + File = {/Users/loos/Zotero/storage/AU5GAG48/13.pdf}, + Issn = {1549-9618, 1549-9626}, + Journal = {Journal of Chemical Theory and Computation}, + Language = {en}, + Month = aug, + Number = {8}, + Pages = {1171--1173}, + Title = {Huge {{Disulfide}}-{{Linkage}}'{{S Electron Capture Variation Induced}} by $\alpha$-{{Helix Orientation}}}, + Volume = {4}, + Year = {2008}, + Bdsk-Url-1 = {https://dx.doi.org/10.1021/ct800161m}} + +@article{Dumont_2009, + Author = {Dumont, {\'E}lise and Laurent, Ad{\`e}le D. and Loos, Pierre-Fran{\c c}ois and Assfeld, Xavier}, + Date-Added = {2018-02-24 12:51:10 +0000}, + Date-Modified = {2018-02-24 12:51:10 +0000}, + Doi = {10.1021/ct900093h}, + File = {/Users/loos/Zotero/storage/DXBEWEYC/15.pdf}, + Issn = {1549-9618, 1549-9626}, + Journal = {Journal of Chemical Theory and Computation}, + Language = {en}, + Month = jun, + Number = {6}, + Pages = {1700--1708}, + Title = {Analyzing the {{Selectivity}} and {{Successiveness}} of a {{Two}}-{{Electron Capture}} on a {{Multiply Disulfide}}-{{Linked Protein}}}, + Volume = {5}, + Year = {2009}, + Bdsk-Url-1 = {https://dx.doi.org/10.1021/ct900093h}} + +@article{Dumont_2010, + Author = {Dumont, {\~A}‰lise and Loos, Pierre-Fran{\~A}\textsection{}ois and Laurent, Ad{\~A}\textasciidieresis{}le D. and Assfeld, Xavier}, + Date-Added = {2018-02-24 12:51:10 +0000}, + Date-Modified = {2018-02-24 12:51:10 +0000}, + Doi = {10.1002/qua.22072}, + File = {/Users/loos/Zotero/storage/4VG63LZM/20.pdf}, + Issn = {00207608, 1097461X}, + Journal = {Int. J. Quantum Chem.}, + Language = {en}, + Month = mar, + Number = {3}, + Pages = {513--523}, + Title = {Electronic Effects and Ring Strain Influences on the Electron Uptake by Selenium-Containing Bonds}, + Volume = {110}, + Year = {2010}, + Bdsk-Url-1 = {https://dx.doi.org/10.1002/qua.22072}} + +@article{Fornili_2006, + Author = {Fornili, Arianna and Loos, Pierre-Fran{\c c}ois and Sironi, Maurizio and Assfeld, Xavier}, + Date-Added = {2018-02-24 12:51:10 +0000}, + Date-Modified = {2018-02-24 12:51:10 +0000}, + Doi = {10.1016/j.cplett.2006.06.095}, + File = {/Users/loos/Zotero/storage/28RWJAZ8/2.pdf}, + Issn = {00092614}, + Journal = {Chem. Phys. Lett.}, + Language = {en}, + Month = aug, + Number = {1-3}, + Pages = {236--240}, + Title = {Frozen Core Orbitals as an Alternative to Specific Frontier Bond Potential in Hybrid {{Quantum Mechanics}}/{{Molecular Mechanics}} Methods}, + Volume = {427}, + Year = {2006}, + Bdsk-Url-1 = {https://dx.doi.org/10.1016/j.cplett.2006.06.095}} + +@article{Garniron_2017, + Author = {Garniron, Yann and Scemama, Anthony and Loos, Pierre-Fran{\c c}ois and Caffarel, Michel}, + Date-Added = {2018-02-24 12:51:10 +0000}, + Date-Modified = {2018-02-24 12:51:10 +0000}, + Doi = {10.1063/1.4992127}, + File = {/Users/loos/Zotero/storage/NHU2BWMZ/57.pdf}, + Issn = {0021-9606, 1089-7690}, + Journal = {J. Chem. Phys.}, + Language = {en}, + Month = jul, + Number = {3}, + Pages = {034101}, + Title = {Hybrid Stochastic-Deterministic Calculation of the Second-Order Perturbative Contribution of Multireference Perturbation Theory}, + Volume = {147}, + Year = {2017}, + Bdsk-Url-1 = {https://dx.doi.org/10.1063/1.4992127}} + +@article{Gill_2012, + Author = {Gill, Peter M. W. and Loos, Pierre-Fran{\c c}ois}, + Date-Added = {2018-02-24 12:51:10 +0000}, + Date-Modified = {2018-04-14 07:30:52 +0000}, + Doi = {10.1007/s00214-011-1069-7}, + File = {/Users/loos/Zotero/storage/A85Y7E9B/32.pdf}, + Issn = {1432-881X, 1432-2234}, + Journal = {Theor. Chem. Acc.}, + Language = {en}, + Month = jan, + Number = {1}, + Pages = {1069}, + Title = {Uniform Electron Gases}, + Volume = {131}, + Year = {2012}, + Bdsk-Url-1 = {https://dx.doi.org/10.1007/s00214-011-1069-7}} + +@article{Gill_2014, + Author = {Gill, Peter M. W. and Loos, Pierre-Fran{\c c}ois and Agboola, Davids}, + Date-Added = {2018-02-24 12:51:10 +0000}, + Date-Modified = {2018-02-24 12:51:10 +0000}, + Doi = {10.1063/1.4903984}, + File = {/Users/loos/Zotero/storage/YM5Q8ST9/43.pdf}, + Issn = {0021-9606, 1089-7690}, + Journal = {J. Chem. Phys.}, + Language = {en}, + Month = dec, + Number = {24}, + Pages = {244102}, + Title = {Basis Functions for Electronic Structure Calculations on Spheres}, + Volume = {141}, + Year = {2014}, + Bdsk-Url-1 = {https://dx.doi.org/10.1063/1.4903984}} + +@article{Loos_2007, + Author = {Loos, Pierre-Fran{\c c}ois and Assfeld, Xavier}, + Date-Added = {2018-02-24 12:51:10 +0000}, + Date-Modified = {2018-02-24 12:51:10 +0000}, + Doi = {10.1002/qua.21410}, + File = {/Users/loos/Zotero/storage/64MPU2ZJ/8.pdf}, + Issn = {00207608, 1097461X}, + Journal = {Int. J. Quantum Chem.}, + Language = {en}, + Number = {12}, + Pages = {2243--2252}, + Title = {Core-Ionized and Core-Excited States of Macromolecules}, + Volume = {107}, + Year = {2007}, + Bdsk-Url-1 = {https://dx.doi.org/10.1002/qua.21410}} + +@article{Loos_2007a, + Author = {Loos, Pierre-Fran{\c c}ois and Assfeld, Xavier and Rivail, Jean-Louis}, + Date-Added = {2018-02-24 12:51:10 +0000}, + Date-Modified = {2018-02-24 12:51:10 +0000}, + Doi = {10.1007/s00214-007-0258-x}, + File = {/Users/loos/Zotero/storage/S6FBKP2M/5.pdf}, + Issn = {1432-881X, 1432-2234}, + Journal = {Theor. Chem. Acc.}, + Language = {en}, + Month = jun, + Number = {1}, + Pages = {165--171}, + Title = {Intramolecular Interactions and Cis Peptidic Bonds}, + Volume = {118}, + Year = {2007}, + Bdsk-Url-1 = {https://dx.doi.org/10.1007/s00214-007-0258-x}} + +@inproceedings{Loos_2007b, + Author = {Loos, Pierre-Fran{\c c}ois and Assfeld, Xavier}, + Booktitle = {{{AIP Conference Proceedings}}}, + Date-Added = {2018-02-24 12:51:10 +0000}, + Date-Modified = {2018-02-24 12:51:10 +0000}, + File = {/Users/loos/Zotero/storage/HGKGXAMT/10.pdf}, + Pages = {308--315}, + Publisher = {{AIP}}, + Title = {On {{The Frontier Bond Location In The QM}}/{{MM Description Of Peptides And Proteins}}.}, + Volume = {963}, + Year = {2007}} + +@article{Loos_2007c, + Author = {Loos, P.-F. and Fornili, A. and Sironi, M. and Assfeld, X.}, + Date-Added = {2018-02-24 12:51:10 +0000}, + Date-Modified = {2018-02-24 12:51:10 +0000}, + File = {/Users/loos/Zotero/storage/CAHLR8H8/9.pdf}, + Journal = {Computing Letters}, + Number = {2-4}, + Pages = {2--4}, + Shorttitle = {Removing Extra Frontier Parameters in {{QM}}/{{MM}} Methods}, + Title = {Removing Extra Frontier Parameters in {{QM}}/{{MM}} Methods: A Tentative with the {{Local Self}}-{{Consistent Field}} Approach}, + Volume = {3}, + Year = {2007}} + +@article{Loos_2007d, + Author = {Loos, Pierre-Fran{\c c}ois and Assfeld, Xavier}, + Date-Added = {2018-02-24 12:51:10 +0000}, + Date-Modified = {2018-02-24 12:51:10 +0000}, + Doi = {10.1021/ct6003214}, + File = {/Users/loos/Zotero/storage/A9TSDVGQ/6.pdf}, + Issn = {1549-9618, 1549-9626}, + Journal = {Journal of Chemical Theory and Computation}, + Language = {en}, + Month = may, + Number = {3}, + Pages = {1047--1053}, + Title = {Self-{{Consistent Strictly Localized Orbitals}}}, + Volume = {3}, + Year = {2007}, + Bdsk-Url-1 = {https://dx.doi.org/10.1021/ct6003214}} + +@article{Loos_2008, + Author = {Loos, Pierre-Fran{\c c}ois and Preat, Julien and Laurent, Ad{\`e}le D. and Michaux, Catherine and Jacquemin, Denis and Perp{\`e}te, Eric A. and Assfeld, Xavier}, + Date-Added = {2018-02-24 12:51:10 +0000}, + Date-Modified = {2018-02-24 12:51:10 +0000}, + Doi = {10.1021/ct700188w}, + File = {/Users/loos/Zotero/storage/LSU72HGK/11.pdf}, + Issn = {1549-9618, 1549-9626}, + Journal = {Journal of Chemical Theory and Computation}, + Language = {en}, + Month = apr, + Number = {4}, + Pages = {637--645}, + Shorttitle = {Theoretical {{Investigation}} of the {{Geometries}} and {{UV}}-vis {{Spectra}} of {{Poly}}( $<$span Style="font-Variant}, + Title = {Theoretical {{Investigation}} of the {{Geometries}} and {{UV}}-vis {{Spectra}} of {{Poly}}( {\textsc{l}} -Glutamic Acid) {{Featuring}} a {{Photochromic Azobenzene Side Chain}}}, + Volume = {4}, + Year = {2008}, + Bdsk-Url-1 = {https://dx.doi.org/10.1021/ct700188w}} + +@article{Loos_2009, + Author = {Loos, Pierre-Fran{\c c}ois and Gill, Peter M. W.}, + Date-Added = {2018-02-24 12:51:10 +0000}, + Date-Modified = {2018-02-24 12:51:10 +0000}, + Doi = {10.1063/1.3275519}, + File = {/Users/loos/Zotero/storage/E9MV4JCJ/19.pdf}, + Issn = {0021-9606, 1089-7690}, + Journal = {J. Chem. Phys.}, + Language = {en}, + Month = dec, + Number = {24}, + Pages = {241101}, + Title = {Correlation Energy of Two Electrons in the High-Density Limit}, + Volume = {131}, + Year = {2009}, + Bdsk-Url-1 = {https://dx.doi.org/10.1063/1.3275519}} + +@article{Loos_2009a, + Author = {Loos, Pierre-Fran{\c c}ois and Gill, Peter M. W.}, + Date-Added = {2018-02-24 12:51:10 +0000}, + Date-Modified = {2018-04-14 07:27:46 +0000}, + Doi = {10.1103/PhysRevA.79.062517}, + File = {/Users/loos/Zotero/storage/R9N5FN2F/17.pdf}, + Issn = {1050-2947, 1094-1622}, + Journal = {Phys. Rev. A}, + Language = {en}, + Month = jun, + Number = {6}, + Pages = {062517}, + Title = {Ground State of Two Electrons on a Sphere}, + Volume = {79}, + Year = {2009}, + Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevA.79.062517}} + +@article{Loos_2009b, + Author = {Loos, Pierre-Fran{\c c}ois and Dumont, Elise and Laurent, Ad{\`e}le D. and Assfeld, Xavier}, + Date-Added = {2018-02-24 12:51:10 +0000}, + Date-Modified = {2018-02-24 12:51:10 +0000}, + Doi = {10.1016/j.cplett.2009.05.041}, + File = {/Users/loos/Zotero/storage/QDEXZPUE/16.pdf}, + Issn = {00092614}, + Journal = {Chem. Phys. Lett.}, + Language = {en}, + Month = jun, + Number = {1-3}, + Pages = {120--123}, + Title = {Important Effects of Neighbouring Nucleotides on Electron Induced {{DNA}} Single-Strand Breaks}, + Volume = {475}, + Year = {2009}, + Bdsk-Url-1 = {https://dx.doi.org/10.1016/j.cplett.2009.05.041}} + +@article{Loos_2009c, + Author = {Loos, Pierre-Fran{\c c}ois and Gill, Peter M. W.}, + Date-Added = {2018-02-24 12:51:10 +0000}, + Date-Modified = {2018-04-14 07:27:56 +0000}, + Doi = {10.1103/PhysRevLett.103.123008}, + File = {/Users/loos/Zotero/storage/GRFHDW5F/18.pdf}, + Issn = {0031-9007, 1079-7114}, + Journal = {Phys. Rev. Lett.}, + Language = {en}, + Month = sep, + Number = {12}, + Pages = {123008}, + Shorttitle = {Two {{Electrons}} on a {{Hypersphere}}}, + Title = {Two {{Electrons}} on a {{Hypersphere}}: {{A Quasiexactly Solvable Model}}}, + Volume = {103}, + Year = {2009}, + Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevLett.103.123008}} + +@article{Loos_2010, + Author = {Loos, Pierre-Fran{\c c}ois and Gill, Peter M.W.}, + Date-Added = {2018-02-24 12:51:10 +0000}, + Date-Modified = {2018-02-24 12:51:10 +0000}, + Doi = {10.1016/j.cplett.2010.09.019}, + File = {/Users/loos/Zotero/storage/DJKJNV2H/27.pdf}, + Issn = {00092614}, + Journal = {Chem. Phys. Lett.}, + Language = {en}, + Month = nov, + Number = {1-3}, + Pages = {1--8}, + Shorttitle = {A Tale of Two Electrons}, + Title = {A Tale of Two Electrons: {{Correlation}} at High Density}, + Volume = {500}, + Year = {2010}, + Bdsk-Url-1 = {https://dx.doi.org/10.1016/j.cplett.2010.09.019}} + +@article{Loos_2010a, + Author = {Loos, Pierre-Fran{\c c}ois and Gill, Peter M. W.}, + Date-Added = {2018-02-24 12:51:10 +0000}, + Date-Modified = {2018-02-24 12:51:10 +0000}, + Doi = {10.1063/1.3455706}, + File = {/Users/loos/Zotero/storage/QWSE9HHH/24.pdf}, + Issn = {0021-9606, 1089-7690}, + Journal = {J. Chem. Phys.}, + Language = {en}, + Month = jun, + Number = {23}, + Pages = {234111}, + Title = {Correlation Energy of Two Electrons in a Ball}, + Volume = {132}, + Year = {2010}, + Bdsk-Url-1 = {https://dx.doi.org/10.1063/1.3455706}} + +@article{Loos_2010b, + Author = {Loos, Pierre-Fran{\c c}ois and Gill, Peter M. W.}, + Date-Added = {2018-02-24 12:51:10 +0000}, + Date-Modified = {2018-04-14 07:28:06 +0000}, + Doi = {10.1103/PhysRevA.81.052510}, + File = {/Users/loos/Zotero/storage/3MZKVWT9/23.pdf}, + Issn = {1050-2947, 1094-1622}, + Journal = {Phys. Rev. A}, + Language = {en}, + Month = may, + Number = {5}, + Pages = {052510}, + Title = {Ground State of Two Electrons on Concentric Spheres}, + Volume = {81}, + Year = {2010}, + Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevA.81.052510}} + +@article{Loos_2010c, + Author = {Loos, Pierre-Fran{\c c}ois}, + Date-Added = {2018-02-24 12:51:10 +0000}, + Date-Modified = {2018-04-14 07:28:12 +0000}, + Doi = {10.1103/PhysRevA.81.032510}, + File = {/Users/loos/Zotero/storage/KJEJ5D77/21.pdf}, + Issn = {1050-2947, 1094-1622}, + Journal = {Phys. Rev. A}, + Language = {en}, + Month = mar, + Number = {3}, + Pages = {032510}, + Title = {Hooke's Law Correlation in Two-Electron Systems}, + Volume = {81}, + Year = {2010}, + Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevA.81.032510}} + +@article{Loos_2010d, + Author = {Loos, Pierre-Fran{\c c}ois and Gill, Peter M. W.}, + Date-Added = {2018-02-24 12:51:10 +0000}, + Date-Modified = {2018-04-14 07:28:17 +0000}, + Doi = {10.1103/PhysRevLett.105.113001}, + File = {/Users/loos/Zotero/storage/I2UH4CU5/26.pdf}, + Issn = {0031-9007, 1079-7114}, + Journal = {Phys. Rev. Lett.}, + Language = {en}, + Month = sep, + Number = {11}, + Pages = {113001}, + Title = {Invariance of the {{Correlation Energy}} at {{High Density}} and {{Large Dimension}} in {{Two}}-{{Electron Systems}}}, + Volume = {105}, + Year = {2010}, + Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevLett.105.113001}} + +@article{Loos_2011, + Author = {Loos, Pierre-Fran{\c c}ois and Gill, Peter M. W.}, + Date-Added = {2018-02-24 12:51:10 +0000}, + Date-Modified = {2018-04-14 07:28:25 +0000}, + Doi = {10.1103/PhysRevB.84.033103}, + File = {/Users/loos/Zotero/storage/NK4SJ24B/29.pdf}, + Issn = {1098-0121, 1550-235X}, + Journal = {Phys. Rev. B}, + Language = {en}, + Month = jul, + Number = {3}, + Pages = {033103}, + Title = {Correlation Energy of the Spin-Polarized Uniform Electron Gas at High Density}, + Volume = {84}, + Year = {2011}, + Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevB.84.033103}} + +@article{Loos_2011a, + Author = {Loos, Pierre-Fran{\c c}ois and Gill, Peter M. W.}, + Date-Added = {2018-02-24 12:51:10 +0000}, + Date-Modified = {2018-04-14 07:28:30 +0000}, + Doi = {10.1103/PhysRevB.83.233102}, + File = {/Users/loos/Zotero/storage/2QNIQXM5/28.pdf}, + Issn = {1098-0121, 1550-235X}, + Journal = {Phys. Rev. B}, + Language = {en}, + Month = jun, + Number = {23}, + Pages = {233102}, + Title = {Exact Energy of the Spin-Polarized Two-Dimensional Electron Gas at High Density}, + Volume = {83}, + Year = {2011}, + Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevB.83.233102}} + +@article{Loos_2011b, + Author = {Loos, Pierre-Fran{\c c}ois and Gill, Peter M. W.}, + Date-Added = {2018-02-24 12:51:10 +0000}, + Date-Modified = {2018-02-24 12:51:10 +0000}, + Doi = {10.1063/1.3665393}, + File = {/Users/loos/Zotero/storage/R8SHV7JI/31.pdf}, + Issn = {0021-9606, 1089-7690}, + Journal = {J. Chem. Phys.}, + Language = {en}, + Month = dec, + Number = {21}, + Pages = {214111}, + Shorttitle = {Thinking Outside the Box}, + Title = {Thinking Outside the Box: {{The}} Uniform Electron Gas on a Hypersphere}, + Volume = {135}, + Year = {2011}, + Bdsk-Url-1 = {https://dx.doi.org/10.1063/1.3665393}} + +@article{Loos_2012, + Author = {Loos, Pierre-Fran{\c c}ois and Gill, Peter M. W.}, + Date-Added = {2018-02-24 12:51:10 +0000}, + Date-Modified = {2018-04-14 07:28:37 +0000}, + Doi = {10.1103/PhysRevLett.108.083002}, + File = {/Users/loos/Zotero/storage/D5YVLEB5/34.pdf}, + Issn = {0031-9007, 1079-7114}, + Journal = {Phys. Rev. Lett.