From b56e90cacf3068d5f167e9a83a3b74d936989988 Mon Sep 17 00:00:00 2001 From: Pierre-Francois Loos Date: Sun, 6 Mar 2022 22:55:44 +0100 Subject: [PATCH] Mike changes --- TrUEGs.bib | 2213 ++++++++++++++++++++++++++-------------------------- TrUEGs.tex | 220 ++++-- 2 files changed, 1243 insertions(+), 1190 deletions(-) diff --git a/TrUEGs.bib b/TrUEGs.bib index 8fd209d..e553a95 100644 --- a/TrUEGs.bib +++ b/TrUEGs.bib @@ -1,7 +1,7 @@ %% This BibTeX bibliography file was created using BibDesk. -%% http://bibdesk.sourceforge.net/ +%% https://bibdesk.sourceforge.io/ -%% Created for Pierre-Francois Loos at 2021-05-23 14:27:26 +0200 +%% Created for Pierre-Francois Loos at 2021-11-26 18:15:28 +0100 %% Saved with string encoding Unicode (UTF-8) @@ -20,7 +20,7 @@ title = {Intracule densities in the strong-interaction limit of density functional theory}, volume = {10}, year = {2008}, - Bdsk-Url-1 = {http://dx.doi.org/10.1039/B803709B}} + bdsk-url-1 = {http://dx.doi.org/10.1039/B803709B}} @article{Pearson_2009, author = {Jason K. Pearson and Peter M.W. Gill and Jesus M. Ugalde and Russell J. Boyd}, @@ -33,7 +33,7 @@ title = {Can correlation bring electrons closer together?}, volume = {107}, year = {2009}, - Bdsk-Url-1 = {https://doi.org/10.1080/00268970902740563}} + bdsk-url-1 = {https://doi.org/10.1080/00268970902740563}} @book{VignaleBook, address = {Cambridge, England}, @@ -69,7 +69,7 @@ title = {Unrestricted {Hartree-Fock} theory and its applications to molecules and chemical reactions}, volume = {20}, year = {1981}, - Bdsk-Url-1 = {https://doi.org/10.1002/qua.560200502}} + bdsk-url-1 = {https://doi.org/10.1002/qua.560200502}} @article{Boyd_1974, abstract = {A new definition of the Fermi hole in many-electron systems is provided in terms of the distribution function falpha alpha (r12) of the interelectronic distance for electrons with parallel spins. By analogy with the Coulomb hole, the Fermi hole is defined as the difference between the values of f22(r12) derived from the Hartree-Fock and the Hartree wavefunctions. this definition, unlike previous ones, provides a simple picture of the Fermi hole as a function of r12. By assuming that the Hartree and Hartree-Fock orbitals are identical, an analytical formula is derived for the Fermi hole. Explicit calculations are presented for the 23S state of He and the ground state of Be. It is observed that the Fermi hole is remarkably similar in these two cases; and that the effects of Coulomb correlation are more long-ranged than those of Fermi correlation.}, @@ -84,7 +84,7 @@ title = {The Fermi hole in atoms}, volume = {7}, year = 1974, - Bdsk-Url-1 = {https://doi.org/10.1088/0022-3700/7/14/006}} + bdsk-url-1 = {https://doi.org/10.1088/0022-3700/7/14/006}} @article{Giner_2016a, author = {Giner,Emmanuel and Tenti,Lorenzo and Angeli,Celestino and Malrieu,Jean-Paul}, @@ -97,7 +97,7 @@ title = {The ``Fermi hole'' and the correlation introduced by the symmetrization or the anti-symmetrization of the wave function}, volume = {145}, year = {2016}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.4963018}} + bdsk-url-1 = {https://doi.org/10.1063/1.4963018}} @article{Becke_1993b, author = {Becke,Axel D.}, @@ -110,7 +110,7 @@ title = {A new mixing of Hartree--Fock and local density‐functional theories}, volume = {98}, year = {1993}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.464304}} + bdsk-url-1 = {https://doi.org/10.1063/1.464304}} @article{Lee_1988, author = {C. Lee and W. Yang and R. G. Parr}, @@ -126,8 +126,8 @@ url = {http://link.aps.org/doi/10.1103/PhysRevB.37.785}, volume = {37}, year = {1988}, - Bdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevB.37.785}, - Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevB.37.785}} + bdsk-url-1 = {http://link.aps.org/doi/10.1103/PhysRevB.37.785}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRevB.37.785}} @article{Wigner_1934, author = {Wigner, E.}, @@ -139,7 +139,7 @@ title = {On the {Interaction} of {Electrons} in {Metals}}, volume = {46}, year = {1934}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRev.46.1002}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRev.46.1002}} @article{Sun_2016, author = {Sun,Jianwei and Perdew,John P. and Yang,Zenghui and Peng,Haowei}, @@ -152,7 +152,7 @@ title = {Communication: Near-locality of exchange and correlation density functionals for 1- and 2-electron systems}, volume = {144}, year = {2016}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.4950845}} + bdsk-url-1 = {https://doi.org/10.1063/1.4950845}} @article{Chachiyo_2016, author = {Chachiyo, Teepanis}, @@ -166,8 +166,8 @@ url = {http://scitation.aip.org/content/aip/journal/jcp/145/2/10.1063/1.4958669}, volume = {145}, year = {2016}, - Bdsk-Url-1 = {http://scitation.aip.org/content/aip/journal/jcp/145/2/10.1063/1.4958669}, - Bdsk-Url-2 = {https://doi.org/10.1063/1.4958669}} + bdsk-url-1 = {http://scitation.aip.org/content/aip/journal/jcp/145/2/10.1063/1.4958669}, + bdsk-url-2 = {https://doi.org/10.1063/1.4958669}} @article{Adamo_1999, author = {C. Adamo and V. Barone}, @@ -181,8 +181,8 @@ url = {http://scitation.aip.org/content/aip/journal/jcp/110/13/10.1063/1.478522}, volume = {110}, year = {1999}, - Bdsk-Url-1 = {http://scitation.aip.org/content/aip/journal/jcp/110/13/10.1063/1.478522}, - Bdsk-Url-2 = {https://doi.org/10.1063/1.478522}} + bdsk-url-1 = {http://scitation.aip.org/content/aip/journal/jcp/110/13/10.1063/1.478522}, + bdsk-url-2 = {https://doi.org/10.1063/1.478522}} @article{Becke_1988b, author = {A. D. Becke}, @@ -196,7 +196,7 @@ url = {http://dx.doi.org/10.1063/1.454274}, volume = {88}, year = {1988}, - Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.454274}} + bdsk-url-1 = {http://dx.doi.org/10.1063/1.454274}} @article{Perdew_1986, author = {J. P. Perdew and W. Yue}, @@ -212,8 +212,8 @@ url = {http://link.aps.org/doi/10.1103/PhysRevB.33.8800}, volume = {33}, year = {1986}, - Bdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevB.33.8800}, - Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevB.33.8800}} + bdsk-url-1 = {http://link.aps.org/doi/10.1103/PhysRevB.33.8800}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRevB.33.8800}} @article{Perdew_1992, author = {J. P. Perdew and Y. Wang}, @@ -229,8 +229,8 @@ url = {http://link.aps.org/doi/10.1103/PhysRevB.45.13244}, volume = {45}, year = {1992}, - Bdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevB.45.13244}, - Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevB.45.13244}} + bdsk-url-1 = {http://link.aps.org/doi/10.1103/PhysRevB.45.13244}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRevB.45.13244}} @article{Perdew_1981, author = {J. P. Perdew and A. Zunger}, @@ -246,8 +246,8 @@ url = {http://link.aps.org/doi/10.1103/PhysRevB.23.5048}, volume = {23}, year = {1981}, - Bdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevB.23.5048}, - Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevB.23.5048}} + bdsk-url-1 = {http://link.aps.org/doi/10.1103/PhysRevB.23.5048}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRevB.23.5048}} @book{DavidsonBook, address = {New York}, @@ -274,8 +274,8 @@ url = {https://link.aps.org/doi/10.1103/PhysRevLett.89.185502}, volume = {89}, year = {2002}, - Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.89.185502}, - Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevLett.89.185502}} + bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.89.185502}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRevLett.89.185502}} @article{Pedersen_2010, author = {Pedersen, Thomas G.}, @@ -292,8 +292,8 @@ url = {https://link.aps.org/doi/10.1103/PhysRevB.81.233406}, volume = {81}, year = {2010}, - Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.81.233406}, - Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevB.81.233406}} + bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.81.233406}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRevB.81.233406}} @article{Louck_1960, author = {J. D. Louck}, @@ -329,8 +329,8 @@ url = {https://link.aps.org/doi/10.1103/PhysRev.36.383}, volume = {36}, year = {1930}, - Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRev.36.383}, - Bdsk-Url-2 = {https://doi.org/10.1103/PhysRev.36.383}} + bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRev.36.383}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRev.36.383}} @article{Sun_2015, author = {Sun, Jianwei and Ruzsinszky, Adrienn and Perdew, John P.}, @@ -347,8 +347,8 @@ url = {https://link.aps.org/doi/10.1103/PhysRevLett.115.036402}, volume = {115}, year = {2015}, - Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.115.036402}, - Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevLett.115.036402}} + bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.115.036402}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRevLett.115.036402}} @article{Becke_1988, author = {A. D. Becke}, @@ -360,7 +360,7 @@ title = {Density-functional exchange-energy approximation with correct asymptotic behavior}, volume = {38}, year = {1988}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevA.38.3098}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRevA.38.3098}} @inproceedings{Perdew_2001, author = {{Perdew}, John P. and {Schmidt}, Karla}, @@ -375,7 +375,7 @@ title = {{Jacob's ladder of density functional approximations for the exchange-correlation energy}}, volume = {577}, year = 2001, - Bdsk-Url-1 = {https://doi.org/10.1063/1.1390175}} + bdsk-url-1 = {https://doi.org/10.1063/1.1390175}} @article{Slater_1951, author = {J. C. Slater}, @@ -391,8 +391,8 @@ url = {http://link.aps.org/doi/10.1103/PhysRev.81.385}, volume = {81}, year = {1951}, - Bdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRev.81.385}, - Bdsk-Url-2 = {https://doi.org/10.1103/PhysRev.81.385}} + bdsk-url-1 = {http://link.aps.org/doi/10.1103/PhysRev.81.385}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRev.81.385}} @article{Thomas_1927, author = {L. H. Thomas}, @@ -409,8 +409,8 @@ url = {http://journals.cambridge.org/article_S0305004100011683}, volume = {23}, year = {1927}, - Bdsk-Url-1 = {http://journals.cambridge.org/article_S0305004100011683}, - Bdsk-Url-2 = {https://doi.org/10.1017/S0305004100011683}} + bdsk-url-1 = {http://journals.cambridge.org/article_S0305004100011683}, + bdsk-url-2 = {https://doi.org/10.1017/S0305004100011683}} @article{Fermi_1927, author = {E. Fermi}, @@ -436,7 +436,7 @@ title = {Calculation of size‐intensive transition moments from the coupled cluster singles and doubles linear response function}, volume = {100}, year = {1994}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.466321}} + bdsk-url-1 = {https://doi.org/10.1063/1.466321}} @article{Stanton_1993, author = {Stanton,John F. and Bartlett,Rodney J.}, @@ -448,7 +448,7 @@ title = {The equation of motion coupled‐cluster method. A systematic biorthogonal approach to molecular excitation energies, transition probabilities, and excited state properties}, volume = {98}, year = {1993}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.464746}} + bdsk-url-1 = {https://doi.org/10.1063/1.464746}} @article{Sarkar_2021, author = {R. Sarkar and M. Boggio-Pasqua and P. F. Loos and D. Jacquemin}, @@ -471,7 +471,7 @@ url = {https://doi.org/10.1063/1.1308557}, volume = {113}, year = {2000}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.1308557}} + bdsk-url-1 = {https://doi.org/10.1063/1.1308557}} @article{Balkova_1994, author = {Balkov{\'a},A. and Bartlett,Rodney J.}, @@ -484,7 +484,7 @@ title = {A multireference coupled‐cluster study of the ground state and lowest excited states of cyclobutadiene}, volume = {101}, year = {1994}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.468025}} + bdsk-url-1 = {https://doi.org/10.1063/1.468025}} @article{qchem4, author = {Shao, Yihan and Gan, Zhengting and Epifanovsky, Evgeny and Gilbert, Andrew T.B. and Wormit, Michael and Kussmann, Joerg and Lange, Adrian W. and Behn, Andrew and Deng, Jia and Feng, Xintian and Ghosh, Debashree and Goldey, Matthew and Horn, Paul R. and Jacobson, Leif D. and Kaliman, Ilya and Khaliullin, Rustam Z. and Ku{\'s}, Tomasz and Landau, Arie and Liu, Jie and Proynov, Emil I. and Rhee, Young Min and Richard, Ryan M. and Rohrdanz, Mary A. and Steele, Ryan P. and Sundstrom, Eric J. and Woodcock, H. Lee and Zimmerman, Paul M. and Zuev, Dmitry and Albrecht, Ben and Alguire, Ethan and Austin, Brian and Beran, Gregory J. O. and Bernard, Yves A. and Berquist, Eric and Brandhorst, Kai and Bravaya, Ksenia B. and Brown, Shawn T. and Casanova, David and Chang, Chun-Min and Chen, Yunqing and Chien, Siu Hung and Closser, Kristina D. and Crittenden, Deborah L. and Diedenhofen, Michael and DiStasio, Robert A. and Do, Hainam and Dutoi, Anthony D. and Edgar, Richard G. and Fatehi, Shervin and Fusti-Molnar, Laszlo and Ghysels, An and Golubeva-Zadorozhnaya, Anna and Gomes, Joseph and Hanson-Heine, Magnus W.D. and Harbach, Philipp H.P. and Hauser, Andreas W. and Hohenstein, Edward G. and Holden, Zachary C. and Jagau, Thomas-C. and Ji, Hyunjun and Kaduk, Benjamin and Khistyaev, Kirill and Kim, Jaehoon and Kim, Jihan and King, Rollin A. and Klunzinger, Phil and Kosenkov, Dmytro and Kowalczyk, Tim and Krauter, Caroline M. and Lao, Ka Un and Laurent, Ad{\`e}le D. and Lawler, Keith V. and Levchenko, Sergey V. and Lin, Ching Yeh and Liu, Fenglai and Livshits, Ester and Lochan, Rohini C. and Luenser, Arne and Manohar, Prashant and Manzer, Samuel F. and Mao, Shan-Ping and Mardirossian, Narbe and Marenich, Aleksandr V. and Maurer, Simon A. and Mayhall, Nicholas J. and Neuscamman, Eric and Oana, C. Melania and Olivares-Amaya, Roberto and O'Neill, Darragh P. and Parkhill, John A. and Perrine, Trilisa M. and Peverati, Roberto and Prociuk, Alexander and Rehn, Dirk R. and Rosta, Edina and Russ, Nicholas J. and Sharada, Shaama M. and Sharma, Sandeep and Small, David W. and Sodt, Alexander and Stein, Tamar and St{\"u}ck, David and Su, Yu-Chuan and Thom, Alex J.W. and Tsuchimochi, Takashi and Vanovschi, Vitalii and Vogt, Leslie and Vydrov, Oleg and Wang, Tao and Watson, Mark A. and Wenzel, Jan and White, Alec and Williams, Christopher F. and Yang, Jun and Yeganeh, Sina and Yost, Shane R. and You, Zhi-Qiang and Zhang, Igor Ying and Zhang, Xing and Zhao, Yan and Brooks, Bernard R. and Chan, Garnet K.L. and Chipman, Daniel M. and Cramer, Christopher J. and Goddard, William A. and Gordon, Mark S. and Hehre, Warren J. and Klamt, Andreas and Schaefer, Henry F. and Schmidt, Michael W. and Sherrill, C. David and Truhlar, Donald G. and Warshel, Arieh and Xu, Xin and Aspuru-Guzik, Al{\'a}n and Baer, Roi and Bell, Alexis T. and Besley, Nicholas A. and Chai, Jeng-Da and Dreuw, Andreas and Dunietz, Barry D. and Furlani, Thomas R. and Gwaltney, Steven R. and Hsu, Chao-Ping and Jung, Yousung and Kong, Jing and Lambrecht, Daniel S. and Liang, WanZhen and Ochsenfeld, Christian and Rassolov, Vitaly A. and Slipchenko, Lyudmila V. and Subotnik, Joseph E. and Van Voorhis, Troy and Herbert, John M. and Krylov, Anna I. and Gill, Peter M.W. and Head-Gordon, Martin}, @@ -496,7 +496,7 @@ title = {Advances in Molecular Quantum Chemistry Contained in the Q-Chem 4 Program Package}, volume = {113}, year = {2015}, - Bdsk-Url-1 = {http://dx.doi.org/10.1080/00268976.2014.952696}} + bdsk-url-1 = {http://dx.doi.org/10.1080/00268976.2014.952696}} @misc{g09, author = {M. J. Frisch and G. W. Trucks and H. B. Schlegel and G. E. Scuseria and M. A. Robb and J. R. Cheeseman and G. Scalmani and V. Barone and B. Mennucci and G. A. Petersson and H. Nakatsuji and M. Caricato and X. Li and H. P. Hratchian and A. F. Izmaylov and J. Bloino and G. Zheng and J. L. Sonnenberg and M. Hada and M. Ehara and K. Toyota and R. Fukuda and J. Hasegawa and M. Ishida and T. Nakajima and Y. Honda and O. Kitao and H. Nakai and T. Vreven and Montgomery, {Jr.}, J. A. and J. E. Peralta and F. Ogliaro and M. Bearpark and J. J. Heyd and E. Brothers and K. N. Kudin and V. N. Staroverov and R. Kobayashi and J. Normand and K. Raghavachari and A. Rendell and J. C. Burant and S. S. Iyengar and J. Tomasi and M. Cossi and N. Rega and J. M. Millam and M. Klene and J. E. Knox and J. B. Cross and V. Bakken and C. Adamo and J. Jaramillo and R. Gomperts and R. E. Stratmann and O. Yazyev and A. J. Austin and R. Cammi and C. Pomelli and J. W. Ochterski and R. L. Martin and K. Morokuma and V. G. Zakrzewski and G. A. Voth and P. Salvador and J. J. Dannenberg and S. Dapprich and A. D. Daniels and {\"O}. Farkas and J. B. Foresman and J. V. Ortiz and J. Cioslowski and D. J. Fox}, @@ -537,7 +537,7 @@ 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}} + bdsk-url-1 = {https://dx.doi.org/10.1063/1.4929353}} @article{Authier_2020, author = {Authier,Juliette and Loos,Pierre-Fran{\c c}ois}, @@ -550,7 +550,7 @@ title = {Dynamical kernels for optical excitations}, volume = {153}, year = {2020}, - Bdsk-Url-1 = {https://doi.org/10.1063/5.0028040}} + bdsk-url-1 = {https://doi.org/10.1063/5.0028040}} @article{Ball_2017, author = {Ball, Caleb J. and Loos, Pierre-Fran{\c c}ois and Gill, Peter M. W.}, @@ -565,7 +565,7 @@ title = {Molecular Electronic Structure in One-Dimensional {{Coulomb}} Systems}, volume = {19}, year = {2017}, - Bdsk-Url-1 = {https://dx.doi.org/10.1039/C6CP06801D}} + 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.}, @@ -581,7 +581,7 @@ 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}} + 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}, @@ -609,7 +609,7 @@ 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}} + bdsk-url-1 = {https://dx.doi.org/10.1016/bs.aiq.2017.03.004}} @article{Benali_2020, author = {Benali,Anouar and Gasperich,Kevin and Jordan,Kenneth D. and Applencourt,Thomas and Luo,Ye and Bennett,M. Chandler and Krogel,Jaron T. and Shulenburger,Luke and Kent,Paul R. C. and Loos,Pierre-Fran{\c c}ois and Scemama,Anthony and Caffarel,Michel}, @@ -622,7 +622,7 @@ title = {Toward a systematic improvement of the fixed-node approximation in diffusion Monte Carlo for solids---A case study in diamond}, volume = {153}, year = {2020}, - Bdsk-Url-1 = {https://doi.org/10.1063/5.0021036}} + bdsk-url-1 = {https://doi.org/10.1063/5.0021036}} @misc{Berger_2020, archiveprefix = {arXiv}, @@ -648,7 +648,7 @@ 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}} + bdsk-url-1 = {https://dx.doi.org/10.1080/00268976.2013.811302}} @article{Blase_2020, author = {Blase, Xavier and Duchemin, Ivan and Jacquemin, Denis and Loos, Pierre-Fran{\c c}ois}, @@ -661,7 +661,7 @@ title = {The Bethe--Salpeter Equation Formalism: From Physics to Chemistry}, volume = {11}, year = {2020}, - Bdsk-Url-1 = {https://doi.org/10.1021/acs.jpclett.0c01875}} + bdsk-url-1 = {https://doi.org/10.1021/acs.jpclett.0c01875}} @article{Burton_2019a, author = {H. G. A. Burton and A. J. W. Thom and P. F. Loos}, @@ -673,7 +673,7 @@ title = {Complex Adiabatic Connection: a Hidden Non-Hermitian Path from Ground to Excited States}, volume = {150}, year = {2019}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.5085121}} + bdsk-url-1 = {https://doi.org/10.1063/1.5085121}} @article{Burton_2019b, author = {H. G. A. Burton and A. J. W. Thom and P. F. Loos}, @@ -685,7 +685,7 @@ title = {Parity-Time Symmetry in Hartree-Fock Theory}, volume = {15}, year = {2019}, - Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.9b00289}} + bdsk-url-1 = {https://doi.org/10.1021/acs.jctc.9b00289}} @article{Chrayteh_2021, author = {Chrayteh, Amara and Blondel, Aymeric and Loos, Pierre-Fran{\c c}ois and Jacquemin, Denis}, @@ -698,7 +698,7 @@ title = {Mountaineering Strategy to Excited States: Highly Accurate Oscillator Strengths and Dipole Moments of Small Molecules}, volume = {0}, year = {0}, - Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.0c01111}} + bdsk-url-1 = {https://doi.org/10.1021/acs.jctc.0c01111}} @article{Dumont_2009, author = {Dumont, Elise and Laurent, Adele D. and Loos, Pierre-Francois and Assfeld, Xavier}, @@ -714,7 +714,7 @@ 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}} + bdsk-url-1 = {https://dx.doi.org/10.1021/ct900093h}} @article{Fornili_2006, author = {Fornili, Arianna and Loos, Pierre-Fran{\c c}ois and Sironi, Maurizio and Assfeld, Xavier}, @@ -730,7 +730,7 @@ 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}} + bdsk-url-1 = {https://dx.doi.org/10.1016/j.cplett.2006.06.095}} @article{Garniron_2017b, author = {Garniron, Yann and Scemama, Anthony and Loos, Pierre-Fran{\c c}ois and Caffarel, Michel}, @@ -746,7 +746,7 @@ url = {http://dx.doi.org/10.1063/1.4992127}, volume = {147}, year = {2017}, - Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.4992127}} + bdsk-url-1 = {http://dx.doi.org/10.1063/1.4992127}} @article{Garniron_2018, author = {Y. Garniron and A. Scemama and E. Giner and M. Caffarel and P. F. Loos}, @@ -758,7 +758,7 @@ title = {Selected Configuration Interaction Dressed by Perturbation}, volume = {149}, year = {2018}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.5044503}} + bdsk-url-1 = {https://doi.org/10.1063/1.5044503}} @article{Garniron_2019, author = {Y. Garniron and K. Gasperich and T. Applencourt and A. Benali and A. Fert{\'e} and J. Paquier and B. Pradines and R. Assaraf and P. Reinhardt and J. Toulouse and P. Barbaresco and N. Renon and G. David and J. P. Malrieu and M. V{\'e}ril and M. Caffarel and P. F. Loos and E. Giner and A. Scemama}, @@ -770,7 +770,7 @@ title = {Quantum Package 2.0: a open-source determinant-driven suite of programs}, volume = {15}, year = {2019}, - Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.9b00176}} + bdsk-url-1 = {https://doi.org/10.1021/acs.jctc.9b00176}} @article{Gill_2012, author = {Gill, Peter M. W. and Loos, Pierre-Fran{\c c}ois}, @@ -786,7 +786,7 @@ title = {Uniform Electron Gases}, volume = {131}, year = {2012}, - Bdsk-Url-1 = {https://dx.doi.org/10.1007/s00214-011-1069-7}} + 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}, @@ -802,7 +802,7 @@ title = {Basis Functions for Electronic Structure Calculations on Spheres}, volume = {141}, year = {2014}, - Bdsk-Url-1 = {https://dx.doi.org/10.1063/1.4903984}} + bdsk-url-1 = {https://dx.doi.org/10.1063/1.4903984}} @article{Giner_2019, author = {E. Giner and A. Scemama and J. Toulouse and P. F. Loos}, @@ -814,7 +814,7 @@ title = {Chemically accurate excitation energies with small basis sets}, volume = {151}, year = {2019}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.5052714}} + bdsk-url-1 = {https://doi.org/10.1063/1.5052714}} @article{Giner_2020, author = {Giner,Emmanuel and Scemama,Anthony and Loos,Pierre-Fran{\c c}ois and Toulouse,Julien}, @@ -827,7 +827,7 @@ title = {A basis-set error correction based on density-functional theory for strongly correlated molecular systems}, volume = {152}, year = {2020}, - Bdsk-Url-1 = {https://doi.org/10.1063/5.0002892}} + bdsk-url-1 = {https://doi.org/10.1063/5.0002892}} @article{Hollett_2020, author = {Hollett,Joshua W. and Loos,Pierre-Fran{\c c}ois}, @@ -840,7 +840,7 @@ title = {Capturing static and dynamic correlation with ΔNO-MP2 and ΔNO-CCSD}, volume = {152}, year = {2020}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.5140669}} + bdsk-url-1 = {https://doi.org/10.1063/1.5140669}} @article{Loos_2007, author = {Loos, Pierre-Fran{\c c}ois and Assfeld, Xavier}, @@ -855,7 +855,7 @@ title = {Core-Ionized and Core-Excited States of Macromolecules}, volume = {107}, year = {2007}, - Bdsk-Url-1 = {https://dx.doi.org/10.1002/qua.21410}} + 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}, @@ -871,7 +871,7 @@ title = {Intramolecular Interactions and Cis Peptidic Bonds}, volume = {118}, year = {2007}, - Bdsk-Url-1 = {https://dx.doi.org/10.1007/s00214-007-0258-x}} + 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}, @@ -899,7 +899,7 @@ title = {Self-{{Consistent Strictly Localized Orbitals}}}, volume = {3}, year = {2007}, - Bdsk-Url-1 = {https://dx.doi.org/10.1021/ct6003214}} + 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}, @@ -916,7 +916,7 @@ 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}} + 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.}, @@ -932,7 +932,7 @@ 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}} + bdsk-url-1 = {https://dx.doi.org/10.1063/1.3275519}} @article{Loos_2009a, author = {Loos, P. F. and Gill, Peter M. W.}, @@ -947,7 +947,7 @@ 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}} + bdsk-url-1 = {https://dx.doi.org/10.1103/PhysRevA.79.062517}} @article{Loos_2009b, author = {Loos, Pierre-Francois and Dumont, Elise and Laurent, Adele D. and Assfeld, Xavier}, @@ -963,7 +963,7 @@ 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}} + bdsk-url-1 = {https://dx.doi.org/10.1016/j.cplett.2009.05.041}} @article{Loos_2009c, author = {Loos, P. F. and Gill, Peter M. W.}, @@ -979,7 +979,7 @@ 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}} + 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.}, @@ -996,7 +996,7 @@ 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}} + 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.}, @@ -1012,7 +1012,7 @@ title = {Correlation Energy of Two Electrons in a Ball}, volume = {132}, year = {2010}, - Bdsk-Url-1 = {https://dx.doi.org/10.1063/1.3455706}} + 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.}, @@ -1028,7 +1028,7 @@ 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}} + bdsk-url-1 = {https://dx.doi.org/10.1103/PhysRevA.81.052510}} @article{Loos_2010c, author = {Loos, Pierre-Fran{\c c}ois}, @@ -1044,7 +1044,7 @@ 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}} + 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.}, @@ -1060,7 +1060,7 @@ 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}} + bdsk-url-1 = {https://dx.doi.org/10.1103/PhysRevLett.105.113001}} @article{Loos_2010e, author = {Loos, Pierre-Fran{\c c}ois and Gill, Peter M.W.}, @@ -1076,7 +1076,7 @@ title = {Excited States of Spherium}, volume = {108}, year = {2010}, - Bdsk-Url-1 = {https://dx.doi.org/10.1080/00268976.2010.508472}} + bdsk-url-1 = {https://dx.doi.org/10.1080/00268976.2010.508472}} @article{Loos_2011, author = {Loos, Pierre-Fran{\c c}ois and Gill, Peter M. W.}, @@ -1092,7 +1092,7 @@ 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}} + 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.}, @@ -1108,7 +1108,7 @@ 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}} + bdsk-url-1 = {https://dx.doi.org/10.1103/PhysRevB.83.233102}} @article{Loos_2011b, author = {Loos, P. F. and Gill, Peter M. W.}, @@ -1124,7 +1124,7 @@ 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}} + 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.}, @@ -1140,7 +1140,7 @@ 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}} + 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.}, @@ -1156,7 +1156,7 @@ title = {Harmonically Trapped Jellium}, volume = {110}, year = {2012}, - Bdsk-Url-1 = {https://dx.doi.org/10.1080/00268976.2012.679634}} + 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.}, @@ -1172,7 +1172,7 @@ 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}} + bdsk-url-1 = {https://dx.doi.org/10.1002/qua.23155}} @article{Loos_2012c, author = {Loos, Pierre-Fran{\c c}ois}, @@ -1188,7 +1188,7 @@ title = {Understanding Excitons Using Spherical Geometry}, volume = {376}, year = {2012}, - Bdsk-Url-1 = {https://dx.doi.org/10.1016/j.physleta.2012.05.010}} + bdsk-url-1 = {https://dx.doi.org/10.1016/j.physleta.2012.05.010}} @article{Loos_2013, author = {Loos, Pierre-Fran{\c c}ois}, @@ -1204,7 +1204,7 @@ 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}} + 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.}, @@ -1220,7 +1220,7 @@ title = {Uniform Electron Gases. {{I}}. {{Electrons}} on a Ring}, volume = {138}, year = {2013}, - Bdsk-Url-1 = {https://dx.doi.org/10.1063/1.4802589}} + 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.}, @@ -1236,7 +1236,7 @@ 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}} + bdsk-url-1 = {https://dx.doi.org/10.1016/j.physleta.2013.11.045}} @article{Loos_2014a, author = {Loos, Pierre-Fran{\c c}ois}, @@ -1252,7 +1252,7 @@ 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}} + 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.}, @@ -1268,7 +1268,7 @@ 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}} + bdsk-url-1 = {https://dx.doi.org/10.1063/1.4867910}} @article{Loos_2015a, author = {Loos, Pierre-Fran{\c c}ois and Bloomfield, Nathaniel J. and Gill, Peter M. W.}, @@ -1285,7 +1285,7 @@ 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}} + bdsk-url-1 = {https://dx.doi.org/10.1063/1.4935374}} @article{Loos_2015b, author = {Loos, Pierre-Fran{\c c}ois and Bressanini, Dario}, @@ -1301,7 +1301,7 @@ title = {Nodal Surfaces and Interdimensional Degeneracies}, volume = {142}, year = {2015}, - Bdsk-Url-1 = {https://dx.doi.org/10.1063/1.4922159}} + bdsk-url-1 = {https://dx.doi.org/10.1063/1.4922159}} @article{Loos_2015c, author = {Loos, Pierre-Fran{\c c}ois and Ball, Caleb J. and Gill, Peter M. W.}, @@ -1316,7 +1316,7 @@ title = {Chemistry in One Dimension}, volume = {17}, year = {2015}, - Bdsk-Url-1 = {https://dx.doi.org/10.1039/C4CP03571B}} + bdsk-url-1 = {https://dx.doi.org/10.1039/C4CP03571B}} @article{Loos_2016, author = {Loos, Pierre-Fran{\c c}ois and Gill, Peter M. W.