}, + Language = {en}, + Month = feb, + Number = {8}, + Pages = {083002}, + Title = {Exact {{Wave Functions}} of {{Two}}-{{Electron Quantum Rings}}}, + Volume = {108}, + Year = {2012}, + Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevLett.108.083002}} + +@article{Loos_2012a, + Author = {Loos, Pierre-Fran{\c c}ois and Gill, Peter M.W.}, + Date-Added = {2018-02-24 12:51:10 +0000}, + Date-Modified = {2018-02-24 12:51:10 +0000}, + Doi = {10.1080/00268976.2012.679634}, + File = {/Users/loos/Zotero/storage/H82N8B89/35.pdf}, + Issn = {0026-8976, 1362-3028}, + Journal = {Mol. Phys.}, + Language = {en}, + Month = oct, + Number = {19-20}, + Pages = {2337--2342}, + Title = {Harmonically Trapped Jellium}, + Volume = {110}, + Year = {2012}, + Bdsk-Url-1 = {https://dx.doi.org/10.1080/00268976.2012.679634}} + +@article{Loos_2012b, + Author = {Loos, Pierre-Fran{\c c}ois and Gill, Peter M. W.}, + Date-Added = {2018-02-24 12:51:10 +0000}, + Date-Modified = {2018-02-24 12:51:10 +0000}, + Doi = {10.1002/qua.23155}, + File = {/Users/loos/Zotero/storage/PMVR53GF/33.pdf}, + Issn = {00207608}, + Journal = {Int. J. Quantum Chem.}, + Language = {en}, + Month = mar, + Number = {6}, + Pages = {1712--1716}, + Title = {Leading-Order Behavior of the Correlation Energy in the Uniform Electron Gas}, + Volume = {112}, + Year = {2012}, + Bdsk-Url-1 = {https://dx.doi.org/10.1002/qua.23155}} + +@article{Loos_2012c, + Author = {Loos, Pierre-Fran{\c c}ois}, + Date-Added = {2018-02-24 12:51:10 +0000}, + Date-Modified = {2018-02-24 12:51:10 +0000}, + Doi = {10.1016/j.physleta.2012.05.010}, + File = {/Users/loos/Zotero/storage/JUPS4RAD/36.pdf}, + Issn = {03759601}, + Journal = {Physics Letters A}, + Language = {en}, + Month = may, + Number = {26-27}, + Pages = {1997--2000}, + Title = {Understanding Excitons Using Spherical Geometry}, + Volume = {376}, + Year = {2012}, + Bdsk-Url-1 = {https://dx.doi.org/10.1016/j.physleta.2012.05.010}} + +@article{Loos_2013, + Author = {Loos, Pierre-Fran{\c c}ois}, + Date-Added = {2018-02-24 12:51:10 +0000}, + Date-Modified = {2018-02-24 12:51:10 +0000}, + Doi = {10.1063/1.4790613}, + File = {/Users/loos/Zotero/storage/47LGX76U/37.pdf}, + Issn = {0021-9606, 1089-7690}, + Journal = {J. Chem. Phys.}, + Language = {en}, + Month = feb, + Number = {6}, + Pages = {064108}, + Title = {High-Density Correlation Energy Expansion of the One-Dimensional Uniform Electron Gas}, + Volume = {138}, + Year = {2013}, + Bdsk-Url-1 = {https://dx.doi.org/10.1063/1.4790613}} + +@article{Loos_2013a, + Author = {Loos, Pierre-Fran{\c c}ois and Gill, Peter M. W.}, + Date-Added = {2018-02-24 12:51:10 +0000}, + Date-Modified = {2018-02-24 12:51:10 +0000}, + Doi = {10.1063/1.4802589}, + File = {/Users/loos/Zotero/storage/5Q2YJGTX/38.pdf}, + Issn = {0021-9606, 1089-7690}, + Journal = {J. Chem. Phys.}, + Language = {en}, + Month = apr, + Number = {16}, + Pages = {164124}, + Title = {Uniform Electron Gases. {{I}}. {{Electrons}} on a Ring}, + Volume = {138}, + Year = {2013}, + Bdsk-Url-1 = {https://dx.doi.org/10.1063/1.4802589}} + +@article{Loos_2014, + Author = {Loos, Pierre-Fran{\c c}ois and Gill, Peter M.W.}, + Date-Added = {2018-02-24 12:51:10 +0000}, + Date-Modified = {2018-02-24 12:51:10 +0000}, + Doi = {10.1016/j.physleta.2013.11.045}, + File = {/Users/loos/Zotero/storage/BRNDKC4F/40.pdf}, + Issn = {03759601}, + Journal = {Physics Letters A}, + Language = {en}, + Month = jan, + Number = {4}, + Pages = {329--333}, + Title = {Exact Wave Functions for Concentric Two-Electron Systems}, + Volume = {378}, + Year = {2014}, + Bdsk-Url-1 = {https://dx.doi.org/10.1016/j.physleta.2013.11.045}} + +@article{Loos_2014a, + Author = {Loos, Pierre-Fran{\c c}ois}, + Date-Added = {2018-02-24 12:51:10 +0000}, + Date-Modified = {2018-04-14 07:28:50 +0000}, + Doi = {10.1103/PhysRevA.89.052523}, + File = {/Users/loos/Zotero/storage/E8XZBSLG/42.pdf}, + Issn = {1050-2947, 1094-1622}, + Journal = {Phys. Rev. A}, + Language = {en}, + Month = may, + Number = {5}, + Pages = {052523}, + Title = {Generalized Local-Density Approximation and One-Dimensional Finite Uniform Electron Gases}, + Volume = {89}, + Year = {2014}, + Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevA.89.052523}} + +@article{Loos_2014b, + Author = {Loos, Pierre-Fran{\c c}ois and Ball, Caleb J. and Gill, Peter M. W.}, + Date-Added = {2018-02-24 12:51:10 +0000}, + Date-Modified = {2018-02-24 12:51:10 +0000}, + Doi = {10.1063/1.4867910}, + File = {/Users/loos/Zotero/storage/QD667QG2/41.pdf}, + Issn = {0021-9606, 1089-7690}, + Journal = {J. Chem. Phys.}, + Language = {en}, + Month = may, + Number = {18}, + Pages = {18A524}, + Title = {Uniform Electron Gases. {{II}}. {{The}} Generalized Local Density Approximation in One Dimension}, + Volume = {140}, + Year = {2014}, + Bdsk-Url-1 = {https://dx.doi.org/10.1063/1.4867910}} + +@article{Loos_2015, + Author = {Loos, Pierre-Fran{\c c}ois and Ball, Caleb J. and Gill, Peter M. W.}, + Date-Added = {2018-02-24 12:51:10 +0000}, + Date-Modified = {2018-02-24 12:51:10 +0000}, + Doi = {10.1039/C4CP03571B}, + File = {/Users/loos/Zotero/storage/4JXMCN8L/44.pdf}, + Issn = {1463-9076, 1463-9084}, + Journal = {Physical Chemistry Chemical Physics}, + Language = {en}, + Number = {5}, + Pages = {3196--3206}, + Title = {Chemistry in One Dimension}, + Volume = {17}, + Year = {2015}, + Bdsk-Url-1 = {https://dx.doi.org/10.1039/C4CP03571B}} + +@article{Loos_2015a, + Author = {Loos, Pierre-Fran{\c c}ois and Bloomfield, Nathaniel J. and Gill, Peter M. W.}, + Date-Added = {2018-02-24 12:51:10 +0000}, + Date-Modified = {2018-02-24 12:51:10 +0000}, + Doi = {10.1063/1.4935374}, + File = {/Users/loos/Zotero/storage/HEH82IUH/47.pdf}, + Issn = {0021-9606, 1089-7690}, + Journal = {J. Chem. Phys.}, + Language = {en}, + Month = nov, + Number = {18}, + Pages = {181101}, + Shorttitle = {Communication}, + Title = {Communication: {{Three}}-Electron Coalescence Points in Two and Three Dimensions}, + Volume = {143}, + Year = {2015}, + Bdsk-Url-1 = {https://dx.doi.org/10.1063/1.4935374}} + +@article{Loos_2015b, + Author = {Loos, Pierre-Fran{\c c}ois and Bressanini, Dario}, + Date-Added = {2018-02-24 12:51:10 +0000}, + Date-Modified = {2018-02-24 12:51:10 +0000}, + Doi = {10.1063/1.4922159}, + File = {/Users/loos/Zotero/storage/UBTEMR7G/45.pdf}, + Issn = {0021-9606, 1089-7690}, + Journal = {J. Chem. Phys.}, + Language = {en}, + Month = jun, + Number = {21}, + Pages = {214112}, + Title = {Nodal Surfaces and Interdimensional Degeneracies}, + Volume = {142}, + Year = {2015}, + Bdsk-Url-1 = {https://dx.doi.org/10.1063/1.4922159}} + +@article{Loos_2016, + Author = {Loos, Pierre-Fran{\c c}ois and Gill, Peter M. W.}, + Date-Added = {2018-02-24 12:51:10 +0000}, + Date-Modified = {2018-02-24 12:51:10 +0000}, + Doi = {10.1002/wcms.1257}, + File = {/Users/loos/Zotero/storage/HEXYAMEN/50.pdf}, + Issn = {17590876}, + Journal = {Wiley Interdiscip. Rev. Comput. Mol. Sci.}, + Language = {en}, + Month = jul, + Number = {4}, + Pages = {410--429}, + Shorttitle = {The Uniform Electron Gas}, + Title = {The Uniform Electron Gas: {{The}} Uniform Electron Gas}, + Volume = {6}, + Year = {2016}, + Bdsk-Url-1 = {https://dx.doi.org/10.1002/wcms.1257}} + +@article{Loos_2017, + Author = {Loos, Pierre-Fran{\c c}ois and Rivail, Jean-Louis and Assfeld, Xavier}, + Date-Added = {2018-02-24 12:51:10 +0000}, + Date-Modified = {2018-02-24 12:51:10 +0000}, + Doi = {10.1007/s00894-017-3347-3}, + File = {/Users/loos/Zotero/storage/BFLICA2H/55.pdf}, + Issn = {1610-2940, 0948-5023}, + Journal = {Journal of Molecular Modeling}, + Language = {en}, + Month = jun, + Number = {6}, + Title = {Iterative Stochastic Subspace Self-Consistent Field Method}, + Volume = {23}, + Year = {2017}, + Bdsk-Url-1 = {https://dx.doi.org/10.1007/s00894-017-3347-3}} + +@article{Moreau_2004, + Author = {Moreau, Y. and Loos, P.-F. and Assfeld, X.}, + Date-Added = {2018-02-24 12:51:10 +0000}, + Date-Modified = {2018-02-24 12:51:10 +0000}, + Doi = {10.1007/s00214-004-0581-4}, + File = {/Users/loos/Zotero/storage/I2GBGPYP/1.pdf}, + Issn = {1432-881X, 1432-2234}, + Journal = {Theor. Chem. Acc.}, + Language = {en}, + Month = sep, + Number = {4}, + Shorttitle = {Solvent Effects on the Asymmetric {{Diels}}?}, + Title = {Solvent Effects on the Asymmetric {{Diels}}?{{Alder}} Reaction between Cyclopentadiene and (?)-Menthyl Acrylate Revisited with the Three-Layer Hybrid Local Self-Consistent Field/Molecular Mechanics/Self-Consistent Reaction Field Method}, + Volume = {112}, + Year = {2004}, + Bdsk-Url-1 = {https://dx.doi.org/10.1007/s00214-004-0581-4}} + +@article{Preat_2007, + Author = {Preat, Julien and Loos, Pierre-Fran{\c c}ois and Assfeld, Xavier and Jacquemin, Denis and Perp{\`e}te, Eric A.}, + Date-Added = {2018-02-24 12:51:10 +0000}, + Date-Modified = {2018-02-24 12:51:10 +0000}, + Doi = {10.1016/j.theochem.2006.12.047}, + File = {/Users/loos/Zotero/storage/4BZSHB49/7.pdf}, + Issn = {01661280}, + Journal = {Journal of Molecular Structure: THEOCHEM}, + Language = {en}, + Month = apr, + Number = {1-3}, + Pages = {85--91}, + Shorttitle = {A {{TD}}-{{DFT}} Investigation of {{UV}} Spectra of Pyrano{\"\i}dic Dyes}, + Title = {A {{TD}}-{{DFT}} Investigation of {{UV}} Spectra of Pyrano{\"\i}dic Dyes: {{A NCM}} vs {{PCM}} Comparison}, + Volume = {808}, + Year = {2007}, + Bdsk-Url-1 = {https://dx.doi.org/10.1016/j.theochem.2006.12.047}} + +@article{Preat_2007a, + Author = {Preat, Julien and Loos, Pierre-Fran{\c c}ois and Assfeld, Xavier and Jacquemin, Denis and Perp{\`e}te, Eric A.}, + Date-Added = {2018-02-24 12:51:10 +0000}, + Date-Modified = {2018-02-24 12:51:10 +0000}, + Doi = {10.1002/qua.21182}, + File = {/Users/loos/Zotero/storage/D5F3ED8Z/4.pdf}, + Issn = {00207608, 1097461X}, + Journal = {Int. J. Quantum Chem.}, + Language = {en}, + Number = {3}, + Pages = {574--585}, + Shorttitle = {{{DFT}} and {{TD}}-{{DFT}} Investigation of {{IR}} and {{UV}} Spectra of Solvated Molecules}, + Title = {{{DFT}} and {{TD}}-{{DFT}} Investigation of {{IR}} and {{UV}} Spectra of Solvated Molecules: {{Comparison}} of Two {{SCRF}} Continuum Models}, + Volume = {107}, + Year = {2007}, + Bdsk-Url-1 = {https://dx.doi.org/10.1002/qua.21182}} + +@inproceedings{Rivail_2006, + Author = {Rivail, J. L. and Bouchy, A. and Loos, P. F.}, + Booktitle = {Anales de La {{Asociaci{\'o}n Qu{\'\i}mica Argentina}}}, + Date-Added = {2018-02-24 12:51:10 +0000}, + Date-Modified = {2018-02-24 12:51:10 +0000}, + File = {/Users/loos/Zotero/storage/XGMNTL9R/3.pdf}, + Pages = {19--26}, + Publisher = {{SciELO Argentina}}, + Title = {Electronic Factors Favouring the Cis Conformation in Proline Peptidic Bonds}, + Volume = {94}, + Year = {2006}} + +@article{Rogers_2016, + Author = {Rogers, Fergus J. M. and Ball, Caleb J. and Loos, Pierre-Fran{\c c}ois}, + Date-Added = {2018-02-24 12:51:10 +0000}, + Date-Modified = {2018-02-24 12:51:10 +0000}, + Doi = {10.1103/PhysRevB.93.235114}, + File = {/Users/loos/Zotero/storage/PD5I8W55/51.pdf}, + Issn = {2469-9950, 2469-9969}, + Journal = {Phys. Rev. B}, + Language = {en}, + Month = jun, + Number = {23}, + Title = {Symmetry-Broken Local-Density Approximation for One-Dimensional Systems}, + Volume = {93}, + Year = {2016}, + Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevB.93.235114}} + +@article{Rogers_2017, + Author = {Rogers, Fergus JM and Loos, Pierre-Fran{\c c}ois}, + Date-Added = {2018-02-24 12:51:10 +0000}, + Date-Modified = {2018-02-24 12:51:10 +0000}, + File = {/Users/loos/Zotero/storage/EJULV3C4/53.pdf}, + Journal = {J. Chem. Phys.}, + Number = {4}, + Pages = {044114}, + Title = {Excited-State {{Wigner}} Crystals}, + Volume = {146}, + Year = {2017}} + +@article{Tognetti_2016, + Author = {Tognetti, Vincent and Loos, Pierre-Fran{\c c}ois}, + Date-Added = {2018-02-24 12:51:10 +0000}, + Date-Modified = {2018-02-24 12:51:10 +0000}, + Doi = {10.1063/1.4940919}, + File = {/Users/loos/Zotero/storage/B35RYULA/48.pdf}, + Issn = {0021-9606, 1089-7690}, + Journal = {J. Chem. Phys.}, + Language = {en}, + Month = feb, + Number = {5}, + Pages = {054108}, + Title = {Natural Occupation Numbers in Two-Electron Quantum Rings}, + Volume = {144}, + Year = {2016}, + Bdsk-Url-1 = {https://dx.doi.org/10.1063/1.4940919}} + +@article{Zhao_2011, + Author = {Zhao, Yan and Loos, Pierre-Fran{\c c}ois and Gill, Peter M. W.}, + Date-Added = {2018-02-24 12:51:10 +0000}, + Date-Modified = {2018-02-24 12:51:10 +0000}, + Doi = {10.1103/PhysRevA.84.032513}, + File = {/Users/loos/Zotero/storage/27Q3DAWX/30.pdf}, + Issn = {1050-2947, 1094-1622}, + Journal = {Phys. Rev. A}, + Language = {en}, + Month = sep, + Number = {3}, + Title = {Correlation Energy of Anisotropic Quantum Dots}, + Volume = {84}, + Year = {2011}, + Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevA.84.032513}} + +@article{Almbladh_1999, + Author = {Almbladh, C.-O. and Barth, U. Von and Leeuwen, R. Van}, + File = {/Users/loos/Zotero/storage/7TN6GPFJ/Almbladh_1999.pdf}, + Journal = {Int. J. Mod. Phys. B}, + Number = {05n06}, + Pages = {535--541}, + Title = {Variational Total Energies from {{$\Phi$}}-and {{$\Psi$}}-Derivable Theories}, + Volume = {13}, + Year = {1999}} + +@article{Bartlett_1981, + Author = {Bartlett, Rodney J.}, + File = {/Users/loos/Zotero/storage/3MKNT5H6/Bartlett_1981.pdf}, + Journal = {Annu. Rev. Phys. Chem.}, + Number = {1}, + Pages = {359--401}, + Title = {Many-Body Perturbation Theory and Coupled Cluster Theory for Electron Correlation in Molecules}, + Volume = {32}, + Year = {1981}} + +@article{Berger_2010, + Author = {Berger, J. A. and Reining, Lucia and Sottile, Francesco}, + Doi = {10.1103/PhysRevB.82.041103}, + File = {/Users/loos/Zotero/storage/6FZPM8KJ/Berger_2010.pdf}, + Issn = {1098-0121, 1550-235X}, + Journal = {Phys. Rev. B}, + Language = {en}, + Month = jul, + Number = {4}, + Shorttitle = {{\emph{Ab Initio}} Calculations of Electronic Excitations}, + Title = {{\emph{Ab Initio}} Calculations of Electronic Excitations: {{Collapsing}} Spectral Sums}, + Volume = {82}, + Year = {2010}, + Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevB.82.041103}} + +@article{Berger_2012, + Author = {Berger, J. A. and Reining, Lucia and Sottile, Francesco}, + Doi = {10.1103/PhysRevB.85.085126}, + File = {/Users/loos/Zotero/storage/LG5MEXAZ/Berger_2012.pdf}, + Issn = {1098-0121, 1550-235X}, + Journal = {Phys. Rev. B}, + Language = {en}, + Month = feb, + Number = {8}, + Shorttitle = {Efficient {{G W}} Calculations for {{SnO}} 2 , {{ZnO}}, and Rubrene}, + Title = {Efficient {{G W}} Calculations for {{SnO}} 2 , {{ZnO}}, and Rubrene: {{The}} Effective-Energy Technique}, + Volume = {85}, + Year = {2012}, + Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevB.85.085126}} + +@article{Berger_2014, + Author = {Berger, J A and Romaniello, Pina and Tandetzky, Falk and Mendoza, Bernardo S and Brouder, Christian and Reining, Lucia}, + Doi = {10.1088/1367-2630/16/11/119601}, + File = {/Users/loos/Zotero/storage/QZKHN82B/Berger_2014.pdf}, + Issn = {1367-2630}, + Journal = {New J. Phys.}, + Month = nov, + Number = {11}, + Pages = {119601}, + Shorttitle = {Erratum}, + Title = {Erratum: {{Solution}} to the Many-Body Problem in One Point ( {{{\emph{New J}}}}{\emph{. }}{{{\emph{Phys}}}}{\emph{.}} {\textbf{16}} 113025)}, + Volume = {16}, + Year = {2014}, + Bdsk-Url-1 = {https://dx.doi.org/10.1088/1367-2630/16/11/119601}} + +@article{Blase_2011, + Author = {Blase, X. and Attaccalite, C. and Olevano, V.}, + Date-Modified = {2018-04-14 07:20:02 +0000}, + Doi = {10.1103/PhysRevB.83.115103}, + File = {/Users/loos/Zotero/storage/ATYGAK7I/Blase_2011.pdf}, + Issn = {1098-0121, 1550-235X}, + Journal = {Phys. Rev. B}, + Language = {en}, + Month = mar, + Number = {11}, + Pages = {115103}, + Title = {First-Principles {{GW}} Calculations for Fullerenes, Porphyrins, Phtalocyanine, and Other Molecules of Interest for Organic Photovoltaic Applications}, + Volume = {83}, + Year = {2011}, + Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevB.83.115103}} + +@article{Blase_2016, + Author = {Blase, Xavier and Boulanger, Paul and Bruneval, Fabien and Fernandez-Serra, Marivi and Duchemin, Ivan}, + Doi = {10.1063/1.4940139}, + File = {/Users/loos/Zotero/storage/LWI3LN6F/Blase_2016.pdf}, + Issn = {0021-9606, 1089-7690}, + Journal = {J. Chem. Phys.