}, @@ -1329,7 +1329,7 @@ title = {{{The}} Uniform Electron Gas}, volume = {6}, year = {2016}, - Bdsk-Url-1 = {https://dx.doi.org/10.1002/wcms.1257}} + bdsk-url-1 = {https://dx.doi.org/10.1002/wcms.1257}} @article{Loos_2017a, author = {Loos, Pierre-Fran{\c c}ois}, @@ -1345,7 +1345,7 @@ title = {Exchange Functionals Based on Finite Uniform Electron Gases}, volume = {146}, year = {2017}, - Bdsk-Url-1 = {https://dx.doi.org/10.1063/1.4978409}} + bdsk-url-1 = {https://dx.doi.org/10.1063/1.4978409}} @article{Loos_2019a, author = {Loos, Pierre-Francois and Jacquemin, Denis}, @@ -1357,7 +1357,7 @@ title = {Chemically Accurate 0-0 Energies with not-so-Accurate Excited State Geometries}, volume = {15}, year = {2019}, - Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.8b01103}} + bdsk-url-1 = {https://doi.org/10.1021/acs.jctc.8b01103}} @article{Loos_2019c, author = {Loos, Pierre-Fran{\c c}ois and Boggio-Pasqua, Martial and Scemama, Anthony and Caffarel, Michel and Jacquemin, Denis}, @@ -1372,7 +1372,7 @@ url = {https://doi.org/10.1021/acs.jctc.8b01205}, volume = {15}, year = {2019}, - Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.8b01205}} + bdsk-url-1 = {https://doi.org/10.1021/acs.jctc.8b01205}} @article{Loos_2019d, author = {P. F. Loos and B. Pradines and A. Scemama and J. Toulouse and E. Giner}, @@ -1384,7 +1384,7 @@ title = {A Density-Based Basis-Set Correction for Wave Function Theory}, volume = {10}, year = {2019}, - Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.8b01103}} + bdsk-url-1 = {https://doi.org/10.1021/acs.jctc.8b01103}} @article{Loos_2020a, author = {P. F. Loos and B. Pradines and A. Scemama and E. Giner and J. Toulouse}, @@ -1394,7 +1394,7 @@ pages = {in press}, title = {A Density-Based Basis-Set Incompleteness Correction for GW Methods}, year = {2020}, - Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.8b01103}} + bdsk-url-1 = {https://doi.org/10.1021/acs.jctc.8b01103}} @article{Loos_2020b, author = {Loos, Pierre-Fran{\c c}ois and Jacquemin, Denis}, @@ -1407,7 +1407,7 @@ title = {Is ADC(3) as Accurate as CC3 for Valence and Rydberg Transition Energies?}, volume = {11}, year = {2020}, - Bdsk-Url-1 = {https://doi.org/10.1021/acs.jpclett.9b03652}} + bdsk-url-1 = {https://doi.org/10.1021/acs.jpclett.9b03652}} @article{Loos_2020c, author = {P. F. Loos and F. Lipparini and M. Boggio-Pasqua and A. Scemama and D. Jacquemin}, @@ -1419,7 +1419,7 @@ title = {A Mountaineering Strategy to Excited States: Highly-Accurate Energies and Benchmarks for Medium Sized Molecules}, volume = {16}, year = {2020}, - Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.9b01216}} + bdsk-url-1 = {https://doi.org/10.1021/acs.jctc.9b01216}} @article{Loos_2020d, author = {Loos, Pierre-Fran{\c c}ois and Scemama, Anthony and Jacquemin, Denis}, @@ -1432,7 +1432,7 @@ title = {The Quest for Highly Accurate Excitation Energies: A Computational Perspective}, volume = {11}, year = {2020}, - Bdsk-Url-1 = {https://doi.org/10.1021/acs.jpclett.0c00014}} + bdsk-url-1 = {https://doi.org/10.1021/acs.jpclett.0c00014}} @article{Loos_2020e, author = {Loos, Pierre-Fran{\c c}ois and Scemama, Anthony and Duchemin, Ivan and Jacquemin, Denis and Blase, Xavier}, @@ -1445,7 +1445,7 @@ title = {Pros and Cons of the Bethe--Salpeter Formalism for Ground-State Energies}, volume = {11}, year = {2020}, - Bdsk-Url-1 = {https://doi.org/10.1021/acs.jpclett.0c00460}} + bdsk-url-1 = {https://doi.org/10.1021/acs.jpclett.0c00460}} @article{Loos_2020f, author = {Loos, Pierre-Fran{\c c}ois and Scemama, Anthony and Boggio-Pasqua, Martial and Jacquemin, Denis}, @@ -1458,7 +1458,7 @@ title = {Mountaineering Strategy to Excited States: Highly Accurate Energies and Benchmarks for Exotic Molecules and Radicals}, volume = {16}, year = {2020}, - Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.0c00227}} + bdsk-url-1 = {https://doi.org/10.1021/acs.jctc.0c00227}} @article{Loos_2020g, author = {Loos,Pierre-Fran{\c c}ois and Fromager,Emmanuel}, @@ -1471,7 +1471,7 @@ title = {A weight-dependent local correlation density-functional approximation for ensembles}, volume = {152}, year = {2020}, - Bdsk-Url-1 = {https://doi.org/10.1063/5.0007388}} + bdsk-url-1 = {https://doi.org/10.1063/5.0007388}} @article{Loos_2020h, author = {Loos,Pierre-Fran{\c c}ois and Blase,Xavier}, @@ -1484,7 +1484,7 @@ title = {Dynamical correction to the Bethe--Salpeter equation beyond the plasmon-pole approximation}, volume = {153}, year = {2020}, - Bdsk-Url-1 = {https://doi.org/10.1063/5.0023168}} + bdsk-url-1 = {https://doi.org/10.1063/5.0023168}} @article{Loos_2020i, author = {Loos,Pierre-Fran{\c c}ois and Damour,Yann and Scemama,Anthony}, @@ -1497,17 +1497,18 @@ title = {The performance of CIPSI on the ground state electronic energy of benzene}, volume = {153}, year = {2020}, - Bdsk-Url-1 = {https://doi.org/10.1063/5.0027617}} + bdsk-url-1 = {https://doi.org/10.1063/5.0027617}} -@misc{Marie_2020, - archiveprefix = {arXiv}, +@article{Marie_2020, author = {Antoine Marie and Hugh G. A. Burton and Pierre-Fran{\c c}ois Loos}, date-added = {2020-12-09 09:59:26 +0100}, - date-modified = {2020-12-09 09:59:26 +0100}, - eprint = {2012.03688}, - primaryclass = {physics.chem-ph}, + date-modified = {2021-11-26 18:15:27 +0100}, + doi = {10.1088/1361-648X/abe795}, + journal = {J. Phys. Condens. Matter}, + pages = {283001}, title = {Perturbation Theory in the Complex Plane: Exceptional Points and Where to Find Them}, - year = {2020}} + volume = {33}, + year = {2021}} @article{Moreau_2004, author = {Moreau, Y. and Loos, P.-F. and Assfeld, X.}, @@ -1523,7 +1524,7 @@ 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}} + bdsk-url-1 = {https://dx.doi.org/10.1007/s00214-004-0581-4}} @article{Preat_2007, author = {Preat, Julien and Loos, Pierre-Francois and Assfeld, Xavier and Jacquemin, Denis and Perpete, Eric A.}, @@ -1540,7 +1541,7 @@ title = {A {{TD}}-{{DFT}} Investigation of {{UV}} Spectra of Pyranoidic Dyes: {{A NCM}} vs {{PCM}} Comparison}, volume = {808}, year = {2007}, - Bdsk-Url-1 = {https://dx.doi.org/10.1016/j.theochem.2006.12.047}} + bdsk-url-1 = {https://dx.doi.org/10.1016/j.theochem.2006.12.047}} @article{Preat_2007a, author = {Preat, Julien and Loos, Pierre-Francois and Assfeld, Xavier and Jacquemin, Denis and Perpete, Eric A.}, @@ -1556,7 +1557,7 @@ 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}} + 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.}, @@ -1580,7 +1581,7 @@ title = {Deterministic Construction Of Nodal Surfaces Within Quantum Monte Carlo: The Case Of {{FeS}}}, volume = {14}, year = {2018}, - Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.7b01250}} + bdsk-url-1 = {https://doi.org/10.1021/acs.jctc.7b01250}} @article{Scemama_2018b, author = {A. Scemama and A. Benali and D. Jacquemin and M. Caffarel and P. F. Loos}, @@ -1592,7 +1593,7 @@ title = {Excitation Energies From Diffusion Monte Carlo Using Selected Configuration Interaction Nodes}, volume = {149}, year = {2018}, - Bdsk-Url-1 = {https://arxiv.org/pdf/1805.09553.pdf}} + bdsk-url-1 = {https://arxiv.org/pdf/1805.09553.pdf}} @article{Scemama_2020, author = {Scemama,Anthony and Giner,Emmanuel and Benali,Anouar and Loos,Pierre-Fran{\c c}ois}, @@ -1605,7 +1606,7 @@ title = {Taming the fixed-node error in diffusion Monte Carlo via range separation}, volume = {153}, year = {2020}, - Bdsk-Url-1 = {https://doi.org/10.1063/5.0026324}} + bdsk-url-1 = {https://doi.org/10.1063/5.0026324}} @misc{Veril_2020, archiveprefix = {arXiv}, @@ -1629,7 +1630,7 @@ url = {https://doi.org/10.1063/1.5044202}, volume = {149}, year = {2018}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.5044202}} + bdsk-url-1 = {https://doi.org/10.1063/1.5044202}} @article{Zhang_2016, author = {Zhang,Du and Yang,Weitao}, @@ -1642,7 +1643,7 @@ title = {Accurate and efficient calculation of excitation energies with the active-space particle-particle random phase approximation}, volume = {145}, year = {2016}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.4964501}} + bdsk-url-1 = {https://doi.org/10.1063/1.4964501}} @article{Yang_2013b, author = {Yang,Yang and van Aggelen,Helen and Yang,Weitao}, @@ -1655,7 +1656,7 @@ title = {Double, Rydberg and charge transfer excitations from pairing matrix fluctuation and particle-particle random phase approximation}, volume = {139}, year = {2013}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.4834875}} + bdsk-url-1 = {https://doi.org/10.1063/1.4834875}} @article{Yang_2014a, author = {Yang,Yang and Peng,Degao and Lu,Jianfeng and Yang,Weitao}, @@ -1668,7 +1669,7 @@ title = {Excitation energies from particle-particle random phase approximation: Davidson algorithm and benchmark studies}, volume = {141}, year = {2014}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.4895792}} + bdsk-url-1 = {https://doi.org/10.1063/1.4895792}} @article{Peng_2014, author = {Peng,Degao and Yang,Yang and Zhang,Peng and Yang,Weitao}, @@ -1681,7 +1682,7 @@ title = {Restricted second random phase approximations and Tamm-Dancoff approximations for electronic excitation energy calculations}, volume = {141}, year = {2014}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.4901716}} + bdsk-url-1 = {https://doi.org/10.1063/1.4901716}} @article{Sutton_2018, author = {Sutton, Christopher and Yang, Yang and Zhang, Du and Yang, Weitao}, @@ -1694,7 +1695,7 @@ title = {Single, Double Electronic Excitations and Exciton Effective Conjugation Lengths in π-Conjugated Systems}, volume = {9}, year = {2018}, - Bdsk-Url-1 = {https://doi.org/10.1021/acs.jpclett.8b01366}} + bdsk-url-1 = {https://doi.org/10.1021/acs.jpclett.8b01366}} @article{Liu_2020, author = {C. Liu and J. Kloppenburg and Y. Yao and X. Ren and H. Appel and Y. Kanai and V. Blum}, @@ -1706,7 +1707,7 @@ title = {All-electron ab initio Bethe-Salpeter equation approach to neutral excitations in molecules with numeric atom-centered orbitals}, volume = {152}, year = {2020}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.5123290}} + bdsk-url-1 = {https://doi.org/10.1063/1.5123290}} @article{Krylov_2008, abstract = { The equation-of-motion coupled-cluster (EOM-CC) approach is a versatile electronic-structure tool that allows one to describe a variety of multiconfigurational wave functions within single-reference formalism. This review provides a guide to established EOM methods illustrated by examples that demonstrate the types of target states currently accessible by EOM. It focuses on applications of EOM-CC to electronically excited and open-shell species. The examples emphasize EOM's advantages for selected situations often perceived as multireference cases [e.g., interacting states of different nature, Jahn-Teller (JT) and pseudo-JT states, dense manifolds of ionized states, diradicals, and triradicals]. I also discuss limitations and caveats and offer practical solutions to some problematic situations. The review also touches on some formal aspects of the theory and important current developments. }, @@ -1720,7 +1721,7 @@ title = {Equation-of-Motion Coupled-Cluster Methods for Open-Shell and Electronically Excited Species: The Hitchhiker's Guide to Fock Space}, volume = {59}, year = {2008}, - Bdsk-Url-1 = {https://doi.org/10.1146/annurev.physchem.59.032607.093602}} + bdsk-url-1 = {https://doi.org/10.1146/annurev.physchem.59.032607.093602}} @article{Manohar_2008, author = {Manohar,Prashant U. and Krylov,Anna I.}, @@ -1733,7 +1734,7 @@ title = {A noniterative perturbative triples correction for the spin-flipping and spin-conserving equation-of-motion coupled-cluster methods with single and double substitutions}, volume = {129}, year = {2008}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.3013087}} + bdsk-url-1 = {https://doi.org/10.1063/1.3013087}} @article{Golubeva_2007, author = {Golubeva, Anna A. and Nemukhin, Alexandr V. and Klippenstein, Stephen J. and Harding, Lawrence B. and Krylov, Anna I.}, @@ -1746,7 +1747,7 @@ title = {Performance of the Spin-Flip and Multireference Methods for Bond Breaking in Hydrocarbons:  A Benchmark Study}, volume = {111}, year = {2007}, - Bdsk-Url-1 = {https://doi.org/10.1021/jp0764079}} + bdsk-url-1 = {https://doi.org/10.1021/jp0764079}} @article{Wang_2005, author = {Wang,Tao and Krylov,Anna I.}, @@ -1759,7 +1760,7 @@ title = {The effect of substituents on electronic states' ordering in meta-xylylene diradicals: Qualitative insights from quantitative studies}, volume = {123}, year = {2005}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.2018645}} + bdsk-url-1 = {https://doi.org/10.1063/1.2018645}} @article{Hossain_2017, author = {Hossain, Ekram and Deng, Shihu M. and Gozem, Samer and Krylov, Anna I. and Wang, Xue-Bin and Wenthold, Paul G.}, @@ -1772,7 +1773,7 @@ title = {Photoelectron Spectroscopy Study of Quinonimides}, volume = {139}, year = {2017}, - Bdsk-Url-1 = {https://doi.org/10.1021/jacs.7b05197}} + bdsk-url-1 = {https://doi.org/10.1021/jacs.7b05197}} @article{Luxon_2018, author = {Luxon, Adam R. and Orms, Natalie and Kanters, Ren{\'e} and Krylov, Anna I. and Parish, Carol A.}, @@ -1785,7 +1786,7 @@ title = {An ab Initio Exploration of the Bergman Cyclization}, volume = {122}, year = {2018}, - Bdsk-Url-1 = {https://doi.org/10.1021/acs.jpca.7b10576}} + bdsk-url-1 = {https://doi.org/10.1021/acs.jpca.7b10576}} @article{Casanova_2012, author = {Casanova,David}, @@ -1798,7 +1799,7 @@ title = {Avoided crossings, conical intersections, and low-lying excited states with a single reference method: The restricted active space spin-flip configuration interaction approach}, volume = {137}, year = {2012}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.4747341}} + bdsk-url-1 = {https://doi.org/10.1063/1.4747341}} @article{Nikiforov_2014, author = {Nikiforov,Alexander and Gamez,Jose A. and Thiel,Walter and Huix-Rotllant,Miquel and Filatov,Michael}, @@ -1811,7 +1812,7 @@ title = {Assessment of approximate computational methods for conical intersections and branching plane vectors in organic molecules}, volume = {141}, year = {2014}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.4896372}} + bdsk-url-1 = {https://doi.org/10.1063/1.4896372}} @article{Lefrancois_2016, author = {Lefrancois,Daniel and Rehn,Dirk R. and Dreuw,Andreas}, @@ -1824,7 +1825,7 @@ title = {Accurate adiabatic singlet-triplet gaps in atoms and molecules employing the third-order spin-flip algebraic diagrammatic construction scheme for the polarization propagator}, volume = {145}, year = {2016}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.4961298}} + bdsk-url-1 = {https://doi.org/10.1063/1.4961298}} @article{Rinkevicius_2010, abstract = {A spin-flip time dependent density functional theory approach with hybrid non-collinear exchange--correlation kernels has been applied to investigate the energy gap between the lowest singlet and triplet states of σ,σ-biradicals. The obtained results indicate that spin-flip time dependent density functional theory is capable to predict the correct ordering of singlet and triplet states among all investigated biradicals and that it gives estimates of singlet--triplet splittings in good agreement with high level correlated ab initio calculations. The theory provides a superior accuracy compared to the conventional broken-symmetry unrestricted density functional theory methods.}, @@ -1840,8 +1841,8 @@ url = {http://www.sciencedirect.com/science/article/pii/S0009261410004859}, volume = {491}, year = {2010}, - Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0009261410004859}, - Bdsk-Url-2 = {https://doi.org/10.1016/j.cplett.2010.03.074}} + bdsk-url-1 = {http://www.sciencedirect.com/science/article/pii/S0009261410004859}, + bdsk-url-2 = {https://doi.org/10.1016/j.cplett.2010.03.074}} @article{Ibeji_2015, abstract = {Over the last few years people have been interested in the process of singlet fission{,} owing to its relevance to solar cell technology. The energetics of singlet fission is intimately related to singlet--triplet (ST) gaps and energies of singlet excited states. However{,} accurate calculations of ST gaps in polyacenes are complicated due to near degeneracies in the π orbitals{,} and therefore{,} have been quite challenging. The spin--flip equation-of-motion coupled-cluster (SF-EOM-CC) and its perturbative approximation have been shown to correctly treat situations involving electronic degeneracies and near degeneracies. In this work{,} we use various spin--flip methods to benchmark the ST gaps of small polyacenes and show that the error in the ST gaps with respect to the experiment is small and does not increase appreciably with the system size. The diradical and polyradical character of the polyacene ground states increase with the system size. However{,} for the small polyacenes the open-shell character of the ground state is still small enough to be treated using single reference methods.}, @@ -1857,7 +1858,7 @@ url = {http://dx.doi.org/10.1039/C5CP00214A}, volume = {17}, year = {2015}, - Bdsk-Url-1 = {http://dx.doi.org/10.1039/C5CP00214A}} + bdsk-url-1 = {http://dx.doi.org/10.1039/C5CP00214A}} @article{Lefrancois_2015, author = {Lefrancois,Daniel and Wormit,Michael and Dreuw,Andreas}, @@ -1870,7 +1871,7 @@ title = {Adapting algebraic diagrammatic construction schemes for the polarization propagator to problems with multi-reference electronic ground states exploiting the spin-flip ansatz}, volume = {143}, year = {2015}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.4931653}} + bdsk-url-1 = {https://doi.org/10.1063/1.4931653}} @article{Mato_2018, abstract = {A new{,} general spin-correct spin-flip configuration interaction (SF-CI) method is introduced by extending the occupation restricted multiple active spaces (ORMAS) CI method in GAMESS. SF-ORMAS is a single reference CI method that utilizes a high-spin restricted open shell determinant on which an arbitrary amount of spin-flipped excitations are carried out to generate a wave function of desired multiplicity. Furthermore{,} the SF-ORMAS method allows for a flexible design of the active space(s) to fit the chemical problem at hand. Therefore{,} a variety of spin-flip schemes can be implemented within this one formalism. As SF-ORMAS mostly accounts for static correlation{,} dynamic correlation is included through perturbation theory. The new method is demonstrated for single and multiple bond breaking{,} diradical systems{,} vertical excitations of linear alkenes{,} and the singlet--triplet energy gap of silicon trimer.}, @@ -1886,7 +1887,7 @@ url = {http://dx.doi.org/10.1039/C7CP06837A}, volume = {20}, year = {2018}, - Bdsk-Url-1 = {http://dx.doi.org/10.1039/C7CP06837A}} + bdsk-url-1 = {http://dx.doi.org/10.1039/C7CP06837A}} @article{Levchenko_2004, author = {Levchenko,Sergey V. and Krylov,Anna I.}, @@ -1899,7 +1900,7 @@ title = {Equation-of-motion spin-flip coupled-cluster model with single and double substitutions: Theory and application to cyclobutadiene}, volume = {120}, year = {2004}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.1630018}} + bdsk-url-1 = {https://doi.org/10.1063/1.1630018}} @article{Krylov_2001a, abstract = {A new approach to the bond-breaking problem is proposed. Both closed and open shell singlet states are described within a single reference formalism as spin-flipping, e.g., α→β, excitations from a triplet (Ms=1) reference state for which both dynamical and non-dynamical correlation effects are much smaller than for the corresponding singlet state. Formally, the new theory can be viewed as an equation-of-motion (EOM) model where excited states are sought in the basis of determinants conserving the total number of electrons but changing the number of α and β electrons. The results for two simplest members of the proposed hierarchy of approximations are presented.}, @@ -1915,8 +1916,8 @@ url = {http://www.sciencedirect.com/science/article/pii/S0009261401002871}, volume = {338}, year = {2001}, - Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0009261401002871}, - Bdsk-Url-2 = {https://doi.org/10.1016/S0009-2614(01)00287-1}} + bdsk-url-1 = {http://www.sciencedirect.com/science/article/pii/S0009261401002871}, + bdsk-url-2 = {https://doi.org/10.1016/S0009-2614(01)00287-1}} @article{Krylov_2002, author = {Krylov,Anna I. and Sherrill,C. David}, @@ -1929,7 +1930,7 @@ title = {Perturbative corrections to the equation-of-motion spin--flip self-consistent field model: Application to bond-breaking and equilibrium properties of diradicals}, volume = {116}, year = {2002}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.1445116}} + bdsk-url-1 = {https://doi.org/10.1063/1.1445116}} @article{Sears_2003, author = {Sears,John S. and Sherrill,C. David and Krylov,Anna I.}, @@ -1942,7 +1943,7 @@ title = {A spin-complete version of the spin-flip approach to bond breaking: What is the impact of obtaining spin eigenfunctions?}, volume = {118}, year = {2003}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.1568735}} + bdsk-url-1 = {https://doi.org/10.1063/1.1568735}} @article{Slipchenko_2002, author = {Slipchenko,Lyudmila V. and Krylov,Anna I.}, @@ -1955,7 +1956,7 @@ title = {Singlet-triplet gaps in diradicals by the spin-flip approach: A benchmark study}, volume = {117}, year = {2002}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.1498819}} + bdsk-url-1 = {https://doi.org/10.1063/1.1498819}} @article{Slipchenko_2003, author = {Slipchenko,Lyudmila V. and Krylov,Anna I.}, @@ -1968,7 +1969,7 @@ title = {Electronic structure of the trimethylenemethane diradical in its ground and electronically excited states: Bonding, equilibrium geometries, and vibrational frequencies}, volume = {118}, year = {2003}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.1561052}} + bdsk-url-1 = {https://doi.org/10.1063/1.1561052}} @article{Sherrill_1998, author = {Sherrill,C. David and Krylov,Anna I. and Byrd,Edward F. C. and Head-Gordon,Martin}, @@ -1983,7 +1984,7 @@ url = {https://doi.org/10.1063/1.477023}, volume = {109}, year = {1998}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.477023}} + bdsk-url-1 = {https://doi.org/10.1063/1.477023}} @article{Krylov_2000a, author = {Krylov,Anna I. and Sherrill,C. David and Head-Gordon,Martin}, @@ -1998,7 +1999,7 @@ url = {https://doi.org/10.1063/1.1311292}, volume = {113}, year = {2000}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.1311292}} + bdsk-url-1 = {https://doi.org/10.1063/1.1311292}} @article{Casanova_2008, author = {Casanova,David and Head-Gordon,Martin}, @@ -2011,7 +2012,7 @@ title = {The spin-flip extended single excitation configuration interaction method}, volume = {129}, year = {2008}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.2965131}} + bdsk-url-1 = {https://doi.org/10.1063/1.2965131}} @article{Casanova_2009b, abstract = {A new formulation of the spin-flip (SF) method is presented. The electronic wave function is specified by the definition of an active space and through α-to-β excitations from a Hartree--Fock reference. The method belongs to the restricted active space (RAS) family{,} where the CI expansion is restricted by classifying the molecular orbitals in three subspaces. Properties such as spin completeness{,} variationality{,} size consistency{,} size intensivity{,} and orbital invariance are discussed. The implementation and applications use a particular truncation of the wave function{,} with the inclusion of hole and particle contributions such that for fixed active space size{,} the number of amplitudes is linear in molecular size. This approach is used to investigate single and double bond-breaking{,} the singlet--triplet gap of linear acenes{,} electronic transitions in three Ni(ii) octahedral complexes{,} the low-lying states of the 2{,}5-didehydrometaxylylene (DDMX) tetraradical and the ground state multiplicity of 28 non-Kekul{\'e} structures. The results suggest that this approach can provide a quite well balanced description of nearly degenerate electronic states at moderate computational cost.}, @@ -2024,7 +2025,7 @@ title = {Restricted active space spin-flip configuration interaction approach: theory{,} implementation and examples}, volume = {11}, year = {2009}, - Bdsk-Url-1 = {http://dx.doi.org/10.1039/B911513G}} + bdsk-url-1 = {http://dx.doi.org/10.1039/B911513G}} @article{Casanova_2009a, author = {Casanova,David and Slipchenko,Lyudmila V. and Krylov,Anna I. and Head-Gordon,Martin}, @@ -2037,7 +2038,7 @@ title = {Double spin-flip approach within equation-of-motion coupled cluster and configuration interaction formalisms: Theory, implementation, and examples}, volume = {130}, year = {2009}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.3066652}} + bdsk-url-1 = {https://doi.org/10.1063/1.3066652}} @article{Mayhall_2014c, abstract = {In this paper{,} we report the development{,} implementation{,} and assessment of a novel method for describing strongly correlated systems{,} spin--flip non-orthogonal configuration interaction (SF-NOCI). The wavefunction is defined to be a linear combination of independently relaxed Slater determinants obtained from all possible spin--flipping excitations within a localized orbital active-space{,} typically taken to be the singly occupied orbitals of a high-spin ROHF wavefunction. The constrained orbital optimization of each CI basis configuration is defined such that only non-active-space orbitals are allowed to relax (all active space orbitals are fixed). A number of simplifications and benefits arise due to the fact that only a restricted number of orbital rotations are permitted{,} (1) basis states cannot coalesce during SCF{,} (2) basis state optimization is better conditioned due to a larger effective HOMO--LUMO gap{,} (3) smooth potential energy surfaces are easily obtained{,} (4) the Hamiltonian coupling between two basis states with non-orthogonal orbitals is greatly simplified. To illustrate the advantages over a conventional orthogonal CI expansion{,} we investigate exchange coupling constants of bimetallic complexes{,} the avoided crossing of the lowest singlet states during LiF dissociation{,} and ligand non-innocence in an organometallic complex. These numerical examples indicate that good qualitative agreement can be obtained with SF-NOCI{,} but dynamical correlation must be included to obtain quantitative accuracy.}, @@ -2050,7 +2051,7 @@ title = {Spin--flip non-orthogonal configuration interaction: a variational and almost black-box method for describing strongly correlated molecules}, volume = {16}, year = {2014}, - Bdsk-Url-1 = {http://dx.doi.org/10.1039/C4CP02818J}} + bdsk-url-1 = {http://dx.doi.org/10.1039/C4CP02818J}} @article{Mayhall_2014b, author = {Mayhall, Nicholas J. and Goldey, Matthew and Head-Gordon, Martin}, @@ -2063,7 +2064,7 @@ title = {A Quasidegenerate Second-Order Perturbation Theory Approximation to RAS-nSF for Excited States and Strong Correlations}, volume = {10}, year = {2014}, - Bdsk-Url-1 = {https://doi.org/10.1021/ct400898p}} + bdsk-url-1 = {https://doi.org/10.1021/ct400898p}} @article{Bell_2013, abstract = {The restricted active space spin-flip (RAS-SF) approach is a multistate{,} spin-complete{,} variational and size consistent method applicable to systems featuring electronic (near-)degeneracies. In contrast to CASSCF it does not involve orbital optimizations and so avoids issues such as root-flipping and state averaging. This also makes RAS-SF calculations roughly 100--1000 times faster. In this paper RAS-SF method is extended to include variable orbital active spaces and three or more spin-flips{,} which allows the study of polynuclear metal systems{,} triple bond dissociations and organic polyradicals featuring more than four unpaired electrons. Benchmark calculations on such systems are carried out and comparison to other wave-function based{,} multi-reference methods{,} such as CASSCF and DMRG yield very good agreement{,} provided that the same active space is employed. Where experimental values are available{,} RAS-SF is found to substantially underestimate the exchange coupling constants{,} if the minimal active space is chosen. However{,} the correct ground state is always obtained. Not surprisingly{,} inclusion of bridge orbitals into the active space can cause the magnitude of the coupling constants to increase substantially. Importantly{,} the ratio of exchange couplings in related systems is in much better agreement with experiment than the magnitude of the coupling. Nevertheless{,} the results indicate the need for the inclusion of dynamic correlation to obtain better accuracy in minimal active spaces.