}, + Language = {en}, + Month = jan, + Number = {3}, + Pages = {034109}, + Title = {{{{\emph{GW}}}} and {{Bethe}}-{{Salpeter}} Study of Small Water Clusters}, + Volume = {144}, + Year = {2016}, + Bdsk-Url-1 = {https://dx.doi.org/10.1063/1.4940139}} + +@article{Blase_2018, + Author = {Blase, Xavier and Duchemin, Ivan and Jacquemin, Denis}, + Doi = {10.1039/C7CS00049A}, + File = {/Users/loos/Zotero/storage/PBGJ3ZVC/Blase_2017.pdf}, + Issn = {0306-0012, 1460-4744}, + Journal = {Chem. Soc. Rev.}, + Language = {en}, + Number = {3}, + Pages = {1022--1043}, + Shorttitle = {The {{Bethe}}\textendash{}{{Salpeter}} Equation in Chemistry}, + Title = {The {{Bethe}}\textendash{}{{Salpeter}} Equation in Chemistry: Relations with {{TD}}-{{DFT}}, Applications and Challenges}, + Volume = {47}, + Year = {2018}, + Bdsk-Url-1 = {https://dx.doi.org/10.1039/C7CS00049A}} + +@article{Boulanger_2014, + Author = {Boulanger, Paul and Jacquemin, Denis and Duchemin, Ivan and Blase, Xavier}, + Doi = {10.1021/ct401101u}, + File = {/Users/loos/Zotero/storage/KTW3SS9F/Boulanger_2014.pdf}, + Issn = {1549-9618, 1549-9626}, + Journal = {J. Chem. Theory Comput.}, + Language = {en}, + Month = mar, + Number = {3}, + Pages = {1212--1218}, + Title = {Fast and {{Accurate Electronic Excitations}} in {{Cyanines}} with the {{Many}}-{{Body Bethe}}\textendash{}{{Salpeter Approach}}}, + Volume = {10}, + Year = {2014}, + Bdsk-Url-1 = {https://dx.doi.org/10.1021/ct401101u}} + +@article{Bruneval_2009, + Author = {Bruneval, Fabien}, + Doi = {10.1103/PhysRevLett.103.176403}, + File = {/Users/loos/Zotero/storage/6XJIUUFE/Bruneval_2009.pdf}, + Issn = {0031-9007, 1079-7114}, + Journal = {Phys. Rev. Lett.}, + Language = {en}, + Month = oct, + Number = {17}, + Title = {G {{W Approximation}} of the {{Many}}-{{Body Problem}} and {{Changes}} in the {{Particle Number}}}, + Volume = {103}, + Year = {2009}, + Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevLett.103.176403}} + +@article{Bruneval_2012, + Author = {Bruneval, Fabien}, + Doi = {10.1063/1.4718428}, + File = {/Users/loos/Zotero/storage/MVP3WBIS/Bruneval_2012a.pdf}, + Issn = {0021-9606, 1089-7690}, + Journal = {J. Chem. Phys.}, + Language = {en}, + Month = may, + Number = {19}, + Pages = {194107}, + Title = {Ionization Energy of Atoms Obtained from {{{\emph{GW}}}} Self-Energy or from Random Phase Approximation Total Energies}, + Volume = {136}, + Year = {2012}, + Bdsk-Url-1 = {https://dx.doi.org/10.1063/1.4718428}} + +@article{Bruneval_2013, + Author = {Bruneval, Fabien and Marques, Miguel A. L.}, + Doi = {10.1021/ct300835h}, + File = {/Users/loos/Zotero/storage/6ERH93TH/Bruneval_2012b.pdf}, + Issn = {1549-9618, 1549-9626}, + Journal = {J. Chem. Theory Comput.}, + Language = {en}, + Month = jan, + Number = {1}, + Pages = {324--329}, + Title = {Benchmarking the {{Starting Points}} of the {{{\emph{GW}}}} {{Approximation}} for {{Molecules}}}, + Volume = {9}, + Year = {2013}, + Bdsk-Url-1 = {https://dx.doi.org/10.1021/ct300835h}} + +@article{Bruneval_2015, + Author = {Bruneval, Fabien and Hamed, Samia M. and Neaton, Jeffrey B.}, + Doi = {10.1063/1.4922489}, + File = {/Users/loos/Zotero/storage/EVU62PAN/Bruneval_2015.pdf}, + Issn = {0021-9606, 1089-7690}, + Journal = {J. Chem. Phys.}, + Language = {en}, + Month = jun, + Number = {24}, + Pages = {244101}, + Title = {A Systematic Benchmark of the {\emph{Ab Initio}} {{Bethe}}-{{Salpeter}} Equation Approach for Low-Lying Optical Excitations of Small Organic Molecules}, + Volume = {142}, + Year = {2015}, + Bdsk-Url-1 = {https://dx.doi.org/10.1063/1.4922489}} + +@article{Bruneval_2016, + Author = {Bruneval, Fabien and Rangel, Tonatiuh and Hamed, Samia M. and Shao, Meiyue and Yang, Chao and Neaton, Jeffrey B.}, + Doi = {10.1016/j.cpc.2016.06.019}, + File = {/Users/loos/Zotero/storage/CHGLK37T/Bruneval_2016a.pdf}, + Issn = {00104655}, + Journal = {Comput. Phys. Commun.}, + Language = {en}, + Month = nov, + Pages = {149--161}, + Shorttitle = {Molgw 1}, + Title = {Molgw 1: {{Many}}-Body Perturbation Theory Software for Atoms, Molecules, and Clusters}, + Volume = {208}, + Year = {2016}, + Bdsk-Url-1 = {https://dx.doi.org/10.1016/j.cpc.2016.06.019}} + +@article{Bruneval_2016a, + Author = {Bruneval, Fabien}, + Doi = {10.1063/1.4972003}, + File = {/Users/loos/Zotero/storage/2TRSI2LP/Bruneval_2016b.pdf}, + Issn = {0021-9606, 1089-7690}, + Journal = {J. Chem. Phys.}, + Language = {en}, + Month = dec, + Number = {23}, + Pages = {234110}, + Title = {Optimized Virtual Orbital Subspace for Faster {{GW}} Calculations in Localized Basis}, + Volume = {145}, + Year = {2016}, + Bdsk-Url-1 = {https://dx.doi.org/10.1063/1.4972003}} + +@article{Caruso_2012, + Author = {Caruso, F. and Rinke, P. and Ren, X. and Scheffler, M. and Rubio, A.}, + Date-Modified = {2018-04-14 07:23:04 +0000}, + Doi = {10.1103/PhysRevB.86.081102}, + File = {/Users/loos/Zotero/storage/2ZGZT4DZ/Caruso_2012.pdf}, + Issn = {1098-0121, 1550-235X}, + Journal = {Phys. Rev. B}, + Language = {en}, + Month = aug, + Number = {8}, + Pages = {081102(R)}, + Shorttitle = {Unified Description of Ground and Excited States of Finite Systems}, + Title = {Unified Description of Ground and Excited States of Finite Systems: {{The}} Self-Consistent {{G W}} Approach}, + Volume = {86}, + Year = {2012}, + Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevB.86.081102}} + +@article{Caruso_2013a, + Author = {Caruso, Fabio and Rinke, Patrick and Ren, Xinguo and Rubio, Angel and Scheffler, Matthias}, + Date-Modified = {2018-04-14 07:22:35 +0000}, + Doi = {10.1103/PhysRevB.88.075105}, + File = {/Users/loos/Zotero/storage/SACFAD2T/Caruso_2013.pdf}, + Issn = {1098-0121, 1550-235X}, + Journal = {Phys. Rev. B}, + Language = {en}, + Month = aug, + Number = {7}, + Pages = {075105}, + Shorttitle = {Self-Consistent {{G W}}}, + Title = {Self-Consistent {{G W}} : {{All}}-Electron Implementation with Localized Basis Functions}, + Volume = {88}, + Year = {2013}, + Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevB.88.075105}} + +@article{Caruso_2013, + Author = {Caruso, Fabio and Rohr, Daniel R. and Hellgren, Maria and Ren, Xinguo and Rinke, Patrick and Rubio, Angel and Scheffler, Matthias}, + Date-Modified = {2018-04-14 07:22:22 +0000}, + Doi = {10.1103/PhysRevLett.110.146403}, + File = {/Users/loos/Zotero/storage/UF9F4UWC/Caruso_2013a.pdf;/Users/loos/Zotero/storage/Y3IZUCIX/Caruso_2013b.pdf}, + Issn = {0031-9007, 1079-7114}, + Journal = {Phys. Rev. Lett.}, + Language = {en}, + Month = apr, + Number = {14}, + Pages = {146403}, + Shorttitle = {Bond {{Breaking}} and {{Bond Formation}}}, + Title = {Bond {{Breaking}} and {{Bond Formation}}: {{How Electron Correlation}} Is {{Captured}} in {{Many}}-{{Body Perturbation Theory}} and {{Density}}-{{Functional Theory}}}, + Volume = {110}, + Year = {2013}, + Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevLett.110.146403}} + +@phdthesis{Caruso_2013b, + Author = {Caruso, Fabio}, + File = {/Users/loos/Zotero/storage/I5Q6ZQCS/Caruso_PhD.pdf}, + School = {Freie Universit{\"a}t Berlin}, + Title = {Self-Consistent {{GW}} Approach for the Unified Description of Ground and Excited States of Finite Systems}, + Type = {{{PhD Thesis}}}, + Year = {2013}} + +@incollection{Corzo_2017, + Author = {Corzo, H{\'e}ctor H. and Ortiz, J. Vince}, + Booktitle = {Advances in Quantum Chemistry}, + Date-Modified = {2018-02-24 19:24:27 +0000}, + Doi = {10.1016/bs.aiq.2016.05.001}, + File = {/Users/loos/Zotero/storage/PT4V59RE/Corzo_2017.pdf}, + Isbn = {978-0-12-809988-9}, + Language = {en}, + Pages = {267--298}, + Publisher = {Elsevier}, + Title = {Electron Propagator Theory}, + Volume = {74}, + Year = {2017}, + Bdsk-Url-1 = {https://dx.doi.org/10.1016/bs.aiq.2016.05.001}} + +@article{Dahlen_2004, + Author = {Dahlen, Nils Erik and von Barth, Ulf}, + Date-Modified = {2018-04-14 07:33:15 +0000}, + Doi = {10.1103/PhysRevB.69.195102}, + File = {/Users/loos/Zotero/storage/JVFRWQV9/Dahlen_2004a.pdf}, + Issn = {1098-0121, 1550-235X}, + Journal = {Phys. Rev. B}, + Language = {en}, + Month = may, + Number = {19}, + Pages = {195102}, + Title = {Variational Energy Functionals Tested on Atoms}, + Volume = {69}, + Year = {2004}, + Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevB.69.195102}} + +@article{Dahlen_2004a, + Author = {Dahlen, Nils Erik and {von Barth}, Ulf}, + Doi = {10.1063/1.1650307}, + File = {/Users/loos/Zotero/storage/6IDAFXL5/Dahlen_2004b.pdf}, + Issn = {0021-9606, 1089-7690}, + Journal = {J. Chem. Phys.}, + Language = {en}, + Month = apr, + Number = {15}, + Pages = {6826--6831}, + Title = {Variational Second-Order {{M{\o}ller}}\textendash{}{{Plesset}} Theory Based on the {{Luttinger}}\textendash{}{{Ward}} Functional}, + Volume = {120}, + Year = {2004}, + Bdsk-Url-1 = {https://dx.doi.org/10.1063/1.1650307}} + +@article{Dahlen_2005a, + Author = {Dahlen, Nils Erik and Van Leeuwen, Robert and Von Barth, Ulf}, + Doi = {10.1002/qua.20306}, + File = {/Users/loos/Zotero/storage/KCXCEUER/Dahlen_2005a.pdf}, + Issn = {0020-7608, 1097-461X}, + Journal = {Int. J. Quantum Chem.}, + Language = {en}, + Number = {5}, + Pages = {512--519}, + Title = {Variational Energy Functionals of the {{Green}} Function Tested on Molecules}, + Volume = {101}, + Year = {2005}, + Bdsk-Url-1 = {https://dx.doi.org/10.1002/qua.20306}} + +@article{Dahlen_2005, + Author = {Dahlen, Nils Erik and {van Leeuwen}, Robert}, + Doi = {10.1063/1.1884965}, + File = {/Users/loos/Zotero/storage/Z984CS8R/Dahlen_2005b.pdf}, + Issn = {0021-9606, 1089-7690}, + Journal = {J. Chem. Phys.}, + Language = {en}, + Month = apr, + Number = {16}, + Pages = {164102}, + Title = {Self-Consistent Solution of the {{Dyson}} Equation for Atoms and Molecules within a Conserving Approximation}, + Volume = {122}, + Year = {2005}, + Bdsk-Url-1 = {https://dx.doi.org/10.1063/1.1884965}} + +@article{Dahlen_2006, + Author = {Dahlen, Nils Erik and {van Leeuwen}, Robert and {von Barth}, Ulf}, + Date-Modified = {2018-04-14 07:33:30 +0000}, + Doi = {10.1103/PhysRevA.73.012511}, + File = {/Users/loos/Zotero/storage/CIIYSNSE/Dahlen_2006.pdf}, + Issn = {1050-2947, 1094-1622}, + Journal = {Phys. Rev. A}, + Language = {en}, + Month = jan, + Number = {1}, + Pages = {012511}, + Title = {Variational Energy Functionals of the {{Green}} Function and of the Density Tested on Molecules}, + Volume = {73}, + Year = {2006}, + Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevA.73.012511}} + +@article{Danovich_2011, + Author = {Danovich, David}, + Doi = {10.1002/wcms.38}, + File = {/Users/loos/Zotero/storage/RQLPMH6E/Danovich_2011.pdf}, + Issn = {17590876}, + Journal = {Wiley Interdiscip. Rev. Comput. Mol. Sci.}, + Language = {en}, + Month = may, + Number = {3}, + Pages = {377--387}, + Shorttitle = {Green's Function Methods for Calculating Ionization Potentials, Electron Affinities, and Excitation Energies}, + Title = {Green's Function Methods for Calculating Ionization Potentials, Electron Affinities, and Excitation Energies: {{GF}} Methods for Calculating {{IPs}}, {{EAs}}, and Excitation Energies}, + Volume = {1}, + Year = {2011}, + Bdsk-Url-1 = {https://dx.doi.org/10.1002/wcms.38}} + +@article{Dreuw_2005, + Author = {Dreuw, Andreas and Head-Gordon, Martin}, + Doi = {10.1021/cr0505627}, + File = {/Users/loos/Zotero/storage/WKGXAHGE/Dreuw_2005.pdf}, + Issn = {0009-2665, 1520-6890}, + Journal = {Chem. Rev.}, + Language = {en}, + Month = nov, + Number = {11}, + Pages = {4009--4037}, + Title = {Single-{{Reference}} Ab {{Initio Methods}} for the {{Calculation}} of {{Excited States}} of {{Large Molecules}}}, + Volume = {105}, + Year = {2005}, + Bdsk-Url-1 = {https://dx.doi.org/10.1021/cr0505627}} + +@article{Dreuw_2015, + Author = {Dreuw, Andreas and Wormit, Michael}, + Doi = {10.1002/wcms.1206}, + File = {/Users/loos/Zotero/storage/ZGBF293U/Dreuw_2015.pdf}, + Issn = {17590876}, + Journal = {Wiley Interdiscip. Rev. Comput. Mol. Sci.}, + Language = {en}, + Month = jan, + Number = {1}, + Pages = {82--95}, + Title = {The Algebraic Diagrammatic Construction Scheme for the Polarization Propagator for the Calculation of Excited States}, + Volume = {5}, + Year = {2015}, + Bdsk-Url-1 = {https://dx.doi.org/10.1002/wcms.1206}} + +@phdthesis{vanFaassen_2005, + Author = {{van Faassen}, Meta}, + File = {/Users/loos/Zotero/storage/PTY6IS9R/Faassen_2015.pdf}, + School = {University Library Groningen][Host]}, + Title = {Time-Dependent {{Current}}-Density-Functional {{Theory}} for {{Molecules}}}, + Type = {{{PhD Thesis}}}, + Year = {2005}} + +@phdthesis{Faber_2014, + Author = {Faber, Carina}, + File = {/Users/loos/Zotero/storage/ZPJDQPGS/Faber_PhD.pdf}, + School = {Universit{\'e} de Grenoble}, + Shorttitle = {Electronic, Excitonic and Polaronic Properties of Organic Systems within the Many-Body {{GW}} and {{Bethe}}-{{Salpeter}} Formalisms}, + Title = {Electronic, Excitonic and Polaronic Properties of Organic Systems within the Many-Body {{GW}} and {{Bethe}}-{{Salpeter}} Formalisms: Towards Organic Photovoltaics}, + Type = {{{PhD Thesis}}}, + Year = {2014}} + +@article{Faleev_2004, + Author = {Faleev, Sergey V. and {van Schilfgaarde}, Mark and Kotani, Takao}, + Date-Modified = {2018-04-14 07:31:23 +0000}, + Doi = {10.1103/PhysRevLett.93.126406}, + File = {/Users/loos/Zotero/storage/YKIDTQ84/Faleev_2004.pdf}, + Issn = {0031-9007, 1079-7114}, + Journal = {Phys. Rev. Lett.}, + Language = {en}, + Month = sep, + Number = {12}, + Pages = {126406}, + Shorttitle = {All-{{Electron Self}}-{{Consistent G W Approximation}}}, + Title = {All-{{Electron Self}}-{{Consistent G W Approximation}}: {{Application}} to {{Si}}, {{MnO}}, and {{NiO}}}, + Volume = {93}, + Year = {2004}, + Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevLett.93.126406}} + +@book{March_1999, + Address = {London}, + Editor = {March, Norman H.}, + File = {/Users/loos/Zotero/storage/7VMQ86HQ/Farid_1999.pdf}, + Isbn = {978-1-86094-200-6}, + Language = {eng}, + Note = {OCLC: 247716792}, + Publisher = {{Imperial College Press}}, + Title = {Electron Correlation in the Solid State}, + Year = {1999}} + +@article{Garcia-Gonzalez_2001, + Author = {Garc{\'\i}a-Gonz{\'a}lez, P. and Godby, R. W.}, + Date-Modified = {2018-04-14 07:24:41 +0000}, + Doi = {10.1103/PhysRevB.63.075112}, + File = {/Users/loos/Zotero/storage/4MI62AQA/GarciaGonzales_2001.pdf}, + Issn = {0163-1829, 1095-3795}, + Journal = {Phys. Rev. B}, + Language = {en}, + Month = jan, + Number = {7}, + Pages = {075112}, + Title = {Self-Consistent Calculation of Total Energies of the Electron Gas Using Many-Body Perturbation Theory}, + Volume = {63}, + Year = {2001}, + Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevB.63.075112}} + +@article{Guzzo_2011, + Author = {Guzzo, Matteo and Lani, Giovanna and Sottile, Francesco and Romaniello, Pina and Gatti, Matteo and Kas, Joshua J. and Rehr, John J. and Silly, Mathieu G. and Sirotti, Fausto and Reining, Lucia}, + Doi = {10.1103/PhysRevLett.107.166401}, + File = {/Users/loos/Zotero/storage/CML472NW/Guzzo_2011.pdf}, + Issn = {0031-9007, 1079-7114}, + Journal = {Phys. Rev. Lett.