}, @@ -2079,7 +2080,7 @@ url = {http://dx.doi.org/10.1039/C2CP43293E}, volume = {15}, year = {2013}, - Bdsk-Url-1 = {http://dx.doi.org/10.1039/C2CP43293E}} + bdsk-url-1 = {http://dx.doi.org/10.1039/C2CP43293E}} @article{Dutta_2013, author = {Dutta,Achintya Kumar and Pal,Sourav and Ghosh,Debashree}, @@ -2092,7 +2093,7 @@ title = {Perturbative approximations to single and double spin flip equation of motion coupled cluster singles doubles methods}, volume = {139}, year = {2013}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.4821936}} + bdsk-url-1 = {https://doi.org/10.1063/1.4821936}} @article{Mayhall_2014a, author = {Mayhall,Nicholas J. and Head-Gordon,Martin}, @@ -2105,7 +2106,7 @@ title = {Increasing spin-flips and decreasing cost: Perturbative corrections for external singles to the complete active space spin flip model for low-lying excited states and strong correlation}, volume = {141}, year = {2014}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.4889918}} + bdsk-url-1 = {https://doi.org/10.1063/1.4889918}} @article{Shao_2003, author = {Shao,Yihan and Head-Gordon,Martin and Krylov,Anna I.}, @@ -2118,7 +2119,7 @@ title = {The spin--flip approach within time-dependent density functional theory: Theory and applications to diradicals}, volume = {118}, year = {2003}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.1545679}} + bdsk-url-1 = {https://doi.org/10.1063/1.1545679}} @article{Bernard_2012, author = {Bernard,Yves A. and Shao,Yihan and Krylov,Anna I.}, @@ -2131,7 +2132,7 @@ title = {General formulation of spin-flip time-dependent density functional theory using non-collinear kernels: Theory, implementation, and benchmarks}, volume = {136}, year = {2012}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.4714499}} + bdsk-url-1 = {https://doi.org/10.1063/1.4714499}} @article{Orms_2018, author = {Orms, Natalie and Rehn, Dirk R. and Dreuw, Andreas and Krylov, Anna I.}, @@ -2144,7 +2145,7 @@ title = {Characterizing Bonding Patterns in Diradicals and Triradicals by Density-Based Wave Function Analysis: A Uniform Approach}, volume = {14}, year = {2018}, - Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.7b01012}} + bdsk-url-1 = {https://doi.org/10.1021/acs.jctc.7b01012}} @article{Manohar_2009, author = {Manohar, Prashant U. and Koziol, Lucas and Krylov, Anna I.}, @@ -2157,7 +2158,7 @@ title = {Effect of a Heteroatom on Bonding Patterns and Triradical Stabilization Energies of 2,4,6-Tridehydropyridine versus 1,3,5-Tridehydrobenzene}, volume = {113}, year = {2009}, - Bdsk-Url-1 = {https://doi.org/10.1021/jp810522e}} + bdsk-url-1 = {https://doi.org/10.1021/jp810522e}} @article{Krylov_2005, author = {Krylov, Anna I.}, @@ -2170,7 +2171,7 @@ title = {Triradicals}, volume = {109}, year = {2005}, - Bdsk-Url-1 = {https://doi.org/10.1021/jp0528212}} + bdsk-url-1 = {https://doi.org/10.1021/jp0528212}} @article{Shibuya_1970, author = {Shibuya, Tai-Ichi and McKoy, Vincent}, @@ -2182,8 +2183,8 @@ title = {Higher Random-Phase Approximation as an Approximation to the Equations of Motion}, volume = {2}, year = {1970}, - Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevA.2.2208}, - Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevA.2.2208}} + bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevA.2.2208}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRevA.2.2208}} @article{Bethe_1931, author = {H. Bethe}, @@ -2195,7 +2196,7 @@ title = {Zur Theorie der Metalle}, volume = {71}, year = {1931}, - Bdsk-Url-1 = {https://doi.org/10.1007/BF01341708}} + bdsk-url-1 = {https://doi.org/10.1007/BF01341708}} @article{Adamo_2013, author = {Adamo, C. and Jacquemin, D.}, @@ -2207,7 +2208,7 @@ title = {The Calculations of Excited-State Properties with Time-Dependent Density Functional Theory}, volume = {42}, year = {2013}, - Bdsk-Url-1 = {https://doi.org/10.1039/C2CS35394F}} + bdsk-url-1 = {https://doi.org/10.1039/C2CS35394F}} @article{Laurent_2013, author = {Laurent, Ad{\`e}le D. and Jacquemin, Denis}, @@ -2219,7 +2220,7 @@ title = {TD-DFT Benchmarks: A Review}, volume = {113}, year = {2013}, - Bdsk-Url-1 = {https://doi.org/10.1002/qua.24438}} + bdsk-url-1 = {https://doi.org/10.1002/qua.24438}} @article{Sneskov_2012, abstract = {Abstract We review coupled cluster (CC) theory for electronically excited states. We outline the basics of a CC response theory framework that allows the transfer of the attractive accuracy and convergence properties associated with CC methods over to the calculation of electronic excitation energies and properties. Key factors affecting the accuracy of CC excitation energy calculations are discussed as are some of the key CC models in this field. To aid both the practitioner as well as the developer of CC excited state methods, we also briefly discuss the key computational steps in a working CC response implementation. Approaches aimed at extending the application range of CC excited state methods either in terms of molecular size and phenomena or in terms of environment (solution and proteins) are also discussed. {\copyright} 2011 John Wiley \& Sons, Ltd. This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods}, @@ -2232,8 +2233,8 @@ title = {Excited State Coupled Cluster Methods}, volume = {2}, year = {2012}, - Bdsk-Url-1 = {https://onlinelibrary.wiley.com/doi/abs/10.1002/wcms.99}, - Bdsk-Url-2 = {https://doi.org/10.1002/wcms.99}} + bdsk-url-1 = {https://onlinelibrary.wiley.com/doi/abs/10.1002/wcms.99}, + bdsk-url-2 = {https://doi.org/10.1002/wcms.99}} @article{Krylov_2006, author = {Krylov, Anna I.}, @@ -2245,7 +2246,7 @@ title = {Spin-Flip Equation-of-Motion Coupled-Cluster Electronic Structure Method for a Description of Excited States, Bond Breaking, Diradicals, and Triradicals}, volume = {39}, year = {2006}, - Bdsk-Url-1 = {https://doi.org/10.1021/ar0402006}} + bdsk-url-1 = {https://doi.org/10.1021/ar0402006}} @article{Piecuch_2002, author = {Piotr Piecuch and Karol Kowalski and Ian S. O. Pimienta and Michael J. Mcguire}, @@ -2258,7 +2259,7 @@ title = {Recent advances in electronic structure theory: Method of moments of coupled-cluster equations and renormalized coupled-cluster approaches}, volume = {21}, year = {2002}, - Bdsk-Url-1 = {https://doi.org/10.1080/0144235021000053811}} + bdsk-url-1 = {https://doi.org/10.1080/0144235021000053811}} @article{Puschnig_2002, author = {Puschnig, Peter and Ambrosch-Draxl, Claudia}, @@ -2275,8 +2276,8 @@ url = {https://link.aps.org/doi/10.1103/PhysRevLett.89.056405}, volume = {89}, year = {2002}, - Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.89.056405}, - Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevLett.89.056405}} + bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.89.056405}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRevLett.89.056405}} @article{Horst_1999, author = {van der Horst, J.-W. and Bobbert, P. A. and Michels, M. A. J. and Brocks, G. and Kelly, P. J.}, @@ -2293,8 +2294,8 @@ url = {https://link.aps.org/doi/10.1103/PhysRevLett.83.4413}, volume = {83}, year = {1999}, - Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.83.4413}, - Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevLett.83.4413}} + bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.83.4413}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRevLett.83.4413}} @article{Rohlfing_1995, author = {Rohlfing, Michael and Kr{\"u}ger, Peter and Pollmann, Johannes}, @@ -2311,8 +2312,8 @@ url = {https://link.aps.org/doi/10.1103/PhysRevB.52.1905}, volume = {52}, year = {1995}, - Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.52.1905}, - Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevB.52.1905}} + bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.52.1905}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRevB.52.1905}} @article{Rohlfing_1998, author = {Rohlfing, Michael and Louie, Steven G.}, @@ -2329,8 +2330,8 @@ url = {https://link.aps.org/doi/10.1103/PhysRevLett.81.2312}, volume = {81}, year = {1998}, - Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.81.2312}, - Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevLett.81.2312}} + bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.81.2312}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRevLett.81.2312}} @article{Rohlfing_1999a, author = {Rohlfing, Michael and Louie, Steven G.}, @@ -2347,8 +2348,8 @@ url = {https://link.aps.org/doi/10.1103/PhysRevLett.82.1959}, volume = {82}, year = {1999}, - Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.82.1959}, - Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevLett.82.1959}} + bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.82.1959}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRevLett.82.1959}} @article{Rohlfing_1999b, author = {Rohlfing, Michael and Louie, Steven G.}, @@ -2365,8 +2366,8 @@ url = {https://link.aps.org/doi/10.1103/PhysRevLett.83.856}, volume = {83}, year = {1999}, - Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.83.856}, - Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevLett.83.856}} + bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.83.856}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRevLett.83.856}} @article{Rohlfing_2012, author = {Rohlfing, Michael}, @@ -2383,8 +2384,8 @@ url = {https://link.aps.org/doi/10.1103/PhysRevLett.108.087402}, volume = {108}, year = {2012}, - Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.108.087402}, - Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevLett.108.087402}} + bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.108.087402}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRevLett.108.087402}} @article{Li_2016, author = {Li, Zhendong and Liu, Wenjian}, @@ -2400,7 +2401,7 @@ url = {https://doi.org/10.1021/acs.jctc.5b01158}, volume = {12}, year = {2016}, - Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.5b01158}} + bdsk-url-1 = {https://doi.org/10.1021/acs.jctc.5b01158}} @article{Li_2010, author = {Li,Zhendong and Liu,Wenjian}, @@ -2413,7 +2414,7 @@ title = {Spin-adapted open-shell random phase approximation and time-dependent density functional theory. I. Theory}, volume = {133}, year = {2010}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.3463799}} + bdsk-url-1 = {https://doi.org/10.1063/1.3463799}} @article{Li_2011b, author = {Li,Zhendong and Liu,Wenjian}, @@ -2426,7 +2427,7 @@ title = {Spin-adapted open-shell time-dependent density functional theory. III. An even better and simpler formulation}, volume = {135}, year = {2011}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.3660688}} + bdsk-url-1 = {https://doi.org/10.1063/1.3660688}} @article{Li_2011a, author = {Li,Zhendong and Liu,Wenjian and Zhang,Yong and Suo,Bingbing}, @@ -2439,7 +2440,7 @@ title = {Spin-adapted open-shell time-dependent density functional theory. II. Theory and pilot application}, volume = {134}, year = {2011}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.3573374}} + bdsk-url-1 = {https://doi.org/10.1063/1.3573374}} @article{Casanova_2020, author = {D. Casanova and A. I. Krylov}, @@ -2451,7 +2452,7 @@ title = {Spin-Flip Methods in Quantum Chemistry}, volume = {22}, year = {2020}, - Bdsk-Url-1 = {https://doi.org/10.1039/c9cp06507e}} + bdsk-url-1 = {https://doi.org/10.1039/c9cp06507e}} @article{Zhang_2004, author = {Zhang, Fan and Burke, Kieron}, @@ -2463,8 +2464,8 @@ title = {Adiabatic connection for near degenerate excited states}, volume = {69}, year = {2004}, - Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevA.69.052510}, - Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevA.69.052510}} + bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevA.69.052510}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRevA.69.052510}} @article{Marut_2020, author = {C. Marut and B. Senjean and E. Fromager and P. F. Loos}, @@ -2476,7 +2477,7 @@ title = {Weight dependence of local exchange-correlation functionals in ensemble density-functional theory: double excitations in two-electron systems}, volume = {224}, year = {2020}, - Bdsk-Url-1 = {https://doi.org/10.1039/d0fd00059k}} + bdsk-url-1 = {https://doi.org/10.1039/d0fd00059k}} @article{Bottcher_1974, author = {C. Bottcher and K. Docken}, @@ -2488,7 +2489,7 @@ title = {Autoionizing States of the Hydrogen Molecule.}, volume = {7}, year = {1974}, - Bdsk-Url-1 = {https://doi.org/10.1088/0022-3700/7/1/002}} + bdsk-url-1 = {https://doi.org/10.1088/0022-3700/7/1/002}} @article{Burges_1995, author = {A. Burgers and D. Wintgen and J.-M. Rost}, @@ -2500,7 +2501,7 @@ title = {Highly doubly excited S states of the helium atom}, volume = {28}, year = {1995}, - Bdsk-Url-1 = {https://doi.org/10.1088/0953-4075/28/15/010}} + bdsk-url-1 = {https://doi.org/10.1088/0953-4075/28/15/010}} @article{Madden_1963, author = {R. P. Madden and K. Codling}, @@ -2512,7 +2513,7 @@ title = {New Autoionizing Atomic Energy Levels in He, Ne, and Ar}, volume = {10}, year = {1963}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevLett.10.516}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRevLett.10.516}} @article{Hesselmann_2011, author = {He{\ss}elmann,Andreas and G{\"o}rling,Andreas}, @@ -2525,7 +2526,7 @@ title = {Efficient exact-exchange time-dependent density-functional theory methods and their relation to time-dependent Hartree--Fock}, volume = {134}, year = {2011}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.3517312}} + bdsk-url-1 = {https://doi.org/10.1063/1.3517312}} @article{Hellgren_2012, author = {Hellgren, Maria and Gross, E. K. U.}, @@ -2537,8 +2538,8 @@ title = {Discontinuities of the exchange-correlation kernel and charge-transfer excitations in time-dependent density-functional theory}, volume = {85}, year = {2012}, - Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevA.85.022514}, - Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevA.85.022514}} + bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevA.85.022514}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRevA.85.022514}} @article{Hellgren_2013, author = {Hellgren, Maria and Gross, E. K. U.}, @@ -2550,8 +2551,8 @@ title = {Discontinuous functional for linear-response time-dependent density-functional theory: The exact-exchange kernel and approximate forms}, volume = {88}, year = {2013}, - Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevA.88.052507}, - Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevA.88.052507}} + bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevA.88.052507}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRevA.88.052507}} @article{Staroverov_1998, abstract = {A technique for reducing computational effort in multireference second-order perturbation theory with very large complete active space {\v Z}CAS. SCF reference functions is proposed. This is achieved by construction of an effective Hamiltonian within the space of configurations dominating the reference function expansion. The method is tested on the standard problems of singlet\textendash{}triplet {\v Z}1A1\textendash{}3B1. separation in the CH 2 radical and vertical excitation energies in formaldehyde. Numerical results show that good accuracy can be obtained even with substantially reduced model spaces. q 1998 Elsevier Science B.V. All rights reserved.}, @@ -2569,7 +2570,7 @@ title = {The Reduced Model Space Method in Multireference Second-Order Perturbation Theory}, volume = {296}, year = {1998}, - Bdsk-Url-1 = {https://doi.org/10.1016/S0009-2614(98)01092-6}} + bdsk-url-1 = {https://doi.org/10.1016/S0009-2614(98)01092-6}} @article{Rawlings_1983, author = {Rawlings, Diane C and Davidson, Ernest R}, @@ -2583,7 +2584,7 @@ title = {{{The Rayleigh}}-{{Schrodinger Bk Method Applied To The Lower Electronic States Of Pyrrole}}}, volume = {98}, year = {1983}, - Bdsk-Url-1 = {https://doi.org/10.1016/0009-2614(83)80080-3}} + bdsk-url-1 = {https://doi.org/10.1016/0009-2614(83)80080-3}} @article{Davidson_1981, author = {Davidson, Ernest R. and McMurchie, Larry E. and Day, Sheryl J.}, @@ -2601,7 +2602,7 @@ title = {The {{{\emph{B}}}} {\textsubscript{ }}{{{\textsubscript{{\emph{K}}}}}}{\textsubscript{ }} Method: {{Application}} to Methylene}, volume = {74}, year = {1981}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.440954}} + bdsk-url-1 = {https://doi.org/10.1063/1.440954}} @article{Nitzsche_1978b, abstract = {A b initio SCF-CI calculations have been performed on several states of N-methylacetamide near the ground-state equilibrium geometry. The 3 m * state is predicted to lie about 0.5-0.6 eV above the 3 n \textasciitilde{} s*tate. The 3 n \textasciitilde{} s*tate is expected to lie about 0.2-0.3 eV below the experimental l n r * state at 5.5 eV. The I K K * , IK\textasciitilde{}P,,and ln3p configurations are predicted to be strongly mixed, giving three states of large oscillator strength in the region of the broad V band of the absorption spectrum.}, @@ -2619,7 +2620,7 @@ title = {Ab Initio Calculation of Some Vertical Excitation Energies of {{N}}-Methylacetamide}, volume = {100}, year = {1978}, - Bdsk-Url-1 = {https://doi.org/10.1021/ja00491a013}} + bdsk-url-1 = {https://doi.org/10.1021/ja00491a013}} @article{LiManni_2013, abstract = {A new multiconfigurational quantum chemical method, SplitGAS, is presented. The configuration interaction expansion, generated from a generalized active space, GAS, wave function is split in two parts, a principal part containing the most relevant configurations and an extended part containing less relevant, but not negligible, configurations. The partition is based on an orbital criterion. The SplitGAS method has been employed to study the HF, N2, and Cr2 molecules. The results on these systems, especially on the challenging, multiconfigurational Cr2 molecule, are satisfactory. While SplitGAS is comparable with the GASSCF method in terms of memory requirements, it performs better than the complete active space method followed by second-order perturbation theory, CASPT2, in terms of equilibrium bond length, dissociation energy, and vibrational properties.}, @@ -2637,7 +2638,7 @@ title = {{{SplitGAS Method}} for {{Strong Correlation}} and the {{Challenging Case}} of {{Cr}} {\textsubscript{2}}}, volume = {9}, year = {2013}, - Bdsk-Url-1 = {https://doi.org/10.1021/ct400046n}} + bdsk-url-1 = {https://doi.org/10.1021/ct400046n}} @article{Gershgorn_1968, author = {Gershgorn, Z. and Shavitt, I.}, @@ -2654,7 +2655,7 @@ title = {An Application of Perturbation Theory Ideas in Configuration Interaction Calculations}, volume = {2}, year = {1968}, - Bdsk-Url-1 = {https://doi.org/10.1002/qua.560020603}} + bdsk-url-1 = {https://doi.org/10.1002/qua.560020603}} @article{Malrieu_1985, abstract = {The theory of effective Hamiltonians is well established. However, limitations appear in its applicability for many problems in molecular physics and quantum chemistry. The standard effective Hamiltonians may become strongly non-Hermitian when there is a large coupling between the model space, in which they are defined, and the outer space Moreover, in the presence of intruder states, discontinuities appear in the matrix elements of these effective Hamiltonians as a function of the internuclear distances. To solve these difficulties, a new class of effective Hamiltonians (called intermediate Hamiltonians) is presented; only one part of their roots are exact eigen-energies of the full Hamiltonian. The theory of these intermediate Hamiltonians is presented by means of a new wave-operator R which is the analogue of the wave-operator Omega in the theory of effective Hamiltonians. Solutions are obtained by a generalised degenerate perturbation theory (GDPT) and by iterative procedures. Two model systems are numerically solved which demonstrate the good convergence properties of GDPT with respect to standard degenerate perturbation theory (DPT). Continuity of the solutions is also checked in the presence of an intruder state.}, @@ -2671,8 +2672,8 @@ url = {https://doi.org/10.1088%2F0305-4470%2F18%2F5%2F014}, volume = {18}, year = 1985, - Bdsk-Url-1 = {https://doi.org/10.1088%2F0305-4470%2F18%2F5%2F014}, - Bdsk-Url-2 = {https://doi.org/10.1088/0305-4470/18/5/014}} + bdsk-url-1 = {https://doi.org/10.1088%2F0305-4470%2F18%2F5%2F014}, + bdsk-url-2 = {https://doi.org/10.1088/0305-4470/18/5/014}} @article{Dvorak_2019b, author = {M. Dvorak and D. Golze and P. Rinke}, @@ -2684,7 +2685,7 @@ title = {Quantum embedding theory in the screened Coulomb interaction: Combining configuration interaction with $GW$/BSE}, volume = {3}, year = {2019}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevB.99.115134}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRevB.99.115134}} @article{Dvorak_2019a, author = {M. Dvorak and P. Rinke}, @@ -2696,7 +2697,7 @@ title = {Dynamical configuration interaction: Quantum embedding that combines wave functions and Green's functions}, volume = {99}, year = {2019}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevB.99.115134}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRevB.99.115134}} @article{Gunnarsson_1976, author = {Gunnarsson, O. and Lundqvist, B. I.}, @@ -2713,8 +2714,8 @@ url = {https://link.aps.org/doi/10.1103/PhysRevB.13.4274}, volume = {13}, year = {1976}, - Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.13.4274}, - Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevB.13.4274}} + bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.13.4274}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRevB.13.4274}} @article{Langreth_1975, author = {D.C. Langreth and J.P. Perdew}, @@ -2729,8 +2730,8 @@ url = {http://www.sciencedirect.com/science/article/pii/0038109879902540}, volume = {31}, year = {1979}, - Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/0038109879902540}, - Bdsk-Url-2 = {https://doi.org/10.1016/0038-1098(79)90254-0}} + bdsk-url-1 = {http://www.sciencedirect.com/science/article/pii/0038109879902540}, + bdsk-url-2 = {https://doi.org/10.1016/0038-1098(79)90254-0}} @article{Teh_2019, author = {H.-H. Teh and J. E. Subotnik}, @@ -2742,7 +2743,7 @@ title = {The Simplest Possible Approach for Simulating S0−S1 Conical Intersections with DFT/TDDFT: Adding One Doubly Excited Configuration}, volume = {10}, year = {2019}, - Bdsk-Url-1 = {https://doi.org/10.1021/acs.jpclett.9b00981}} + bdsk-url-1 = {https://doi.org/10.1021/acs.jpclett.9b00981}} @article{Lowdin_1963, author = {P. L{\"o}wdin}, @@ -2754,7 +2755,7 @@ title = {Studies in perturbation theory: Part I. An elementary iteration-variation procedure for solving the Schr{\"o}dinger equation by partitioning technique}, volume = {10}, year = {1963}, - Bdsk-Url-1 = {https://doi.org/10.1016/0022-2852(63)90151-6}} + bdsk-url-1 = {https://doi.org/10.1016/0022-2852(63)90151-6}} @article{Petersilka_1996, author = {M. Petersilka and U. J. Gossmann and E. K. U. Gross}, @@ -2766,7 +2767,7 @@ title = {Excitation Energies From Time-Dependent Density-Functional Theory}, volume = {76}, year = {1996}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevLett.76.1212}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRevLett.76.1212}} @article{Nielsen_1980, author = {Egon S. Nielsen and Poul Jorgensen}, @@ -2778,7 +2779,7 @@ title = {Transition moments and dynamic polarizabilities in a second order polarization propagator approach}, volume = {73}, year = {1980}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.440119}} + bdsk-url-1 = {https://doi.org/10.1063/1.440119}} @article{Oddershede_1977, author = {Jens Oddershede and Poul Jorgensen}, @@ -2790,7 +2791,7 @@ title = {An order analysis of the particle--hole propagator}, volume = {66}, year = {1977}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.434118}} + bdsk-url-1 = {https://doi.org/10.1063/1.434118}} @phdthesis{Huix-Rotllant_PhD, author = {M. Huix-Rotllant}, @@ -2800,7 +2801,7 @@ title = {Improved correlation kernels for linear-response time-dependent density-functional theory}, url = {https://tel.archives-ouvertes.fr/tel-00680039/}, year = {2011}, - Bdsk-Url-1 = {https://tel.archives-ouvertes.fr/tel-01027522}} + bdsk-url-1 = {https://tel.archives-ouvertes.fr/tel-01027522}} @article{Maitra_2016, author = {N. T. Maitra}, @@ -2812,7 +2813,7 @@ title = {Fundamental aspects of time-dependent density functional theory}, volume = {144}, year = {2016}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.4953039}} + bdsk-url-1 = {https://doi.org/10.1063/1.4953039}} @article{Christiansen_1995a, author = {Ove Christiansen and Henrik Koch and Poul J{\o}rgensen}, @@ -2826,8 +2827,8 @@ url = {http://www.sciencedirect.com/science/article/pii/000926149500841Q}, volume = {243}, year = {1995}, - Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/000926149500841Q}, - Bdsk-Url-2 = {http://dx.doi.org/10.1016/0009-2614(95)00841-Q}} + bdsk-url-1 = {http://www.sciencedirect.com/science/article/pii/000926149500841Q}, + bdsk-url-2 = {http://dx.doi.org/10.1016/0009-2614(95)00841-Q}} @article{Wambach_1988, author = {J. Wambach}, @@ -2839,7 +2840,7 @@ title = {Damping of small-amplitude nuclear collective motion}, volume = {51}, year = {1988}, - Bdsk-Url-1 = {https://doi.org/10.1088/0034-4885/51/7/002}} + bdsk-url-1 = {https://doi.org/10.1088/0034-4885/51/7/002}} @article{Sakkinen_2012, author = {N. Sakkinen and M. Manninen and R. van Leeuwen}, @@ -2851,7 +2852,7 @@ title = {The Kadanoff-Baym approach to double excitations in finite systems}, volume = {14}, year = {2012}, - Bdsk-Url-1 = {https://doi.org/10.1088/1367-2630/14/1/013032}} + bdsk-url-1 = {https://doi.org/10.1088/1367-2630/14/1/013032}} @article{Myohanen_2008, author = {P. My{\"o}h{\"a}nen and A. Stan and G. Stefanucci and R. van Leeuwen}, @@ -2863,7 +2864,7 @@ title = {A many-body approach to quantum transport dynamics: Initial correlations and memory effects}, volume = {84}, year = {2008}, - Bdsk-Url-1 = {https://doi.org/10.1209/0295-5075/84/67001}} + bdsk-url-1 = {https://doi.org/10.1209/0295-5075/84/67001}} @article{Casida_2005, author = {M. E. Casida}, @@ -2875,7 +2876,7 @@ title = {Propagator corrections to adiabatic time- dependent density-functional theory linear response theory}, volume = {122}, year = {2005}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.1836757}} + bdsk-url-1 = {https://doi.org/10.1063/1.1836757}} @article{Casida_2016, author = {M. E. Casida and M. {Huix-Rotllant}}, @@ -2887,7 +2888,7 @@ title = {{{Many-Body Perturbation Theory (MBPT) and Time-Dependent Density-Functional Theory (TD-DFT): MBPT Insights About What Is Missing In, and Corrections To, the TD-DFT Adiabatic Approximation}}}, volume = {368}, year = {2016}, - Bdsk-Url-1 = {https://doi.org/10.1007/128_2015_632}} + bdsk-url-1 = {https://doi.org/10.1007/128_2015_632}} @phdthesis{Rebolini_PhD, author = {E. Rebolini}, @@ -2897,7 +2898,7 @@ title = {Range-Separated Density-Functional Theory for Molecular Excitation Energies}, url = {https://tel.archives-ouvertes.fr/tel-01027522}, year = {2014}, - Bdsk-Url-1 = {https://tel.archives-ouvertes.fr/tel-01027522}} + bdsk-url-1 = {https://tel.archives-ouvertes.fr/tel-01027522}} @article{Baumeier_2012a, author = {Baumeier, Bj\"{o}rn and Andrienko, Denis and Rohlfing, Michael}, @@ -2910,7 +2911,7 @@ title = {Frenkel and Charge-Transfer Excitations in Donor--Acceptor Complexes From Many-Body Green's Functions Theory}, volume = {8}, year = {2012}, - Bdsk-Url-1 = {https://doi.org/10.1021/ct300311x}} + bdsk-url-1 = {https://doi.org/10.1021/ct300311x}} @article{Ma_2009a, author = {Ma, Yuchen and Rohlfing, Michael and Molteni, Carla}, @@ -2927,8 +2928,8 @@ url = {https://link.aps.org/doi/10.1103/PhysRevB.80.241405}, volume = {80}, year = {2009}, - Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.80.241405}, - Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevB.80.241405}} + bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.80.241405}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRevB.80.241405}} @misc{QuAcK, author = {P. F. Loos}, @@ -2940,8 +2941,8 @@ title = {{{QuAcK: a software for emerging quantum electronic structure methods}}}, url = {https://github.com/pfloos/QuAcK}, year = {2019}, - Bdsk-Url-1 = {https://github.com/LCPQ/quantum_package}, - Bdsk-Url-2 = {http://dx.doi.org/10.5281/zenodo.200970}} + bdsk-url-1 = {https://github.com/LCPQ/quantum_package}, + bdsk-url-2 = {http://dx.doi.org/10.5281/zenodo.200970}} @article{Loos_2018a, author = {P. F. Loos and A. Scemama and A. Blondel and Y. Garniron and M. Caffarel and D. Jacquemin}, @@ -2953,7 +2954,7 @@ title = {A Mountaineering Strategy to Excited States: Highly-Accurate Reference Energies and Benchmarks}, volume = {14}, year = {2018}, - Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.8b00406}} + bdsk-url-1 = {https://doi.org/10.1021/acs.jctc.8b00406}} @article{Albrecht_1997, author = {Albrecht, Stefan and Onida, Giovanni and Reining, Lucia}, @@ -2970,8 +2971,8 @@ url = {https://link.aps.org/doi/10.1103/PhysRevB.55.10278}, volume = {55}, year = {1997}, - Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.55.10278}, - Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevB.55.10278}} + bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.55.10278}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRevB.55.10278}} @article{Almlof_1991, abstract = {It is shown how the energy denominators encountered in various schemes for electronics structure calculation can be removed by a Laplace transform technique. The method is applicable to a wide variety of electronic structure calculations.}, @@ -2987,8 +2988,8 @@ url = {http://www.sciencedirect.com/science/article/pii/000926149180078C}, volume = {181}, year = {1991}, - Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/000926149180078C}, - Bdsk-Url-2 = {https://doi.org/10.1016/0009-2614(91)80078-C}} + bdsk-url-1 = {http://www.sciencedirect.com/science/article/pii/000926149180078C}, + bdsk-url-2 = {https://doi.org/10.1016/0009-2614(91)80078-C}} @article{Angeli_2012, author = {Angeli, Celestino and Cimiraglia, Renzo and Pastore, Mariachiara}, @@ -3005,7 +3006,7 @@ title = {A Comparison of Various Approaches in Internally Contracted Multireference Configuration Interaction: The Carbon Dimer as a Test Case}, volume = {110}, year = {2012}, - Bdsk-Url-1 = {https://doi.org/10.1080/00268976.2012.689872}} + bdsk-url-1 = {https://doi.org/10.1080/00268976.2012.689872}} @article{Azarias_2017, author = {Azarias, Clo{\'e} and Habert, Chlo\'{e} and Budz\'{a}k, \check{S}imon and Blase, Xavier and Duchemin, Ivan and Jacquemin, Denis}, @@ -3021,7 +3022,7 @@ url = {https://doi.org/10.1021/acs.jpca.7b05222}, volume = {121}, year = {2017}, - Bdsk-Url-1 = {https://doi.org/10.1021/acs.jpca.7b05222}} + bdsk-url-1 = {https://doi.org/10.1021/acs.jpca.7b05222}} @article{Barth_1995, abstract = {A recently derived approximation scheme for the polarisation propagator has been applied in a study of discrete K-shell excitations in N2 and CO. The new scheme referred to as second-order algebraic diagrammatic construction (ADC(2)) provides a direct approach to excitation energies and transition moments and gives a consistent second-order and first-order treatment for transitions to singly and doubly excited states, respectively. The essential computational requisite is a Hermitean eigenvalue problem in the space of single and double excitations on the Hartree-Fock ground state. Spin-free decoupled ADC(2) working equations for the singlet-singlet and singlet-triplet transitions have been formulated and employed. As the only additional approximation, the mixing between configurations with a different number of excited core-level electrons has been neglected. The calculated excitation energies of both the core-valence and core-Rydberg transitions are in very good agreement with the experimental data and are distinctly improved with respect to previous theoretical work, including extended configuration interaction treatments. The authors emphasise the accuracy achieved for the oscillator strengths which yield a very satisfactory description for the intensity ratios of the dipole-allowed transitions. The absolute dipole oscillator strengths are in excellent accord with the experimental values of Kay et al. (1977).}, @@ -3038,8 +3039,8 @@ url = {https://doi.org/10.1088%2F0022-3700%2F18%2F5%2F008}, volume = {18}, year = 1995, - Bdsk-Url-1 = {https://doi.org/10.1088%2F0022-3700%2F18%2F5%2F008}, - Bdsk-Url-2 = {https://doi.org/10.1088/0022-3700/18/5/008}} + bdsk-url-1 = {https://doi.org/10.1088%2F0022-3700%2F18%2F5%2F008}, + bdsk-url-2 = {https://doi.org/10.1088/0022-3700/18/5/008}} @article{Bauernschmitt_1996, author = {Bauernschmitt,R{\"u}diger and Ahlrichs,Reinhart}, @@ -3054,7 +3055,7 @@ url = {https://doi.org/10.1063/1.471637}, volume = {104}, year = {1996}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.471637}} + bdsk-url-1 = {https://doi.org/10.1063/1.471637}} @article{Baym_1961, author = {Baym, Gordon and Kadanoff, Leo P.}, @@ -3070,7 +3071,7 @@ title = {Conservation {{Laws}} and {{Correlation Functions}}}, volume = {124}, year = {1961}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRev.124.287}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRev.124.287}} @article{Baym_1962, author = {Baym, Gordon}, @@ -3086,7 +3087,7 @@ title = {Self-{{Consistent Approximations}} in {{Many}}-{{Body Systems}}}, volume = {127}, year = {1962}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRev.127.1391}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRev.127.1391}} @article{Beigi_2003, author = {Ismail-Beigi, Sohrab and Louie, Steven G.}, @@ -3103,8 +3104,8 @@ url = {https://link.aps.org/doi/10.1103/PhysRevLett.90.076401}, volume = {90}, year = {2003}, - Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.90.076401}, - Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevLett.90.076401}} + bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.90.076401}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRevLett.90.076401}} @article{Benedict_1998, author = {Benedict, Lorin X. and Shirley, Eric L. and Bohn, Robert B.}, @@ -3121,8 +3122,8 @@ url = {https://link.aps.org/doi/10.1103/PhysRevLett.80.4514}, volume = {80}, year = {1998}, - Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.80.4514}, - Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevLett.80.4514}} + bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.80.4514}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRevLett.80.4514}} @article{Bernardi_1990, author = {Bernardi, Fernando and De, Sushovan and Olivucci, Massimo and Robb, Michael A.}, @@ -3139,7 +3140,7 @@ title = {The Mechanism of Ground-State-Forbidden Photochemical Pericyclic Reactions: Evidence for Real Conical Intersections}, volume = {112}, year = {1990}, - Bdsk-Url-1 = {https://doi.org/10.1021/ja00161a013}} + bdsk-url-1 = {https://doi.org/10.1021/ja00161a013}} @article{Bernardi_1996, author = {Bernardi, Fernando and Olivucci, Massimo and Robb, Michael A.}, @@ -3154,7 +3155,7 @@ title = {Potential Energy Surface Crossings in Organic Photochemistry}, volume = {25}, year = {1996}, - Bdsk-Url-1 = {https://doi.org/10.1039/cs9962500321}} + bdsk-url-1 = {https://doi.org/10.1039/cs9962500321}} @article{Blase_1994, author = {Blase, X. and Zhu, Xuejun and Louie, Steven G.}, @@ -3171,8 +3172,8 @@ url = {https://link.aps.org/doi/10.1103/PhysRevB.49.4973}, volume = {49}, year = {1994}, - Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.49.4973}, - Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevB.49.4973}} + bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.49.4973}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRevB.49.4973}} @article{Blase_1995, author = {Blase, X. and Rubio, Angel and Louie, Steven G. and Cohen, Marvin L.}, @@ -3189,8 +3190,8 @@ url = {https://link.aps.org/doi/10.1103/PhysRevB.51.6868}, volume = {51}, year = {1995}, - Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.51.6868}, - Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevB.51.6868}} + bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.51.6868}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRevB.51.6868}} @article{Blase_2011, author = {Blase,X. and Attaccalite,C.}, @@ -3203,7 +3204,7 @@ title = {Charge-Transfer Excitations in Molecular Donor-Acceptor Complexes within the Many-Body Bethe-Salpeter Approach}, volume = {99}, year = {2011}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.3655352}} + bdsk-url-1 = {https://doi.org/10.1063/1.3655352}} @article{Blase_2018, author = {Blase, Xavier and Duchemin, Ivan and Jacquemin, Denis}, @@ -3218,7 +3219,7 @@ url = {http://dx.doi.org/10.1039/C7CS00049A}, volume = {47}, year = {2018}, - Bdsk-Url-1 = {http://dx.doi.org/10.1039/C7CS00049A}} + bdsk-url-1 = {http://dx.doi.org/10.1039/C7CS00049A}} @article{Botti_2004, author = {Botti, Silvana and Sottile, Francesco and Vast, Nathalie and Olevano, Valerio and Reining, Lucia and Weissker, Hans-Christian and Rubio, Angel and Onida, Giovanni and Del Sole, Rodolfo and Godby, R. W.}, @@ -3235,8 +3236,8 @@ url = {https://link.aps.org/doi/10.1103/PhysRevB.69.155112}, volume = {69}, year = {2004}, - Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.69.155112}, - Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevB.69.155112}} + bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.69.155112}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRevB.69.155112}} @article{Bredas_2014, author = {Bredas, Jean-Luc}, @@ -3252,7 +3253,7 @@ title = {Mind the Gap!}, volume = {1}, year = {2014}, - Bdsk-Url-1 = {https://doi.org/10.1039/C3MH00098B}} + bdsk-url-1 = {https://doi.org/10.1039/C3MH00098B}} @article{Bruneval_2008, author = {Bruneval, Fabien and Gonze, Xavier}, @@ -3269,8 +3270,8 @@ url = {https://link.aps.org/doi/10.1103/PhysRevB.78.085125}, volume = {78}, year = {2008}, - Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.78.085125}, - Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevB.78.085125}} + bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.78.085125}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRevB.78.085125}} @article{Bruneval_2015, author = {Bruneval,Fabien and Hamed,Samia M. and Neaton,Jeffrey B.}, @@ -3283,7 +3284,7 @@ title = {A systematic benchmark of the ab initio Bethe-Salpeter equation approach for low-lying optical excitations of small organic molecules}, volume = {142}, year = {2015}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.4922489}} + bdsk-url-1 = {https://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.}, @@ -3300,7 +3301,7 @@ 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}} + bdsk-url-1 = {https://dx.doi.org/10.1016/j.cpc.2016.06.019}} @article{Campillo_1999, author = {Campillo, I. and Pitarke, J. M. and Rubio, A. and Zarate, E. and Echenique, P. M.}, @@ -3317,8 +3318,8 @@ url = {https://link.aps.org/doi/10.1103/PhysRevLett.83.2230}, volume = {83}, year = {1999}, - Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.83.2230}, - Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevLett.83.2230}} + bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.83.2230}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRevLett.83.2230}} @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}, @@ -3336,7 +3337,7 @@ 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}} + bdsk-url-1 = {https://dx.doi.org/10.1103/PhysRevLett.110.146403}} @article{Caruso_2016, author = {F. Caruso and M. Dauth and M. J. {van Setten} and P. Rinke}, @@ -3348,7 +3349,7 @@ 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}} + bdsk-url-1 = {https://doi.org/10.1021/acs.jctc.6b00774}} @inbook{Casida_1995, author = {M. E. Casida}, @@ -3361,7 +3362,7 @@ series = {Recent Advances in Density Functional Methods}, title = {Time-Dependent Density Functional Response Theory for Molecules}, year = {1995}, - Bdsk-Url-1 = {https://doi.org/10.1142/9789812830586_0005}} + bdsk-url-1 = {https://doi.org/10.1142/9789812830586_0005}} @article{Casida_1998, author = {Casida, Mark E. and Jamorski, Christine and Casida, Kim C. and Salahub, Dennis R.}, @@ -3378,7 +3379,7 @@ title = {Molecular Excitation Energies to High-Lying Bound States from Time-Dependent Density-Functional Response Theory: {{Characterization}} and Correction of the Time-Dependent Local Density Approximation Ionization Threshold}, volume = {108}, year = {1998}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.475855}} + bdsk-url-1 = {https://doi.org/10.1063/1.475855}} @article{Casida_2000, author = {Casida, Mark E. and Salahub, Dennis R.}, @@ -3395,7 +3396,7 @@ title = {Asymptotic Correction Approach to Improving Approximate Exchange\textendash{}Correlation Potentials: {{Time}}-Dependent Density-Functional Theory Calculations of Molecular Excitation Spectra}, volume = {113}, year = {2000}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.1319649}} + bdsk-url-1 = {https://doi.org/10.1063/1.1319649}} @article{Casida_2012, author = {Casida, M.E. and Huix-Rotllant, M.}, @@ -3419,8 +3420,8 @@ url = {http://scitation.aip.org/content/aip/journal/jcp/103/17/10.1063/1.470315}, volume = {103}, year = {1995}, - Bdsk-Url-1 = {http://scitation.aip.org/content/aip/journal/jcp/103/17/10.1063/1.470315}, - Bdsk-Url-2 = {http://dx.doi.org/10.1063/1.470315}} + bdsk-url-1 = {http://scitation.aip.org/content/aip/journal/jcp/103/17/10.1063/1.470315}, + bdsk-url-2 = {http://dx.doi.org/10.1063/1.470315}} @article{Colonna_2014, author = {Nicola Colonna and Maria Hellgren and Stefano {de Gironcoli}}, @@ -3432,7 +3433,7 @@ title = {Correlation Energy Within Exact-Exchange Adiabatic Connection Fluctuation-Dissipation Theory: Systematic Development and Simple Approximations}, volume = {90}, year = {2014}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevB.90.125150}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRevB.90.125150}} @article{Cudazzo_2010, author = {Cudazzo, Pierluigi and Attaccalite, Claudio and Tokatly, Ilya V. and Rubio, Angel}, @@ -3449,8 +3450,8 @@ url = {https://link.aps.org/doi/10.1103/PhysRevLett.104.226804}, volume = {104}, year = {2010}, - Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.104.226804}, - Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevLett.104.226804}} + bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.104.226804}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRevLett.104.226804}} @article{Cudazzo_2013, author = {Cudazzo, Pierluigi and Gatti, Matteo and Rubio, Angel and Sottile, Francesco}, @@ -3467,8 +3468,8 @@ url = {https://link.aps.org/doi/10.1103/PhysRevB.88.195152}, volume = {88}, year = {2013}, - Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.88.195152}, - Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevB.88.195152}} + bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.88.195152}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRevB.88.195152}} @article{Dahlen_2006, author = {Dahlen, Nils Erik and {van Leeuwen}, Robert and {von Barth}, Ulf}, @@ -3485,7 +3486,7 @@ 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}} + bdsk-url-1 = {https://dx.doi.org/10.1103/PhysRevA.73.012511}} @article{deGroot_1995, author = {{de Groot}, H. J. and Bobbert, P. A. and {van Haeringen}, W.}, @@ -3501,7 +3502,7 @@ 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}} + bdsk-url-1 = {https://dx.doi.org/10.1103/PhysRevB.52.11000}} @article{Delerue_2000, author = {Delerue, C. and Lannoo, M. and Allan, G.}, @@ -3518,8 +3519,8 @@ url = {https://link.aps.org/doi/10.1103/PhysRevLett.84.2457}, volume = {84}, year = {2000}, - Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.84.2457}, - Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevLett.84.2457}} + bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.84.2457}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRevLett.84.2457}} @article{DiSabatino_2016, author = {Di Sabatino, Stefano and Berger, J. A. and Reining, Lucia and Romaniello, Pina}, @@ -3536,7 +3537,7 @@ 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}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRevB.94.155141}} @article{DiSabatino_2019, author = {S. {Di Sabatino} and J. A. Berger and P. Romaniello}, @@ -3548,7 +3549,7 @@ title = {Many-Body Effective Energy Theory: Photoemission at Strong Correlation}, volume = {15}, year = {2019}, - Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.9b00427}} + bdsk-url-1 = {https://doi.org/10.1021/acs.jctc.9b00427}} @article{Dreuw_2005, author = {Dreuw, Andreas and Head-Gordon, Martin}, @@ -3560,7 +3561,7 @@ 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}} + bdsk-url-1 = {https://dx.doi.org/10.1021/cr0505627}} @article{Duchemin_2019, author = {Duchemin,Ivan and Blase,Xavier}, @@ -3573,7 +3574,7 @@ title = {Separable resolution-of-the-identity with all-electron Gaussian bases: Application to cubic-scaling RPA}, volume = {150}, year = {2019}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.5090605}} + bdsk-url-1 = {https://doi.org/10.1063/1.5090605}} @article{Duchemin_2020, author = {Ivan Duchemin and Xavier Blase}, @@ -3585,7 +3586,7 @@ title = {Robust Analytic-Continuation Approach to Many-Body {{GW}} Calculations}, volume = {16}, year = {2020}, - Bdsk-Url-1 = {}} + bdsk-url-1 = {}} @article{Dunning_1989, author = {T. H. {Dunning, Jr.}}, @@ -3597,7 +3598,7 @@ title = {Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen}, volume = {90}, year = {1989}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.456153}} + bdsk-url-1 = {https://doi.org/10.1063/1.456153}} @article{Elliott_2019, author = {Elliott, Joshua D. and Colonna, Nicola and Marsili, Margherita and Marzari, Nicola and Umari, Paolo}, @@ -3613,7 +3614,7 @@ url = {https://doi.org/10.1021/acs.jctc.8b01271}, volume = {15}, year = {2019}, - Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.8b01271}} + bdsk-url-1 = {https://doi.org/10.1021/acs.jctc.8b01271}} @article{Faber_2011, author = {Faber, Carina and Attaccalite, Claudio and Olevano, V. and Runge, E. and Blase, X.}, @@ -3629,7 +3630,7 @@ 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}} + bdsk-url-1 = {https://dx.doi.org/10.1103/PhysRevB.83.115123}} @article{Faber_2011b, author = {Faber, Carina and Janssen, Jonathan Laflamme and C\^ot\'e, Michel and Runge, E. and Blase, X.}, @@ -3646,8 +3647,8 @@ url = {https://link.aps.org/doi/10.1103/PhysRevB.84.155104}, volume = {84}, year = {2011}, - Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.84.155104}, - Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevB.84.155104}} + bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.84.155104}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRevB.84.155104}} @phdthesis{Faber_2014, author = {Faber, Carina}, @@ -3682,7 +3683,7 @@ url = {https://doi.org/10.1063/1.3624731}, volume = {135}, year = {2011}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.3624731}} + bdsk-url-1 = {https://doi.org/10.1063/1.3624731}} @article{Friedrich_2006, author = {Friedrich, Christoph and Schindlmayr, Arno and Bl{\"u}gel, Stefan and Kotani, Takao}, @@ -3698,7 +3699,7 @@ 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}} + bdsk-url-1 = {https://dx.doi.org/10.1103/PhysRevB.74.045104}} @article{Fuchs_2008, author = {Fuchs, F. and R\"odl, C. and Schleife, A. and Bechstedt, F.}, @@ -3715,8 +3716,8 @@ url = {https://link.aps.org/doi/10.1103/PhysRevB.78.085103}, volume = {78}, year = {2008}, - Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.78.085103}, - Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevB.78.085103}} + bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.78.085103}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRevB.78.085103}} @article{Furche_2008, author = {Furche, Filipp}, @@ -3733,7 +3734,7 @@ 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}} + bdsk-url-1 = {https://dx.doi.org/10.1063/1.2977789}} @article{Gao_2020, author = {Gao, Weiwei and Chelikowsky, James R.}, @@ -3749,7 +3750,7 @@ url = {https://doi.org/10.1021/acs.jctc.9b01025}, volume = {16}, year = {2020}, - Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.9b01025}} + bdsk-url-1 = {https://doi.org/10.1021/acs.jctc.9b01025}} @article{Garcia-Gonzalez_2001, author = {Garc{\'\i}a-Gonz{\'a}lez, P. and Godby, R. W.}, @@ -3766,7 +3767,7 @@ 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}} + bdsk-url-1 = {https://dx.doi.org/10.1103/PhysRevB.63.075112}} @article{Gatti_2007, author = {M. Gatti and V. Olevano and L. Reining,and I. V. Tokatly}, @@ -3778,7 +3779,7 @@ title = {Transforming Nonlocality into a Frequency Dependence: A Shortcut to Spectroscopy}, volume = {99}, year = {2007}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevLett.99.057401}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRevLett.99.057401}} @article{Giustino_2010, author = {Giustino, Feliciano and Cohen, Marvin L. and Louie, Steven G.}, @@ -3795,8 +3796,8 @@ url = {https://link.aps.org/doi/10.1103/PhysRevB.81.115105}, volume = {81}, year = {2010}, - Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.81.115105}, - Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevB.81.115105}} + bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.81.115105}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRevB.81.115105}} @article{Godby_1988, author = {Godby, R. W. and Schl\"uter, M. and Sham, L. J.}, @@ -3813,8 +3814,8 @@ url = {http://link.aps.org/doi/10.1103/PhysRevB.37.10159}, volume = {37}, year = {1988}, - Bdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevB.37.10159}, - Bdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevB.37.10159}} + bdsk-url-1 = {http://link.aps.org/doi/10.1103/PhysRevB.37.10159}, + bdsk-url-2 = {http://dx.doi.org/10.1103/PhysRevB.37.10159}} @article{Gui_2018, author = {Gui, Xin and Holzer, Christof and Klopper, Wim}, @@ -3827,7 +3828,7 @@ title = {Accuracy Assessment of GW Starting Points for Calculating Molecular Excitation Energies Using the Bethe--Salpeter Formalism}, volume = {14}, year = {2018}, - Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.8b00014}} + bdsk-url-1 = {https://doi.org/10.1021/acs.jctc.8b00014}} @article{Hanke_1980, author = {W. Hanke and L. J. Sham}, @@ -3839,7 +3840,7 @@ title = {Many-Particle Effects in the Optical Spectrum of a Semiconductor}, volume = {21}, year = {1980}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevB.21.4656}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRevB.21.4656}} @article{Haser_1992, author = {H{\"{a}}ser,Marco and Alml{\"{o}}f,Jan}, @@ -3854,7 +3855,7 @@ url = {https://doi.org/10.1063/1.462485}, volume = {96}, year = {1992}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.462485}} + bdsk-url-1 = {https://doi.org/10.1063/1.462485}} @article{Hirose_2017, author = {Hirose,Daichi and Noguchi,Yoshifumi and Sugino,Osamu}, @@ -3869,7 +3870,7 @@ url = {https://doi.org/10.1063/1.4974320}, volume = {146}, year = {2017}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.4974320}} + bdsk-url-1 = {https://doi.org/10.1063/1.4974320}} @article{Hohenberg_1964, annote = {Hohenberg-Kohn theorem}, @@ -3882,7 +3883,7 @@ title = {Inhomogeneous electron gas}, volume = {136}, year = {1964}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRev.136.B864}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRev.136.B864}} @article{Holm_1999, author = {Holm, Bengt}, @@ -3898,7 +3899,7 @@ title = {Total {{Energies}} from {{GW Calculations}}}, volume = {83}, year = {1999}, - Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevLett.83.788}} + bdsk-url-1 = {https://dx.doi.org/10.1103/PhysRevLett.83.788}} @article{Holm_2000, author = {Holm, B. and Aryasetiawan, F.}, @@ -3923,7 +3924,7 @@ title = {Communication: A hybrid Bethe--Salpeter/time-dependent density-functional-theory approach for excitation energies}, volume = {149}, year = {2018}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.5051028}} + bdsk-url-1 = {https://doi.org/10.1063/1.5051028}} @article{Holzer_2019, author = {Holzer,Christof and Teale,Andrew M. and Hampe,Florian and Stopkowicz,Stella and Helgaker,Trygve and Klopper,Wim}, @@ -3936,7 +3937,7 @@ title = {GW Quasiparticle Energies of Atoms in Strong Magnetic Fields}, volume = {150}, year = {2019}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.5093396}} + bdsk-url-1 = {https://doi.org/10.1063/1.5093396}} @article{Huix-Rotllant_2010, author = {{Huix-Rotllant}, Miquel and Natarajan, Bhaarathi and Ipatov, Andrei and Muhavini Wawire, C. and Deutsch, Thierry and Casida, Mark E.}, @@ -3951,7 +3952,7 @@ title = {Assessment of Noncollinear Spin-Flip {{Tamm}}\textendash{{Dancoff}} Approximation Time-Dependent Density-Functional Theory for the Photochemical Ring-Opening of Oxirane}, volume = {12}, year = {2010}, - Bdsk-Url-1 = {https://doi.org/10.1039/c0cp00273a}} + bdsk-url-1 = {https://doi.org/10.1039/c0cp00273a}} @article{Huix-Rotllant_2011, author = {{Huix-Rotllant}, Miquel and Ipatov, Andrei and Rubio, Angel and Casida, Mark E.}, @@ -3963,7 +3964,7 @@ title = {Assessment of Dressed Time-Dependent Density-Functional Theory for the Low-Lying Valence States of 28 Organic Chromophores}, volume = {391}, year = {2011}, - Bdsk-Url-1 = {https://doi.org/10.1016/j.chemphys.2011.03.019}} + bdsk-url-1 = {https://doi.org/10.1016/j.chemphys.2011.03.019}} @article{Hummer_2004, author = {Hummer, Kerstin and Puschnig, Peter and Ambrosch-Draxl, Claudia}, @@ -3980,8 +3981,8 @@ url = {https://link.aps.org/doi/10.1103/PhysRevLett.92.147402}, volume = {92}, year = {2004}, - Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.92.147402}, - Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevLett.92.147402}} + bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.92.147402}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRevLett.92.147402}} @article{Hummer_2005, author = {Hummer, Kerstin and Ambrosch-Draxl, Claudia}, @@ -3998,8 +3999,8 @@ url = {https://link.aps.org/doi/10.1103/PhysRevB.71.081202}, volume = {71}, year = {2005}, - Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.71.081202}, - Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevB.71.081202}} + bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.71.081202}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRevB.71.081202}} @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}, @@ -4017,7 +4018,7 @@ 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}} + 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}, @@ -4034,7 +4035,7 @@ 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}} + bdsk-url-1 = {https://dx.doi.org/10.1021/acs.jctc.7b00123}} @article{Hybertsen_1985, author = {Hybertsen, Mark S. and Louie, Steven G.}, @@ -4064,7 +4065,7 @@ 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}} + bdsk-url-1 = {https://dx.doi.org/10.1103/PhysRevB.34.5390}} @article{Jacquemin_2015a, author = {Jacquemin, Denis and Duchemin, Ivan and Blase, Xavier}, @@ -4078,7 +4079,7 @@ 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}} + bdsk-url-1 = {https://doi.org/10.1021/acs.jctc.5b00304}} @article{Jacquemin_2015b, author = {Jacquemin, Denis and Duchemin, Ivan and Blase, Xavier}, @@ -4091,7 +4092,7 @@ title = {0--0 Energies Using Hybrid Schemes: Benchmarks of TD-DFT, CIS(D), ADC(2), CC2, and BSE/GW formalisms for 80 Real-Life Compounds}, volume = {11}, year = {2015}, - Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.5b00619}} + bdsk-url-1 = {https://doi.org/10.1021/acs.jctc.5b00619}} @article{Jacquemin_2017a, author = {Jacquemin, Denis and Duchemin, Ivan and Blase, Xavier}, @@ -4104,7 +4105,7 @@ title = {Is the Bethe--Salpeter Formalism Accurate for Excitation Energies? Comparisons with TD-DFT, CASPT2, and EOM-CCSD}, volume = {8}, year = {2017}, - Bdsk-Url-1 = {https://doi.org/10.1021/acs.jpclett.7b00381}} + bdsk-url-1 = {https://doi.org/10.1021/acs.jpclett.7b00381}} @article{Jacquemin_2017b, author = {Jacquemin, Denis and Duchemin, Ivan and Blondel, Aymeric and Blase, Xavier}, @@ -4117,7 +4118,7 @@ title = {Benchmark of Bethe-Salpeter for Triplet Excited-States}, volume = {13}, year = {2017}, - Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.6b01169}} + bdsk-url-1 = {https://doi.org/10.1021/acs.jctc.6b01169}} @article{Kaczmarski_2010, author = {Kaczmarski, Marcin S. and Ma, Yuchen and Rohlfing, Michael}, @@ -4134,8 +4135,8 @@ url = {https://link.aps.org/doi/10.1103/PhysRevB.81.115433}, volume = {81}, year = {2010}, - Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.81.115433}, - Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevB.81.115433}} + bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.81.115433}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRevB.81.115433}} @article{Kaltak_2014, author = {Kaltak, Merzuk and Klime\v{s}, Ji\v{i}\'{i} and Kresse, Georg}, @@ -4151,7 +4152,7 @@ url = {https://doi.org/10.1021/ct5001268}, volume = {10}, year = {2014}, - Bdsk-Url-1 = {https://doi.org/10.1021/ct5001268}} + bdsk-url-1 = {https://doi.org/10.1021/ct5001268}} @article{Korbel_2014, author = {K{\"{o}}rbel, Sabine and Boulanger, Paul and Duchemin, Ivan and Blase, Xavier and Marques, Miguel A. L. and Botti, Silvana}, @@ -4164,7 +4165,7 @@ title = {Benchmark Many-Body GW and Bethe--Salpeter Calculations for Small Transition Metal Molecules}, volume = {10}, year = {2014}, - Bdsk-Url-1 = {https://doi.org/10.1021/ct5003658}} + bdsk-url-1 = {https://doi.org/10.1021/ct5003658}} @article{Kotani_2007, author = {Kotani, Takao and {van Schilfgaarde}, Mark and Faleev, Sergey V.}, @@ -4182,7 +4183,7 @@ title = {Quasiparticle Self-Consistent {{G W}} Method: {{A}} Basis for the Independent-Particle Approximation}, volume = {76}, year = {2007}, - Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevB.76.165106}} + bdsk-url-1 = {https://dx.doi.org/10.1103/PhysRevB.76.165106}} @article{Kraisler_2013, author = {Kraisler, Eli and Kronik, Leeor}, @@ -4200,7 +4201,7 @@ title = {Piecewise {{Linearity}} of {{Approximate Density Functionals Revisited}}: {{Implications}} for {{Frontier Orbital Energies}}}, volume = {110}, year = {2013}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevLett.110.126403}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRevLett.110.126403}} @article{Krause_2017, abstract = {A software update solving the Bethe−Salpeter equation ...}, @@ -4214,8 +4215,8 @@ title = {Implementation of the Bethe-Salpeter equation in the TURBOMOLE program}, volume = {38}, year = {2017}, - Bdsk-Url-1 = {https://onlinelibrary.wiley.com/doi/abs/10.1002/jcc.24688}, - Bdsk-Url-2 = {https://doi.org/10.1002/jcc.24688}} + bdsk-url-1 = {https://onlinelibrary.wiley.com/doi/abs/10.1002/jcc.24688}, + bdsk-url-2 = {https://doi.org/10.1002/jcc.24688}} @article{Kronik_2012, author = {Leeor Kronik and Tamar Stein and Sivan {Refaely-Abramson} and Roi Baer}, @@ -4227,7 +4228,7 @@ title = {Excitation Gaps of Finite-Sized Systems from Optimally Tuned Range-Separated Hybrid Functionals}, volume = {8}, year = {2012}, - Bdsk-Url-1 = {https://doi.org/10.1021/ct2009363}} + bdsk-url-1 = {https://doi.org/10.1021/ct2009363}} @article{Kutepov_2016, author = {Kutepov, Andrey L.