}, + Language = {en}, + Month = oct, + Number = {16}, + Shorttitle = {Valence {{Electron Photoemission Spectrum}} of {{Semiconductors}}}, + Title = {Valence {{Electron Photoemission Spectrum}} of {{Semiconductors}}: {{{\emph{Ab Initio}}}} {{Description}} of {{Multiple Satellites}}}, + Volume = {107}, + Year = {2011}, + Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevLett.107.166401}} + +@article{vanSchilfgaarde_2006, + Author = {{van Schilfgaarde}, M. and Kotani, Takao and Faleev, S.}, + Date-Modified = {2018-04-14 07:31:33 +0000}, + Doi = {10.1103/PhysRevLett.96.226402}, + File = {/Users/loos/Zotero/storage/6S8FDHP8/vanSchilfgaarde_2006.pdf}, + Issn = {0031-9007, 1079-7114}, + Journal = {Phys. Rev. Lett.}, + Language = {en}, + Month = jun, + Number = {22}, + Pages = {226402}, + Title = {Quasiparticle {{Self}}-{{Consistent G W Theory}}}, + Volume = {96}, + Year = {2006}, + Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevLett.96.226402}} + +@article{Furche_2008, + Author = {Furche, Filipp}, + Doi = {10.1063/1.2977789}, + File = {/Users/loos/Zotero/storage/FWTKB6W5/Furche_2008.pdf}, + Issn = {0021-9606, 1089-7690}, + Journal = {J. Chem. Phys.}, + Language = {en}, + Month = sep, + Number = {11}, + Pages = {114105}, + Title = {Developing the Random Phase Approximation into a Practical Post-{{Kohn}}\textendash{}{{Sham}} Correlation Model}, + Volume = {129}, + Year = {2008}, + Bdsk-Url-1 = {https://dx.doi.org/10.1063/1.2977789}} + +@article{Hattig_2002, + Author = {H{\"a}ttig, Christof and Hald, Kasper}, + Doi = {10.1039/b110847f}, + File = {/Users/loos/Zotero/storage/C9SZ4GHZ/Hattig_2002.pdf}, + Issn = {14639076, 14639084}, + Journal = {Phys. Chem. Chem. Phys.}, + Month = may, + Number = {11}, + Pages = {2111--2118}, + Title = {Implementation of {{RI}}-{{CC2}} Triplet Excitation Energies with an Application to Trans-Azobenzene}, + Volume = {4}, + Year = {2002}, + Bdsk-Url-1 = {https://dx.doi.org/10.1039/b110847f}} + +@article{Ismail-Beigi_2010, + Author = {Ismail-Beigi, Sohrab}, + Doi = {10.1103/PhysRevB.81.195126}, + File = {/Users/loos/Zotero/storage/DAFHBKV5/Ismail-Beigi_2010.pdf}, + Issn = {1098-0121, 1550-235X}, + Journal = {Phys. Rev. B}, + Language = {en}, + Month = may, + Number = {19}, + Shorttitle = {Correlation Energy Functional within the {{G W}} -{{RPA}}}, + Title = {Correlation Energy Functional within the {{G W}} -{{RPA}}: {{Exact}} Forms, Approximate Forms, and Challenges}, + Volume = {81}, + Year = {2010}, + Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevB.81.195126}} + +@article{Jacquemin_2017, + Author = {Jacquemin, Denis and Duchemin, Ivan and Blondel, Aymeric and Blase, Xavier}, + Doi = {10.1021/acs.jctc.6b01169}, + File = {/Users/loos/Zotero/storage/T7RT7DS8/Jacquemin_2017.pdf}, + Issn = {1549-9618, 1549-9626}, + Journal = {J. Chem. Theory Comput.}, + Language = {en}, + Month = feb, + Number = {2}, + Pages = {767--783}, + Title = {Benchmark of {{Bethe}}-{{Salpeter}} for {{Triplet Excited}}-{{States}}}, + Volume = {13}, + Year = {2017}, + Bdsk-Url-1 = {https://dx.doi.org/10.1021/acs.jctc.6b01169}} + +@article{LaflammeJanssen_2015, + Author = {Laflamme Janssen, Jonathan and Rousseau, Bruno and C{\^o}t{\'e}, Michel}, + Doi = {10.1103/PhysRevB.91.125120}, + File = {/Users/loos/Zotero/storage/IT4XRL8J/Janssen_2015.pdf}, + Issn = {1098-0121, 1550-235X}, + Journal = {Phys. Rev. B}, + Language = {en}, + Month = mar, + Number = {12}, + Title = {Efficient Dielectric Matrix Calculations Using the {{Lanczos}} Algorithm for Fast Many-Body {{G}} 0 {{W}} 0 Implementations}, + Volume = {91}, + Year = {2015}, + Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevB.91.125120}} + +@article{Kaplan_2015, + Author = {Kaplan, F. and Weigend, F. and Evers, F. and {van Setten}, M. J.}, + Doi = {10.1021/acs.jctc.5b00394}, + File = {/Users/loos/Zotero/storage/Y8FW5KVR/Kaplan_2015.pdf}, + Issn = {1549-9618, 1549-9626}, + Journal = {J. Chem. Theory Comput.}, + Language = {en}, + Month = nov, + Number = {11}, + Pages = {5152--5160}, + Shorttitle = {Off-{{Diagonal Self}}-{{Energy Terms}} and {{Partially Self}}-{{Consistency}} in {{{\emph{GW}}}} {{Calculations}} for {{Single Molecules}}}, + Title = {Off-{{Diagonal Self}}-{{Energy Terms}} and {{Partially Self}}-{{Consistency}} in {{{\emph{GW}}}} {{Calculations}} for {{Single Molecules}}: {{Efficient Implementation}} and {{Quantitative Effects}} on {{Ionization Potentials}}}, + Volume = {11}, + Year = {2015}, + Bdsk-Url-1 = {https://dx.doi.org/10.1021/acs.jctc.5b00394}} + +@article{Kaplan_2016, + 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}, + File = {/Users/loos/Zotero/storage/MWYM8YMS/Kaplan_2016.pdf}, + Issn = {1549-9618, 1549-9626}, + Journal = {J. Chem. Theory Comput.}, + Language = {en}, + Month = jun, + Number = {6}, + Pages = {2528--2541}, + Title = {Quasi-{{Particle Self}}-{{Consistent}} {{{\emph{GW}}}} for {{Molecules}}}, + Volume = {12}, + Year = {2016}, + Bdsk-Url-1 = {https://dx.doi.org/10.1021/acs.jctc.5b01238}} + +@article{Rangel_2017, + Author = {Rangel, Tonatiuh and Hamed, Samia M. and Bruneval, Fabien and Neaton, Jeffrey B.}, + Doi = {10.1063/1.4983126}, + File = {/Users/loos/Zotero/storage/IPXGTRK7/Rangel_2017.pdf}, + Issn = {0021-9606, 1089-7690}, + Journal = {J. Chem. Phys.}, + Language = {en}, + Month = may, + Number = {19}, + Pages = {194108}, + Title = {An Assessment of Low-Lying Excitation Energies and Triplet Instabilities of Organic Molecules with an {\emph{Ab Initio}} {{Bethe}}-{{Salpeter}} Equation Approach and the {{Tamm}}-{{Dancoff}} Approximation}, + Volume = {146}, + Year = {2017}, + Bdsk-Url-1 = {https://dx.doi.org/10.1063/1.4983126}} + +@article{Reining_2017, + Author = {Reining, Lucia}, + Doi = {10.1002/wcms.1344}, + File = {/Users/loos/Zotero/storage/VDXYCLGF/Reining_2017.pdf}, + Issn = {17590876}, + Journal = {Wiley Interdiscip. Rev. Comput. Mol. Sci.}, + Language = {en}, + Month = dec, + Pages = {e1344}, + Shorttitle = {The {{GW}} Approximation}, + Title = {The {{GW}} Approximation: Content, Successes and Limitations: {{The GW}} Approximation}, + Year = {2017}, + Bdsk-Url-1 = {https://dx.doi.org/10.1002/wcms.1344}} + +@article{Ren_2013, + Author = {Ren, Xinguo and Rinke, Patrick and Scuseria, Gustavo E. and Scheffler, Matthias}, + Date-Modified = {2018-04-14 07:32:03 +0000}, + Doi = {10.1103/PhysRevB.88.035120}, + File = {/Users/loos/Zotero/storage/HMTI4LPK/Ren_2013.pdf}, + Issn = {1098-0121, 1550-235X}, + Journal = {Phys. Rev. B}, + Language = {en}, + Month = jul, + Number = {3}, + Pages = {035120}, + Shorttitle = {Renormalized Second-Order Perturbation Theory for the Electron Correlation Energy}, + Title = {Renormalized Second-Order Perturbation Theory for the Electron Correlation Energy: {{Concept}}, Implementation, and Benchmarks}, + Volume = {88}, + Year = {2013}, + Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevB.88.035120}} + +@article{Zhang_2017, + Author = {Zhang, Du and Su, Neil Qiang and Yang, Weitao}, + Doi = {10.1021/acs.jpclett.7b01275}, + File = {/Users/loos/Zotero/storage/ZJ4HTDNE/Zhang_2017.pdf}, + Issn = {1948-7185}, + Journal = {J. Phys. Chem. 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B}, + Language = {en}, + Month = oct, + Number = {15}, + Title = {{{GW}} + {{T}} Theory of Excited Electron Lifetimes in Metals}, + Volume = {72}, + Year = {2005}, + Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevB.72.155109}} + +@article{Vlcek_2017, + Author = {Vl{\v c}ek, Vojt{\v e}ch and Rabani, Eran and Neuhauser, Daniel and Baer, Roi}, + Doi = {10.1021/acs.jctc.7b00770}, + File = {/Users/loos/Zotero/storage/HBVLY4QJ/Vlcek_2017.pdf}, + Issn = {1549-9618, 1549-9626}, + Journal = {J. Chem. Theory Comput.}, + Language = {en}, + Month = oct, + Number = {10}, + Pages = {4997--5003}, + Title = {Stochastic {{GW Calculations}} for {{Molecules}}}, + Volume = {13}, + Year = {2017}, + Bdsk-Url-1 = {https://dx.doi.org/10.1021/acs.jctc.7b00770}} + +@article{Sun_2004, + Author = {Sun, Ping and Kotliar, Gabriel}, + Doi = {10.1103/PhysRevLett.92.196402}, + File = {/Users/loos/Zotero/storage/HQRU6MCS/Sun_2004.pdf}, + Issn = {0031-9007, 1079-7114}, + Journal = {Phys. Rev. Lett.}, + Language = {en}, + Month = may, + Number = {19}, + Title = {Many-{{Body Approximation Scheme}} beyond {{GW}}}, + Volume = {92}, + Year = {2004}, + Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevLett.92.196402}} + +@article{Yang_2013, + Author = {Yang, Yang and {van Aggelen}, Helen and Steinmann, Stephan N. and Peng, Degao and Yang, Weitao}, + Doi = {10.1063/1.4828728}, + File = {/Users/loos/Zotero/storage/9LZMQQNK/Yang_2013.pdf}, + Issn = {0021-9606, 1089-7690}, + Journal = {J. Chem. Phys.}, + Language = {en}, + Month = nov, + Number = {17}, + Pages = {174110}, + Title = {Benchmark Tests and Spin Adaptation for the Particle-Particle Random Phase Approximation}, + Volume = {139}, + Year = {2013}, + Bdsk-Url-1 = {https://dx.doi.org/10.1063/1.4828728}} + +@article{Willow_2013, + Author = {Willow, Soohaeng Yoo and Kim, Kwang S. and Hirata, So}, + Doi = {10.1063/1.4801862}, + File = {/Users/loos/Zotero/storage/F8QZMTFD/Willow_2013b.pdf}, + Issn = {0021-9606, 1089-7690}, + Journal = {J. Chem. Phys.}, + Language = {en}, + Month = apr, + Number = {16}, + Pages = {164111}, + Title = {Stochastic Evaluation of Second-Order {{Dyson}} Self-Energies}, + Volume = {138}, + Year = {2013}, + Bdsk-Url-1 = {https://dx.doi.org/10.1063/1.4801862}} + +@article{Stan_2009, + Author = {Stan, Adrian and Dahlen, Nils Erik and {van Leeuwen}, Robert}, + Doi = {10.1063/1.3089567}, + File = {/Users/loos/Zotero/storage/M4YMAWCH/Stan_2009.pdf}, + Issn = {0021-9606, 1089-7690}, + Journal = {J. Chem. Phys.}, + Language = {en}, + Month = mar, + Number = {11}, + Pages = {114105}, + Title = {Levels of Self-Consistency in the {{GW}} Approximation}, + Volume = {130}, + Year = {2009}, + Bdsk-Url-1 = {https://dx.doi.org/10.1063/1.3089567}} + +@article{Leng_2016, + Author = {Leng, Xia and Jin, Fan and Wei, Min and Ma, Yuchen}, + Doi = {10.1002/wcms.1265}, + Issn = {17590876}, + Journal = {Wiley Interdiscip. Rev. Comput. Mol. Sci.}, + Language = {en}, + Month = sep, + Number = {5}, + Pages = {532--550}, + Shorttitle = {{{GW}} Method and {{Bethe}}-{{Salpeter}} Equation for Calculating Electronic Excitations}, + Title = {{{GW}} Method and {{Bethe}}-{{Salpeter}} Equation for Calculating Electronic Excitations: {{GW}} Method and {{Bethe}}-{{Salpeter}} Equation}, + Volume = {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}, + Doi = {10.1103/PhysRevB.84.205415}, + File = {/Users/loos/Zotero/storage/98P28A6E/Ke_2011.pdf}, + Issn = {1098-0121, 1550-235X}, + Journal = {Phys. Rev. B}, + Language = {en}, + Month = nov, + Number = {20}, + Pages = {205415}, + Shorttitle = {All-Electron {{G W}} Methods Implemented in Molecular Orbital Space}, + Title = {All-Electron {{G W}} Methods Implemented in Molecular Orbital Space: {{Ionization}} Energy and Electron Affinity of Conjugated Molecules}, + Volume = {84}, + Year = {2011}, + Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevB.84.205415}} + +@article{Knowles_1985, + Author = {Knowles, P. J. and Somasundram, K. and Handy, N. C. and Hirao, K.}, + File = {/Users/loos/Zotero/storage/KGTI53ND/Knowles_1985.pdf}, + Journal = {Chem. Phys. Lett.}, + Number = {1}, + Pages = {8--12}, + Title = {The Calculation of Higher-Order Energies in the Many-Body Perturbation Theory Series}, + Volume = {113}, + Year = {1985}} + +@article{Knowles_1989, + Author = {Knowles, Peter J. and Handy, Nicholas C.}, + File = {/Users/loos/Zotero/storage/XWJJMYAA/Knowles_1989.pdf}, + Journal = {Comput. Phys. 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Chem.}, + Language = {en}, + Month = mar, + Number = {6}, + Pages = {383--388}, + Title = {Implementation Of The {{Bethe}}-{{Salpeter}} Equation In The {{Turbomole}} Program}, + Volume = {38}, + Year = {2017}, + Bdsk-Url-1 = {https://dx.doi.org/10.1002/jcc.24688}} + +@article{Ku_2002, + Author = {Ku, Wei and Eguiluz, Adolfo G.}, + Date-Modified = {2018-04-14 07:25:01 +0000}, + Doi = {10.1103/PhysRevLett.89.126401}, + File = {/Users/loos/Zotero/storage/AATBUYZP/Ku_2002.pdf}, + Issn = {0031-9007, 1079-7114}, + Journal = {Phys. Rev. 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V.}, + Doi = {10.1063/1.4994837}, + File = {/Users/loos/Zotero/storage/XYSAJSW4/Hirata_2017.pdf}, + Issn = {0021-9606, 1089-7690}, + Journal = {J. Chem. Phys.}, + Language = {en}, + Month = jul, + Number = {4}, + Pages = {044108}, + Shorttitle = {One-Particle Many-Body {{Green}}'s Function Theory}, + Title = {One-Particle Many-Body {{Green}}'s Function Theory: {{Algebraic}} Recursive Definitions, Linked-Diagram Theorem, Irreducible-Diagram Theorem, and General-Order Algorithms}, + Volume = {147}, + Year = {2017}, + Bdsk-Url-1 = {https://dx.doi.org/10.1063/1.4994837}} + +@article{Hung_2016, + Author = {Hung, Linda and {da Jornada}, Felipe H. and Souto-Casares, Jaime and Chelikowsky, James R. and Louie, Steven G. and {\"O}{\u g}{\"u}t, Serdar}, + Date-Modified = {2018-04-14 07:21:28 +0000}, + Doi = {10.1103/PhysRevB.94.085125}, + File = {/Users/loos/Zotero/storage/YVJNGCM7/Hung_2016.pdf}, + Issn = {2469-9950, 2469-9969}, + Journal = {Phys. Rev. B}, + Language = {en}, + Month = aug, + Number = {8}, + Pages = {085125}, + Shorttitle = {Excitation Spectra of Aromatic Molecules within a Real-Space {{G W}} -{{BSE}} Formalism}, + Title = {Excitation Spectra of Aromatic Molecules within a Real-Space {{G W}} -{{BSE}} Formalism: {{Role}} of Self-Consistency and Vertex Corrections}, + Volume = {94}, + Year = {2016}, + Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevB.94.085125}} + +@article{Hung_2017, + Author = {Hung, Linda and Bruneval, Fabien and Baishya, Kopinjol and {\"O}{\u g}{\"u}t, Serdar}, + Doi = {10.1021/acs.jctc.7b00123}, + File = {/Users/loos/Zotero/storage/PHJQ6KXT/Hung_2017.pdf}, + Issn = {1549-9618, 1549-9626}, + Journal = {J. Chem. Theory Comput.}, + Language = {en}, + Month = may, + Number = {5}, + Pages = {2135--2146}, + Title = {Benchmarking the {{{\emph{GW}}}} {{Approximation}} and {{Bethe}}\textendash{}{{Salpeter Equation}} for {{Groups IB}} and {{IIB Atoms}} and {{Monoxides}}}, + Volume = {13}, + Year = {2017}, + Bdsk-Url-1 = {https://dx.doi.org/10.1021/acs.jctc.7b00123}} + +@article{Wilhelm_2018, + Author = {Wilhelm, Jan and Golze, Dorothea and Talirz, Leopold and Hutter, J{\"u}rg and Pignedoli, Carlo A.}, + Doi = {10.1021/acs.jpclett.7b02740}, + File = {/Users/loos/Zotero/storage/3Q9NY2YU/Wilhelm_2018.pdf}, + Issn = {1948-7185}, + Journal = {J. Phys. Chem. Lett.}, + Language = {en}, + Month = jan, + Number = {2}, + Pages = {306--312}, + Title = {Toward {{{\emph{GW}}}} {{Calculations}} on {{Thousands}} of {{Atoms}}}, + Volume = {9}, + Year = {2018}, + Bdsk-Url-1 = {https://dx.doi.org/10.1021/acs.jpclett.7b02740}} + +@article{vanSetten_2018, + Author = {{van Setten}, Michiel J. and Costa, Ramon and Vi{\~n}es, Francesc and Illas, Francesc}, + Doi = {10.1021/acs.jctc.7b01192}, + File = {/Users/loos/Zotero/storage/2KY9G5DS/vanSetten_2018.pdf}, + Issn = {1549-9618, 1549-9626}, + Journal = {J. Chem. Theory Comput.}, + Language = {en}, + Month = feb, + Number = {2}, + Pages = {877--883}, + Title = {Assessing {{{\emph{GW}}}} {{Approaches}} for {{Predicting Core Level Binding Energies}}}, + Volume = {14}, + Year = {2018}, + Bdsk-Url-1 = {https://dx.doi.org/10.1021/acs.jctc.7b01192}} + +@article{vanAggelen_2013, + Author = {{van Aggelen}, Helen and Yang, Yang and Yang, Weitao}, + Doi = {10.1103/PhysRevA.88.030501}, + File = {/Users/loos/Zotero/storage/QWPW6HYS/vanAggelen_2013.pdf}, + Issn = {1050-2947, 1094-1622}, + Journal = {Phys. Rev. A}, + Language = {en}, + Month = sep, + Number = {3}, + Title = {Exchange-Correlation Energy from Pairing Matrix Fluctuation and the Particle-Particle Random-Phase Approximation}, + Volume = {88}, + Year = {2013}, + Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevA.88.030501}} + +@article{vanAggelen_2014, + Author = {{van Aggelen}, Helen and Yang, Yang and Yang, Weitao}, + Doi = {10.1063/1.4865816}, + File = {/Users/loos/Zotero/storage/JPZDDCA4/vanAggelen_2014.pdf}, + Issn = {0021-9606, 1089-7690}, + Journal = {J. Chem. Phys.