}, @@ -4244,7 +4245,7 @@ title = {Electronic Structure of {{Na}}, {{K}}, {{Si}}, and {{LiF}} from Self-Consistent Solution of {{Hedin}}'s Equations Including Vertex Corrections}, volume = {94}, year = {2016}, - Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevB.94.155101}} + bdsk-url-1 = {https://dx.doi.org/10.1103/PhysRevB.94.155101}} @article{Kutepov_2017, author = {Kutepov, A. L. and Kotliar, G.}, @@ -4261,7 +4262,7 @@ title = {One-Electron Spectra and Susceptibilities of the Three-Dimensional Electron Gas from Self-Consistent Solutions of {{Hedin}}'s Equations}, volume = {96}, year = {2017}, - Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevB.96.035108}} + bdsk-url-1 = {https://dx.doi.org/10.1103/PhysRevB.96.035108}} @article{Lazzeri_2008, author = {Lazzeri, Michele and Attaccalite, Claudio and Wirtz, Ludger and Mauri, Francesco}, @@ -4278,8 +4279,8 @@ url = {https://link.aps.org/doi/10.1103/PhysRevB.78.081406}, volume = {78}, year = {2008}, - Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.78.081406}, - Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevB.78.081406}} + bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.78.081406}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRevB.78.081406}} @article{Lettmann_2019, author = {Tobias Lettmann and Michael Rohlfing}, @@ -4291,7 +4292,7 @@ title = {Electronic Excitations of Polythiophene within Many-Body Perturbation Theory with and without the Tamm-Dancoff Approximation}, volume = {15}, year = {2019}, - Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.9b00223}} + bdsk-url-1 = {https://doi.org/10.1021/acs.jctc.9b00223}} @article{Li_2019, author = {J. 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Scemama}, @@ -4560,7 +4561,7 @@ title = {Quantum Package 2.0: A Open-Source Determinant-Driven Suite Of Programs}, volume = {15}, year = {2019}, - Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.9b00176}} + bdsk-url-1 = {https://doi.org/10.1021/acs.jctc.9b00176}} @article{Rabani_2015, author = {Rabani, Eran and Baer, Roi and Neuhauser, Daniel}, @@ -4577,8 +4578,8 @@ url = {https://link.aps.org/doi/10.1103/PhysRevB.91.235302}, volume = {91}, year = {2015}, - Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.91.235302}, - Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevB.91.235302}} + bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.91.235302}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRevB.91.235302}} @article{Rebolini_2016, author = {Rebolini,Elisa and Toulouse,Julien}, @@ -4591,7 +4592,7 @@ title = {Range-separated time-dependent density-functional theory with a frequency-dependent second-order Bethe-Salpeter correlation kernel}, volume = {144}, year = {2016}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.4943003}} + bdsk-url-1 = {https://doi.org/10.1063/1.4943003}} @article{Refaely-Abramson_2012, author = {Sivan Refaely-Abramson and Sahar Sharifzadeh and Niranjan Govind and Jochen Autschbach and Jeffrey B. Neaton and Roi Baer and Leeor Kronik}, @@ -4603,7 +4604,7 @@ title = {Quasiparticle Spectra from a Nonempirical Optimally Tuned Range-Separated Hybrid Density Functional}, volume = {109}, year = {2012}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevLett.109.226405}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRevLett.109.226405}} @article{Reining_2017, author = {Reining, Lucia}, @@ -4615,7 +4616,7 @@ title = {The {{GW}} Approximation: Content, Successes and Limitations: {{The GW}} Approximation}, volume = {8}, year = {2017}, - Bdsk-Url-1 = {https://dx.doi.org/10.1002/wcms.1344}} + bdsk-url-1 = {https://dx.doi.org/10.1002/wcms.1344}} @book{ReiningBook, author = {Martin, R.M. and Reining, L. and Ceperley, D.M.}, @@ -4639,7 +4640,7 @@ publisher = {{John Wiley \& Sons, Inc.}}, title = {A {{Computational Strategy}} for {{Organic Photochemistry}}}, year = {2007}, - Bdsk-Url-1 = {https://doi.org/10.1002/9780470125922.ch2}} + bdsk-url-1 = {https://doi.org/10.1002/9780470125922.ch2}} @article{Rohlfing_1999, author = {Rohlfing, Michael and Louie, Steven G.}, @@ -4656,8 +4657,8 @@ url = {https://link.aps.org/doi/10.1103/PhysRevLett.83.856}, volume = {83}, year = {1999}, - Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.83.856}, - Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevLett.83.856}} + bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.83.856}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRevLett.83.856}} @article{Rohlfing_2000, author = {Rohlfing, Michael and Louie, Steven G.}, @@ -4674,8 +4675,8 @@ url = {https://link.aps.org/doi/10.1103/PhysRevB.62.4927}, volume = {62}, year = {2000}, - Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.62.4927}, - Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevB.62.4927}} + bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.62.4927}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRevB.62.4927}} @article{Romaniello_2009a, author = {Romaniello, P. and Guyot, S. and Reining, L.}, @@ -4687,7 +4688,7 @@ 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}} + bdsk-url-1 = {https://dx.doi.org/10.1063/1.3249965}} @article{Romaniello_2009b, author = {Romaniello,P. and Sangalli,D. and Berger,J. A. and Sottile,F. and Molinari,L. G. and Reining,L. and Onida,G.}, @@ -4700,7 +4701,7 @@ title = {Double excitations in finite systems}, volume = {130}, year = {2009}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.3065669}} + bdsk-url-1 = {https://doi.org/10.1063/1.3065669}} @article{Romaniello_2012, author = {Romaniello, Pina and Bechstedt, Friedhelm and Reining, Lucia}, @@ -4718,7 +4719,7 @@ 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}} + bdsk-url-1 = {https://dx.doi.org/10.1103/PhysRevB.85.155131}} @article{Rostgaard_2010, author = {Rostgaard, C. and Jacobsen, K. W. and Thygesen, K. S.}, @@ -4735,7 +4736,7 @@ title = {Fully Self-Consistent {{GW}} Calculations for Molecules}, volume = {81}, year = {2010}, - Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevB.81.085103}} + bdsk-url-1 = {https://dx.doi.org/10.1103/PhysRevB.81.085103}} @article{Runge_1984, author = {Runge, E. and Gross, E. K. U.}, @@ -4747,7 +4748,7 @@ title = {Density-Functional Theory for Time-Dependent Systems}, volume = 52, year = 1984, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevLett.52.997}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRevLett.52.997}} @article{Sangalli_2011, author = {Sangalli, Davide and Romaniello, Pina and Onida, Giovanni and Marini, Andrea}, @@ -4759,7 +4760,7 @@ title = {Double Excitations in Correlated Systems: {{A}} Many\textendash{}Body Approach}, volume = {134}, year = {2011}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.3518705}} + bdsk-url-1 = {https://doi.org/10.1063/1.3518705}} @article{Schirmer_1982, author = {Jochen Schirmer}, @@ -4771,7 +4772,7 @@ title = {Beyond the Random-Phase Approximation: a new Approximation Scheme for the Polarization Propagator}, volume = 26, year = 1982, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevA.26.2395}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRevA.26.2395}} @article{Schirmer_1991, author = {Jochen Schirmer}, @@ -4783,7 +4784,7 @@ title = {Closed-Form Intermediate Representations of Many-Body Propagators and Resolvent Matrices}, volume = {43}, year = {1991}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevA.43.4647}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRevA.43.4647}} @article{Schirmer_2004d, author = {Schirmer, J. and Trofimov, A. 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J. and Schl\"uter, M.}, @@ -4880,8 +4881,8 @@ url = {https://link.aps.org/doi/10.1103/PhysRevLett.51.1888}, volume = {51}, year = {1983}, - Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.51.1888}, - Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevLett.51.1888}} + bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.51.1888}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRevLett.51.1888}} @article{Sharifzadeh_2013, author = {Sharifzadeh, Sahar and Darancet, Pierre and Kronik, Leeor and Neaton, Jeffrey B.}, @@ -4896,7 +4897,7 @@ url = {https://doi.org/10.1021/jz401069f}, volume = {4}, year = {2013}, - Bdsk-Url-1 = {https://doi.org/10.1021/jz401069f}} + bdsk-url-1 = {https://doi.org/10.1021/jz401069f}} @article{Shishkin_2007, author = {Shishkin, M. and Kresse, G.}, @@ -4913,7 +4914,7 @@ title = {Self-Consistent {{G W}} Calculations for Semiconductors and Insulators}, volume = {75}, year = {2007}, - Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevB.75.235102}} + bdsk-url-1 = {https://dx.doi.org/10.1103/PhysRevB.75.235102}} @article{Sottile_2003, author = {Francesco Sottile and Valerio Olevano and Lucia Reining}, @@ -4925,7 +4926,7 @@ title = {Parameter-Free Calculation of Response Functions in Time-Dependent Density-Functional Theory}, volume = {91}, year = {2003}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevLett.91.056402}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRevLett.91.056402}} @article{Stan_2009, author = {Stan, Adrian and Dahlen, Nils Erik and {van Leeuwen}, Robert}, @@ -4942,7 +4943,7 @@ title = {Levels of Self-Consistency in the {{GW}} Approximation}, volume = {130}, year = {2009}, - Bdsk-Url-1 = {https://dx.doi.org/10.1063/1.3089567}} + bdsk-url-1 = {https://dx.doi.org/10.1063/1.3089567}} @article{Stein_2009, author = {Stein, Tamar and Kronik, Leeor and Baer, Roi}, @@ -4955,7 +4956,7 @@ title = {Reliable Prediction of Charge Transfer Excitations in Molecular Complexes Using Time-Dependent Density Functional Theory}, volume = {131}, year = {2009}, - Bdsk-Url-1 = {https://doi.org/10.1021/ja8087482}} + bdsk-url-1 = {https://doi.org/10.1021/ja8087482}} @article{Stein_2010, author = {Tamar Stein and Helen Eisenberg and Leeor Kronik and Roi Baer}, @@ -4967,7 +4968,7 @@ title = {Fundamental Gaps in Finite Systems from Eigenvalues of a Generalized Kohn-Sham Method}, volume = {105}, year = {2010}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevLett.105.266802}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRevLett.105.266802}} @article{Stein_2012, author = {Tamar Stein and Jochen Autschbach and Niranjan Govind and Leeor Kronik and Roi Baer}, @@ -4979,7 +4980,7 @@ title = {Curvature and Frontier Orbital Energies in Density Functional Theory}, volume = {3}, year = {2012}, - Bdsk-Url-1 = {https://doi.org/10.1021/jz3015937}} + bdsk-url-1 = {https://doi.org/10.1021/jz3015937}} @article{Strinati_1980, author = {Strinati, G. and Mattausch, H. J. and Hanke, W.}, @@ -4996,8 +4997,8 @@ url = {http://link.aps.org/doi/10.1103/PhysRevLett.45.290}, volume = {45}, year = {1980}, - Bdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevLett.45.290}, - Bdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevLett.45.290}} + bdsk-url-1 = {http://link.aps.org/doi/10.1103/PhysRevLett.45.290}, + bdsk-url-2 = {http://dx.doi.org/10.1103/PhysRevLett.45.290}} @article{Strinati_1988, author = {Strinati, G.}, @@ -5009,7 +5010,7 @@ 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}} + bdsk-url-1 = {https://dx.doi.org/10.1007/BF02725962}} @article{Toulouse_2005, author = {J. Toulouse and P. Gori-Giorgi and A. Savin}, @@ -5035,8 +5036,8 @@ url = {http://www.sciencedirect.com/science/article/pii/S0301010496003035}, volume = {214}, year = {1997}, - Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0301010496003035}, - Bdsk-Url-2 = {https://doi.org/10.1016/S0301-0104(96)00303-5}} + bdsk-url-1 = {http://www.sciencedirect.com/science/article/pii/S0301010496003035}, + bdsk-url-2 = {https://doi.org/10.1016/S0301-0104(96)00303-5}} @article{Trofimov_1997b, abstract = {The electronic spectrum of furan is investigated theoretically beyond the previous vertical-electronic description. A polarization propagator method referred to as second-order algebraic-diagrammatic construction (ADC(2)) has been used in the electronic structure calculations. The vibrational excitation accompanying the electronic transitions is described with the aid of a linear electron-vibrational coupling model. The spectral information thereby obtained permits extensive comparison with experiment. The average accuracy of the present method, estimated by comparing adiabatic transition energies, is better than 0.4 eV. Only for the lowest π-π∗ valance transition, V′(1A1) and V′(1B2), and for the Rydberg excitations agree The results for the other π-π∗ valence transitions, V(1B2), and for the Rydberg excitations agree well with findings of previous experimental and theoretical work. A (multistate) vibronic coupling effect involving the V′(1A1) and V(1B2) valence transitions and the 3s(1A2 Rydberg excitation is suggested as the reason for the highly diffuse character of the 5.7--6.7 eV photoabsorption band.}, @@ -5052,8 +5053,8 @@ url = {http://www.sciencedirect.com/science/article/pii/S0301010497002565}, volume = {224}, year = {1997}, - Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0301010497002565}, - Bdsk-Url-2 = {https://doi.org/10.1016/S0301-0104(97)00256-5}} + bdsk-url-1 = {http://www.sciencedirect.com/science/article/pii/S0301010497002565}, + bdsk-url-2 = {https://doi.org/10.1016/S0301-0104(97)00256-5}} @article{Umari_2010, author = {Umari, P. and Stenuit, Geoffrey and Baroni, Stefano}, @@ -5070,8 +5071,8 @@ url = {https://link.aps.org/doi/10.1103/PhysRevB.81.115104}, volume = {81}, year = {2010}, - Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.81.115104}, - Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevB.81.115104}} + bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.81.115104}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRevB.81.115104}} @article{Verdozzi_1995, author = {Verdozzi, C. and Godby, R. 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P. and Kutepov, A. and Kotliar, G.}, @@ -5188,8 +5189,8 @@ url = {https://link.aps.org/doi/10.1103/PhysRevX.3.021011}, volume = {3}, year = {2013}, - Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevX.3.021011}, - Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevX.3.021011}} + bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevX.3.021011}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRevX.3.021011}} @article{Zhang_2013, author = {Zhang,Du and Steinmann,Stephan N. and Yang,Weitao}, @@ -5202,7 +5203,7 @@ title = {Dynamical second-order Bethe-Salpeter equation kernel: A method for electronic excitation beyond the adiabatic approximation}, volume = {139}, year = {2013}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.4824907}} + bdsk-url-1 = {https://doi.org/10.1063/1.4824907}} @article{Ziaei_2016, author = {Ziaei,Vafa and Bredow,Thomas}, @@ -5217,7 +5218,7 @@ url = {https://doi.org/10.1063/1.4966920}, volume = {145}, year = {2016}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.4966920}} + bdsk-url-1 = {https://doi.org/10.1063/1.4966920}} @article{Golze_2019, author = {Golze, Dorothea and Dvorak, Marc and Rinke, Patrick}, @@ -5229,8 +5230,8 @@ title = {The GW Compendium: A Practical Guide to Theoretical Photoemission Spectroscopy}, volume = {7}, year = {2019}, - Bdsk-Url-1 = {https://www.frontiersin.org/article/10.3389/fchem.2019.00377}, - Bdsk-Url-2 = {https://doi.org/10.3389/fchem.2019.00377}} + bdsk-url-1 = {https://www.frontiersin.org/article/10.3389/fchem.2019.00377}, + bdsk-url-2 = {https://doi.org/10.3389/fchem.2019.00377}} @misc{MRCC, author = {M. 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Eugene and Hohenstein, Edward G. and Bozkaya, U{\u g}ur and Sokolov, Alexander Yu. and Di Remigio, Roberto and Richard, Ryan M. and Gonthier, J{\'e}r{\^o}me F. and James, Andrew M. and McAlexander, Harley R. and Kumar, Ashutosh and Saitow, Masaaki and Wang, Xiao and Pritchard, Benjamin P. and Verma, Prakash and Schaefer, Henry F. and Patkowski, Konrad and King, Rollin A. and Valeev, Edward F. and Evangelista, Francesco A. and Turney, Justin M. and Crawford, T. Daniel and Sherrill, C. David}, @@ -5271,7 +5272,7 @@ url = {https://doi.org/10.1021/acs.jctc.7b00174}, volume = {13}, year = {2017}, - Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.7b00174}} + bdsk-url-1 = {https://doi.org/10.1021/acs.jctc.7b00174}} @article{Harding_2008, author = {M. E. Harding and J. Vazquez and B. Ruscic and A. K. Wilson and J. Gauss and J. F. Stanton}, @@ -5283,7 +5284,7 @@ title = {High-Accuracy Extrapolated ab Initio Thermochemistry. III. Additional Improvements and Overview}, volume = {128}, year = {2008}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.2835612}} + bdsk-url-1 = {https://doi.org/10.1063/1.2835612}} @article{dalton, author = {Aidas, Kestutis and Angeli, Celestino and Bak, Keld L. and Bakken, Vebj{\o}rn and Bast, Radovan and Boman, Linus and Christiansen, Ove and Cimiraglia, Renzo and Coriani, Sonia and Dahle, P{\aa}l and Dalskov, Erik K. and Ekstr{\"o}m, Ulf and Enevoldsen, Thomas and Eriksen, Janus J. and Ettenhuber, Patrick and Fern{\'a}ndez, Berta and Ferrighi, Lara and Fliegl, Heike and Frediani, Luca and Hald, Kasper and Halkier, Asger and H{\"a}ttig, Christof and Heiberg, Hanne and Helgaker, Trygve and Hennum, Alf Christian and Hettema, Hinne and Hjerten{\ae}s, Eirik and H{\o}st, Stinne and H{\o}yvik, Ida-Marie and Iozzi, Maria Francesca and Jans{\'\i}k, Branislav and Jensen, Hans J{\o}rgen Aa. and Jonsson, Dan and J{\o}rgensen, Poul and Kauczor, Joanna and Kirpekar, Sheela and Kj{\ae}rgaard, Thomas and Klopper, Wim and Knecht, Stefan and Kobayashi, Rika and Koch, Henrik and Kongsted, Jacob and Krapp, Andreas and Kristensen, Kasper and Ligabue, Andrea and Lutn{\ae}s, Ola B. and Melo, Juan I. and Mikkelsen, Kurt V. and Myhre, Rolf H. and Neiss, Christian and Nielsen, Christian B. and Norman, Patrick and Olsen, Jeppe and Olsen, J{\'o}gvan Magnus H. and Osted, Anders and Packer, Martin J. and Pawlowski, Filip and Pedersen, Thomas B. and Provasi, Patricio F. and Reine, Simen and Rinkevicius, Zilvinas and Ruden, Torgeir A. and Ruud, Kenneth and Rybkin, Vladimir V. and Sa{\l}ek, Pawel and Samson, Claire C. M. and de Mer{\'a}s, Alfredo S{\'a}nchez and Saue, Trond and Sauer, Stephan P. A. and Schimmelpfennig, Bernd and Sneskov, Kristian and Steindal, Arnfinn H. and Sylvester-Hvid, Kristian O. and Taylor, Peter R. and Teale, Andrew M. and Tellgren, Erik I. and Tew, David P. and Thorvaldsen, Andreas J. and Th{\o}gersen, Lea and Vahtras, Olav and Watson, Mark A. and Wilson, David J. D. and Ziolkowski, Marcin and {\AA}gren, Hans}, @@ -5298,7 +5299,7 @@ url = {http://dx.doi.org/10.1002/wcms.1172}, volume = {4}, year = {2014}, - Bdsk-Url-1 = {http://dx.doi.org/10.1002/wcms.1172}} + bdsk-url-1 = {http://dx.doi.org/10.1002/wcms.1172}} @article{Chr95, abstract = {An approximate coupled cluster singles and doubles model is presented, denoted CC2. The \{CC2\} total energy is of second-order M{\o}ller-Plesset perturbation theory (MP2) quality. The \{CC2\} linear response function is derived. Unlike MP2, excitation energies and transition moments can be obtained in CC2. A hierarchy of coupled cluster models, CCS, CC2, CCSD, CC3, \{CCSDT\} etc., is presented where \{CC2\} and \{CC3\} are approximate coupled cluster models defined by similar approximations. Higher levels give increased accuracy at increased computational effort. The scaling of CCS, CC2, CCSD, \{CC3\} and \{CCSDT\} is N4, N5, N6, \{N7\} and N8, respectively where N is th the number of orbitals. Calculations on Be, \{N2\} and \{C2H4\} are performed and results compared with those obtained in the second-order polarization propagator approach SOPPA. }, @@ -5313,8 +5314,8 @@ url = {http://www.sciencedirect.com/science/article/pii/000926149500841Q}, volume = {243}, year = {1995}, - Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/000926149500841Q}, - Bdsk-Url-2 = {http://dx.doi.org/10.1016/0009-2614(95)00841-Q}} + bdsk-url-1 = {http://www.sciencedirect.com/science/article/pii/000926149500841Q}, + bdsk-url-2 = {http://dx.doi.org/10.1016/0009-2614(95)00841-Q}} @article{Furche_2005, author = {Filipp Furche and Troy {Van Voorhis}}, @@ -5326,7 +5327,7 @@ title = {Fluctuation-Dissipation Theorem Density-Functional Theory}, volume = {122}, year = {2005}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.1884112}} + bdsk-url-1 = {https://doi.org/10.1063/1.1884112}} @article{Toulouse_2009, author = {Julien Toulouse and Iann C. Gerber and Georg Jansen and Andreas Savin and Janos G. Angyan}, @@ -5338,7 +5339,7 @@ title = {Adiabatic-Connection Fluctuation-Dissipation Density-Functional Theory Based on Range Separation}, volume = {102}, year = {2009}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevLett.102.096404}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRevLett.102.096404}} @article{Toulouse_2010, author = {Julien Toulouse and Wuming Zhu and Janos G. Angyan and Andreas Savin}, @@ -5350,7 +5351,7 @@ title = {Range-Separated Density-Functional Theory With the Random-Phase Approximation: Detailed Formalism and Illustrative Applications}, volume = {82}, year = {2010}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevA.82.032502}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRevA.82.032502}} @article{Angyan_2011, author = {J. G. Angyan and R.-F. Liu and J. Toulouse and G. Jansen}, @@ -5362,7 +5363,7 @@ title = {Correlation Energy Expressions from the Adiabatic-Connection Fluctuation Dissipation Theorem Approach}, volume = {7}, year = {2011}, - Bdsk-Url-1 = {https://doi.org/10.1021/ct200501r}} + bdsk-url-1 = {https://doi.org/10.1021/ct200501r}} @article{Ghosh_2018, author = {Ghosh, Soumen and Verma, Pragya and Cramer, Christopher J. and Gagliardi, Laura and Truhlar, Donald G.}, @@ -5375,7 +5376,7 @@ title = {Combining Wave Function Methods with Density Functional Theory for Excited States}, volume = {118}, year = {2018}, - Bdsk-Url-1 = {https://doi.org/10.1021/acs.chemrev.8b00193}} + bdsk-url-1 = {https://doi.org/10.1021/acs.chemrev.8b00193}} @incollection{Grimme_2004a, author = {Stefan Grimme}, @@ -5400,7 +5401,7 @@ title = {Progress and Challenges in the Calculation of Electronic Excited States}, volume = {13}, year = {2012}, - Bdsk-Url-1 = {https://doi.org/10.1002/cphc.201100200}} + bdsk-url-1 = {https://doi.org/10.1002/cphc.201100200}} @article{Holzer_2018b, author = {Christof Holzer and Xin Gui and Michael E. Harding and Georg Kresse and Trygve Helgaker and Wim Klopper}, @@ -5412,7 +5413,7 @@ title = {Bethe--Salpeter Correlation Energies of Atoms and Molecules}, volume = {149}, year = {2018}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.5047030}} + bdsk-url-1 = {https://doi.org/10.1063/1.5047030}} @article{Olsen_2014, author = {T. Olsen and K. S. Thygesen}, @@ -5424,7 +5425,7 @@ title = {Static Correlation Beyond the Random Phase Approximation: Dissociating H2 With the Bethe-Salpeter Equation and Time-Dependent GW}, volume = {140}, year = {2014}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.4871875}} + bdsk-url-1 = {https://doi.org/10.1063/1.4871875}} @book{Schuck_Book, author = {P. Ring and P. Schuck}, @@ -5444,7 +5445,7 @@ title = {Linearized Many-Body Problem}, volume = {135}, year = {1964}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRev.135.A932}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRev.135.A932}} @article{Rowe_1968, author = {D. J. Rowe}, @@ -5456,7 +5457,7 @@ title = {Methods for Calculating Ground-State Correlations of Vibrational Nuclei}, volume = {175}, year = {1968}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRev.175.1283}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRev.175.1283}} @article{Salpeter_1951, author = {E. E. Salpeter and H. A. Bethe}, @@ -5468,7 +5469,7 @@ title = {A Relativistic Equation for Bound-State Problems}, volume = {84}, year = {1951}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRev.84.1232}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRev.84.1232}} @incollection{Rebolini_2013, author = {E. Rebolini and J. Toulouse and A. Savin}, @@ -5493,7 +5494,7 @@ title = {Dynamical Shift and Broadening of Core Excitons in Semiconductors}, volume = {49}, year = {1982}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevLett.49.1519}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRevLett.49.1519}} @article{Strinati_1984, author = {G. Strinati}, @@ -5505,7 +5506,7 @@ title = {Effects of Dynamical Screening on Resonances at Inner-Shell Thresholds in Semiconductors}, volume = {29}, year = {1984}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevB.29.5718}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRevB.29.5718}} @article{Loos_2019b, author = {Loos, Pierre-Francois and Jacquemin, Denis}, @@ -5517,7 +5518,7 @@ title = {Evaluating 0-0 Energies with Theoretical Tools: a Short Review}, volume = {3}, year = {2019}, - Bdsk-Url-1 = {https://doi.org/10.1002/cptc.201900070}} + bdsk-url-1 = {https://doi.org/10.1002/cptc.201900070}} @article{Furche_2002, author = {F. Furche and R. Ahlrichs}, @@ -5529,7 +5530,7 @@ title = {Adiabatic Time-Dependent Density Functional Methods for Excited State Properties}, volume = {117}, year = {2002}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.1508368}} + bdsk-url-1 = {https://doi.org/10.1063/1.1508368}} @article{Roca-Sanjuan_2011, author = {Daniel {Roca-Sanjuan} and Mickael G. Delcey and Isabelle Navizet and Nicolas Ferre and Ya-Jun Liu and Roland Lindh}, @@ -5541,7 +5542,7 @@ title = {Chemiluminescence and Fluorescence States of a Small Model for Coelenteramide and Cypridina Oxyluciferin: A CASSCF/CASPT2 Study}, volume = {7}, year = {2011}, - Bdsk-Url-1 = {https://doi.org/10.1021/ct2004758}} + bdsk-url-1 = {https://doi.org/10.1021/ct2004758}} @article{Navizet_2011, author = {Isabelle Navizet and Ya-Jun Liu and Nicolas Ferre and Daniel {Roca-Sanjun} and Roland Lindh}, @@ -5553,7 +5554,7 @@ title = {The Chemistry of Bioluminescence: An Analysis of Chemical Functionalities}, volume = {12}, year = {2011}, - Bdsk-Url-1 = {https://doi.org/10.1002/cphc.201100504}} + bdsk-url-1 = {https://doi.org/10.1002/cphc.201100504}} @article{Gell-Mann_1957, author = {Gell-Mann, Murray and Brueckner, Keith A.}, @@ -5568,7 +5569,7 @@ title = {Correlation Energy of an Electron Gas at High Density}, volume = {106}, year = {1957}, - Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRev.106.364}} + bdsk-url-1 = {http://dx.doi.org/10.1103/PhysRev.106.364}} @article{Sawada_1957a, author = {Sawada, Katuro}, @@ -5584,7 +5585,7 @@ title = {Correlation Energy of an Electron Gas at High Density}, volume = {106}, year = {1957}, - Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRev.106.372}} + bdsk-url-1 = {http://dx.doi.org/10.1103/PhysRev.106.372}} @article{Sawada_1957b, author = {Sawada, K. and Brueckner, K. A. and Fukuda, N. and Brout, R.}, @@ -5600,7 +5601,7 @@ title = {Correlation Energy of an Electron Gas at High Density: Plasma Oscillations}, volume = {108}, year = {1957}, - Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRev.108.507}} + bdsk-url-1 = {http://dx.doi.org/10.1103/PhysRev.108.507}} @book{Martin_2016, author = {Richard M. Martin and Lucia Reining and David M. Ceperley}, @@ -5625,7 +5626,7 @@ url = {http://dx.doi.org/10.1016/j.cplett.2005.06.107}, volume = {412}, year = {2005}, - Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.cplett.2005.06.107}} + bdsk-url-1 = {http://dx.doi.org/10.1016/j.cplett.2005.06.107}} @article{Alam_2016, author = {Alam, Md. Mehboob and Knecht, Stefan and Fromager, Emmanuel}, @@ -5642,7 +5643,7 @@ title = {Ghost-Interaction Correction in Ensemble Density-Functional Theory for Excited States with and without Range Separation}, volume = {94}, year = {2016}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevA.94.012511}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRevA.94.012511}} @article{Alam_2017, author = {Alam, Md. Mehboob and Deur, Killian and Knecht, Stefan and Fromager, Emmanuel}, @@ -5659,7 +5660,7 @@ title = {Combining Extrapolation with Ghost Interaction Correction in Range-Separated Ensemble Density Functional Theory for Excited States}, volume = {147}, year = {2017}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.4999825}} + bdsk-url-1 = {https://doi.org/10.1063/1.4999825}} @article{Angeli_2001a, author = {Angeli, Celestino and Cimiraglia, Renzo and Malrieu, Jean-Paul}, @@ -5676,7 +5677,7 @@ title = {N-Electron Valence State Perturbation Theory: A Fast Implementation of the Strongly Contracted Variant}, volume = {350}, year = {2001}, - Bdsk-Url-1 = {https://doi.org/10.1016/S0009-2614(01)01303-3}} + bdsk-url-1 = {https://doi.org/10.1016/S0009-2614(01)01303-3}} @article{Angeli_2001b, author = {Angeli, C. and Cimiraglia, R. and Evangelisti, S. and Leininger, T. and Malrieu, J.-P.