}, + Language = {en}, + Month = may, + Number = {18}, + Pages = {18A511}, + Title = {Exchange-Correlation Energy from Pairing Matrix Fluctuation and the Particle-Particle Random Phase Approximation}, + Volume = {140}, + Year = {2014}, + Bdsk-Url-1 = {https://dx.doi.org/10.1063/1.4865816}} + +@article{vanSetten_2013, + Author = {{van Setten}, M. J. and Weigend, F. and Evers, F.}, + Doi = {10.1021/ct300648t}, + File = {/Users/loos/Zotero/storage/SLTIFNCK/vanSetten_2013.pdf}, + Issn = {1549-9618, 1549-9626}, + Journal = {J. Chem. Theory Comput.}, + Language = {en}, + Month = jan, + Number = {1}, + Pages = {232--246}, + Shorttitle = {The {{{\emph{GW}}}} -{{Method}} for {{Quantum Chemistry Applications}}}, + Title = {The {{{\emph{GW}}}} -{{Method}} for {{Quantum Chemistry Applications}}: {{Theory}} and {{Implementation}}}, + Volume = {9}, + Year = {2013}, + Bdsk-Url-1 = {https://dx.doi.org/10.1021/ct300648t}} + +@article{Trofimov_2002, + Author = {Trofimov, A. B. and Stelter, G. and Schirmer, J.}, + Doi = {10.1063/1.1504708}, + File = {/Users/loos/Zotero/storage/BFV2TPGP/Trofimov_2002.pdf}, + Issn = {0021-9606, 1089-7690}, + Journal = {J. Chem. Phys.}, + Language = {en}, + Month = oct, + Number = {14}, + Pages = {6402--6410}, + Shorttitle = {Electron Excitation Energies Using a Consistent Third-Order Propagator Approach}, + Title = {Electron Excitation Energies Using a Consistent Third-Order Propagator Approach: {{Comparison}} with Full Configuration Interaction and Coupled Cluster Results}, + Volume = {117}, + Year = {2002}, + Bdsk-Url-1 = {https://dx.doi.org/10.1063/1.1504708}} + +@article{Trofimov_2005, + Author = {Trofimov, A. B. and Schirmer, J.}, + Doi = {10.1063/1.2047550}, + File = {/Users/loos/Zotero/storage/DVPFF5F8/Trofimov_2005.pdf}, + Issn = {0021-9606, 1089-7690}, + Journal = {J. Chem. Phys.}, + Language = {en}, + Month = oct, + Number = {14}, + Pages = {144115}, + Title = {Molecular Ionization Energies and Ground- and Ionic-State Properties Using a Non-{{Dyson}} Electron Propagator Approach}, + Volume = {123}, + Year = {2005}, + Bdsk-Url-1 = {https://dx.doi.org/10.1063/1.2047550}} + +@article{Trofimov_2006, + Author = {Trofimov, A.B. and Krivdina, I.L. and Weller, J. and Schirmer, J.}, + Doi = {10.1016/j.chemphys.2006.07.015}, + File = {/Users/loos/Zotero/storage/IYH37EES/Trofimov_2006.pdf}, + Issn = {03010104}, + Journal = {Chem. Phys.}, + Language = {en}, + Month = oct, + Number = {1-3}, + Pages = {1--10}, + Title = {Algebraic-Diagrammatic Construction Propagator Approach to Molecular Response Properties}, + Volume = {329}, + Year = {2006}, + Bdsk-Url-1 = {https://dx.doi.org/10.1016/j.chemphys.2006.07.015}} + +@article{Umari_2009, + Author = {Umari, P. and Stenuit, Geoffrey and Baroni, Stefano}, + Doi = {10.1103/PhysRevB.79.201104}, + File = {/Users/loos/Zotero/storage/PXE8MFW3/Umari_2009.pdf}, + Issn = {1098-0121, 1550-235X}, + Journal = {Phys. Rev. B}, + Language = {en}, + Month = may, + Number = {20}, + Title = {Optimal Representation of the Polarization Propagator for Large-Scale {{G W}} Calculations}, + Volume = {79}, + Year = {2009}, + Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevB.79.201104}} + +@article{Tiago_2006, + Author = {Tiago, Murilo L. and Chelikowsky, James R.}, + Doi = {10.1103/PhysRevB.73.205334}, + File = {/Users/loos/Zotero/storage/3YTWEDNW/Tiago_2006.pdf}, + Issn = {1098-0121, 1550-235X}, + Journal = {Phys. Rev. B}, + Language = {en}, + Month = may, + Number = {20}, + Title = {Optical Excitations in Organic Molecules, Clusters, and Defects Studied by First-Principles {{Green}}'s Function Methods}, + Volume = {73}, + Year = {2006}, + Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevB.73.205334}} + +@article{Ou_2016, + Author = {Ou, Qi and Subotnik, Joseph E.}, + Doi = {10.1021/acs.jpca.6b03294}, + File = {/Users/loos/Zotero/storage/9L34S2JP/Ou_2016.pdf}, + Issn = {1089-5639, 1520-5215}, + Journal = {J. Phys. Chem. A}, + Language = {en}, + Month = jul, + Number = {26}, + Pages = {4514--4525}, + Shorttitle = {Comparison between {{{\emph{GW}}}} and {{Wave}}-{{Function}}-{{Based Approaches}}}, + Title = {Comparison between {{{\emph{GW}}}} and {{Wave}}-{{Function}}-{{Based Approaches}}: {{Calculating}} the {{Ionization Potential}} and {{Electron Affinity}} for {{1D Hubbard Chains}}}, + Volume = {120}, + Year = {2016}, + Bdsk-Url-1 = {https://dx.doi.org/10.1021/acs.jpca.6b03294}} + +@article{Ou_2018, + Author = {Ou, Qi and Subotnik, Joseph E.}, + Doi = {10.1021/acs.jctc.7b00246}, + File = {/Users/loos/Zotero/storage/2J2XU5F7/Ou_2017.pdf}, + Issn = {1549-9618, 1549-9626}, + Journal = {J. Chem. Theory Comput.}, + Language = {en}, + Month = feb, + Number = {2}, + Pages = {527--542}, + Shorttitle = {Comparison between the {{Bethe}}\textendash{}{{Salpeter Equation}} and {{Configuration Interaction Approaches}} for {{Solving}} a {{Quantum Chemistry Problem}}}, + Title = {Comparison between the {{Bethe}}\textendash{}{{Salpeter Equation}} and {{Configuration Interaction Approaches}} for {{Solving}} a {{Quantum Chemistry Problem}}: {{Calculating}} the {{Excitation Energy}} for {{Finite 1D Hubbard Chains}}}, + Volume = {14}, + Year = {2018}, + Bdsk-Url-1 = {https://dx.doi.org/10.1021/acs.jctc.7b00246}} + +@article{Romaniello_2009, + Author = {Romaniello, P. and Guyot, S. and Reining, L.}, + Doi = {10.1063/1.3249965}, + File = {/Users/loos/Zotero/storage/WCWVRT3M/Romaniello_2009.pdf}, + Issn = {0021-9606, 1089-7690}, + Journal = {J. Chem. Phys.}, + Language = {en}, + Month = oct, + Number = {15}, + Pages = {154111}, + Shorttitle = {The Self-Energy beyond {{GW}}}, + Title = {The Self-Energy beyond {{GW}}: {{Local}} and Nonlocal Vertex Corrections}, + Volume = {131}, + Year = {2009}, + Bdsk-Url-1 = {https://dx.doi.org/10.1063/1.3249965}} + +@article{Romaniello_2012, + Author = {Romaniello, Pina and Bechstedt, Friedhelm and Reining, Lucia}, + Date-Modified = {2018-04-14 07:32:24 +0000}, + Doi = {10.1103/PhysRevB.85.155131}, + File = {/Users/loos/Zotero/storage/PLHVA772/Romaniello_2012.pdf}, + Issn = {1098-0121, 1550-235X}, + Journal = {Phys. Rev. B}, + Language = {en}, + Month = apr, + Number = {15}, + Pages = {155131}, + Shorttitle = {Beyond the {{G W}} Approximation}, + Title = {Beyond the {{G W}} Approximation: {{Combining}} Correlation Channels}, + Volume = {85}, + Year = {2012}, + Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevB.85.155131}} + +@article{Tarantino_2017, + Author = {Tarantino, Walter and Romaniello, Pina and Berger, J. A. and Reining, Lucia}, + Date-Modified = {2018-04-14 07:27:03 +0000}, + Doi = {10.1103/PhysRevB.96.045124}, + File = {/Users/loos/Zotero/storage/PE5YGU7F/Romaniello_2017.pdf}, + Issn = {2469-9950, 2469-9969}, + Journal = {Phys. Rev. B}, + Language = {en}, + Month = jul, + Number = {4}, + Pages = {045124}, + Shorttitle = {Self-Consistent {{Dyson}} Equation and Self-Energy Functionals}, + Title = {Self-Consistent {{Dyson}} Equation and Self-Energy Functionals: {{An}} Analysis and Illustration on the Example of the {{Hubbard}} Atom}, + Volume = {96}, + Year = {2017}, + Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevB.96.045124}} + +@article{Rostgaard_2010, + Author = {Rostgaard, C. and Jacobsen, K. W. and Thygesen, K. S.}, + Date-Modified = {2018-04-14 07:23:37 +0000}, + Doi = {10.1103/PhysRevB.81.085103}, + File = {/Users/loos/Zotero/storage/4665L3NK/Rostgaard_2010.pdf}, + Issn = {1098-0121, 1550-235X}, + Journal = {Phys. Rev. B}, + Language = {en}, + Month = feb, + Number = {8}, + Pages = {085103}, + Title = {Fully Self-Consistent {{GW}} Calculations for Molecules}, + Volume = {81}, + Year = {2010}, + Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevB.81.085103}} + +@article{Takada_2001, + Author = {Takada, Yasutami}, + Doi = {10.1103/PhysRevLett.87.226402}, + File = {/Users/loos/Zotero/storage/N3BXLFU9/Takada_2001.pdf}, + Issn = {0031-9007, 1079-7114}, + Journal = {Phys. Rev. Lett.}, + Language = {en}, + Month = nov, + Number = {22}, + Title = {Inclusion of {{Vertex Corrections}} in the {{Self}}-{{Consistent Calculation}} of {{Quasiparticles}} in {{Metals}}}, + Volume = {87}, + Year = {2001}, + Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevLett.87.226402}} + +@article{Tempere_2002, + Author = {Tempere, J. and Silvera, I. F. and Devreese, J. T.}, + Doi = {10.1103/PhysRevB.65.195418}, + File = {/Users/loos/Zotero/storage/W8QP2SXG/Tempere_2002.pdf}, + Issn = {0163-1829, 1095-3795}, + Journal = {Phys. Rev. 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Sci.}, + Language = {en}, + Month = mar, + Number = {2}, + Pages = {123--142}, + Shorttitle = {Electron Propagator Theory}, + Title = {Electron Propagator Theory: An Approach to Prediction and Interpretation in Quantum Chemistry: {{Electron}} Propagator Theory}, + Volume = {3}, + Year = {2013}, + Bdsk-Url-1 = {https://dx.doi.org/10.1002/wcms.1116}} + +@article{Pavlyukh_2016, + Author = {Pavlyukh, Y. and Uimonen, A.-M. and Stefanucci, G. and {van Leeuwen}, R.}, + Doi = {10.1103/PhysRevLett.117.206402}, + File = {/Users/loos/Zotero/storage/CB7B27J4/Pavlyukh_2006.pdf}, + Issn = {0031-9007, 1079-7114}, + Journal = {Phys. Rev. Lett.}, + Language = {en}, + Month = nov, + Number = {20}, + Title = {Vertex {{Corrections}} for {{Positive}}-{{Definite Spectral Functions}} of {{Simple Metals}}}, + Volume = {117}, + Year = {2016}, + Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevLett.117.206402}} + +@article{Pavosevic_2017, + Author = {Pavo{\v s}evi{\'c}, Fabijan and Peng, Chong and Ortiz, J. V. and Valeev, Edward F.}, + Doi = {10.1063/1.5000916}, + File = {/Users/loos/Zotero/storage/CPREHP25/Pavosevic_2017.pdf}, + Issn = {0021-9606, 1089-7690}, + Journal = {J. Chem. Phys.}, + Language = {en}, + Month = sep, + Number = {12}, + Pages = {121101}, + Shorttitle = {Communication}, + Title = {Communication: {{Explicitly}} Correlated Formalism for Second-Order Single-Particle {{Green}}'s Function}, + Volume = {147}, + Year = {2017}, + Bdsk-Url-1 = {https://dx.doi.org/10.1063/1.5000916}} + +@article{Peng_2013, + Author = {Peng, Degao and Steinmann, Stephan N. and {van Aggelen}, Helen and Yang, Weitao}, + Doi = {10.1063/1.4820556}, + File = {/Users/loos/Zotero/storage/2PKBAZ2I/Peng_2013.pdf}, + Issn = {0021-9606, 1089-7690}, + Journal = {J. Chem. Phys.}, + Language = {en}, + Month = sep, + Number = {10}, + Pages = {104112}, + Title = {Equivalence of Particle-Particle Random Phase Approximation Correlation Energy and Ladder-Coupled-Cluster Doubles}, + Volume = {139}, + Year = {2013}, + Bdsk-Url-1 = {https://dx.doi.org/10.1063/1.4820556}} + +@article{Stan_2015, + Author = {Adrian Stan and Pina Romaniello and Santiago Rigamonti and Lucia Reining and J A Berger}, + Date-Modified = {2018-07-05 09:39:07 +0000}, + Doi = {10.1088/1367-2630/17/9/093045}, + Journal = {New J. Phys.}, + Number = {9}, + Pages = {093045}, + Title = {Unphysical and physical solutions in many-body theories: from weak to strong correlation}, + Volume = {17}, + Year = {2015}, + Bdsk-Url-1 = {https://doi.org/10.1088/1367-2630/17/9/093045}} + +@article{Tarantino_2018, + Author = {Walter Tarantino and Bernardo S Mendoza and Pina Romaniello and J A Berger and Lucia Reining}, + Journal = {J. Phys.: Condensed Matter}, + Number = {13}, + Pages = {135602}, + Title = {Many-body perturbation theory and non-perturbative approaches: screened interaction as the key ingredient}, + 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}, + Issue = {15}, + Journal = {Phys. Rev. Lett.}, + Month = {Apr}, + Numpages = {5}, + Pages = {156402}, + Publisher = {American Physical Society}, + Title = {Nonexistence of the Luttinger-Ward Functional and Misleading Convergence of Skeleton Diagrammatic Series for Hubbard-Like Models}, + Volume = {114}, + Year = {2015}, + Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevLett.114.156402}} + +@article{Schaefer_2013, + Author = {Sch\"afer, T. and Rohringer, G. and Gunnarsson, O. and Ciuchi, S. and Sangiovanni, G. and Toschi, A.}, + Doi = {10.1103/PhysRevLett.110.246405}, + Issue = {24}, + Journal = {Phys. Rev. Lett.}, + Month = {Jun}, + Numpages = {5}, + Pages = {246405}, + Publisher = {American Physical Society}, + Title = {Divergent Precursors of the Mott-Hubbard Transition at the Two-Particle Level}, + Volume = {110}, + Year = {2013}, + Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevLett.110.246405}} + +@article{Schaefer_2016, + Author = {Sch\"afer, T. and Ciuchi, S. and Wallerberger, M. and Thunstr\"om, P. and Gunnarsson, O. and Sangiovanni, G. and Rohringer, G. and Toschi, A.}, + Doi = {10.1103/PhysRevB.94.235108}, + Issue = {23}, + Journal = {Phys. Rev. B}, + Month = {Dec}, + Numpages = {25}, + Pages = {235108}, + Publisher = {American Physical Society}, + Title = {Nonperturbative landscape of the Mott-Hubbard transition: Multiple divergence lines around the critical endpoint}, + Url = {https://link.aps.org/doi/10.1103/PhysRevB.94.235108}, + Volume = {94}, + Year = {2016}, + Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.94.235108}, + Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevB.94.235108}} + +@article{Rossi_2015, + Abstract = {Recently, Kozik, Ferrero and Georges discovered numerically that for a family of fundamental models of interacting fermions, the self-energy ##IMG## [http://ej.iop.org/images/1751-8121/48/48/485202/jpaaa05f8ieqn1.gif] {${\rm{\Sigma }}[G]$} is a multi-valued functional of the fully dressed single-particle propagator G , and that the skeleton diagrammatic series ##IMG## [http://ej.iop.org/images/1751-8121/48/48/485202/jpaaa05f8ieqn2.gif] {${{\rm{\Sigma }}}_{{\rm{bold}}}[G]$} converges to the wrong branch above a critical interaction strength. We consider the zero space-time dimensional case, where the same mathematical phenomena appear from elementary algebra. We also find a similar phenomenology for the fully bold formalism built on the fully dressed single-particle propagator and pair propagator.}, + Author = {Riccardo Rossi and F{\'e}lix Werner}, + Date-Modified = {2018-07-18 13:15:08 +0000}, + Journal = {J. Phys. A: Math. Theor.}, + Number = {48}, + Pages = {485202}, + Title = {Skeleton series and multivaluedness of the self-energy functional in zero space-time dimensions}, + Url = {http://stacks.iop.org/1751-8121/48/i=48/a=485202}, + Volume = {48}, + Year = {2015}, + Bdsk-Url-1 = {http://stacks.iop.org/1751-8121/48/i=48/a=485202}} + +@article{Gunnarsson_2017, + Author = {Gunnarsson, O. and Rohringer, G. and Sch\"afer, T. and Sangiovanni, G. and Toschi, A.}, + Doi = {10.1103/PhysRevLett.119.056402}, + Issue = {5}, + Journal = {Phys. Rev. Lett.