}, @@ -5692,7 +5693,7 @@ title = {Introduction of {\emph{n}} -Electron Valence States for Multireference Perturbation Theory}, volume = {114}, year = {2001}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.1361246}} + bdsk-url-1 = {https://doi.org/10.1063/1.1361246}} @article{Angeli_2002, author = {Angeli, Celestino and Cimiraglia, Renzo and Malrieu, Jean-Paul}, @@ -5709,7 +5710,7 @@ title = {{\emph{N}} -Electron Valence State Perturbation Theory: {{A}} Spinless Formulation and an Efficient Implementation of the Strongly Contracted and of the Partially Contracted Variants}, volume = {117}, year = {2002}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.1515317}} + bdsk-url-1 = {https://doi.org/10.1063/1.1515317}} @article{Angeli_2008, author = {C. Angeli}, @@ -5742,7 +5743,7 @@ pages = {NA-NA}, title = {An Analysis of the Dynamic $\sigma$ Polarization in the {{V}} State of Ethene}, year = {2010}, - Bdsk-Url-1 = {https://doi.org/10.1002/qua.22597}} + bdsk-url-1 = {https://doi.org/10.1002/qua.22597}} @article{Applencourt_2014, author = {Peter Belohorec and Stuart M. Rothstein and Jan Vrbik}, @@ -5756,8 +5757,8 @@ url = {https://doi.org/10.1063/1.464838}, volume = {98}, year = {1993}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.464838}, - Bdsk-Url-2 = {http://dx.doi.org/10.1063/1.464838}} + bdsk-url-1 = {https://doi.org/10.1063/1.464838}, + bdsk-url-2 = {http://dx.doi.org/10.1063/1.464838}} @article{Aquilante_2003, author = {Aquilante, Francesco and Barone, Vincenzo and Roos, Bj\"orn O.}, @@ -5773,7 +5774,7 @@ title = {A Theoretical Investigation of Valence and {{Rydberg}} Electronic States of Acrolein}, volume = {119}, year = {2003}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.1625363}} + bdsk-url-1 = {https://doi.org/10.1063/1.1625363}} @article{Arenas_2006, author = {Arenas, Juan F. and Otero, Juan C. and Pel{\'a}ez, Daniel and Soto, Juan}, @@ -5788,7 +5789,7 @@ url = {http://dx.doi.org/10.1021/jo051897r}, volume = {71}, year = {2006}, - Bdsk-Url-1 = {http://dx.doi.org/10.1021/jo051897r}} + bdsk-url-1 = {http://dx.doi.org/10.1021/jo051897r}} @article{arxiv, author = {Michel Caffarel and Thomas Applencourt and Emmanuel Giner and Anthony Scemama}, @@ -5798,7 +5799,7 @@ eprint = {arXiv:1607.06742}, title = {Using CIPSI nodes in diffusion Monte Carlo}, year = {2016}, - Bdsk-Url-1 = {https://dx.doi.org/10.1021/bk-2016-1234.ch002}} + bdsk-url-1 = {https://dx.doi.org/10.1021/bk-2016-1234.ch002}} @article{Aspuru-Guzik_2004, author = {Aspuru-Guzik, Al{\'a}n and El Akramine, Ouafae and Grossman, Jeffrey C. and Lester, William A.}, @@ -5815,7 +5816,7 @@ title = {Quantum {{Monte Carlo}} for Electronic Excitations of Free-Base Porphyrin}, volume = {120}, year = {2004}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.1646356}} + bdsk-url-1 = {https://doi.org/10.1063/1.1646356}} @article{Assaraf_2000, author = {Assaraf, Roland and Caffarel, Michel and Khelif, Anatole}, @@ -5832,8 +5833,8 @@ url = {http://dx.doi.org/10.1103/PhysRevE.61.4566}, volume = {61}, year = {2000}, - Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevE.61.4566}, - Bdsk-Url-2 = {http://dx.doi.org/10.1103/physreve.61.4566}} + bdsk-url-1 = {http://dx.doi.org/10.1103/PhysRevE.61.4566}, + bdsk-url-2 = {http://dx.doi.org/10.1103/physreve.61.4566}} @article{Assaraf_2007, author = {Assaraf, Roland and Caffarel, Michel and Scemama, Anthony}, @@ -5849,8 +5850,8 @@ url = {http://dx.doi.org/10.1103/PhysRevE.75.035701}, volume = {75}, year = {2007}, - Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevE.75.035701}, - Bdsk-Url-2 = {http://dx.doi.org/10.1103/physreve.75.035701}} + bdsk-url-1 = {http://dx.doi.org/10.1103/PhysRevE.75.035701}, + bdsk-url-2 = {http://dx.doi.org/10.1103/physreve.75.035701}} @article{Astrakharchik_2011, author = {G. E. Astrakharchik and M. D. Girardeau}, @@ -5877,7 +5878,7 @@ url = {http://dx.doi.org/10.1021/cr2001564}, volume = {112}, year = {2012}, - Bdsk-Url-1 = {http://dx.doi.org/10.1021/cr2001564}} + bdsk-url-1 = {http://dx.doi.org/10.1021/cr2001564}} @article{Avery_1993, author = {J. Avery}, @@ -5889,7 +5890,7 @@ title = {Selected applications of hyperspherical harmonics in quantum theory}, volume = {97}, year = {1993}, - Bdsk-Url-1 = {https://doi.org/10.1021/j100112a048}} + bdsk-url-1 = {https://doi.org/10.1021/j100112a048}} @book{AveryBook, address = {Dordrecht}, @@ -5909,7 +5910,7 @@ pages = {137}, title = {Time‐independent density functional theory for degenerate excited states of Coulomb systems}, year = {2018}, - Bdsk-Url-1 = {https://doi.org/10.1007/s00214-018-2352-7}} + bdsk-url-1 = {https://doi.org/10.1007/s00214-018-2352-7}} @article{Bajdich_2005, author = {M. Bajdich and L. Mitas and G. Drobny and L. K. Wagner}, @@ -5936,7 +5937,7 @@ title = {Rydberg States with Quantum {{Monte Carlo}}}, volume = {124}, year = {2006}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.2180773}} + bdsk-url-1 = {https://doi.org/10.1063/1.2180773}} @article{Bande_2008, author = {Bande, Annika and L{\"u}chow, Arne}, @@ -5952,7 +5953,7 @@ url = {http://dx.doi.org/10.1039/b803571g}, volume = {10}, year = {2008}, - Bdsk-Url-1 = {http://dx.doi.org/10.1039/b803571g}} + bdsk-url-1 = {http://dx.doi.org/10.1039/b803571g}} @article{Barca_2018a, author = {Barca, Giuseppe M. J. and Gilbert, Andrew T. B. and Gill, Peter M. W.}, @@ -5964,7 +5965,7 @@ title = {Simple {{Models}} for {{Difficult Electronic Excitations}}}, volume = {14}, year = {2018}, - Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.7b00994}} + bdsk-url-1 = {https://doi.org/10.1021/acs.jctc.7b00994}} @article{Barca_2018b, author = {Barca, Giuseppe M. J. and Gilbert, Andrew T. B. and Gill, Peter M. W.}, @@ -5982,7 +5983,7 @@ title = {Excitation {{Number}}: {{Characterizing Multiply Excited States}}}, volume = {14}, year = {2018}, - Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.7b00963}} + bdsk-url-1 = {https://doi.org/10.1021/acs.jctc.7b00963}} @article{Bauschlicher_1995, author = {Bauschlicher, Charles W. and Ma\^{i}tre, Philippe}, @@ -5998,7 +5999,7 @@ url = {http://dx.doi.org/10.1007/s002140050068}, volume = {90}, year = {1995}, - Bdsk-Url-1 = {http://dx.doi.org/10.1007/s002140050068}} + bdsk-url-1 = {http://dx.doi.org/10.1007/s002140050068}} @article{Belohorec_93, author = {Peter Belohorec and Stuart M. Rothstein and Jan Vrbik}, @@ -6012,8 +6013,8 @@ url = {https://doi.org/10.1063/1.464838}, volume = {98}, year = {1993}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.464838}, - Bdsk-Url-2 = {http://dx.doi.org/10.1063/1.464838}} + bdsk-url-1 = {https://doi.org/10.1063/1.464838}, + bdsk-url-2 = {http://dx.doi.org/10.1063/1.464838}} @article{Bender_1969, author = {Bender, Charles F. and Davidson, Ernest R.}, @@ -6030,7 +6031,7 @@ url = {http://dx.doi.org/10.1103/physrev.183.23}, volume = {183}, year = {1969}, - Bdsk-Url-1 = {http://dx.doi.org/10.1103/physrev.183.23}} + bdsk-url-1 = {http://dx.doi.org/10.1103/physrev.183.23}} @article{Berge_s_2008, author = {Berg{\`e}s, Jacqueline and Varmenot, Nicolas and Scemama, Anthony and Abedinzadeh, Zohreh and Bobrowski, Krzysztof}, @@ -6047,7 +6048,7 @@ url = {http://dx.doi.org/10.1021/jp711944v}, volume = {112}, year = {2008}, - Bdsk-Url-1 = {http://dx.doi.org/10.1021/jp711944v}} + bdsk-url-1 = {http://dx.doi.org/10.1021/jp711944v}} @article{Blunt_2015, author = {Blunt, N. S. and Smart, Simon D. and Booth, George H. and Alavi, Ali}, @@ -6063,7 +6064,7 @@ title = {An Excited-State Approach within Full Configuration Interaction Quantum {{Monte Carlo}}}, volume = {143}, year = {2015}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.4932595}} + bdsk-url-1 = {https://doi.org/10.1063/1.4932595}} @article{Blunt_2017, author = {Blunt, N. S. and Neuscamman, Eric}, @@ -6080,7 +6081,7 @@ title = {Charge-Transfer Excited States: {{Seeking}} a Balanced and Efficient Wave Function Ansatz in Variational {{Monte Carlo}}}, volume = {147}, year = {2017}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.4998197}} + bdsk-url-1 = {https://doi.org/10.1063/1.4998197}} @article{Blunt_2018, author = {N. S. Blunt}, @@ -6092,7 +6093,7 @@ title = {An efficient and accurate perturbative correction to initiator full configuration interaction quantum Monte Carlo}, volume = {148}, year = {2018}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.5037923}} + bdsk-url-1 = {https://doi.org/10.1063/1.5037923}} @article{Boblest_2014, author = {S. Boblest and C. Schimeczek and G. Wunner}, @@ -6113,7 +6114,7 @@ title = {Luttinger-liquid behaviour in carbon nanotubes}, volume = {397}, year = {1999}, - Bdsk-Url-1 = {https://doi.org/10.1038/17569}} + bdsk-url-1 = {https://doi.org/10.1038/17569}} @article{Boggio-Pasqua_2000, abstract = {Realistic analytical representations of the twelve lowest singlet and triplet electronic adiabatic potential energy curves of C2 molecule are given in this article. The corresponding electronic states are correlated with C atoms both in their 3P state. A new set of high level MRCI calculations coupled with a double many-body expansion analytical \textregistered{}tting based on the extended Hartree$\pm$Fock approximate correlation energy model have been used in this work. Using RKR data available in the literature, comparison is made between our results and RKR turning points concerning the four lowest singlet states X1Sg1, A1Pu, B1Dg and BH 1Sg1 of C2. The agreement is very satisfying. q 2000 Elsevier Science B.V. All rights reserved.}, @@ -6131,7 +6132,7 @@ title = {Analytical Representations of High Level Ab Initio Potential Energy Curves of the {{C}} 2 Molecule}, volume = {531}, year = {2000}, - Bdsk-Url-1 = {https://doi.org/10.1016/S0166-1280(00)00442-5}} + bdsk-url-1 = {https://doi.org/10.1016/S0166-1280(00)00442-5}} @article{Boggio-Pasqua_2004, author = {{Boggio-Pasqua}, Martial and Bearpark, Michael J. and Klene, Michael and Robb, Michael A.}, @@ -6147,7 +6148,7 @@ title = {A Computational Strategy for Geometry Optimization of Ionic and Covalent Excited States, Applied to Butadiene and Hexatriene}, volume = {120}, year = {2004}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.1690756}} + bdsk-url-1 = {https://doi.org/10.1063/1.1690756}} @article{Boggio-Pasqua_2007, author = {{Boggio-Pasqua}, Martial and Bearpark, Michael J. and Robb, Michael A.}, @@ -6159,7 +6160,7 @@ title = {Toward a {{Mechanistic Understanding}} of the {{Photochromism}} of {{Dimethyldihydropyrenes}}}, volume = {72}, year = {2007}, - Bdsk-Url-1 = {https://doi.org/10.1021/jo070452v}} + bdsk-url-1 = {https://doi.org/10.1021/jo070452v}} @article{Bomble_2004, author = {Bomble, Yannick J. and Sattelmeyer, Kurt W. and Stanton, John F. and Gauss, J\"urgen}, @@ -6175,7 +6176,7 @@ title = {On the Vertical Excitation Energy of Cyclopentadiene}, volume = {121}, year = {2004}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.1780159}} + bdsk-url-1 = {https://doi.org/10.1063/1.1780159}} @article{Booth_2009, author = {Booth, George H. and Thom, Alex J. W. and Alavi, Ali}, @@ -6194,8 +6195,8 @@ urldate = {2017-11-13}, volume = {131}, year = {2009}, - Bdsk-Url-1 = {http://aip.scitation.org/doi/full/10.1063/1.3193710}, - Bdsk-Url-2 = {http://dx.doi.org/10.1063/1.3193710}} + bdsk-url-1 = {http://aip.scitation.org/doi/full/10.1063/1.3193710}, + bdsk-url-2 = {http://dx.doi.org/10.1063/1.3193710}} @article{Booth_2011, author = {Booth, George H. and Cleland, Deidre and Thom, Alex J. W. and Alavi, Ali}, @@ -6212,7 +6213,7 @@ title = {Breaking the Carbon Dimer: {{The}} Challenges of Multiple Bond Dissociation with Full Configuration Interaction Quantum {{Monte Carlo}} Methods}, volume = {135}, year = {2011}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.3624383}} + bdsk-url-1 = {https://doi.org/10.1063/1.3624383}} @article{Borgoo_2015, abstract = {This expression gives the difference between an excitation energy E1 - E0 and the corresponding Kohn\textendash{}Sham orbital energy difference $\epsilon$1 - $\epsilon$0 as a partial derivative of the exchange-correlation energy of an ensemble of states Exc,w[$\rho$]. Through Lieb maximisation, on input full-CI density functions, the exchange-correlation energy is evaluated accurately and the partial derivative is evaluated numerically using finite difference. The equality is studied numerically for different geometries of the H2 molecule and different ensemble weights. We explore the adiabatic connection for the ensemble exchange-correlation energy. The latter may prove useful when modelling the unknown weight dependence of the exchange-correlation energy.}, @@ -6228,7 +6229,7 @@ title = {Excitation Energies from Ensemble {{DFT}}}, volume = {1702}, year = {2015}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.4938857}} + bdsk-url-1 = {https://doi.org/10.1063/1.4938857}} @article{Boschen_2014, author = {Boschen, Jeffery S. and Theis, Daniel and Ruedenberg, Klaus and Windus, Theresa L.}, @@ -6243,7 +6244,7 @@ title = {Accurate Ab Initio Potential Energy Curves and Spectroscopic Properties of the Four Lowest Singlet States of {{C2}}}, volume = {133}, year = {2014}, - Bdsk-Url-1 = {https://doi.org/10.1007/s00214-013-1425-x}} + bdsk-url-1 = {https://doi.org/10.1007/s00214-013-1425-x}} @article{Bouabca_2009, author = {Bouab{\c c}a, Thomas and Ben Amor, Nadia and Maynau, Daniel and Caffarel, Michel}, @@ -6261,7 +6262,7 @@ title = {A Study of the Fixed-Node Error in Quantum {{Monte Carlo}} Calculations of Electronic Transitions: {{The}} Case of the Singlet N$\rightarrow\pi{_\ast}$ ({{CO}}) Transition of the Acrolein}, volume = {130}, year = {2009}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.3086023}} + bdsk-url-1 = {https://doi.org/10.1063/1.3086023}} @incollection{Bressanini_2001, author = {D. Bressanini and D. M. Ceperley and P. Reynolds}, @@ -6327,7 +6328,7 @@ title = {Periodic trends in the diatomic monoxides and monosulfides of the 3d transition metals}, url = {http://dx.doi.org/10.1039/a906523g}, year = {2000}, - Bdsk-Url-1 = {http://dx.doi.org/10.1039/a906523g}} + bdsk-url-1 = {http://dx.doi.org/10.1039/a906523g}} @article{Budzak_2017, author = {Budz{\'a}k, {\v S}. and Scalmani, G. and Jacquemin, D.}, @@ -6352,8 +6353,8 @@ url = {http://www.sciencedirect.com/science/article/pii/S0009261406010372}, volume = {428}, year = {2006}, - Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0009261406010372}, - Bdsk-Url-2 = {https://doi.org/10.1016/j.cplett.2006.07.027}} + bdsk-url-1 = {http://www.sciencedirect.com/science/article/pii/S0009261406010372}, + bdsk-url-2 = {https://doi.org/10.1016/j.cplett.2006.07.027}} @article{Buendia_2013, author = {E. Buend{\'\i}a and F.J. G{\'a}lvez and P. Maldonado and A. Sarsa}, @@ -6368,8 +6369,8 @@ url = {http://www.sciencedirect.com/science/article/pii/S0009261413000079}, volume = {559}, year = {2013}, - Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0009261413000079}, - Bdsk-Url-2 = {https://doi.org/10.1016/j.cplett.2012.12.055}} + bdsk-url-1 = {http://www.sciencedirect.com/science/article/pii/S0009261413000079}, + bdsk-url-2 = {https://doi.org/10.1016/j.cplett.2012.12.055}} @article{Buenker_1968, author = {Buenker, Robert J. and Peyerimhoff, Sigrid D.}, @@ -6384,7 +6385,7 @@ title = {{{CI}} Method for the Study of General Molecular Potentials}, volume = {12}, year = {1968}, - Bdsk-Url-1 = {https://doi.org/10.1007/BF00528266}} + bdsk-url-1 = {https://doi.org/10.1007/BF00528266}} @article{Buenker_2014, author = {Buenker, Robert J. and Phillips, Robin A. and Krebs, Stefan and Liebermann, Heinz-Peter and Alekseyev, Aleksey B. and Funke, Peter}, @@ -6403,8 +6404,8 @@ urldate = {2017-11-13}, volume = {133}, year = {2014}, - Bdsk-Url-1 = {https://link.springer.com/article/10.1007/s00214-014-1468-7}, - Bdsk-Url-2 = {http://dx.doi.org/10.1007/s00214-014-1468-7}} + bdsk-url-1 = {https://link.springer.com/article/10.1007/s00214-014-1468-7}, + bdsk-url-2 = {http://dx.doi.org/10.1007/s00214-014-1468-7}} @article{Bunge_2006, author = {Bunge, Carlos F. and Carb{\'o}-Dorca, Ramon}, @@ -6422,8 +6423,8 @@ urldate = {2017-11-17}, volume = {125}, year = {2006}, - Bdsk-Url-1 = {http://aip.scitation.org/doi/abs/10.1063/1.2207621}, - Bdsk-Url-2 = {http://dx.doi.org/10.1063/1.2207621}} + bdsk-url-1 = {http://aip.scitation.org/doi/abs/10.1063/1.2207621}, + bdsk-url-2 = {http://dx.doi.org/10.1063/1.2207621}} @article{Burkatzki_2007, author = {Burkatzki, M. and Filippi, C. and Dolg, M.}, @@ -6440,7 +6441,7 @@ url = {http://dx.doi.org/10.1063/1.2741534}, volume = {126}, year = {2007}, - Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.2741534}} + bdsk-url-1 = {http://dx.doi.org/10.1063/1.2741534}} @article{Burkatzki_2008, author = {Burkatzki, M. and Filippi, Claudia and Dolg, M.}, @@ -6457,7 +6458,7 @@ url = {http://dx.doi.org/10.1063/1.2987872}, volume = {129}, year = {2008}, - Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.2987872}} + bdsk-url-1 = {http://dx.doi.org/10.1063/1.2987872}} @article{Burnett_1993, author = {K. Burnett and V. C. Reed and P. L. Knight}, @@ -6484,7 +6485,7 @@ url = {http://dx.doi.org/10.1016/j.chemphys.2008.11.021}, volume = {356}, year = {2009}, - Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.chemphys.2008.11.021}} + bdsk-url-1 = {http://dx.doi.org/10.1016/j.chemphys.2008.11.021}} @article{Caffarel_2005, author = {Michel Caffarel and Jean-Pierre Daudey and Jean-Louis Heully and Alejandro Ram{\'\i}rez-Sol{\'\i}s}, @@ -6498,8 +6499,8 @@ url = {https://doi.org/10.1063/1.2011393}, volume = {123}, year = {2005}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.2011393}, - Bdsk-Url-2 = {http://dx.doi.org/10.1063/1.2011393}} + bdsk-url-1 = {https://doi.org/10.1063/1.2011393}, + bdsk-url-2 = {http://dx.doi.org/10.1063/1.2011393}} @article{Caffarel_2007, author = {Caffarel, Michel and Hern{\'a}ndez-Lamoneda, Ram{\'o}n and Scemama, Anthony and Ram{\'\i}rez-Sol{\'\i}s, Alejandro}, @@ -6515,8 +6516,8 @@ url = {http://dx.doi.org/10.1103/PhysRevLett.99.153001}, volume = {99}, year = {2007}, - Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevLett.99.153001}, - Bdsk-Url-2 = {http://dx.doi.org/10.1103/physrevlett.99.153001}} + bdsk-url-1 = {http://dx.doi.org/10.1103/PhysRevLett.99.153001}, + bdsk-url-2 = {http://dx.doi.org/10.1103/physrevlett.99.153001}} @article{Caffarel_2009, author = {Caffarel, Michel and Scemama, Anthony and Ram{\'\i}rez-Sol{\'\i}s, Alejandro}, @@ -6533,7 +6534,7 @@ url = {http://dx.doi.org/10.1007/s00214-009-0713-y}, volume = {126}, year = {2009}, - Bdsk-Url-1 = {http://dx.doi.org/10.1007/s00214-009-0713-y}} + bdsk-url-1 = {http://dx.doi.org/10.1007/s00214-009-0713-y}} @article{Caffarel_2010, author = {Thomas Bouab\c{c}a and Beno\^{i}t Bra\"{\i}da and Michel Caffarel}, @@ -6547,8 +6548,8 @@ url = {https://doi.org/10.1063/1.3457364}, volume = {133}, year = {2010}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.3457364}, - Bdsk-Url-2 = {http://dx.doi.org/10.1063/1.3457364}} + bdsk-url-1 = {https://doi.org/10.1063/1.3457364}, + bdsk-url-2 = {http://dx.doi.org/10.1063/1.3457364}} @article{Caffarel_2014, author = {Caffarel, Michel and Giner, Emmanuel and Scemama, Anthony and Ram{\'\i}rez-Sol{\'\i}s, Alejandro}, @@ -6565,7 +6566,7 @@ url = {http://dx.doi.org/10.1021/ct5004252}, volume = {10}, year = {2014}, - Bdsk-Url-1 = {http://dx.doi.org/10.1021/ct5004252}} + bdsk-url-1 = {http://dx.doi.org/10.1021/ct5004252}} @article{Caffarel_2016, author = {Caffarel, Michel and Applencourt, Thomas and Giner, Emmanuel and Scemama, Anthony}, @@ -6582,7 +6583,7 @@ url = {http://dx.doi.org/10.1063/1.4947093}, volume = {144}, year = {2016}, - Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.4947093}} + bdsk-url-1 = {http://dx.doi.org/10.1063/1.4947093}} @inbook{Caffarel_2016b, author = {Michel Caffarel and Thomas Applencourt and Emmanuel Giner and Anthony Scemama}, @@ -6595,8 +6596,8 @@ title = {Using CIPSI Nodes in Diffusion Monte Carlo}, url = {http://pubs.acs.org/doi/abs/10.1021/bk-2016-1234.ch002}, year = {2016}, - Bdsk-Url-1 = {http://pubs.acs.org/doi/abs/10.1021/bk-2016-1234.ch002}, - Bdsk-Url-2 = {http://dx.doi.org/10.1021/bk-2016-1234.ch002}} + bdsk-url-1 = {http://pubs.acs.org/doi/abs/10.1021/bk-2016-1234.ch002}, + bdsk-url-2 = {http://dx.doi.org/10.1021/bk-2016-1234.ch002}} @article{Cai_2000c, author = {Zheng-Li Cai and David J. Tozer and Jeffrey R. Reimers}, @@ -6610,7 +6611,7 @@ url = {https://doi.org/10.1063/1.1312826}, volume = {113}, year = {2000}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.1312826}} + bdsk-url-1 = {https://doi.org/10.1063/1.1312826}} @article{Caricato_2010, author = {Caricato, M. and Trucks, G. W. and Frisch, M. J. and Wiberg, K. B.}, @@ -6639,7 +6640,7 @@ title = {The {{Hubbard}} Dimer: A Density Functional Case Study of a Many-Body Problem}, volume = {27}, year = {2015}, - Bdsk-Url-1 = {https://doi.org/10.1088/0953-8984/27/39/393001}} + bdsk-url-1 = {https://doi.org/10.1088/0953-8984/27/39/393001}} @article{Carrascal_2018, abstract = {The asymmetric Hubbard dimer is used to study the density-dependence of the exact frequencydependent kernel of linear-response time-dependent density functional theory. The exact form of the kernel is given, and the limitations of the adiabatic approximation utilizing the exact ground-state functional are shown. The oscillator strength sum rule is proven for lattice Hamiltonians, and relative oscillator strengths are defined appropriately. The method of Casida for extracting oscillator strengths from a frequencydependent kernel is demonstrated to yield the exact result with this kernel. An unambiguous way of labelling the nature of excitations is given. The fluctuation-dissipation theorem is proven for the groundstate exchange-correlation energy. The distinction between weak and strong correlation is shown to depend on the ratio of interaction to asymmetry. A simple interpolation between carefully defined weak-correlation and strong-correlation regimes yields a density-functional approximation for the kernel that gives accurate transition frequencies for both the single and double excitations, including charge-transfer excitations. Many exact results, limits, and expansions about those limits are given in the Appendices.}, @@ -6652,7 +6653,7 @@ title = {Linear Response Time-Dependent Density Functional Theory of the {{Hubbard}} Dimer}, volume = {91}, year = {2018}, - Bdsk-Url-1 = {https://doi.org/10.1140/epjb/e2018-90114-9}} + bdsk-url-1 = {https://doi.org/10.1140/epjb/e2018-90114-9}} @inbook{Casida, author = {M. E. Casida}, @@ -6665,7 +6666,7 @@ series = {Recent Advances in Density Functional Methods}, title = {Time-Dependent Density Functional Response Theory for Molecules}, year = {1995}, - Bdsk-Url-1 = {https://doi.org/10.1142/9789812830586_0005}} + bdsk-url-1 = {https://doi.org/10.1142/9789812830586_0005}} @article{Casula_2006, author = {Casula, Michele}, @@ -6681,8 +6682,8 @@ url = {http://dx.doi.org/10.1103/PhysRevB.74.161102}, volume = {74}, year = {2006}, - Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevB.74.161102}, - Bdsk-Url-2 = {http://dx.doi.org/10.1103/physrevb.74.161102}} + bdsk-url-1 = {http://dx.doi.org/10.1103/PhysRevB.74.161102}, + bdsk-url-2 = {http://dx.doi.org/10.1103/physrevb.74.161102}} @article{Casula_2009, author = {Casula, Michele and Marchi, Mariapia and Azadi, Sam and Sorella, Sandro}, @@ -6699,7 +6700,7 @@ url = {http://dx.doi.org/10.1016/j.cplett.2009.07.005}, volume = {477}, year = {2009}, - Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.cplett.2009.07.005}} + bdsk-url-1 = {http://dx.doi.org/10.1016/j.cplett.2009.07.005}} @article{Casula_2010, author = {Casula, Michele and Moroni, Saverio and Sorella, Sandro and Filippi, Claudia}, @@ -6716,7 +6717,7 @@ url = {http://dx.doi.org/10.1063/1.3380831}, volume = {132}, year = {2010}, - Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.3380831}} + bdsk-url-1 = {http://dx.doi.org/10.1063/1.3380831}} @article{Catalan_2006, author = {Catal\'an, J. and {de Paz}, J. L. G.}, @@ -6733,7 +6734,7 @@ title = {On the Photophysics of All- {\emph{Trans}} Polyenes: {{Hexatriene}} versus Octatetraene}, volume = {124}, year = {2006}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.2158992}} + bdsk-url-1 = {https://doi.org/10.1063/1.2158992}} @article{Cave_1988b, author = {Cave, Robert J. and Davidson, Ernest R.}, @@ -6749,7 +6750,7 @@ title = {Theoretical Investigation of Several Low-Lying States of Trans, Trans-1, 3,5-Hexatriene}, volume = {92}, year = {1988}, - Bdsk-Url-1 = {https://doi.org/10.1021/j100314a009}} + bdsk-url-1 = {https://doi.org/10.1021/j100314a009}} @article{Cave_2004, author = {Cave, Robert J. and Zhang, Fan and Maitra, Neepa T. and Burke, Kieron}, @@ -6761,7 +6762,7 @@ 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}} + bdsk-url-1 = {https://doi.org/10.1016/j.cplett.2004.03.051}} @inbook{Ceperley_1979, author = {D. M. Ceperley and M. H. Kalos}, @@ -6782,7 +6783,7 @@ title = {Ground State of the Electron Gas by a Stochastic Method}, volume = {45}, year = {1980}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevLett.45.566}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRevLett.45.566}} @article{Ceperley_1991, author = {D. M. Ceperley}, @@ -6809,8 +6810,8 @@ url = {https://link.aps.org/doi/10.1103/PhysRevB.94.220102}, volume = {94}, year = {2016}, - Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.94.220102}, - Bdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevB.94.220102}} + bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.94.220102}, + bdsk-url-2 = {http://dx.doi.org/10.1103/PhysRevB.94.220102}} @article{Chien_2018, author = {Chien, Alan D. and Holmes, Adam A. and Otten, Matthew and Umrigar, C. J. and Sharma, Sandeep and Zimmerman, Paul M.}, @@ -6827,7 +6828,7 @@ title = {Excited {{States}} of {{Methylene}}, {{Polyenes}}, and {{Ozone}} from {{Heat}}-{{Bath Configuration Interaction}}}, volume = {122}, year = {2018}, - Bdsk-Url-1 = {https://doi.org/10.1021/acs.jpca.8b01554}} + bdsk-url-1 = {https://doi.org/10.1021/acs.jpca.8b01554}} @article{Christiansen_1991, author = {P. A. Christiansen}, @@ -6841,8 +6842,8 @@ url = {https://doi.org/10.1063/1.461491}, volume = {95}, year = {1991}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.461491}, - Bdsk-Url-2 = {http://dx.doi.org/10.1063/1.461491}} + bdsk-url-1 = {https://doi.org/10.1063/1.461491}, + bdsk-url-2 = {http://dx.doi.org/10.1063/1.461491}} @article{Christiansen_1998, author = {Christiansen, Ove and Stanton, John F. and Gauss, J\"urgen}, @@ -6858,7 +6859,7 @@ title = {A Coupled Cluster Study of the 1 {{1A1g}} and 1 {{1B2u}} States of Benzene}, volume = {108}, year = {1998}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.475801}} + bdsk-url-1 = {https://doi.org/10.1063/1.475801}} @article{Chuvylkin_2010, author = {N. D. Chuvylkin and E. A. Smolenskiі and N. S. Zefirov}, @@ -6897,8 +6898,8 @@ urldate = {2017-11-14}, volume = {83}, year = {1985}, - Bdsk-Url-1 = {http://aip.scitation.org/doi/10.1063/1.449362}, - Bdsk-Url-2 = {http://dx.doi.org/10.1063/1.449362}} + bdsk-url-1 = {http://aip.scitation.org/doi/10.1063/1.449362}, + bdsk-url-2 = {http://dx.doi.org/10.1063/1.449362}} @article{Cimiraglia_1987, author = {Cimiraglia, Renzo and Persico, Maurizio}, @@ -6928,7 +6929,7 @@ url = {http://dx.doi.org/10.1016/j.cplett.2007.01.073}, volume = {436}, year = {2007}, - Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.cplett.2007.01.073}} + bdsk-url-1 = {http://dx.doi.org/10.1016/j.cplett.2007.01.073}} @article{Cohen_2007, author = {Cohen, Aron J. and {Mori-S\'anchez}, Paula and Yang, Weitao}, @@ -6945,7 +6946,7 @@ title = {Development of Exchange-Correlation Functionals with Minimal Many-Electron Self-Interaction Error}, volume = {126}, year = {2007}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.2741248}} + bdsk-url-1 = {https://doi.org/10.1063/1.2741248}} @article{Cohen_2008, author = {Cohen, Aron J. and {Mori-S\'anchez}, Paula and Yang, Weitao}, @@ -6961,7 +6962,7 @@ title = {Fractional Charge Perspective on the Band Gap in Density-Functional Theory}, volume = {77}, year = {2008}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevB.77.115123}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRevB.77.115123}} @article{Cohen_2008a, author = {Cohen, Aron J. and {Mori-S\'anchez}, Paula and Yang, Weitao}, @@ -6978,7 +6979,7 @@ title = {Fractional Spins and Static Correlation Error in Density Functional Theory}, volume = {129}, year = {2008}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.2987202}} + bdsk-url-1 = {https://doi.org/10.1063/1.2987202}} @article{Cohen_2009, abstract = {In this work the behavior of MP2 for fractional occupations is investigated. The consideration of fractional charge behavior gives a simple derivation of an expression for the chemical potential (or the derivative of energy with respect to the number of electrons) of MP2. A generalized optimized effective potential formalism (OEP) has been developed in which the OEP is a nonlocal potential, which can be applied to explicit functionals of the orbitals and eigenvalues and also facilitates the evaluation of the chemical potential. The MP2 derivative improves upon the corresponding Koopmans' theorem in Hartree-Fock theory for the ionization energy and also gives a good estimate of the electron affinity. In strongly correlated systems with degeneracies and fractional spins, MP2 diverges, and another corrected second-order perturbative method ameliorates this failure for the energy but still does not recapture the correct behavior for the energy derivatives that yield the gap. Overall we present a view of wave function based methods and their behavior for fractional charges and spins that offers insight into the application of these methods to challenging chemical problems.