}, + Month = {Aug}, + Numpages = {5}, + Pages = {056402}, + Publisher = {American Physical Society}, + Title = {Breakdown of Traditional Many-Body Theories for Correlated Electrons}, + Url = {https://link.aps.org/doi/10.1103/PhysRevLett.119.056402}, + Volume = {119}, + Year = {2017}, + Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.119.056402}, + Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevLett.119.056402}} diff --git a/JCTC_revision/GW-srDFT.tex b/JCTC_revision/GW-srDFT.tex new file mode 100644 index 0000000..5a2d04b --- /dev/null +++ b/JCTC_revision/GW-srDFT.tex @@ -0,0 +1,698 @@ +\documentclass[aip,jcp,reprint,noshowkeys]{revtex4-1} +\usepackage{graphicx,dcolumn,bm,xcolor,microtype,multirow,amscd,amsmath,amssymb,amsfonts,physics,mhchem,longtable,wrapfig,txfonts} + +\usepackage{natbib} +\usepackage[extra]{tipa} +\bibliographystyle{achemso} +\AtBeginDocument{\nocite{achemso-control}} + +\usepackage{hyperref} +\hypersetup{ + colorlinks=true, + linkcolor=blue, + filecolor=blue, + urlcolor=blue, + citecolor=blue +} +\urlstyle{same} + +\newcommand{\alert}[1]{\textcolor{red}{#1}} +\definecolor{darkgreen}{HTML}{009900} +\usepackage[normalem]{ulem} +\newcommand{\titou}[1]{\textcolor{red}{#1}} +\newcommand{\jt}[1]{\textcolor{purple}{#1}} +\newcommand{\manu}[1]{\textcolor{darkgreen}{#1}} +\newcommand{\toto}[1]{\textcolor{brown}{#1}} +\newcommand{\trashPFL}[1]{\textcolor{red}{\sout{#1}}} +\newcommand{\trashJT}[1]{\textcolor{purple}{\sout{#1}}} +\newcommand{\trashMG}[1]{\textcolor{darkgreen}{\sout{#1}}} +\newcommand{\trashAS}[1]{\textcolor{brown}{\sout{#1}}} +\newcommand{\MG}[1]{\manu{(\underline{\bf MG}: #1)}} +\newcommand{\JT}[1]{\juju{(\underline{\bf JT}: #1)}} +\newcommand{\PFL}[1]{\titou{(\underline{\bf PFL}: #1)}} +\newcommand{\AS}[1]{\toto{(\underline{\bf AS}: #1)}} + +\newcommand{\mc}{\multicolumn} +\newcommand{\fnm}{\footnotemark} +\newcommand{\fnt}{\footnotetext} +\newcommand{\tabc}[1]{\multicolumn{1}{c}{#1}} +\newcommand{\SI}{\textcolor{blue}{supporting information}} +\newcommand{\QP}{\textsc{quantum package}} + +% methods +\newcommand{\HF}{\text{HF}} +\newcommand{\KS}{\text{KS}} +\newcommand{\GOWO}{$G_0W_0$} +\newcommand{\evGW}{ev$GW$} +\newcommand{\qsGW}{qs$GW$} +\newcommand{\GW}{$GW$} +\newcommand{\Hxc}{\text{Hxc}} +\newcommand{\Hx}{\text{Hx}} +\newcommand{\xc}{\text{xc}} + +\newcommand{\Bas}{\mathcal{B}} +\newcommand{\cD}{\mathcal{D}} +\newcommand{\Ne}{N} +\newcommand{\Nbas}{N_\text{bas}} + + +% energies +\newcommand{\Ec}{E_\text{c}} +\newcommand{\Egap}{E_\text{gap}} +\newcommand{\IP}{\text{IP}} +\newcommand{\EA}{\text{EA}} +\newcommand{\CBS}{\text{CBS}} +\newcommand{\LDA}{\text{LDA}} +\newcommand{\PBE}{\text{PBE}} +\newcommand{\PBEO}{\text{PBE0}} +\newcommand{\srLDA}{\text{srLDA}} +\newcommand{\srPBE}{\text{srPBE}} + +% orbital energies +\newcommand{\e}[1]{\epsilon_{#1}} +\newcommand{\eHF}[1]{\epsilon^\text{HF}_{#1}} +\newcommand{\eKS}[1]{\epsilon^\text{KS}_{#1}} +\newcommand{\eQP}[1]{\epsilon^\text{QP}_{#1}} +\newcommand{\eGOWO}[1]{\epsilon^\text{\GOWO}_{#1}} +\newcommand{\beGOWO}[1]{\Bar{\epsilon}^\text{\GOWO}_{#1}} +\newcommand{\Om}[1]{\Omega_{#1}} +\newcommand{\eHOMO}{\epsilon_\text{HOMO}} +\newcommand{\eLUMO}{\epsilon_\text{LUMO}} +\newcommand{\HOMO}{\text{HOMO}} +\newcommand{\LUMO}{\text{LUMO}} + +% Matrix elements and operators +\newcommand{\A}[1]{A_{#1}} +\newcommand{\B}[1]{B_{#1}} +\newcommand{\G}[2]{G_{#1}^{#2}} +\newcommand{\Gs}[1]{G_\text{f}^{#1}} +\newcommand{\F}[2]{F_{#1}^{#2}} +\newcommand{\Po}[2]{P_{#1}^{#2}} +\newcommand{\W}[2]{W_{#1}^{#2}} +\newcommand{\Wc}[1]{W_{#1}^\text{c}} +\newcommand{\vc}[2]{\varv_{#1}^{#2}} +\newcommand{\pot}[2]{v_{#1}^{#2}} +\newcommand{\Pot}[2]{V_{#1}^{#2}} +\newcommand{\bpot}[2]{\Bar{v}_{#1}^{#2}} +\newcommand{\bPot}[2]{\Bar{V}_{#1}^{#2}} +\newcommand{\Sig}[2]{\Sigma_{#1}^{#2}} +\newcommand{\bSig}[2]{\Bar{\Sigma}_{#1}^{#2}} +\newcommand{\Z}[1]{Z_{#1}} +\newcommand{\Gam}[2]{\Gamma_{#1}^{#2}} +\newcommand{\fc}{f_\text{c}} +\newcommand{\Vc}{V_\text{c}} +\newcommand{\vne}{v_\text{ne}} +\newcommand{\hT}{\Hat{T}} +\newcommand{\hWee}[1]{\Hat{W}_\text{ee}^{#1}} +\newcommand{\MO}[1]{\phi_{#1}} +\newcommand{\stat}[1]{\underset{#1}{\text{stat}}} + +% Matrices +\newcommand{\bOm}{\boldsymbol{\Omega}} +\newcommand{\bA}{\boldsymbol{A}} +\newcommand{\bB}{\boldsymbol{B}} +\newcommand{\bX}{\boldsymbol{X}} +\newcommand{\bY}{\boldsymbol{Y}} + + +% coordinates +\newcommand{\br}[1]{\mathbf{r}_{#1}} +\newcommand{\dbr}[1]{d\br{#1}} + +\newcommand{\n}[2]{n_{#1}^{#2}} +\newcommand{\E}[2]{E_{#1}^{#2}} +\newcommand{\bE}[2]{\Bar{E}_{#1}^{#2}} +\newcommand{\bEc}[1]{\Bar{E}_\text{c,md}^{#1}} +\newcommand{\bec}[1]{\Bar{e}^{#1}} +\newcommand{\wf}[2]{\Psi_{#1}^{#2}} +\newcommand{\hn}[2]{\Hat{n}_{#1}^{#2}} +\newcommand{\rsmu}[2]{\mu_{#1}^{#2}} + +% units +\newcommand{\IneV}[1]{#1 eV} +\newcommand{\InAU}[1]{#1 a.u.} +\newcommand{\InAA}[1]{#1 \AA} +\newcommand{\kcal}{kcal/mol} + +\newcommand{\ISCD}{Institut des Sciences du Calcul et des Donn\'ees, Sorbonne Universit\'e, Paris, France} +\newcommand{\LCPQ}{Laboratoire de Chimie et Physique Quantiques (UMR 5626), Universit\'e de Toulouse, CNRS, UPS, France} +\newcommand{\LCT}{Laboratoire de Chimie Th\'eorique (UMR 7616), Sorbonne Universit\'e, CNRS, Paris, France} +\newcommand{\IUF}{Institut Universitaire de France, Paris, France} + +\begin{document} + +\title{A Density-Based Basis-Set Incompleteness Correction for GW Methods} + +\author{Pierre-Fran\c{c}ois Loos} +\email[Corresponding author: ]{loos@irsamc.ups-tlse.fr} +\affiliation{\LCPQ} +\author{Barth\'el\'emy Pradines} +\affiliation{\LCT} +\affiliation{\ISCD} +\author{Anthony Scemama} +\affiliation{\LCPQ} +\author{Emmanuel Giner} +\affiliation{\LCT} +\author{Julien Toulouse} +\email[Corresponding author: ]{toulouse@lct.jussieu.fr} +\affiliation{\LCT} +\affiliation{\IUF} + +\begin{abstract} +\begin{wrapfigure}[12]{o}[-1.25cm]{0.4\linewidth} + \centering + \includegraphics[width=\linewidth]{TOC} +\end{wrapfigure} +Similar to other electron correlation methods, many-body perturbation theory methods based on Green functions, such as the so-called $GW$ approximation, suffer from the usual slow convergence of energetic properties with respect to the size of the one-electron basis set. +This displeasing feature is due to lack of explicit electron-electron terms modeling the infamous Kato electron-electron cusp and the correlation Coulomb hole around it. +Here, we propose a computationally efficient density-based basis set correction based on short-range correlation density functionals which significantly speeds up the convergence of energetics towards the complete basis set limit. +The performance of this density-based correction is illustrated by computing the ionization potentials of the twenty smallest atoms and molecules of the GW100 test set at the perturbative $GW$ (or $G_0W_0$) level using increasingly large basis sets. +We also compute the ionization potentials of the five canonical nucleobases (adenine, cytosine, thymine, guanine, and uracil) and show that, here again, a significant improvement is obtained. +\end{abstract} + +\maketitle + +%%%%%%%%%%%%%%%%%%%%%%%% +\section{Introduction} +\label{sec:intro} +%%%%%%%%%%%%%%%%%%%%%%%% +The purpose of many-body perturbation theory (MBPT) based on Green functions is to solve the formidable many-body problem by adding the electron-electron Coulomb interaction perturbatively starting from an independent-particle model. \cite{Martin_2016} +In this approach, the \textit{screening} of the Coulomb interaction is an essential quantity. \cite{Aryasetiawan_1998, Onida_2002, Reining_2017} + +The so-called {\GW} approximation is the workhorse of MBPT and has a long and successful history in the calculation of the electronic structure of solids. \cite{Aryasetiawan_1998, Onida_2002, Reining_2017} +{\GW} is getting increasingly popular in molecular systems \cite{Blase_2011, Faber_2011, Bruneval_2012, Bruneval_2015, Bruneval_2016, Bruneval_2016a, Boulanger_2014, Blase_2016, Li_2017, Hung_2016, Hung_2017, vanSetten_2015, vanSetten_2018, Ou_2016, Ou_2018, Faber_2014} thanks to efficient implementation relying on plane waves \cite{Marini_2009, Deslippe_2012, Maggio_2017} or local basis functions. \cite{Blase_2011, Blase_2018, Bruneval_2016, vanSetten_2013, Kaplan_2015, Kaplan_2016, Krause_2017, Caruso_2012, Caruso_2013, Caruso_2013a, Caruso_2013b} +The {\GW} approximation stems from the acclaimed Hedin's equations \cite{Hedin_1965} +\begin{subequations} +\begin{align} + \label{eq:G} + & \G{}{}(12) = \G{0}{}(12) + \int \G{0}{}(13) \Sig{}{}(34) \G{}{}(42) d(34), + \\ + \label{eq:Gamma} + & \Gam{}{}(123) = \delta(12) \delta(13) + \notag + \\ + & \qquad \qquad + \int \fdv{\Sig{}{}(12)}{\G{}{}(45)} \G{}{}(46) G(75) \Gam{}{}(673) d(4567), + \\ + \label{eq:P} + & \Po{}{}(12) = - i \int G(13) \Gam{}{}(324) G(41) d(34), + \\ + \label{eq:W} + & \W{}{}(12) = \vc{}{}(12) + \int \vc{}{}(13) \Po{}{}(34) \W{}{}(42) d(34), + \\ + \label{eq:Sig} + & \Sig{}{}(12) = i \int \G{}{}(13) \W{}{}(14) \Gam{}{}(324) d(34), +\end{align} +\end{subequations} +which connects the Green function $\G{}{}$, its non-interacting version $\G{0}{}$, the irreducible vertex function $\Gam{}{}$, the irreducible polarizability $\Po{}{}$, the dynamically-screened Coulomb interaction $\W{}{}$ +and the self-energy $\Sig{}{}$, where $\vc{}{}$ is the bare Coulomb interaction, $\delta(12)$ is the Dirac delta function \cite{NISTbook} and $1$ is a composite coordinate gathering space, spin, and time variables $(\br{1},\sigma_1,t_1)$. +Within the {\GW} approximation, one bypasses the calculation of the vertex corrections by setting +\begin{equation} + \label{eq:GW} + \Gam{}{}(123) \stackrel{GW}{\approx} \delta(12) \delta(13). +\end{equation} +Depending on the degree of self-consistency one is willing to perform, there exists several types of {\GW} calculations. \cite{Loos_2018} +The simplest and most popular variant of {\GW} is perturbative {\GW}, or {\GOWO}. \cite{Hybertsen_1985a, Hybertsen_1986} +Although obviously starting-point dependent, \cite{Bruneval_2013, Jacquemin_2016, Gui_2018} it has been widely used in the literature to study solids, atoms and molecules. \cite{Bruneval_2012, Bruneval_2013, vanSetten_2015, vanSetten_2018} +For finite systems such as atoms and molecules, partially \cite{Hybertsen_1986, Shishkin_2007, Blase_2011, Faber_2011} or fully self-consistent \cite{Caruso_2012, Caruso_2013, Caruso_2013a, Caruso_2013b} {\GW} methods have shown great promise. \cite{Ke_2011, Blase_2011, Faber_2011, Koval_2014, Hung_2016, Blase_2018, Jacquemin_2017} + +Similar to other electron correlation methods, MBPT methods suffer from the usual slow convergence of energetic properties with respect to the size of the one-electron basis set. +This can be tracked down to the lack of explicit electron-electron terms modeling the infamous electron-electron coalescence point (also known as Kato cusp \cite{Kato_1957}) and, more specifically, the Coulomb correlation hole around it. +Pioneered by Hylleraas \cite{Hylleraas_1929} in the 1930's and popularized in the 1990's by Kutzelnigg and coworkers \cite{Kutzelnigg_1985, Noga_1994, Kutzelnigg_1991} (and subsequently others \cite{Kong_2012, Hattig_2012, Tenno_2012a, Tenno_2012b, Gruneis_2017}), the so-called F12 methods overcome this slow convergence by employing geminal basis functions that closely resemble the correlation holes in electronic wave functions. +F12 methods are now routinely employed in computational chemistry and provide robust tools for electronic structure calculations where small basis sets may be used to obtain near complete basis set (CBS) limit accuracy. \cite{Tew_2007} + +The basis-set correction presented here follow a different route, and relies on the range-separated density-functional theory (RS-DFT) formalism to capture, thanks to a short-range correlation functional, the missing part of the short-range correlation effects. \cite{Giner_2018} +As shown in recent studies on both ground- and excited-state properties, \cite{Loos_2019, Giner_2019} similar to F12 methods, it significantly speeds up the convergence of energetics towards the CBS limit while avoiding the usage of the large auxiliary basis sets that are used in F12 methods to avoid the numerous three- and four-electron integrals. \cite{Kong_2012, Hattig_2012, Tenno_2012a, Tenno_2012b, Gruneis_2017, Barca_2016, Barca_2017, Barca_2018} + +Explicitly correlated F12 correction schemes have been derived for second-order Green function methods (GF2) \cite{SzaboBook, Casida_1989, Casida_1991, Stefanucci_2013, Ortiz_2013, Phillips_2014, Phillips_2015, Rusakov_2014, Rusakov_2016, Hirata_2015, Hirata_2017, Loos_2018} by Ten-no and coworkers \cite{Ohnishi_2016, Johnson_2018} and Valeev and coworkers. \cite{Pavosevic_2017, Teke_2019} +However, to the best of our knowledge, a F12-based correction for {\GW} has not been designed yet. + +In the present manuscript, we illustrate the performance of the density-based basis set correction developed in Refs.~\onlinecite{Giner_2018, Loos_2019, Giner_2019} on ionization potentials obtained within {\GOWO}. +Note that the present basis set correction can be straightforwardly applied to other properties (\textit{e.g.}, electron affinities and fundamental gap), as well as other flavors of (self-consistent) {\GW} or Green function-based methods, such as GF2 (and its higher-order variants). + +The paper is organized as follows. +In Sec.~\ref{sec:theory}, we provide details about the theory behind the present basis set correction and its adaptation to {\GW} methods. +Results for a large collection of molecular systems are reported and discussed in Sec.~\ref{sec:results}. +Finally, we draw our conclusions in Sec.~\ref{sec:conclusion}. +Unless otherwise stated, atomic units are used throughout. + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{Theory} +\label{sec:theory} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsection{MBPT with DFT basis set correction} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +Following Ref.~\onlinecite{Giner_2018}, we start by defining, for a $\Ne$-electron system with nuclei-electron potential $\vne(\br{})$, the approximate ground-state energy for one-electron densities $\n{}{}$ which are ``representable'' in a finite basis set $\Bas$ +\begin{equation} + \E{0}{\Bas} = \min_{\n{}{} \in \cD^\Bas} \qty{ \F{}{}[n] + \int \vne(\br{}) \n{}{}(\br{}) \dbr{} }, +\label{eq:E0B} +\end{equation} +where $\cD^\Bas$ is the set of $\Ne$-representable densities which can be extracted from a wave function $\wf{}{\Bas}$ expandable in the Hilbert space generated by $\Bas$. +In this expression, +\begin{equation} + \F{}{}[n] = \min_{\wf{}{} \rightsquigarrow \n{}{}} \mel*{\wf{}{}}{\hT + \hWee{}}{\wf{}{}} +\end{equation} +is the exact Levy-Lieb universal density functional, \cite{Levy_1979, Levy_1982, Lieb_1983} where the notation $\wf{}{} \rightsquigarrow \n{}{}$ in Eq.~\eqref{eq:E0B} states that $\wf{}{}$ yields the one-electron density $\n{}{}$. +$\hT$ and $\hWee{}$ are the kinetic and electron-electron interaction operators. +The exact Levy-Lieb universal density functional is then decomposed as +\begin{equation} + \F{}{}[\n{}{}] = \F{}{\Bas}[\n{}{}] + \bE{}{\Bas}[\n{}{}], +\label{eq:Fn} +\end{equation} +where $\F{}{\Bas}[\n{}{}]$ is the Levy-Lieb density functional with wave functions $\wf{}{\Bas}$ expandable in the Hilbert space generated by $\Bas$ +\begin{equation} + \F{}{\Bas}[\n{}{}] = \min_{\wf{}{\Bas} \rightsquigarrow \n{}{}} \mel*{\wf{}{\Bas}}{ \hT + \hWee{}}{\wf{}{\Bas}}, +\end{equation} +and $\bE{}{\Bas}[\n{}{}]$ is the complementary basis-correction density functional. \cite{Giner_2018} +In the present work, instead of using wave-function methods for calculating $\F{}{\Bas}[\n{}{}]$, we use Green-function methods. +We assume that there exists a functional $\Omega^\Bas[\G{}{\Bas}]$ of $\Ne$-representable one-electron Green functions $\G{}{\Bas}(\br{},\br{}',\omega)$ representable in the basis set $\Bas$ and yielding the density $\n{}{}$ which gives $\F{}{\Bas}[\n{}{}]$ at a stationary point +\begin{equation} + \F{}{\Bas}[\n{}{}] = \stat{\G{}{\Bas} \rightsquigarrow \n{}{}} \Omega^\Bas[\G{}{\Bas}]. +\label{eq:FBn} +\end{equation} +The reason why we use a stationary condition rather than a minimization condition is that only a stationary property is generally known for functionals of the Green function. +For example, we can choose for $\Omega^\Bas[\G{}{}]$ a Klein-like energy functional (see, \textit{e.g.