}, @@ -6996,7 +6997,7 @@ title = {Second-{{Order Perturbation Theory}} with {{Fractional Charges}} and {{Fractional Spins}}}, volume = {5}, year = {2009}, - Bdsk-Url-1 = {https://doi.org/10.1021/ct8005419}} + bdsk-url-1 = {https://doi.org/10.1021/ct8005419}} @article{Cohen_2012, author = {Cohen, Aron J. and {Mori-S\'anchez}, Paula and Yang, Weitao}, @@ -7013,7 +7014,7 @@ title = {Challenges for {{Density Functional Theory}}}, volume = {112}, year = {2012}, - Bdsk-Url-1 = {https://doi.org/10.1021/cr200107z}} + bdsk-url-1 = {https://doi.org/10.1021/cr200107z}} @article{Cohen_2016, author = {Cohen, Aron J. and {Mori-S\'anchez}, Paula}, @@ -7029,7 +7030,7 @@ title = {Landscape of an Exact Energy Functional}, volume = {93}, year = {2016}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevA.93.042511}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRevA.93.042511}} @article{Crack_2014, author = {Crack, Jason C. and Green, Jeffrey and Thomson, Andrew J. and Brun, Nick E. Le}, @@ -7046,7 +7047,7 @@ url = {http://dx.doi.org/10.1021/ar5002507}, volume = {47}, year = {2014}, - Bdsk-Url-1 = {http://dx.doi.org/10.1021/ar5002507}} + bdsk-url-1 = {http://dx.doi.org/10.1021/ar5002507}} @article{Daday_2012, author = {Daday, Csaba and Smart, Simon and Booth, George H. and Alavi, Ali and Filippi, Claudia}, @@ -7064,7 +7065,7 @@ title = {Full {{Configuration Interaction Excitations}} of {{Ethene}} and {{Butadiene}}: {{Resolution}} of an {{Ancient Question}}}, volume = {8}, year = {2012}, - Bdsk-Url-1 = {https://doi.org/10.1021/ct300486d}} + bdsk-url-1 = {https://doi.org/10.1021/ct300486d}} @article{Dallos_2004, author = {Dallos, Michal and Lischka, Hans}, @@ -7079,7 +7080,7 @@ title = {A Systematic Theoretical Investigation of the Lowest Valence- and {{Rydberg}}-Excited Singlet States of Trans-Butadiene. {{The}} Character of the 1 1 {{B}} u ({{V}}) State Revisited}, volume = {112}, year = {2004}, - Bdsk-Url-1 = {https://doi.org/10.1007/s00214-003-0557-9}} + bdsk-url-1 = {https://doi.org/10.1007/s00214-003-0557-9}} @article{Dash_2018, author = {M. Dash and S. Moroni and A. Scemama and C. Filippi}, @@ -7103,7 +7104,7 @@ title = {Organic Photovoltaics: A Chemical Approach}, volume = {46}, year = {2010}, - Bdsk-Url-1 = {https://doi.org/10.1039/c003088k}} + bdsk-url-1 = {https://doi.org/10.1039/c003088k}} @article{Deshpande_2008, author = {Vikram V. Deshpande and Marc Bockrath}, @@ -7115,7 +7116,7 @@ title = {The one-dimensional Wigner crystal in carbon nanotubes}, volume = {4}, year = {2008}, - Bdsk-Url-1 = {https://doi.org/10.1038/nphys895}} + bdsk-url-1 = {https://doi.org/10.1038/nphys895}} @article{Deshpande_2010, author = {Vikram V. Deshpande and Marc Bockrath and Leonid I. Glazman and Amir Yacoby}, @@ -7128,7 +7129,7 @@ title = {Electron liquids and solids in one dimension}, volume = {464}, year = {2010}, - Bdsk-Url-1 = {https://doi.org/10.1038/nature08918}} + bdsk-url-1 = {https://doi.org/10.1038/nature08918}} @article{Deur_2017, author = {Deur, Killian and Mazouin, Laurent and Fromager, Emmanuel}, @@ -7146,7 +7147,7 @@ title = {Exact Ensemble Density Functional Theory for Excited States in a Model System: {{Investigating}} the Weight Dependence of the Correlation Energy}, volume = {95}, year = {2017}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevB.95.035120}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRevB.95.035120}} @article{Deur_2018, abstract = {Gross\textendash{}Oliveira\textendash{}Kohn density-functional theory (GOK-DFT) is an extension of DFT to excited states where the basic variable is the ensemble density, i.e. the weighted sum of ground- and excitedstate densities. The ensemble energy (i.e. the weighted sum of ground- and excited-state energies) can be obtained variationally as a functional of the ensemble density. Like in DFT, the key ingredient to model in GOK-DFT is the exchange-correlation functional. Developing density-functional approximations (DFAs) for ensembles is a complicated task as both density and weight dependencies should in principle be reproduced. In a recent paper [Phys. Rev. B 95, 035120 (2017)], the authors applied exact GOK-DFT to the simple but nontrivial Hubbard dimer in order to investigate (numerically) the importance of weight dependence in the calculation of excitation energies. In this work, we derive analytical DFAs for various density and correlation regimes by means of a Legendre\textendash{}Fenchel transform formalism. Both functional and density driven errors are evaluated for each DFA. Interestingly, when the ensemble exact-exchange-only functional is used, these errors can be large, in particular if the dimer is symmetric, but they cancel each other so that the excitation energies obtained by linear interpolation are always accurate, even in the strongly correlated regime.}, @@ -7165,7 +7166,7 @@ title = {Exploring Weight-Dependent Density-Functional Approximations for Ensembles in the {{Hubbard}} Dimer}, volume = {91}, year = {2018}, - Bdsk-Url-1 = {https://doi.org/10.1140/epjb/e2018-90124-7}} + bdsk-url-1 = {https://doi.org/10.1140/epjb/e2018-90124-7}} @article{Deur_2019, author = {K. Deur and E. Fromager}, @@ -7177,7 +7178,7 @@ title = {Ground and excited energy levels can be extracted exactly from a single ensemble density-functional theory calculation}, volume = {150}, year = {2019}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.5084312}} + bdsk-url-1 = {https://doi.org/10.1063/1.5084312}} @article{Diedrich_2005, author = {Diedrich, Christian and L{\"u}chow, Arne and Grimme, Stefan}, @@ -7194,7 +7195,7 @@ url = {http://dx.doi.org/10.1063/1.1846654}, volume = {122}, year = {2005}, - Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.1846654}} + bdsk-url-1 = {http://dx.doi.org/10.1063/1.1846654}} @article{Dierksen_2004, author = {Dierksen, M. and Grimme, S.}, @@ -7216,7 +7217,7 @@ title = {Note on Exchange Phenomena in the Thomas Atom}, volume = 26, year = 1930, - Bdsk-Url-1 = {https://doi.org/10.1017/S0305004100016108}} + bdsk-url-1 = {https://doi.org/10.1017/S0305004100016108}} @article{Doblhoff_Dier_2016, author = {Doblhoff-Dier, Katharina and Meyer, J{\"o}rg and Hoggan, Philip E. and Kroes, Geert-Jan and Wagner, Lucas K.}, @@ -7233,7 +7234,7 @@ url = {http://dx.doi.org/10.1021/acs.jctc.6b00160}, volume = {12}, year = {2016}, - Bdsk-Url-1 = {http://dx.doi.org/10.1021/acs.jctc.6b00160}} + bdsk-url-1 = {http://dx.doi.org/10.1021/acs.jctc.6b00160}} @article{Dolgov_2004, author = {Dolgov, Eugeniy K. and Bataev, Vadim A. and Pupyshev, Vladimir I. and Godunov, Igor A.}, @@ -7250,7 +7251,7 @@ url = {http://dx.doi.org/10.1002/qua.10745}, volume = {96}, year = {2004}, - Bdsk-Url-1 = {http://dx.doi.org/10.1002/qua.10745}} + bdsk-url-1 = {http://dx.doi.org/10.1002/qua.10745}} @article{Dolgov_2004b, author = {Dolgov, Eugeniy K. and Bataev, Vadim A. and Godunov, Igor A.}, @@ -7265,7 +7266,7 @@ url = {http://dx.doi.org/10.1002/qua.10683}, volume = {96}, year = {2004}, - Bdsk-Url-1 = {http://dx.doi.org/10.1002/qua.10683}} + bdsk-url-1 = {http://dx.doi.org/10.1002/qua.10683}} @article{Dolgov_2004c, author = {Dolgov, Eugeniy K. and Bataev, Vadim A. and Pupyshev, Vladimir I. and Godunov, Igor A.}, @@ -7282,7 +7283,7 @@ url = {http://dx.doi.org/10.1002/qua.20186}, volume = {100}, year = {2004}, - Bdsk-Url-1 = {http://dx.doi.org/10.1002/qua.20186}} + bdsk-url-1 = {http://dx.doi.org/10.1002/qua.20186}} @article{Dreuw_2003, author = {Dreuw, Andreas and Weisman, Jennifer L. and {Head-Gordon}, Martin}, @@ -7298,7 +7299,7 @@ title = {Long-Range Charge-Transfer Excited States in Time-Dependent Density Functional Theory Require Non-Local Exchange}, volume = {119}, year = {2003}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.1590951}} + bdsk-url-1 = {https://doi.org/10.1063/1.1590951}} @article{Dreuw_2004, author = {Dreuw, Andreas and Head-Gordon, Martin}, @@ -7316,7 +7317,7 @@ title = {Failure of {{Time}}-{{Dependent Density Functional Theory}} for {{Long}}-{{Range Charge}}-{{Transfer Excited States}}: {{The Zincbacteriochlorin}}-{{Bacteriochlorin}} and {{Bacteriochlorophyll}}-{{Spheroidene Complexes}}}, volume = {126}, year = {2004}, - Bdsk-Url-1 = {https://doi.org/10.1021/ja039556n}} + bdsk-url-1 = {https://doi.org/10.1021/ja039556n}} @article{Drowart_1967, author = {J. Drowart and A. Pattoret and S. Smoes}, @@ -7343,7 +7344,7 @@ url = {http://dx.doi.org/10.1021/acs.chemrev.5b00577}, volume = {116}, year = {2016}, - Bdsk-Url-1 = {http://dx.doi.org/10.1021/acs.chemrev.5b00577}} + bdsk-url-1 = {http://dx.doi.org/10.1021/acs.chemrev.5b00577}} @article{Dubecky_2010, author = {Dubeck{\'y}, M. and Derian, R. and Mitas, L. and {\v S}tich, I.}, @@ -7361,7 +7362,7 @@ title = {Ground and Excited Electronic States of Azobenzene: {{A}} Quantum {{Monte Carlo}} Study}, volume = {133}, year = {2010}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.3506028}} + bdsk-url-1 = {https://doi.org/10.1063/1.3506028}} @article{Dumont_2008b, author = {Dumont, Elise and Loos, Pierre-Fran{\c c}ois and Laurent, Ad\`ele D. and Assfeld, Xavier}, @@ -7378,7 +7379,7 @@ title = {Huge {{Disulfide}}-{{Linkage}}'{{S Electron Capture Variation Induced}} by $\alpha$-{{Helix Orientation}}}, volume = {4}, year = {2008}, - Bdsk-Url-1 = {https://doi.org/10.1021/ct800161m}} + bdsk-url-1 = {https://doi.org/10.1021/ct800161m}} @article{Dumont_2010, author = {Dumont, \~A‰lise and Loos, Pierre-Fran\~A\textsection{}ois and Laurent, Ad\~A\textasciidieresis{}le D. and Assfeld, Xavier}, @@ -7395,7 +7396,7 @@ title = {Electronic Effects and Ring Strain Influences on the Electron Uptake by Selenium-Containing Bonds}, volume = {110}, year = {2010}, - Bdsk-Url-1 = {https://doi.org/10.1002/qua.22072}} + bdsk-url-1 = {https://doi.org/10.1002/qua.22072}} @article{Dupuy_2015, author = {Dupuy, Nicolas and Bouaouli, Samira and Mauri, Francesco and Sorella, Sandro and Casula, Michele}, @@ -7413,7 +7414,7 @@ title = {Vertical and Adiabatic Excitations in Anthracene from Quantum {{Monte Carlo}}: {{Constrained}} Energy Minimization for Structural and Electronic Excited-State Properties in the {{JAGP}} Ansatz}, volume = {142}, year = {2015}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.4922048}} + bdsk-url-1 = {https://doi.org/10.1063/1.4922048}} @article{Durig_1984, author = {Durig, J.R. and Whang, C.M. and Attia, G.M. and Li, Y.S.}, @@ -7429,7 +7430,7 @@ title = {Microwave Spectra, Structure, and Barrier to Internal Rotation of {{CH3SnH2D}}, {{CH3SnHD2}} and {{CH3SnD3}}}, volume = {108}, year = {1984}, - Bdsk-Url-1 = {https://doi.org/10.1016/0022-2852(84)90182-6}} + bdsk-url-1 = {https://doi.org/10.1016/0022-2852(84)90182-6}} @article{Dykstra_1977, author = {Dykstra, Clifford E. and Lucchese, Robert R. and Schaefer, Henry F.}, @@ -7444,7 +7445,7 @@ title = {Electron Correlation Effects on the Excitation Energies of the Lowest Triplet States of Glyoxal}, volume = {67}, year = {1977}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.435214}} + bdsk-url-1 = {https://doi.org/10.1063/1.435214}} @article{Dykstra_1977a, author = {Dykstra, Clifford E. and Lucchese, Robert R. and Schaefer, Henry F.}, @@ -7459,7 +7460,7 @@ title = {Electron Correlation Effects on the Excitation Energies of the Lowest Triplet States of Glyoxal}, volume = {67}, year = {1977}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.435214}} + bdsk-url-1 = {https://doi.org/10.1063/1.435214}} @article{Dzubak_2017, author = {Dzubak, Allison L. and Krogel, Jaron T. and Reboredo, Fernando A.}, @@ -7476,7 +7477,7 @@ url = {http://dx.doi.org/10.1063/1.4991414}, volume = {147}, year = {2017}, - Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.4991414}} + bdsk-url-1 = {http://dx.doi.org/10.1063/1.4991414}} @article{Ehara_2011, author = {Ehara, Masahiro and Oyagi, Fumito and Abe, Yoko and Fukuda, Ryoichi and Nakatsuji, Hiroshi}, @@ -7492,7 +7493,7 @@ title = {Excited-State Geometries and Vibrational Frequencies Studied Using the Analytical Energy Gradients of the Direct Symmetry-Adapted Cluster\textendash{}Configuration Interaction Method. {{I}}. {{HAX}}-Type Molecules}, volume = {135}, year = {2011}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.3617233}} + bdsk-url-1 = {https://doi.org/10.1063/1.3617233}} @article{Elliott_2011, author = {Elliott, Peter and Goldson, Sharma and Canahui, Chris and Maitra, Neepa T.}, @@ -7509,7 +7510,7 @@ title = {Perspectives on Double-Excitations in {{TDDFT}}}, volume = {391}, year = {2011}, - Bdsk-Url-1 = {https://doi.org/10.1016/j.chemphys.2011.03.020}} + bdsk-url-1 = {https://doi.org/10.1016/j.chemphys.2011.03.020}} @article{Ernsting_1978, author = {Ernsting, Nikolaus P. and Pfab, Josef and Romelt, Joachim}, @@ -7524,7 +7525,7 @@ url = {http://dx.doi.org/10.1039/F29787402286}, volume = {74}, year = {1978}, - Bdsk-Url-1 = {http://dx.doi.org/10.1039/F29787402286}} + bdsk-url-1 = {http://dx.doi.org/10.1039/F29787402286}} @article{Evangelista_2014, author = {Evangelista, Francesco A.}, @@ -7541,7 +7542,7 @@ url = {http://dx.doi.org/10.1063/1.4869192}, volume = {140}, year = {2014}, - Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.4869192}} + bdsk-url-1 = {http://dx.doi.org/10.1063/1.4869192}} @article{Evangelisti_1983, author = {Evangelisti, Stefano and Daudey, Jean-Pierre and Malrieu, Jean-Paul}, @@ -7558,7 +7559,7 @@ url = {http://dx.doi.org/10.1016/0301-0104(83)85011-3}, volume = {75}, year = {1983}, - Bdsk-Url-1 = {http://dx.doi.org/10.1016/0301-0104(83)85011-3}} + bdsk-url-1 = {http://dx.doi.org/10.1016/0301-0104(83)85011-3}} @article{Fahy_1990, author = {Fahy, S. and Wang, X. W. and Louie, Steven G.}, @@ -7575,8 +7576,8 @@ url = {https://link.aps.org/doi/10.1103/PhysRevB.42.3503}, volume = {42}, year = {1990}, - Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.42.3503}, - Bdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevB.42.3503}} + bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.42.3503}, + bdsk-url-2 = {http://dx.doi.org/10.1103/PhysRevB.42.3503}} @article{Feller_2014, author = {David Feller and Kirk A. Peterson and Ernest R. Davidson}, @@ -7591,7 +7592,7 @@ url = {http://dx.doi.org/10.1063/1.4894482}, volume = {141}, year = {2014}, - Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.4894482}} + bdsk-url-1 = {http://dx.doi.org/10.1063/1.4894482}} @article{Feng_2003, author = {Feng, Liang and van der Hart, Hugo W}, @@ -7608,7 +7609,7 @@ title = {Two-Photon Double Ionization of {{He}}}, volume = {36}, year = {2003}, - Bdsk-Url-1 = {https://doi.org/10.1088/0953-4075/36/1/101}} + bdsk-url-1 = {https://doi.org/10.1088/0953-4075/36/1/101}} @article{Filatov_1999, abstract = {The energy and density of situations with strong non-dynamic correlation are formulated as weighted sums {\v Z}ensembles. of energies and densities of symmetry-adapted reference KS determinants. A computational scheme termed the spin-restricted ensemble-referenced Kohn\textendash{}Sham {\v Z}REKS. method is devised for these cases. An optimal set of orthonormal one-electron orbitals and their optimal occupation numbers are obtained from minimization of the ground state energy with respect to the density. The REKS method is applied to several model problems, rotation in C2 H 4, dissociation of H 2, and the singlet-triplet energy gaps in substituted trimethylene diradicals. q 1999 Elsevier Science B.V. All rights reserved.}, @@ -7626,7 +7627,7 @@ title = {A Spin-Restricted Ensemble-Referenced {{Kohn}}\textendash{{Sham}} Method and Its Application to Diradicaloid Situations}, volume = {304}, year = {1999}, - Bdsk-Url-1 = {https://doi.org/10.1016/S0009-2614(99)00336-X}} + bdsk-url-1 = {https://doi.org/10.1016/S0009-2614(99)00336-X}} @article{Filatov_2015, author = {Filatov, Michael and {Huix-Rotllant}, Miquel and Burghardt, Irene}, @@ -7643,7 +7644,7 @@ title = {Ensemble Density Functional Theory Method Correctly Describes Bond Dissociation, Excited State Electron Transfer, and Double Excitations}, volume = {142}, year = {2015}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.4919773}} + bdsk-url-1 = {https://doi.org/10.1063/1.4919773}} @inbook{Filatov_2015b, abstract = {Ensemble density functional theory (DFT) is a novel time-independent formalism for obtaining excitation energies of many-body fermionic systems. A considerable advantage of ensemble DFT over the more common Kohn\textendash{}Sham (KS) DFT and time-dependent DFT formalisms is that it enables one to account for strong non-dynamic electron correlation in the ground and excited states of molecular systems in a transparent and accurate fashion. Despite its positive aspects, ensemble DFT has not so far found its way into the repertoire of methods of modern computational chemistry, probably because of the perceived lack of practically affordable implementations of the theory. The spin-restricted ensemble-referenced KS (REKS) method is perhaps the first computationally feasible implementation of the ideas behind ensemble DFT which enables one to describe accurately electronic transitions in a wide class of molecular systems, including strongly correlated molecules (biradicals, molecules undergoing bond breaking/formation), extended $\pi$-conjugated systems, donor\textendash{}acceptor charge transfer adducts, etc.}, @@ -7661,7 +7662,7 @@ title = {Ensemble {{DFT Approach}} to {{Excited States}} of {{Strongly Correlated Molecular Systems}}}, volume = {368}, year = {2015}, - Bdsk-Url-1 = {https://doi.org/10.1007/128_2015_630}} + bdsk-url-1 = {https://doi.org/10.1007/128_2015_630}} @article{Filatov_2015c, author = {Filatov, Michael}, @@ -7679,7 +7680,7 @@ title = {Spin-Restricted Ensemble-Referenced {{Kohn}}-{{Sham}} Method: Basic Principles and Application to Strongly Correlated Ground and Excited States of Molecules}, volume = {5}, year = {2015}, - Bdsk-Url-1 = {https://doi.org/10.1002/wcms.1209}} + bdsk-url-1 = {https://doi.org/10.1002/wcms.1209}} @incollection{Filatov_2015d, abstract = {Ensemble density functional theory (DFT) is a novel time-independent formalism for obtaining excitation energies of many-body fermionic systems. A considerable advantage of ensemble DFT over the more common Kohn\textendash{}Sham (KS) DFT and time-dependent DFT formalisms is that it enables one to account for strong non-dynamic electron correlation in the ground and excited states of molecular systems in a transparent and accurate fashion. Despite its positive aspects, ensemble DFT has not so far found its way into the repertoire of methods of modern computational chemistry, probably because of the perceived lack of practically affordable implementations of the theory. The spin-restricted ensemble-referenced KS (REKS) method is perhaps the first computationally feasible implementation of the ideas behind ensemble DFT which enables one to describe accurately electronic transitions in a wide class of molecular systems, including strongly correlated molecules (biradicals, molecules undergoing bond breaking/formation), extended $\pi$-conjugated systems, donor\textendash{}acceptor charge transfer adducts, etc.}, @@ -7698,7 +7699,7 @@ title = {Ensemble {{DFT Approach}} to {{Excited States}} of {{Strongly Correlated Molecular Systems}}}, volume = {368}, year = {2015}, - Bdsk-Url-1 = {https://doi.org/10.1007/128_2015_630}} + bdsk-url-1 = {https://doi.org/10.1007/128_2015_630}} @article{Filatov_2015e, author = {Filatov, Michael}, @@ -7716,7 +7717,7 @@ title = {Spin-Restricted Ensemble-Referenced {{Kohn}}-{{Sham}} Method: Basic Principles and Application to Strongly Correlated Ground and Excited States of Molecules}, volume = {5}, year = {2015}, - Bdsk-Url-1 = {https://doi.org/10.1002/wcms.1209}} + bdsk-url-1 = {https://doi.org/10.1002/wcms.1209}} @article{Filatov_2015f, author = {Filatov, Michael and {Huix-Rotllant}, Miquel and Burghardt, Irene}, @@ -7733,7 +7734,7 @@ title = {Ensemble Density Functional Theory Method Correctly Describes Bond Dissociation, Excited State Electron Transfer, and Double Excitations}, volume = {142}, year = {2015}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.4919773}} + bdsk-url-1 = {https://doi.org/10.1063/1.4919773}} @article{Filippi_2016, author = {Guareschi, Riccardo and Zulfikri, Habiburrahman and Daday, Csaba and Floris, Franca Maria and Amovilli, Claudio and Mennucci, Benedetta and Filippi, Claudia}, @@ -7748,7 +7749,7 @@ url = {http://dx.doi.org/10.1021/acs.jctc.6b00044}, volume = {12}, year = {2016}, - Bdsk-Url-1 = {http://dx.doi.org/10.1021/acs.jctc.6b00044}} + bdsk-url-1 = {http://dx.doi.org/10.1021/acs.jctc.6b00044}} @article{Flicker_1977, author = {Flicker, Wayne M. and Mosher, Oren A. and Kuppermann, Aron}, @@ -7764,7 +7765,7 @@ title = {Low Energy, Variable Angle Electron-Impact Excitation of 1,3,5-Hexatriene}, volume = {45}, year = {1977}, - Bdsk-Url-1 = {https://doi.org/10.1016/0009-2614(77)80073-0}} + bdsk-url-1 = {https://doi.org/10.1016/0009-2614(77)80073-0}} @article{Flscher_1994, author = {Fulscher, M. P. and Roos, B. O.}, @@ -7781,7 +7782,7 @@ title = {The Excited States of Pyrazine: {{A}} Basis Set Study}, volume = {87}, year = {1994}, - Bdsk-Url-1 = {https://doi.org/10.1007/BF01113393}} + bdsk-url-1 = {https://doi.org/10.1007/BF01113393}} @article{Fogler_2005a, author = {M. M. Fogler}, @@ -7793,7 +7794,7 @@ title = {Ground-State Energy of the Electron Liquid in Ultrathin Wires}, volume = {94}, year = {2005}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevLett.94.056405}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRevLett.94.056405}} @article{Fogler_2005b, author = {Fogler, Michael M. and Pivovarov, Eugene}, @@ -7841,7 +7842,7 @@ title = {Symmetry Constraints and Variational Principles in Diffusion Quantum {{Monte Carlo}} Calculations of Excited-State Energies}, volume = {60}, year = {1999}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevB.60.4558}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRevB.60.4558}} @article{Franck_2014, author = {Franck, Odile and Fromager, Emmanuel}, @@ -7859,7 +7860,7 @@ title = {Generalised Adiabatic Connection in Ensemble Density-Functional Theory for Excited States: Example of the {{H}} {\textsubscript{2}} Molecule}, volume = {112}, year = {2014}, - Bdsk-Url-1 = {https://doi.org/10.1080/00268976.2013.858191}} + bdsk-url-1 = {https://doi.org/10.1080/00268976.2013.858191}} @article{Fridh_1972, author = {Fridh, C. and \AA{}sbrink, L. and Jonsson, B.\"o. and Lindholm, E.}, @@ -7875,7 +7876,7 @@ title = {Rydberg Series in Small Molecules}, volume = {9}, year = {1972}, - Bdsk-Url-1 = {https://doi.org/10.1016/0020-7381(72)80032-9}} + bdsk-url-1 = {https://doi.org/10.1016/0020-7381(72)80032-9}} @article{Fukuto_2005, author = {Fukuto, Jon M. and Switzer, Christopher H. and Miranda, Katrina M. and Wink, David A.}, @@ -7892,7 +7893,7 @@ title = {{{NITROXYL}} ({{HNO}}): {{Chemistry}}, {{Biochemistry}}, and {{Pharmacology}}}, volume = {45}, year = {2005}, - Bdsk-Url-1 = {https://doi.org/10.1146/annurev.pharmtox.45.120403.095959}} + bdsk-url-1 = {https://doi.org/10.1146/annurev.pharmtox.45.120403.095959}} @article{Fulscher_1992, author = {Fulscher, Markus P. and Andersson, Kerstin and Roos, Bjoern O.}, @@ -7909,7 +7910,7 @@ title = {Toward an Accurate Molecular Orbital Theory for Excited States: The Azabenzenes}, volume = {96}, year = {1992}, - Bdsk-Url-1 = {https://doi.org/10.1021/j100202a026}} + bdsk-url-1 = {https://doi.org/10.1021/j100202a026}} @article{Galvez_2002, author = {G\'alvez, F. J. and Buend\i\'a, E. and Sarsa, A.}, @@ -7925,7 +7926,7 @@ title = {Excited States of Beryllium Atom from Explicitly Correlated Wave Functions}, volume = {117}, year = {2002}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.1503776}} + bdsk-url-1 = {https://doi.org/10.1063/1.1503776}} @article{Garniron_2017, author = {Garniron, Yann and Scemama, Anthony and Loos, Pierre-Fran{\c c}ois and Caffarel, Michel}, @@ -7942,7 +7943,7 @@ title = {Hybrid Stochastic-Deterministic Calculation of the Second-Order Perturbative Contribution of Multireference Perturbation Theory}, volume = {147}, year = {2017}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.4992127}} + bdsk-url-1 = {https://doi.org/10.1063/1.4992127}} @article{Garniron_2017a, author = {Garniron, Yann and Giner, Emmanuel and Malrieu, Jean-Paul and Scemama, Anthony}, @@ -7959,7 +7960,7 @@ url = {http://dx.doi.org/10.1063/1.4980034}, volume = {146}, year = {2017}, - Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.4980034}} + bdsk-url-1 = {http://dx.doi.org/10.1063/1.4980034}} @article{Garziano_2016, author = {Garziano, Luigi and Macr\`i, Vincenzo and Stassi, Roberto and Di Stefano, Omar and Nori, Franco and Savasta, Salvatore}, @@ -7975,7 +7976,7 @@ title = {One {{Photon Can Simultaneously Excite Two}} or {{More Atoms}}}, volume = {117}, year = {2016}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevLett.117.043601}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRevLett.117.043601}} @article{Giarrusso_2018, abstract = {Using the formalism of the conditional amplitude, we study the response part of the exchange-correlation potential in the strong-coupling limit of density functional theory, analyzing its peculiar features and comparing it with the response potential averaged over the coupling constant for small atoms and for the hydrogen molecule. We also use a simple one-dimensional model of a stretched heteronuclear molecule to derive exact properties of the response potential in the strong-coupling limit. The simplicity of the model allows us to unveil relevant features also of the exact Kohn-Sham potential and its different components, namely the appearance of a second peak in the correlation kinetic potential on the side of the most electronegative atom.}, @@ -7994,7 +7995,7 @@ title = {Response {{Potential}} in the {{Strong}}-{{Interaction Limit}} of {{Density Functional Theory}}: {{Analysis}} and {{Comparison}} with the {{Coupling}}-{{Constant Average}}}, volume = {14}, year = {2018}, - Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.8b00386}} + bdsk-url-1 = {https://doi.org/10.1021/acs.jctc.8b00386}} @article{Giarrusso_2018a, abstract = {The response part of the exchange-correlation potential of Kohn\textendash{}Sham density functional theory plays a very important role, for example for the calculation of accurate band gaps and excitation energies. Here we analyze this part of the potential in the limit of infinite interaction in density functional theory, showing that in the one-dimensional case it satisfies a very simple sum rule.}, @@ -8011,7 +8012,7 @@ title = {Sum-Rules of the Response Potential in the Strongly-Interacting Limit of {{DFT}}}, volume = {91}, year = {2018}, - Bdsk-Url-1 = {https://doi.org/10.1140/epjb/e2018-90301-8}} + bdsk-url-1 = {https://doi.org/10.1140/epjb/e2018-90301-8}} @article{Gidopoulos_2002, author = {Gidopoulos, N. I. and Papaconstantinou, P. G. and Gross, E. K. U.}, @@ -8025,7 +8026,7 @@ title = {Spurious {{Interactions}}, and {{Their Correction}}, in the {{Ensemble}}-{{Kohn}}-{{Sham Scheme}} for {{Excited States}}}, volume = {88}, year = {2002}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevLett.88.033003}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRevLett.88.033003}} @article{Giner_2013, author = {Giner, Emmanuel and Scemama, Anthony and Caffarel, Michel}, @@ -8042,7 +8043,7 @@ url = {http://dx.doi.org/10.1139/cjc-2013-0017}, volume = {91}, year = {2013}, - Bdsk-Url-1 = {http://dx.doi.org/10.1139/cjc-2013-0017}} + bdsk-url-1 = {http://dx.doi.org/10.1139/cjc-2013-0017}} @article{Giner_2015, author = {Emmanuel Giner and Anthony Scemama and Michel Caffarel}, @@ -8059,7 +8060,7 @@ url = {http://dx.doi.org/10.1063/1.4905528}, volume = {142}, year = {2015}, - Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.4905528}} + bdsk-url-1 = {http://dx.doi.org/10.1063/1.4905528}} @article{Giner_2016, author = {Giner, E. and David, G. and Scemama, A. and Malrieu, J. P.}, @@ -8076,7 +8077,7 @@ url = {http://dx.doi.org/10.1063/1.4940781}, volume = {144}, year = {2016}, - Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.4940781}} + bdsk-url-1 = {http://dx.doi.org/10.1063/1.4940781}} @article{Giner_2017a, author = {Giner, Emmanuel and Angeli, Celestino and Garniron, Yann and Scemama, Anthony and Malrieu, Jean-Paul}, @@ -8093,7 +8094,7 @@ url = {http://dx.doi.org/10.1063/1.4984616}, volume = {146}, year = {2017}, - Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.4984616}} + bdsk-url-1 = {http://dx.doi.org/10.1063/1.4984616}} @article{Giner_2017b, author = {Giner, E. and Angeli, C. and Scemama, A. and Malrieu, J.-P.