}, Refs.~\onlinecite{Stefanucci_2013, Martin_2016, Dahlen_2005, Dahlen_2005a, Dahlen_2006}) +\begin{equation} + \Omega^\Bas[\G{}{}] = \Tr[\ln( - \G{}{} ) ] - \Tr[ (\Gs{\Bas})^{-1} \G{}{} - 1 ] + \Phi_\Hxc^\Bas[\G{}{}], +\label{eq:OmegaB} +\end{equation} +where $(\Gs{\Bas})^{-1}$ is the projection into $\Bas$ of the inverse free-particle Green function +\begin{equation} + (\Gs{})^{-1}(\br{},\br{}',\omega)= \qty(\omega + \frac{\nabla^2_{\br{}}}{2} ) \delta(\br{}-\br{}'), +\end{equation} +and we have introduced the trace +\begin{equation} + \Tr[A B] = \int_{-\infty}^{+\infty} \frac{d\omega}{2\pi i} e^{i \omega 0^+} \iint A(\br{},\br{}',\omega) B(\br{}',\br{}{},\omega) \dbr{} \dbr{}'. +\end{equation} +In Eq.~\eqref{eq:OmegaB}, $\Phi_\Hxc^\Bas[\G{}{}]$ is a Hartree-exchange-correlation ($\Hxc$) functional of the Green function such that its functional derivatives yields the $\Hxc$ self-energy in the basis +\begin{equation} + \fdv{\Phi_\Hxc^\Bas[\G{}{}]}{\G{}{}(\br{},\br{}',\omega)} = \Sig{\Hxc}{\Bas}[\G{}{}](\br{},\br{}',\omega). +\end{equation} +Inserting Eqs.~\eqref{eq:Fn} and \eqref{eq:FBn} into Eq.~\eqref{eq:E0B}, we finally arrive at +\begin{equation} + \E{0}{\Bas} = \stat{\G{}{\Bas}} \qty{ \Omega^\Bas[\G{}{\Bas}] + \int \vne(\br{}) \n{\G{}{\Bas}}{}(\br{}) \dbr{} + \bE{}{\Bas}[\n{\G{}{\Bas}}{}] }, +\label{eq:E0BGB} +\end{equation} +where the stationary point is searched over $\Ne$-representable one-electron Green functions $\G{}{\Bas}(\br{},\br{}',\omega)$ representable in the basis set $\Bas$. + +The stationary condition from Eq.~\eqref{eq:E0BGB} is +\begin{multline} + \fdv{}{\G{}{\Bas}} \Bigg( \Omega^\Bas[\G{}{\Bas}] + \int \vne(\br{}) \n{\G{}{\Bas}}{}(\br{}) \dbr{} + \bE{}{\Bas}[\n{\G{}{\Bas}}{}] + \\ + - \lambda \int \n{\G{}{\Bas}}{}(\br{}) \dbr{} \Bigg) = 0, +\label{eq:stat} +\end{multline} +where $\lambda$ is the chemical potential (enforcing the electron number). +It leads the following Dyson equation +\begin{equation} + (\G{}{\Bas})^{-1} = (\G{0}{\Bas})^{-1}- \Sig{\Hxc}{\Bas}[\G{}{\Bas}]- \bSig{}{\Bas}[\n{\G{}{\Bas}}{}], +\label{eq:Dyson} +\end{equation} +where $(\G{0}{\Bas})^{-1}$ is the basis projection of the inverse non-interacting Green function with potential $\vne(\br{})$, \textit{i.e.}, +\begin{equation} + (\G{0}{})^{-1}(\br{},\br{}',\omega)= \qty(\omega + \frac{\nabla_{\br{}}^2}{2} - \vne(\br{}) + \lambda) \delta(\br{}-\br{}'), +\end{equation} +and $\bSig{}{\Bas}$ is a frequency-independent local self-energy coming from the functional derivative of the complementary basis-correction density functional +\begin{equation} + \bSig{}{\Bas}[\n{}{}](\br{},\br{}') = \bpot{}{\Bas}[\n{}{}](\br{}) \delta(\br{}-\br{}'), +\end{equation} +with $\bpot{}{\Bas}[\n{}{}](\br{}) = \delta \bE{}{\Bas}[\n{}{}] / \delta \n{}{}(\br{})$. +This is found from Eq.~\eqref{eq:stat} by using the chain rule, +\begin{equation} + \pdv{\bE{}{\Bas}[\n{}{}]}{\G{}{}(\br{},\br{}',\omega)} = \int \pdv{\bE{}{\Bas}[\n{}{}]}{\n{}{}(\br{}'')} \frac{\delta \n{}{}(\br{}'')}{\delta \G{}{}(\br{},\br{}',\omega)} \dbr{}'', +\end{equation} +and +\begin{equation} + \n{}{}(\br{}) = \int_{-\infty}^{+\infty} \frac{d\omega}{2\pi i} e^{i \omega 0^+} \G{}{}(\br{},\br{},\omega). +\end{equation} +The solution of the Dyson equation \eqref{eq:Dyson} gives the Green function $\G{}{\Bas}(\br{},\br{}',\omega)$ which is not exact (even using the exact complementary basis-correction density functional $\bSig{}{\Bas}[\n{}{}]$) but should converge more rapidly with the basis set thanks to the presence of the basis-set correction $\bSig{}{\Bas}$. +Of course, in the CBS limit, the basis-set correction vanishes and the Green function becomes exact, \textit{i.e.}, +\begin{align} + \lim_{\Bas \to \CBS} \bSig{}{\Bas} & = 0, + & + \lim_{\Bas \to \CBS} \G{}{\Bas} & = \G{}{}. +\end{align} + +The Dyson equation \eqref{eq:Dyson} can also be written with an arbitrary reference +\begin{equation} + (\G{}{\Bas})^{-1} = (\G{\text{ref}}{\Bas})^{-1} - \qty( \Sig{\Hxc}{\Bas}[\G{}{\Bas}]- \Sig{\text{ref}}{\Bas} ) - \bSig{}{\Bas}[\n{\G{}{\Bas}}{}], +\end{equation} +where $(\G{\text{ref}}{\Bas})^{-1} = (\G{0}{\Bas})^{-1} - \Sig{\text{ref}}{\Bas}$. +For example, if the reference is Hartree-Fock ($\HF$), $\Sig{\text{ref}}{\Bas}(\br{},\br{}') = \Sig{\Hx}{\Bas}(\br{},\br{}')$ is the $\HF$ nonlocal self-energy, and if the reference is Kohn-Sham ($\KS$), $\Sig{\text{ref}}{\Bas}(\br{},\br{}') = \pot{\Hxc}{\Bas}(\br{}) \delta(\br{}-\br{}')$ is the local $\Hxc$ potential. + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsection{The {\GW} Approximation} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +In this subsection, we provide the minimal set of equations required to describe {\GOWO}. +More details can be found, for example, in Refs.~\citenum{vanSetten_2013, Kaplan_2016, Bruneval_2016}. +For the sake of simplicity, we only give the equations for closed-shell systems with a $\KS$ single-particle reference. +The one-electron energies $\e{p}$ and their corresponding (real-valued) orbitals $\MO{p}(\br{})$ (which defines the basis set $\Bas$) are then $\KS$ energies and orbitals. + +Within the {\GW} approximation, the correlation part of the self-energy reads +\begin{equation} +\label{eq:SigC} +\begin{split} + \Sig{\text{c},p}{\Bas}(\omega) + & = \mel*{\MO{p}}{\Sig{\text{c}}{\Bas}(\omega)}{\MO{p}} + \\ + & = 2 \sum_{i}^\text{occ} \sum_{m} \frac{[pi|m]^2}{\omega - \e{i} + \Om{m} - i \eta} + \\ + & + 2 \sum_{a}^\text{virt} \sum_{m} \frac{[pa|m]^2}{\omega - \e{a} - \Om{m} + i \eta}, +\end{split} +\end{equation} +where $m$ labels excited states and $\eta$ is a positive infinitesimal. +The screened two-electron integrals +\begin{equation} + [pq|m] = \sum_{ia} (pq|ia) (\bX_m+\bY_m)_{ia} +\end{equation} +are obtained via the contraction of the bare two-electron integrals \cite{Gill_1994} +\begin{equation} + (pq|rs) = \iint \frac{\MO{p}(\br{}) \MO{q}(\br{}) \MO{r}(\br{}') \MO{s}(\br{}')}{\abs*{\br{} - \br{}'}} \dbr{} \dbr{}', +\end{equation} +and the transition densities $(\bX_m+\bY_m)_{ia}$ originating from a (direct) random-phase approximation (RPA) calculation \cite{Casida_1995, Dreuw_2005} +\begin{equation} +\label{eq:LR} + \begin{pmatrix} + \bA & \bB \\ + -\bB & -\bA \\ + \end{pmatrix} + \begin{pmatrix} + \bX_m \\ + \bY_m \\ + \end{pmatrix} + = + \Om{m} + \begin{pmatrix} + \bX_m \\ + \bY_m \\ + \end{pmatrix}, +\end{equation} +with +\begin{align} +\label{eq:RPA} + A_{ia,jb} & = \delta_{ij} \delta_{ab} (\e{a} - \e{i}) + 2 (ia|bj), + & + B_{ia,jb} & = 2 (ia|jb), +\end{align} +and $\delta_{pq}$ is the Kronecker delta. \cite{NISTbook} +Equation \eqref{eq:LR} also provides the RPA neutral excitation energies $\Om{m}$ which represent the poles of the screened Coulomb interaction $\W{}{}(\omega)$. + +The {\GOWO} quasiparticle energies $\eGOWO{p}$ are provided by the solution of the (non-linear) quasiparticle equation \cite{Hybertsen_1985a, vanSetten_2013, Veril_2018} +\begin{equation} +\label{eq:QP-G0W0} + \omega = \e{p} - \Pot{\xc,p}{\Bas} + \Sig{\text{x},p}{\Bas} + \Re[\Sig{\text{c},p}{\Bas}(\omega)]. +\end{equation} +with the largest renormalization weight (or factor) +\begin{equation} +\label{eq:Z} + \Z{p} = \qty[ 1 - \left. \pdv{\Re[\Sig{\text{c},p}{\Bas}(\omega)]}{\omega} \right|_{\omega = \e{p}}]^{-1}. +\end{equation} +Because of sum rules, \cite{Martin_1959, Baym_1961, Baym_1962, vonBarth_1996} the other solutions, known as satellites, share the remaining weight. +In Eq.~\eqref{eq:QP-G0W0}, $\Sig{\text{x},p}{\Bas} = \mel*{\MO{p}}{\Sig{\text{x}}{\Bas}}{\MO{p}}$ is the (static) exchange part of the self-energy and +\begin{equation} + \Pot{\xc,p}{\Bas} = \int \MO{p}(\br{}) \pot{\xc}{\Bas}(\br{}) \MO{p}(\br{}) \dbr{}. +\end{equation} +In particular, the ionization potential (IP) and electron affinity (EA) are extracted thanks to the following relationships: \cite{SzaboBook} +\begin{align} + \IP & = -\eGOWO{\HOMO}, + & + \EA & = -\eGOWO{\LUMO}, +\end{align} +where $\eGOWO{\HOMO}$ and $\eGOWO{\LUMO}$ are the HOMO and LUMO orbital energies, respectively. + +%%%%%%%%%%%%%%%%%%%%%%%% +\subsection{Short-range correlation functionals} +\label{sec:srDFT} +%%%%%%%%%%%%%%%%%%%%%%%% + +The frequency-independent local self-energy $\bSig{}{\Bas}[\n{}{}](\br{},\br{}') = \bpot{}{\Bas}[\n{}{}](\br{}) \delta(\br{}-\br{}')$ originates from the functional derivative of complementary basis-correction density functionals $\bpot{}{\Bas}[\n{}{}](\br{}) = \delta \bE{}{\Bas}[\n{}{}] / \delta \n{}{}(\br{})$. +Here, we employ two types of complementary, short-range correlation functionals $\bE{}{\Bas}[\n{}{}]$: a short-range local-density approximation ($\srLDA$) functional with multideterminant reference \cite{Toulouse_2005, Paziani_2006} and a short-range Perdew-Burke-Ernzerhof ($\srPBE$) correlation functional \cite{Ferte_2019, Loos_2019} which interpolates between the usual PBE functional \cite{Perdew_1996} at $\mu = 0$ and the exact large-$\mu$ behavior~\cite{Toulouse_2004, Gori-Giorgi_2006, Paziani_2006} using the on-top pair density from the uniform-electron gas. \cite{Loos_2019} +Additionally to the one-electron density calculated from the HF or KS orbitals, these RS-DFT functionals require a range-separation function $\rsmu{}{\Bas}(\br{})$ which automatically adapts to the spatial inhomogeneity of the basis-set incompleteness error and is computed using the HF or KS opposite-spin pair-density matrix in the basis set $\Bas$. +We refer the interested reader to Refs.~\onlinecite{Giner_2018, Loos_2019, Giner_2019} where our procedure is thoroughly detailed and the explicit expressions of these two short-range correlation functionals are provided. + +The basis set corrected {\GOWO} quasiparticle energies are thus given by +\begin{equation} + \beGOWO{p} = \eGOWO{p} + \bPot{p}{\Bas} + \label{eq:QP-corrected} +\end{equation} +with +\begin{equation} +\begin{split} + \bPot{p}{\Bas} + & = \int \MO{p}(\br{}) \bSig{}{\Bas}[\n{}{}](\br{},\br{}') \MO{p}(\br{}') \dbr{} \dbr{}' + \\ + & = \int \MO{p}(\br{}) \bpot{}{\Bas}[\n{}{}](\br{}) \MO{p}(\br{}) \dbr{}. +\end{split} +\end{equation} +As evidenced by Eq.~\eqref{eq:QP-corrected}, the present basis set correction is a non-self-consistent, \textit{post}-{\GW} correction. +Although outside the scope of this study, various other strategies can be potentially designed, for example, within linearized {\GOWO} or self-consistent {\GW} calculations. + +%%% TABLE I %%% +\begin{squeezetable} +\begin{table*} +\caption{ +IPs (in eV) of the 20 smallest molecules of the GW100 set computed at the {\GOWO}@HF level of theory with various basis sets and corrections. +The mean absolute deviation (MAD), root-mean-square deviation (RMSD), and maximum deviation (MAX) with respect to the {\GOWO}@HF/CBS values are also reported. +\label{tab:GW20_HF} +} + \begin{ruledtabular} + \begin{tabular}{lccccccccccccc} + & \mc{4}{c}{{\GOWO}@HF} & \mc{4}{c}{{\GOWO}@HF+srLDA} & \mc{4}{c}{{\GOWO}@HF+srPBE} & \mc{1}{c}{{\GOWO}@HF} \\ + \cline{2-5} \cline{6-9} \cline{10-13} \cline{14-14} + Mol. & cc-pVDZ & cc-pVTZ & cc-pVQZ & cc-pV5Z & cc-pVDZ & cc-pVTZ & cc-pVQZ & cc-pV5Z & cc-pVDZ & cc-pVTZ & cc-pVQZ & cc-pV5Z & CBS \\ + \hline + \ce{He} & 24.36 & 24.57 & 24.67 & 24.72 & 24.63 & 24.69 & 24.73 & 24.74 & 24.66 & 24.69 & 24.72 & 24.74 & 24.75 \\ + \ce{Ne} & 20.87 & 21.39 & 21.63 & 21.73 & 21.38 & 21.67 & 21.80 & 21.84 & 21.56 & 21.73 & 21.81 & 21.83 & 21.82 \\ + \ce{H2} & 16.25 & 16.48 & 16.56 & 16.58 & 16.42 & 16.54 & 16.58 & 16.60 & 16.42 & 16.53 & 16.58 & 16.60 & 16.61 \\ + \ce{Li2} & 5.23 & 5.34 & 5.39 & 5.42 & 5.31 & 5.37 & 5.41 & 5.43 & 5.28 & 5.37 & 5.41 & 5.43 & 5.44 \\ + \ce{LiH} & 7.96 & 8.16 & 8.25 & 8.28 & 8.13 & 8.23 & 8.28 & 8.30 & 8.10 & 8.21 & 8.27 & 8.30 & 8.31 \\ + \ce{HF} & 15.54 & 16.16 & 16.42 & 16.52 & 16.01 & 16.41 & 16.57 & 16.61 & 16.15 & 16.45 & 16.57 & 16.61 & 16.62 \\ + \ce{Ar} & 15.40 & 15.72 & 15.93 & 16.08 & 15.85 & 15.98 & 16.09 & 16.18 & 15.91 & 15.99 & 16.08 & 16.17 & 16.15 \\ + \ce{H2O} & 12.16 & 12.79 & 13.04 & 13.14 & 12.58 & 13.01 & 13.16 & 13.21 & 12.68 & 13.03 & 13.16 & 13.20 & 13.23 \\ + \ce{LiF} & 10.75 & 11.35 & 11.59 & 11.70 & 11.21 & 11.60 & 11.73 & 11.79 & 11.34 & 11.63 & 11.73 & 11.78 & 11.79 \\ + \ce{HCl} & 12.40 & 12.77 & 12.96 & 13.05 & 12.79 & 12.99 & 13.10 & 13.13 & 12.83 & 12.99 & 13.09 & 13.12 & 13.12 \\ + \ce{BeO} & 9.47 & 9.77 & 9.98 & 10.09 & 9.85 & 9.97 & 10.09 & 10.15 & 9.93 & 9.98 & 10.08 & 10.15 & 10.16 \\ + \ce{CO} & 14.66 & 15.02 & 15.17 & 15.24 & 14.99 & 15.18 & 15.26 & 15.29 & 15.04 & 15.18 & 15.25 & 15.29 & 15.30 \\ + \ce{N2} & 15.87 & 16.31 & 16.48 & 16.56 & 16.22 & 16.50 & 16.59 & 16.62 & 16.30 & 16.50 & 16.58 & 16.62 & 16.62 \\ + \ce{CH4} & 14.43 & 14.74 & 14.86 & 14.90 & 14.69 & 14.85 & 14.91 & 14.93 & 14.73 & 14.85 & 14.90 & 14.93 & 14.95 \\ + \ce{BH3} & 13.35 & 13.64 & 13.74 & 13.78 & 13.57 & 13.73 & 13.78 & 13.80 & 13.58 & 13.72 & 13.78 & 13.80 & 13.82 \\ + \ce{NH3} & 10.59 & 11.13 & 11.32 & 11.40 & 10.93 & 11.30 & 11.41 & 11.45 & 10.99 & 11.30 & 11.41 & 11.44 & 11.47 \\ + \ce{BF} & 11.08 & 11.30 & 11.38 & 11.42 & 11.29 & 11.40 & 11.43 & 11.45 & 11.29 & 11.38 & 11.42 & 11.45 & 11.45 \\ + \ce{BN} & 11.35 & 11.69 & 11.85 & 11.92 & 11.67 & 11.85 & 11.94 & 11.98 & 11.72 & 11.85 & 11.93 & 11.97 & 11.98 \\ + \ce{SH2} & 10.10 & 10.49 & 10.65 & 10.72 & 10.44 & 10.67 & 10.76 & 10.78 & 10.45 & 10.66 & 10.74 & 10.77 & 10.78 \\ + \ce{F2} & 15.93 & 16.30 & 16.51 & 16.61 & 16.42 & 16.56 & 16.67 & 16.71 & 16.58 & 16.61 & 16.67 & 16.71 & 16.69 \\ + \hline + MAD & 0.66 & 0.30 & 0.13 & 0.06 & 0.33 & 0.13 & 0.04 & 0.01 & 0.27 & 0.12 & 0.04 & 0.01 \\ + RMSD & 0.71 & 0.32 & 0.14 & 0.06 & 0.37 & 0.14 & 0.04 & 0.01 & 0.30 & 0.13 & 0.05 & 0.01 \\ + MAX & 1.08 & 0.46 & 0.22 & 0.10 & 0.65 & 0.22 & 0.07 & 0.03 & 0.54 & 0.20 & 0.08 & 0.03 \\ + \end{tabular} + \end{ruledtabular} +\end{table*} +\end{squeezetable} + +%%% TABLE II %%% +\begin{squeezetable} +\begin{table*} +\caption{ +IPs (in eV) of the 20 smallest molecules of the GW100 set computed at the {\GOWO}@PBE0 level of theory with various basis sets and corrections. +The mean absolute deviation (MAD), root-mean-square deviation (RMSD), and maximum deviation (MAX) with respect to the {\GOWO}@PBE0/CBS values are also reported. +\label{tab:GW20_PBE0} +} + \begin{ruledtabular} + \begin{tabular}{lccccccccccccc} + & \mc{4}{c}{{\GOWO}@PBE0} & \mc{4}{c}{{\GOWO}@PBE0+srLDA} & \mc{4}{c}{{\GOWO}@PBE0+srPBE} & \mc{1}{c}{{\GOWO}@PBE0}\\ + \cline{2-5} \cline{6-9} \cline{10-13} \cline{14-14} + Mol. & cc-pVDZ & cc-pVTZ & cc-pVQZ & cc-pV5Z & cc-pVDZ & cc-pVTZ & cc-pVQZ & cc-pV5Z & cc-pVDZ & cc-pVTZ & cc-pVQZ & cc-pV5Z & CBS \\ + \hline + \ce{He} & 23.99 & 23.98 & 24.03 & 24.04 & 24.26 & 24.09 & 24.09 & 24.07 & 24.29 & 24.10 & 24.08 & 24.07 & 24.06 \\ + \ce{Ne} & 20.35 & 20.88 & 21.05 & 21.05 & 20.86 & 21.16 & 21.22 & 21.16 & 21.05 & 21.22 & 21.23 & 21.15 & 21.12 \\ + \ce{H2} & 15.98 & 16.13 & 16.19 & 16.21 & 16.16 & 16.20 & 16.22 & 16.22 & 16.16 & 16.19 & 16.22 & 16.22 & 16.23 \\ + \ce{Li2} & 5.15 & 5.24 & 5.28 & 5.31 & 5.23 & 5.28 & 5.30 & 5.32 & 5.21 & 5.27 & 5.30 & 5.32 & 5.32 \\ + \ce{LiH} & 7.32 & 7.49 & 7.56 & 7.59 & 7.48 & 7.55 & 7.59 & 7.61 & 7.45 & 7.54 & 7.58 & 7.61 & 7.62 \\ + \ce{HF} & 14.95 & 15.61 & 15.82 & 15.85 & 15.41 & 15.85 & 15.97 & 15.94 & 15.56 & 15.89 & 15.97 & 15.93 & 15.94 \\ + \ce{Ar} & 14.93 & 15.25 & 15.42 & 15.50 & 15.37 & 15.50 & 15.58 & 15.60 & 15.44 & 15.52 & 15.58 & 15.59 & 15.56 \\ + \ce{H2O} & 11.53 & 12.21 & 12.43 & 12.47 & 11.95 & 12.43 & 12.55 & 12.54 & 12.05 & 12.45 & 12.55 & 12.54 & 12.56 \\ + \ce{LiF} & 9.89 & 10.60 & 10.82 & 10.94 & 10.35 & 10.84 & 10.96 & 11.02 & 10.48 & 10.87 & 10.96 & 11.02 & 11.02 \\ + \ce{HCl} & 11.96 & 12.34 & 12.50 & 12.57 & 12.35 & 12.56 & 12.64 & 12.65 & 12.39 & 12.56 & 12.63 & 12.64 & 12.63 \\ + \ce{BeO} & 9.16 & 9.44 & 9.63 & 9.74 & 9.53 & 9.64 & 9.74 & 9.80 & 9.61 & 9.65 & 9.74 & 9.79 & 9.80 \\ + \ce{CO} & 13.67 & 14.02 & 14.13 & 14.18 & 14.00 & 14.18 & 14.22 & 14.23 & 14.05 & 14.18 & 14.22 & 14.23 & 14.22 \\ + \ce{N2} & 14.84 & 15.30 & 15.44 & 15.50 & 15.22 & 15.50 & 15.55 & 15.56 & 15.31 & 15.51 & 15.54 & 15.55 & 15.55 \\ + \ce{CH4} & 13.85 & 14.15 & 14.27 & 14.30 & 14.11 & 14.27 & 14.32 & 14.33 & 14.15 & 14.27 & 14.32 & 14.33 & 14.35 \\ + \ce{BH3} & 12.87 & 13.13 & 13.22 & 13.26 & 13.09 & 13.23 & 13.27 & 13.28 & 13.10 & 13.22 & 13.26 & 13.28 & 13.29 \\ + \ce{NH3} & 9.96 & 10.56 & 10.73 & 10.75 & 10.31 & 10.72 & 10.82 & 10.80 & 10.37 & 10.72 & 10.81 & 10.79 & 10.82 \\ + \ce{BF} & 10.66 & 10.87 & 10.92 & 10.94 & 10.88 & 10.96 & 10.97 & 10.97 & 10.88 & 10.95 & 10.96 & 10.97 & 10.96 \\ + \ce{BN} & 11.07 & 11.40 & 11.54 & 11.60 & 11.40 & 11.56 & 11.63 & 11.65 & 11.45 & 11.56 & 11.62 & 11.65 & 11.65 \\ + \ce{SH2} & 9.69 & 10.10 & 10.25 & 10.30 & 10.03 & 10.28 & 10.35 & 10.36 & 10.04 & 10.27 & 10.34 & 10.35 & 10.36 \\ + \ce{F2} & 14.92 & 15.38 & 15.57 & 15.64 & 15.41 & 15.65 & 15.73 & 15.74 & 15.57 & 15.69 & 15.73 & 15.73 & 15.71 \\ + \hline + MAD & 0.60 & 0.24 & 0.10 & 0.05 & 0.29 & 0.07 & 0.02 & 0.01 & 0.23 & 0.07 & 0.03 & 0.01 \\ + RMSD & 0.66 & 0.26 & 0.11 & 0.06 & 0.33 & 0.08 & 0.03 & 0.02 & 0.27 & 0.08 & 0.04 & 0.01 \\ + MAX & 1.12 & 0.42 & 0.19 & 0.09 & 0.67 & 0.18 & 0.09 & 0.04 & 0.54 & 0.15 & 0.10 & 0.03 \\ + \end{tabular} + \end{ruledtabular} +\end{table*} +\end{squeezetable} + +%%%%%%%%%%%%%%%%%%%%%%%% +\section{Computational details} +\label{sec:compdetails} +%%%%%%%%%%%%%%%%%%%%%%%% +All the geometries have been extracted from the GW100 set. \cite{vanSetten_2015} +Unless otherwise stated, all the {\GOWO} calculations have been performed with the MOLGW software developed by Bruneval and coworkers. \cite{Bruneval_2016a} +The HF, PBE, and PBE0 calculations as well as the srLDA and srPBE basis set corrections have been computed with Quantum Package, \cite{QP2} which by default uses the SG-2 quadrature grid for the numerical integrations. +Frozen-core (FC) calculations are systematically performed. +The FC density-based basis set correction~\cite{Loos_2019} is used consistently with the FC approximation in the {\GOWO} calculations. +The {\GOWO} quasiparticle energies have been obtained ``graphically'', \textit{i.e.}, by solving the non-linear, frequency-dependent quasiparticle equation \eqref{eq:QP-G0W0} (without linearization). +Moreover, the infinitesimal $\eta$ in Eq.~\eqref{eq:SigC} has been set to zero. + +Compared to the conventional $\order*{\Nbas^6}$ computational cost of {\GW} (where $\Nbas$ is the number of basis functions), the present basis set correction represents a marginal additional cost as further discussed in Refs.~\onlinecite{Loos_2019, Giner_2019}. +Note, however, that the formal $\order*{\Nbas^6}$ cost of {\GW} can be significantly reduced thanks to resolution-of-the-identity techniques \cite{vanSetten_2013, Bruneval_2016, Duchemin_2017} and other tricks. \cite{Rojas_1995, Duchemin_2019} + +%%% FIG 1 %%% +\begin{figure*} + \includegraphics[width=0.45\linewidth]{fig1a} + \hspace{1cm} + \includegraphics[width=0.45\linewidth]{fig1b} + \caption{ + IP (in eV) of the water molecule computed at the {\GOWO} (black circles), {\GOWO}+srLDA (red squares), and {\GOWO}+srPBE (blue diamonds) levels of theory with increasingly large Dunning's basis sets \cite{Dunning_1989} (cc-pVDZ, cc-pVTZ, cc-pVQZ, and cc-pV5Z) with two different starting points: HF (left) and PBE0 (right). + The thick black line represents the CBS value obtained by extrapolation (see text for more details). + The green area corresponds to chemical accuracy (\textit{i.e.}, error below $1$ {\kcal} or $0.043$ eV). + \label{fig:IP_G0W0_H2O} + } +\end{figure*} + +%%%%%%%%%%%%%%%%%%%%%%%% +\section{Results and Discussion} +\label{sec:results} +%%%%%%%%%%%%%%%%%%%%%%%% +In this section, we study a subset of atoms and molecules from the GW100 test set. \cite{vanSetten_2015} +In particular, we study the 20 smallest molecules of the GW100 set, a subset that we label as GW20. +This subset has been recently considered by Lewis and Berkelbach to study the effect of vertex corrections to $\W{}{}$ on IPs of molecules. \cite{Lewis_2019a} +Later in this section, we also study the five canonical nucleobases (adenine, cytosine, thymine, guanine, and uracil) which are also part of the GW100 test set. + +%%%%%%%%%%%%%%%%%%%%%%%% +\subsection{GW20} +\label{sec:GW20} +%%%%%%%%%%%%%%%%%%%%%%%% +The IPs of the GW20 set obtained at the {\GOWO}@{\HF} and {\GOWO}@{\PBEO} levels with increasingly larger Dunning's basis sets cc-pVXZ (X $=$ D, T, Q, and 5) are reported in Tables \ref{tab:GW20_HF} and \ref{tab:GW20_PBE0}, respectively. +The corresponding statistical deviations (with respect to the CBS values) are also reported: mean absolute deviation (MAD), root-mean-square deviation (RMSD), and maximum deviation (MAX). +These reference CBS values have been obtained with the usual X$^{-3}$ extrapolation procedure using the three largest basis sets. \cite{Bruneval_2012} + +The convergence of the IP of the water molecule with respect to the basis set size is depicted in Fig.~\ref{fig:IP_G0W0_H2O}. +This represents a typical example. +Additional graphs reporting the convergence of the IPs of each molecule of the GW20 subset at the {\GOWO}@{\HF} and {\GOWO}@{\PBEO} levels are reported in the {\SI}. + +Tables \ref{tab:GW20_HF} and \ref{tab:GW20_PBE0} (as well as Fig.~\ref{fig:IP_G0W0_H2O}) clearly evidence that the present basis set correction significantly increases the rate of convergence of IPs. +At the {\GOWO}@{\HF} (see Table \ref{tab:GW20_HF}), the MAD of the conventional calculations (\textit{i.e}, without basis set correction) is roughly divided by two each time one increases the basis set size (MADs of $0.60$, $0.24$, $0.10$, and $0.05$ eV going from cc-pVDZ to cc-pV5Z) with maximum errors higher than $1$ eV for molecules such as \ce{HF}, \ce{H2O}, and \ce{LiF} with the smallest basis set. +Even with the largest quintuple-$\zeta$ basis, the MAD is still above chemical accuracy (\textit{i.e.}, error below $1$ {\kcal} or $0.043$ eV). + +For each basis set, the correction brought by the short-range correlation functionals reduces by roughly half or more the MAD, RMSD, and MAX compared to the correction-free calculations. +For example, we obtain MADs of $0.27$, $0.12$, $0.04$, and $0.01$ eV at the {\GOWO}@HF+srPBE level with increasingly larger basis sets. +Interestingly, in most cases, the srPBE correction is slightly larger than the srLDA one. +This observation is clear at the cc-pVDZ level but, for larger basis sets, the two RS-DFT-based corrections are basically equivalent. +Note also that, in some cases, the corrected IPs slightly overshoot the CBS values. +However, it is hard to know if it is not due to the extrapolation error. +In a nutshell, the present basis set correction provides cc-pVQZ quality results at the cc-pVTZ level. +Besides, it allows to reach chemical accuracy with the quadruple-$\zeta$ basis set, an accuracy that could not be reached even with the cc-pV5Z basis set for the conventional calculations. + +Very similar conclusions are drawn at the {\GOWO}@{\PBEO} level (see Table \ref{tab:GW20_PBE0}) with a slightly faster convergence to the CBS limit. +For example, at the {\GOWO}@PBE0+srLDA/cc-pVQZ level, the MAD is only $0.02$ eV with a maximum error as small as $0.09$ eV. + +It is worth pointing out that, for ground-state properties such as atomization and correlation energies, the density-based correction brought a more significant basis set reduction. +For example, we evidenced in Ref.~\onlinecite{Loos_2019} that quintuple-$\zeta$ quality atomization and correlation energies are recovered with triple-$\zeta$ basis sets. +Here, the overall gain seems to be less important. +The potential reasons for this could be: i) potential-based DFT corrections are usually less accurate than the ones based directly on energies, \cite{Kim_2013} and ii) because the present scheme only corrects the basis set incompleteness error originating from the electron-electron cusp, some incompleteness remains at the HF or KS level. \cite{Adler_2007} + +%%% TABLE III %%% +\begin{table*} +\caption{ +IPs (in eV) of the five canonical nucleobases (adenine, cytosine, thymine, guanine, and uracil) computed at the {\GOWO}@PBE level of theory for various basis sets. +The deviation with respect to the {\GOWO}@PBE/def2-TQZVP extrapolated values are reported in square brackets. +The extrapolation error is reported in parenthesis. +The CCSD(T)/def2-TZVPP and experimental results are reported for comparison purposes. +\label{tab:DNA_IP} +} + \begin{ruledtabular} + \begin{tabular}{llccccc} + & & \mc{5}{c}{IPs of nucleobases (eV)} \\ + \cline{3-7} + Method & Basis & \tabc{Adenine} & \tabc{Cytosine} & \tabc{Guanine} & \tabc{Thymine} & \tabc{Uracil} \\ + \hline + {\GOWO}@PBE\fnm[1] & def2-SVP & $7.27$[$-0.88$] & $7.53$[$-0.92$] & $6.95$[$-0.92$] & $8.02$[$-0.85$] & $8.38$[$-1.00$] \\ + {\GOWO}@PBE+srLDA\fnm[1] & def2-SVP & $7.60$[$-0.55$] & $7.95$[$-0.50$] & $7.29$[$-0.59$] & $8.36$[$-0.51$] & $8.80$[$-0.58$] \\ + {\GOWO}@PBE+srPBE\fnm[1] & def2-SVP & $7.64$[$-0.51$] & $8.06$[$-0.39$] & $7.34$[$-0.54$] & $8.41$[$-0.45$] & $8.91$[$-0.47$] \\ + {\GOWO}@PBE\fnm[1] & def2-TZVP & $7.74$[$-0.41$] & $8.06$[$-0.39$] & $7.45$[$-0.42$] & $8.48$[$-0.38$] & $8.86$[$-0.52$] \\ + {\GOWO}@PBE+srLDA\fnm[1] & def2-TZVP & $7.92$[$-0.23$] & $8.26$[$-0.19$] & $7.64$[$-0.23$] & $8.67$[$-0.20$] & $9.25$[$-0.13$] \\ + {\GOWO}@PBE+srPBE\fnm[1] & def2-TZVP & $7.92$[$-0.23$] & $8.27$[$-0.18$] & $7.64$[$-0.23$] & $8.68$[$-0.19$] & $9.27$[$-0.11$] \\ + {\GOWO}@PBE\fnm[2] & def2-QZVP & $7.98$[$-0.18$] & $8.29$[$-0.16$] & $7.69$[$-0.18$] & $8.71$[$-0.16$] & $9.22$[$-0.16$] \\ + {\GOWO}@PBE\fnm[3] & def2-TQZVP & $8.16(1)$ & $8.44(1)$ & $7.87(1)$ & $8.87(1)$ & $9.38(1)$ \\ + \hline + CCSD(T)\fnm[4] & def2-TZVPP & $8.33$ & $9.51$ & $8.03$ & $9.08$ & $10.13$ \\ + Experiment\fnm[5] & & $8.48$ & $8.94$ & $8.24$ & $9.20$ & $9.68$ \\ + \end{tabular} + \end{ruledtabular} + \fnt[1]{This work.} + \fnt[2]{Unpublished data taken from \url{https://gw100.wordpress.com} obtained with TURBOMOLE v7.0.} + \fnt[3]{Extrapolated values obtained from the def2-TZVP and def2-QZVP values.} + \fnt[4]{Reference \onlinecite{Krause_2015}.} + \fnt[5]{Experimental values are taken from Ref.~\onlinecite{vanSetten_2015} and correspond to vertical ionization energies.} +\end{table*} + +%%% FIG 2 %%% +\begin{figure*} + \includegraphics[width=\linewidth]{fig2} + \caption{ + Error (in eV) with respect to the {\GOWO}@PBE/def2-TQZVP extrapolated values for the IPs of the five canonical nucleobases (adenine, cytosine, thymine, guanine, and uracil) computed at the {\GOWO}@PBE level of theory for various basis sets. + \label{fig:DNA_IP} + } +\end{figure*} + +%%%%%%%%%%%%%%%%%%%%%%%% +\subsection{Nucleobases} +\label{sec:DNA} +%%%%%%%%%%%%%%%%%%%%%%%% +In order to check the transferability of the present observations to larger systems, we have computed the values of the IPs of the five canonical nucleobases (adenine, cytosine, thymine, guanine, and uracil) at the {\GOWO}@PBE level of theory with a different basis set family. \cite{Weigend_2003a, Weigend_2005a} +The numerical values are reported in Table \ref{tab:DNA_IP}, and their error with respect to the {\GOWO}@PBE/def2-TQZVP extrapolated values \cite{vanSetten_2015} (obtained via extrapolation of the def2-TZVP and def2-QZVP results) are shown in Fig.~\ref{fig:DNA_IP}. +The CCSD(T)/def2-TZVPP computed by Krause \textit{et al.} \cite{Krause_2015} as well as the experimental results extracted from Ref.~\onlinecite{vanSetten_2015} are reported for comparison purposes. + +For these five systems, the IPs are all of the order of $8$ or $9$ eV with an amplitude of roughly $1$ eV between the smallest basis set (def2-SVP) and the CBS value. +The conclusions that we have drawn in the previous subsection do apply here as well. +For the smallest double-$\zeta$ basis def2-SVP, the basis set correction reduces by roughly half an eV the basis set incompleteness error. +It is particularly interesting to note that the basis-set corrected def2-TZVP results are on par with the correction-free def2-QZVP numbers. +This is quite remarkable as the number of basis functions jumps from $371$ to $777$ for the largest system (guanine). + +%%%%%%%%%%%%%%%%%%%%%%%% +\section{Conclusion} +\label{sec:conclusion} +%%%%%%%%%%%%%%%%%%%%%%%% +In the present manuscript, we have shown that the density-based basis set correction developed by some of the authors in Ref.~\onlinecite{Giner_2018} and applied recently to ground- and excited-state properties \cite{Loos_2019, Giner_2019} can also be successfully applied to Green function methods such as {\GW}. +In particular, we have evidenced that the present basis set correction (which relies on LDA- or PBE-based short-range correlation functionals) significantly speeds up the convergence of IPs for small and larger molecules towards the CBS limit. +These findings have been observed for different {\GW} starting points (HF, PBE, and PBE0). + +As mentioned earlier, the present basis set correction can be straightforwardly applied to other properties of interest such as electron affinities or fundamental gap. +It is also applicable to other flavors of {\GW} such as the partially self-consistent {\evGW} or {\qsGW} methods. +We are currently investigating the performance of the present approach within linear response theory in order to speed up the convergence of excitation energies obtained within the RPA and Bethe-Salpeter equation (BSE) \cite{Strinati_1988, Leng_2016, Blase_2018} formalisms. +We hope to report on this in the near future. + +%%%%%%%%%%%%%%%%%%%%%%%% +\section*{Supporting Information} +%%%%%%%%%%%%%%%%%%%%%%%% +See {\SI} for additional graphs reporting the convergence of the ionization potentials of the GW20 subset with respect to the size of the basis set. + +%%%%%%%%%%%%%%%%%%%%%%%% +\begin{acknowledgements} +PFL would like to thank Fabien Bruneval for technical assistance. +PFL and JT would like to thank Arjan Berger and Pina Romaniello for stimulating discussions. +This work was performed using HPC resources from GENCI-TGCC (Grant No.~2018-A0040801738) and CALMIP (Toulouse) under allocation 2019-18005. +Funding from the \textit{``Centre National de la Recherche Scientifique''} is acknowledged. +This work has been supported through the EUR grant NanoX ANR-17-EURE-0009 in the framework of the \textit{``Programme des Investissements d'Avenir''}. +\end{acknowledgements} +%%%%%%%%%%%%%%%%%%%%%%%% + +\bibliography{GW-srDFT,GW-srDFT-control} + +\end{document} diff --git a/JCTC_revision/TOC.pdf b/JCTC_revision/TOC.pdf new file mode 100644 index 0000000000000000000000000000000000000000..3eab9ba40fd04981853252208cc681343ca3cf0b GIT binary patch literal 686716 zcmd?Rby!s0*FSs+NfAM$hDHTNq`Q=qMo_vD$)USZLWKcQO6l(IE&&DUln!Blp*x4) z8NBcB^E|IU@Adxi`|suQn%Q&KT6=v~?6vkev&XwClG3akk9hFzR%{fW;c?Tk)7ctZ z;t31Wu_>6^m^qo#@qm|9@#yI2*rYA2olG6TcWWajQ%O@3+n1(zqM~??P7bCOH;LsY4%++f>t}eT zHZT8?21h8pC}pU3P#q5kij4Ze^&e1IFr?g^WYnBM2z0{2s0-j9n-M$sfsRe$2^|L= zn~4$l3IYQOzhBujm5nV;O`NWH+<57DQ6`~i;J<%#aQ;UJ9outvJ5xF~6(cj#D}5?P z4yHCv;FSORLDBT3g^{?e8=Ve#iJgvvot>SIM}UV;?}}Z**2W3sccer4^0(t;9BiHK 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