}, @@ -8109,7 +8110,7 @@ url = {http://dx.doi.org/10.1016/j.comptc.2017.03.001}, volume = {1116}, year = {2017}, - Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.comptc.2017.03.001}} + bdsk-url-1 = {http://dx.doi.org/10.1016/j.comptc.2017.03.001}} @article{Gordon_1979, author = {Robert D. Gordon and Paula Luck}, @@ -8124,8 +8125,8 @@ url = {http://www.sciencedirect.com/science/article/pii/0009261479802766}, volume = {65}, year = {1979}, - Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/0009261479802766}, - Bdsk-Url-2 = {http://dx.doi.org/10.1016/0009-2614(79)80276-6}} + bdsk-url-1 = {http://www.sciencedirect.com/science/article/pii/0009261479802766}, + bdsk-url-2 = {http://dx.doi.org/10.1016/0009-2614(79)80276-6}} @article{Gori-Giorgi_2009, author = {{Gori-Giorgi}, Paola and Seidl, Michael and Vignale, G.}, @@ -8141,7 +8142,7 @@ title = {Density-{{Functional Theory}} for {{Strongly Interacting Electrons}}}, volume = {103}, year = {2009}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevLett.103.166402}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRevLett.103.166402}} @article{Gorling_2015, author = {G\"orling, Andreas}, @@ -8157,7 +8158,7 @@ title = {Exchange-Correlation Potentials with Proper Discontinuities for Physically Meaningful {{Kohn}}-{{Sham}} Eigenvalues and Band Structures}, volume = {91}, year = {2015}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevB.91.245120}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRevB.91.245120}} @article{Gould_2013, author = {Gould, Tim and Dobson, John F.}, @@ -8175,7 +8176,7 @@ title = {The Flexible Nature of Exchange, Correlation, and {{Hartree}} Physics: {{Resolving}} ``Delocalization'' Errors in a ``Correlation Free'' Density Functional}, volume = {138}, year = {2013}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.4773284}} + bdsk-url-1 = {https://doi.org/10.1063/1.4773284}} @article{Gould_2014, author = {Gould, Tim and Toulouse, Julien}, @@ -8192,7 +8193,7 @@ title = {Kohn-{{Sham}} Potentials in Exact Density-Functional Theory at Noninteger Electron Numbers}, volume = {90}, year = {2014}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevA.90.050502}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRevA.90.050502}} @article{Gould_2017, author = {Gould, Tim and Pittalis, Stefano}, @@ -8210,7 +8211,7 @@ title = {Hartree and {{Exchange}} in {{Ensemble Density Functional Theory}}: {{Avoiding}} the {{Nonuniqueness Disaster}}}, volume = {119}, year = {2017}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevLett.119.243001}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRevLett.119.243001}} @article{Gould_2018, author = {Gould, Tim and Kronik, Leeor and Pittalis, Stefano}, @@ -8227,7 +8228,7 @@ title = {Charge Transfer Excitations from Exact and Approximate Ensemble {{Kohn}}-{{Sham}} Theory}, volume = {148}, year = {2018}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.5022832}} + bdsk-url-1 = {https://doi.org/10.1063/1.5022832}} @article{Gould_2019, author = {Gould, Tim and Pittalis, Stefano}, @@ -8239,7 +8240,7 @@ title = {Density-Driven Correlations in Many-Electron Ensembles: Theory and Application for Excited States}, volume = {123}, year = {2019}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevLett.123.016401}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRevLett.123.016401}} @article{Gozem_2012, abstract = {The ground state potential energy surface of the retinal chromophore of visual pigments (e.g., bovine rhodopsin) features a low-lying conical intersection surrounded by regions with variable charge-transfer and diradical electronic structures. This implies that dynamic electron correlation may have a large effect on the shape of the force fields driving its reactivity. To investigate this effect, we focus on mapping the potential energy for three paths located along the ground state CASSCF potential energy surface of the penta-2,4-dieniminium cation taken as a minimal model of the retinal chromophore. The first path spans the bond length alternation coordinate and intercepts a conical intersection point. The other two are minimum energy paths along two distinct but kinetically competitive thermal isomerization coordinates. We show that the effect of introducing the missing dynamic electron correlation variationally (with MRCISD) and perturbatively (with the CASPT2, NEVPT2, and XMCQDPT2 methods) leads, invariably, to a stabilization of the regions with charge transfer character and to a significant reshaping of the reference CASSCF potential energy surface and suggesting a change in the dominating isomerization mechanism. The possible impact of such a correction on the photoisomerization of the retinal chromophore is discussed.}, @@ -8257,7 +8258,7 @@ title = {Dynamic {{Electron Correlation Effects}} on the {{Ground State Potential Energy Surface}} of a {{Retinal Chromophore Model}}}, volume = {8}, year = {2012}, - Bdsk-Url-1 = {https://doi.org/10.1021/ct3003139}} + bdsk-url-1 = {https://doi.org/10.1021/ct3003139}} @article{Gozem_2013, abstract = {This work investigates the performance of equation-ofmotion coupled-cluster (EOM-CC) methods for describing the changes in the potential energy surfaces of the penta-2,4-dieniminium cation, a reduced model of the retinal chromophore of visual pigments, due to dynamical electron correlation effects. The groundstate wave function of this model includes charge-transfer and diradical configurations whose weights vary along different displacements and are rapidly changing at the conical intersection between the ground and the first excited states, making the shape of the potential energy surface sensitive to a balanced description of nondynamical and dynamical correlation. Recently, variational (MRCISD) and perturbative (MRPT2) approaches for including dynamical correlation in CASSCF-based calculations were tested along three representative ground state paths. Here, we use the same three paths to compare the performance of single-reference EOM-CC methods against MRCISD and MRCISD+Q. We find that the spin-flip variant of EOM-CCSD with perturbative inclusion of triple excitations (dT or fT) produces potential energy profiles of the two lowest electronic states in quantitative agreement with MRCISD+Q (our highest-quality reference method). The nonparallelity errors and differences in vertical energy differences of the two surfaces along these scans are less than 1.4 kcal/mol (EOM-SF-CCSD(dT) versus MRCISD+Q). For comparison, the largest error of MRCISD versus MRCISD+Q is 1.7 kcal/mol. Our results show that the EOM-CC methods provide an alternative to multireference approaches and may be used to study photochemical systems like the one used in this work.}, @@ -8276,7 +8277,7 @@ title = {Conical {{Intersection}} and {{Potential Energy Surface Features}} of a {{Model Retinal Chromophore}}: {{Comparison}} of {{EOM}}-{{CC}} and {{Multireference Methods}}}, volume = {9}, year = {2013}, - Bdsk-Url-1 = {https://doi.org/10.1021/ct300759z}} + bdsk-url-1 = {https://doi.org/10.1021/ct300759z}} @article{Gozem_2013a, author = {Gozem, Samer and Melaccio, Federico and Lindh, Roland and Krylov, Anna I. and Granovsky, Alexander A. and Angeli, Celestino and Olivucci, Massimo}, @@ -8293,7 +8294,7 @@ title = {Mapping the {{Excited State Potential Energy Surface}} of a {{Retinal Chromophore Model}} with {{Multireference}} and {{Equation}}-of-{{Motion Coupled}}-{{Cluster Methods}}}, volume = {9}, year = {2013}, - Bdsk-Url-1 = {https://doi.org/10.1021/ct400460h}} + bdsk-url-1 = {https://doi.org/10.1021/ct400460h}} @article{Gozem_2014, abstract = {We report and characterize ground-state and excited-state potential energy profiles using a variety of electronic structure methods along a loop lying on the branching plane associated with a conical intersection (CI) of a reduced retinal model, the penta-2,4-dieniminium cation (PSB3). Whereas the performance of the equation-of-motion coupled-cluster, density functional theory, and multireference methods had been tested along the excited- and ground-state paths of PSB3 in our earlier work, the ability of these methods to correctly describe the potential energy surface shape along a CI branching plane has not yet been investigated. This is the focus of the present contribution. We find, in agreement with earlier studies by others, that standard time-dependent DFT (TDDFT) does not yield the correct two-dimensional (i.e., conical) crossing along the branching plane but rather a one-dimensional (i.e., linear) crossing along the same plane. The same type of behavior is found for SS-CASPT2(IPEA=0), SS-CASPT2(IPEA=0.25), spin-projected SF-TDDFT, EOM-SF-CCSD, and, finally, for the reference MRCISD+Q method. In contrast, we found that MRCISD, CASSCF, MS-CASPT2(IPEA=0), MS-CASPT2(IPEA=0.25), XMCQDPT2, QD-NEVPT2, non-spin-projected SF-TDDFT, and SI-SA-REKS yield the expected conical crossing. To assess the effect of the different crossing topologies (i.e., linear or conical) on the PSB3 photoisomerization efficiency, we discuss the results of 100 semiclassical trajectories computed by CASSCF and SS-CASPT2(IPEA=0.25) for a PSB3 derivative. We show that for the same initial conditions, the two methods yield similar dynamics leading to isomerization quantum yields that differ by only a few percent.}, @@ -8311,7 +8312,7 @@ title = {Shape of {{Multireference}}, {{Equation}}-of-{{Motion Coupled}}-{{Cluster}}, and {{Density Functional Theory Potential Energy Surfaces}} at a {{Conical Intersection}}}, volume = {10}, year = {2014}, - Bdsk-Url-1 = {https://doi.org/10.1021/ct500154k}} + bdsk-url-1 = {https://doi.org/10.1021/ct500154k}} @article{Grimme_2004, author = {Grimme, S. and Izgorodina, E. I.}, @@ -8338,7 +8339,7 @@ title = {Rayleigh-{{Ritz}} Variational Principle for Ensembles of Fractionally Occupied States}, volume = {37}, year = {1988}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevA.37.2805}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRevA.37.2805}} @article{Gross_1988b, author = {Gross, E. K. U. and Oliveira, L. N. and Kohn, W.}, @@ -8355,7 +8356,7 @@ title = {Density-Functional Theory for Ensembles of Fractionally Occupied States. {{I}}. {{Basic}} Formalism}, volume = {37}, year = {1988}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevA.37.2809}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRevA.37.2809}} @article{Gross_1988c, author = {Gross, E. K. U. and Oliveira, L. N. and Kohn, W.}, @@ -8372,7 +8373,7 @@ title = {Rayleigh-{{Ritz}} Variational Principle for Ensembles of Fractionally Occupied States}, volume = {37}, year = {1988}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevA.37.2805}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRevA.37.2805}} @article{Grossi_2017, abstract = {Exact pieces of information on the adiabatic connection integrand, W$\lambda$[$\rho$], which allows evaluation of the exchange-correlation energy of Kohn-Sham density functional theory, can be extracted from the leading terms in the strong coupling limit ($\lambda$ $\rightarrow$ $\infty$, where $\lambda$ is the strength of the electron-electron interaction). In this work, we first compare the theoretical prediction for the two leading terms in the strong coupling limit with data obtained via numerical implementation of the exact Levy functional in the simple case of two electrons confined in one dimension, confirming the asymptotic exactness of these two terms. We then carry out a first study on the incorporation of the Fermionic statistics at large coupling $\lambda$, both numerical and theoretical, confirming that spin effects enter at orders $\sim$e-$\surd\lambda$.}, @@ -8390,7 +8391,7 @@ title = {Fermionic {{Statistics}} in the {{Strongly Correlated Limit}} of {{Density Functional Theory}}}, volume = {13}, year = {2017}, - Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.7b00998}} + bdsk-url-1 = {https://doi.org/10.1021/acs.jctc.7b00998}} @article{Grossman_2001, author = {Grossman, Jeffrey C. and Rohlfing, Michael and Mitas, Lubos and Louie, Steven G. and Cohen, Marvin L.}, @@ -8407,7 +8408,7 @@ title = {High {{Accuracy Many}}-{{Body Calculational Approaches}} for {{Excitations}} in {{Molecules}}}, volume = {86}, year = {2001}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevLett.86.472}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRevLett.86.472}} @article{Grossman_2002, author = {Grossman, Jeffrey C.}, @@ -8424,7 +8425,7 @@ url = {http://dx.doi.org/10.1063/1.1487829}, volume = {117}, year = {2002}, - Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.1487829}} + bdsk-url-1 = {http://dx.doi.org/10.1063/1.1487829}} @article{Guareschi_2013, author = {Guareschi, Riccardo and Filippi, Claudia}, @@ -8441,7 +8442,7 @@ title = {Ground- and {{Excited}}-{{State Geometry Optimization}} of {{Small Organic Molecules}} with {{Quantum Monte Carlo}}}, volume = {9}, year = {2013}, - Bdsk-Url-1 = {https://doi.org/10.1021/ct400876y}} + bdsk-url-1 = {https://doi.org/10.1021/ct400876y}} @article{Guareschi_2014, author = {Guareschi, Riccardo and Floris, Franca Maria and Amovilli, Claudio and Filippi, Claudia}, @@ -8458,7 +8459,7 @@ title = {Solvent {{Effects}} on {{Excited}}-{{State Structures}}: {{A Quantum Monte Carlo}} and {{Density Functional Study}}}, volume = {10}, year = {2014}, - Bdsk-Url-1 = {https://doi.org/10.1021/ct500723s}} + bdsk-url-1 = {https://doi.org/10.1021/ct500723s}} @article{Guareschi_2016a, author = {Guareschi, Riccardo and Zulfikri, Habiburrahman and Daday, Csaba and Floris, Franca Maria and Amovilli, Claudio and Mennucci, Benedetta and Filippi, Claudia}, @@ -8475,7 +8476,7 @@ title = {Introducing {{QMC}}/{{MMpol}}: {{Quantum Monte Carlo}} in {{Polarizable Force Fields}} for {{Excited States}}}, volume = {12}, year = {2016}, - Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.6b00044}} + bdsk-url-1 = {https://doi.org/10.1021/acs.jctc.6b00044}} @article{Gwaltney_1995, author = {Steven R. Gwaltney and Rodney J. Bartlett}, @@ -8490,8 +8491,8 @@ url = {http://www.sciencedirect.com/science/article/pii/0009261495006087}, volume = {241}, year = {1995}, - Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/0009261495006087}, - Bdsk-Url-2 = {https://doi.org/10.1016/0009-2614(95)00608-7}} + bdsk-url-1 = {http://www.sciencedirect.com/science/article/pii/0009261495006087}, + bdsk-url-2 = {https://doi.org/10.1016/0009-2614(95)00608-7}} @article{Ha_1972, author = {Ha, Tae-Kyu}, @@ -8507,7 +8508,7 @@ title = {Ab Initio Calculation of Cis-Trans Isomerization in Glyoxal}, volume = {12}, year = {1972}, - Bdsk-Url-1 = {https://doi.org/10.1016/0022-2860(72)85029-4}} + bdsk-url-1 = {https://doi.org/10.1016/0022-2860(72)85029-4}} @article{Hadad_1993, author = {Hadad, Christopher M. and Foresman, James B. and Wiberg, Kenneth B.}, @@ -8521,7 +8522,7 @@ url = {http://dx.doi.org/10.1021/j100119a010}, volume = {97}, year = {1993}, - Bdsk-Url-1 = {http://dx.doi.org/10.1021/j100119a010}} + bdsk-url-1 = {http://dx.doi.org/10.1021/j100119a010}} @article{Haghighi_Mood_2017, author = {Haghighi Mood, Kaveh and L{\"u}chow, Arne}, @@ -8538,7 +8539,7 @@ url = {http://dx.doi.org/10.1021/acs.jpca.7b05798}, volume = {121}, year = {2017}, - Bdsk-Url-1 = {http://dx.doi.org/10.1021/acs.jpca.7b05798}} + bdsk-url-1 = {http://dx.doi.org/10.1021/acs.jpca.7b05798}} @article{Hald_2002, author = {Hald, Kasper and J\o{}rgensen, Poul and Christiansen, Ove and Koch, Henrik}, @@ -8554,7 +8555,7 @@ title = {Implementation of Electronic Ground States and Singlet and Triplet Excitation Energies in Coupled Cluster Theory with Approximate Triples Corrections}, volume = {116}, year = {2002}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.1457431}} + bdsk-url-1 = {https://doi.org/10.1063/1.1457431}} @article{Hammond_1987, author = {Brian L. Hammond and Peter J. Reynolds and William A. Lester}, @@ -8570,8 +8571,8 @@ url = {https://doi.org/10.1063%2F1.453345}, volume = {87}, year = 1987, - Bdsk-Url-1 = {https://doi.org/10.1063%2F1.453345}, - Bdsk-Url-2 = {http://dx.doi.org/10.1063/1.453345}} + bdsk-url-1 = {https://doi.org/10.1063%2F1.453345}, + bdsk-url-2 = {http://dx.doi.org/10.1063/1.453345}} @article{Handy_1999, author = {Handy, Nicholas C. and Tozer, David J.}, @@ -8587,7 +8588,7 @@ title = {Excitation Energies of Benzene from {{Kohn}}-{{Sham}} Theory}, volume = {20}, year = {1999}, - Bdsk-Url-1 = {https://doi.org/10.1002/(SICI)1096-987X(19990115)20:1%3C106::AID-JCC11%3E3.0.CO;2-P}} + bdsk-url-1 = {https://doi.org/10.1002/(SICI)1096-987X(19990115)20:1%3C106::AID-JCC11%3E3.0.CO;2-P}} @article{Harbach_2014, author = {Harbach, Philipp H. P. and Wormit, Michael and Dreuw, Andreas}, @@ -8605,7 +8606,7 @@ title = {The Third-Order Algebraic Diagrammatic Construction Method ({{ADC}}(3)) for the Polarization Propagator for Closed-Shell Molecules: {{Efficient}} Implementation and Benchmarking}, volume = {141}, year = {2014}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.4892418}} + bdsk-url-1 = {https://doi.org/10.1063/1.4892418}} @article{Hashimoto_1996, author = {Hashimoto, T. and Nakano, H. and Hirao, K.}, @@ -8623,7 +8624,7 @@ title = {Theoretical Study of the Valence $\Pi\rightarrow\pi$* Excited States of Polyacenes: {{Benzene}} and Naphthalene}, volume = {104}, year = {1996}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.471286}} + bdsk-url-1 = {https://doi.org/10.1063/1.471286}} @article{Hashimoto_1996a, author = {Hashimoto, T. and Nakano, H. and Hirao, K.}, @@ -8641,7 +8642,7 @@ title = {Theoretical Study of the Valence $\Pi\rightarrow\pi$* Excited States of Polyacenes: {{Benzene}} and Naphthalene}, volume = {104}, year = {1996}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.471286}} + bdsk-url-1 = {https://doi.org/10.1063/1.471286}} @article{Hattig_2000, author = {H\"attig, C. and Weigend, F.}, @@ -8676,7 +8677,7 @@ title = {{\emph{Ab Initio}} Configuration Interaction Studies of the $\pi$-Electron States of Benzene}, volume = {60}, year = {1974}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.1681456}} + bdsk-url-1 = {https://doi.org/10.1063/1.1681456}} @article{Head-Gordon_1994, author = {M. Head-Gordon and R. J. Rico and M. Oumi and T. J. Lee}, @@ -8711,7 +8712,7 @@ title = {Time-Dependent Density-Functional and Reduced Density-Matrix Methods for Few Electrons: {{Exact}} versus Adiabatic Approximations}, volume = {391}, year = {2011}, - Bdsk-Url-1 = {https://doi.org/10.1016/j.chemphys.2011.06.010}} + bdsk-url-1 = {https://doi.org/10.1016/j.chemphys.2011.06.010}} @book{Helgakerbook, author = {T. Helgaker and P. J{\o}rgensen and J. Olsen}, @@ -8737,7 +8738,7 @@ title = {Direct Cluster Expansion Method. {{Application}} to Glyoxal}, volume = {79}, year = {1983}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.445594}} + bdsk-url-1 = {https://doi.org/10.1063/1.445594}} @article{Hirata_2000, author = {Hirata, So and Nooijen, Marcel and Bartlett, Rodney J.}, @@ -8753,7 +8754,7 @@ title = {High-Order Determinantal Equation-of-Motion Coupled-Cluster Calculations for Electronic Excited States}, volume = {326}, year = {2000}, - Bdsk-Url-1 = {https://doi.org/10.1016/S0009-2614(00)00772-7}} + bdsk-url-1 = {https://doi.org/10.1016/S0009-2614(00)00772-7}} @article{Hollauer_1991, author = {Hollauer, Eduardo and Nascimento, Marco Antonio Chaer}, @@ -8769,7 +8770,7 @@ title = {A {{CASSCF}} Description of the N$\pi$* Singlet and Triplet Electronic Excited States of the Trans-Glyoxal Molecule}, volume = {181}, year = {1991}, - Bdsk-Url-1 = {https://doi.org/10.1016/0009-2614(91)90381-I}} + bdsk-url-1 = {https://doi.org/10.1016/0009-2614(91)90381-I}} @article{Holmes_2016, author = {Holmes, Adam A. and Tubman, Norm M. and Umrigar, C. J.}, @@ -8786,7 +8787,7 @@ url = {http://dx.doi.org/10.1021/acs.jctc.6b00407}, volume = {12}, year = {2016}, - Bdsk-Url-1 = {http://dx.doi.org/10.1021/acs.jctc.6b00407}} + bdsk-url-1 = {http://dx.doi.org/10.1021/acs.jctc.6b00407}} @article{Holmes_2017, author = {Holmes, Adam A. and Umrigar, C. J. and Sharma, Sandeep}, @@ -8803,7 +8804,7 @@ url = {http://dx.doi.org/10.1063/1.4998614}, volume = {147}, year = {2017}, - Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.4998614}} + bdsk-url-1 = {http://dx.doi.org/10.1063/1.4998614}} @article{Hoyer_2016, author = {Hoyer, Chad E. and Ghosh, Soumen and Truhlar, Donald G. and Gagliardi, Laura}, @@ -8817,7 +8818,7 @@ url = {http://dx.doi.org/10.1021/acs.jpclett.5b02773}, volume = {7}, year = {2016}, - Bdsk-Url-1 = {http://dx.doi.org/10.1021/acs.jpclett.5b02773}} + bdsk-url-1 = {http://dx.doi.org/10.1021/acs.jpclett.5b02773}} @article{Hsu_2001, author = {Hsu, Chao-Ping and Hirata, So and {Head-Gordon}, Martin}, @@ -8835,7 +8836,7 @@ title = {Excitation {{Energies}} from {{Time}}-{{Dependent Density Functional Theory}} for {{Linear Polyene Oligomers}}: {{Butadiene}} to {{Decapentaene}}}, volume = {105}, year = {2001}, - Bdsk-Url-1 = {https://doi.org/10.1021/jp0024367}} + bdsk-url-1 = {https://doi.org/10.1021/jp0024367}} @article{Hubner_1998, author = {H{\"u}bner, Olaf and Termath, Volker and Berning, Andreas and Sauer, Joachim}, @@ -8852,8 +8853,8 @@ url = {http://dx.doi.org/10.1016/S0009-2614(98)00792-1}, volume = {294}, year = {1998}, - Bdsk-Url-1 = {http://dx.doi.org/10.1016/S0009-2614(98)00792-1}, - Bdsk-Url-2 = {http://dx.doi.org/10.1016/s0009-2614(98)00792-1}} + bdsk-url-1 = {http://dx.doi.org/10.1016/S0009-2614(98)00792-1}, + bdsk-url-2 = {http://dx.doi.org/10.1016/s0009-2614(98)00792-1}} @article{Huron_1973, author = {Huron, B. and Malrieu, J. P. and Rancurel, P.}, @@ -8870,7 +8871,7 @@ url = {http://dx.doi.org/10.1063/1.1679199}, volume = {58}, year = {1973}, - Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.1679199}} + bdsk-url-1 = {http://dx.doi.org/10.1063/1.1679199}} @article{Hylleraas_1930, author = {E. Hylleraas and B. Undheim}, @@ -8898,8 +8899,8 @@ urldate = {2017-11-14}, volume = {89}, year = {1988}, - Bdsk-Url-1 = {http://aip.scitation.org/doi/10.1063/1.455405}, - Bdsk-Url-2 = {http://dx.doi.org/10.1063/1.455405}} + bdsk-url-1 = {http://aip.scitation.org/doi/10.1063/1.455405}, + bdsk-url-2 = {http://dx.doi.org/10.1063/1.455405}} @article{Innes_1988, author = {Innes, K.K. and Ross, I.G. and Moomaw, William R.}, @@ -8916,7 +8917,7 @@ title = {Electronic States of Azabenzenes and Azanaphthalenes: {{A}} Revised and Extended Critical Review}, volume = {132}, year = {1988}, - Bdsk-Url-1 = {https://doi.org/10.1016/0022-2852(88)90343-8}} + bdsk-url-1 = {https://doi.org/10.1016/0022-2852(88)90343-8}} @article{Ishii_2003, author = {H. Ishii and H. Kataura and H. Shiozawa and H. Yoshioka and H. Otsubo and Y. Takayama and T. Miyahara and S. Suzuki and Y. Achiba and M. Nakatake and T. Narimura and M. Higashiguchi and K. Shimada and H. Namatame and M. Taniguchi}, @@ -8928,7 +8929,7 @@ title = {Direct observation of Tomonaga-Luttinger-liquid state in carbon nanotubes at low temperatures}, volume = {426}, year = {2003}, - Bdsk-Url-1 = {https://doi.org/10.1038/nature02074}} + bdsk-url-1 = {https://doi.org/10.1038/nature02074}} @article{Kallay_2004, author = {K{\'a}llay, Mih{\'a}ly and Gauss, J{\"u}rgen}, @@ -8942,8 +8943,8 @@ url = {http://scitation.aip.org/content/aip/journal/jcp/121/19/10.1063/1.1805494}, volume = {121}, year = {2004}, - Bdsk-Url-1 = {http://scitation.aip.org/content/aip/journal/jcp/121/19/10.1063/1.1805494}, - Bdsk-Url-2 = {http://dx.doi.org/10.1063/1.1805494}} + bdsk-url-1 = {http://scitation.aip.org/content/aip/journal/jcp/121/19/10.1063/1.1805494}, + bdsk-url-2 = {http://dx.doi.org/10.1063/1.1805494}} @article{Kalos_1974, author = {M. H. Kalos and D. Levesque and L. Verlet}, @@ -8969,7 +8970,7 @@ url = {http://dx.doi.org/10.1063/1.4901980}, volume = {141}, year = {2014}, - Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.4901980}} + bdsk-url-1 = {http://dx.doi.org/10.1063/1.4901980}} @article{Kazaryan_2008, author = {Kazaryan, Andranik and Heuver, Jeroen and Filatov, Michael}, @@ -8987,7 +8988,7 @@ title = {Excitation {{Energies}} from {{Spin}}-{{Restricted Ensemble}}-{{Referenced Kohn}}-{{Sham Method}}: {{A State}}-{{Average Approach}} {\textsuperscript{\textdagger}}}, volume = {112}, year = {2008}, - Bdsk-Url-1 = {https://doi.org/10.1021/jp8033837}} + bdsk-url-1 = {https://doi.org/10.1021/jp8033837}} @article{Kazaryan_2008a, author = {Kazaryan, Andranik and Heuver, Jeroen and Filatov, Michael}, @@ -9005,7 +9006,7 @@ title = {Excitation {{Energies}} from {{Spin}}-{{Restricted Ensemble}}-{{Referenced Kohn}}-{{Sham Method}}: {{A State}}-{{Average Approach}} {\textsuperscript{\textdagger}}}, volume = {112}, year = {2008}, - Bdsk-Url-1 = {https://doi.org/10.1021/jp8033837}} + bdsk-url-1 = {https://doi.org/10.1021/jp8033837}} @article{Kitao_1987, author = {Kitao, O. and Nakatsuji, H.}, @@ -9021,7 +9022,7 @@ title = {Cluster Expansion of the Wave Function. {{Valence}} and {{Rydberg}} Excitations and Ionizations of Benzene}, volume = {87}, year = {1987}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.453297}} + bdsk-url-1 = {https://doi.org/10.1063/1.453297}} @article{Kitao_1988, author = {Kitao, O. and Nakatsuji, H.}, @@ -9038,7 +9039,7 @@ title = {Cluster Expansion of the Wavefunction: {{Valence}} and {{Rydberg}} Excitations of Trans- and Cis-Butadiene}, volume = {143}, year = {1988}, - Bdsk-Url-1 = {https://doi.org/10.1016/0009-2614(88)87060-X}} + bdsk-url-1 = {https://doi.org/10.1016/0009-2614(88)87060-X}} @article{Klahm_2014, author = {Klahm, Sebastian and L{\"u}chow, Arne}, @@ -9054,7 +9055,7 @@ url = {http://dx.doi.org/10.1016/j.cplett.2014.03.044}, volume = {600}, year = {2014}, - Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.cplett.2014.03.044}} + bdsk-url-1 = {http://dx.doi.org/10.1016/j.cplett.2014.03.044}} @article{Klein_1976, author = {D. J. Klein and H. M. Pickett}, @@ -9102,7 +9103,7 @@ url = {http://dx.doi.org/10.1080/00268976.2014.1003621}, volume = {113}, year = {2015}, - Bdsk-Url-1 = {http://dx.doi.org/10.1080/00268976.2014.1003621}} + bdsk-url-1 = {http://dx.doi.org/10.1080/00268976.2014.1003621}} @article{Koch_1990, author = {Koch, Henrik and Jensen, Hans Jo/rgen Aa. and Jo/rgensen, Poul and Helgaker, Trygve}, @@ -9115,7 +9116,7 @@ title = {Excitation Energies from the Coupled Cluster Singles and Doubles Linear Response Function ({{CCSDLR}}). {{Applications}} to {{Be}}, {{CH}} {\textsuperscript{+}} , {{CO}}, and {{H}} {\textsubscript{2}} {{O}}}, volume = {93}, year = {1990}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.458815}} + bdsk-url-1 = {https://doi.org/10.1063/1.458815}} @article{Koch_1997, author = {Koch, Henrik and Christiansen, Ove and Jorgensen, Poul and Sanchez de Mer{\'a}s, Alfredo M. and Helgaker, Trygve}, @@ -9129,8 +9130,8 @@ url = {http://scitation.aip.org/content/aip/journal/jcp/106/5/10.1063/1.473322}, volume = {106}, year = {1997}, - Bdsk-Url-1 = {http://scitation.aip.org/content/aip/journal/jcp/106/5/10.1063/1.473322}, - Bdsk-Url-2 = {http://dx.doi.org/10.1063/1.473322}} + bdsk-url-1 = {http://scitation.aip.org/content/aip/journal/jcp/106/5/10.1063/1.473322}, + bdsk-url-2 = {http://dx.doi.org/10.1063/1.473322}} @article{Koga_1999, author = {Koga, Toshikatsu and Tatewaki, Hiroshi and Matsuyama, Hisashi and Satoh, Yasuharu}, @@ -9147,7 +9148,7 @@ url = {http://dx.doi.org/10.1007/s002140050479}, volume = {102}, year = {1999}, - Bdsk-Url-1 = {http://dx.doi.org/10.1007/s002140050479}} + bdsk-url-1 = {http://dx.doi.org/10.1007/s002140050479}} @article{Kohn_1986, author = {Kohn, Walter}, @@ -9164,7 +9165,7 @@ title = {Density-Functional Theory for Excited States in a Quasi-Local-Density Approximation}, volume = {34}, year = {1986}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevA.34.737}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRevA.34.737}} @article{Kolorenc_2011, author = {J. Kolorenc and L. 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P.}, @@ -9963,7 +9964,7 @@ title = {Valence Transitions in 1,3-cyclopentadiene, 1,3-cyclohexadiene, and 1,3-cycloheptadiene}, volume = {83}, year = {1985}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.449304}} + bdsk-url-1 = {https://doi.org/10.1063/1.449304}} @article{McDiarmid_1988, author = {McDiarmid, Ruth and Sheybani, Abdol-Hakim}, @@ -9979,7 +9980,7 @@ title = {Reinterpretation of the Main Absorption Band of 1,3-butadiene}, volume = {89}, year = {1988}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.455177}} + bdsk-url-1 = {https://doi.org/10.1063/1.455177}} @article{McDonald_1933, author = {J. K. L. 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Matveev}, @@ -10033,7 +10034,7 @@ title = {Wigner crystal physics in quantum wires}, volume = {21}, year = {2009}, - Bdsk-Url-1 = {https://doi.org/10.1088/0953-8984/21/2/023203}} + bdsk-url-1 = {https://doi.org/10.1088/0953-8984/21/2/023203}} @article{Minezawa_2009, author = {Minezawa, Noriyuki and Gordon, Mark S.}, @@ -10050,7 +10051,7 @@ title = {Optimizing {{Conical Intersections}} by {{Spin}}-{{Flip Density Functional Theory}}: {{Application}} to {{Ethylene}}}, volume = {113}, year = {2009}, - Bdsk-Url-1 = {https://doi.org/10.1021/jp908032x}} + bdsk-url-1 = {https://doi.org/10.1021/jp908032x}} @article{Minezawa_2009a, author = {Minezawa, Noriyuki and Gordon, Mark S.}, @@ -10067,7 +10068,7 @@ title = {Optimizing {{Conical Intersections}} by {{Spin}}-{{Flip Density Functional Theory}}: {{Application}} to {{Ethylene}}}, volume = {113}, year = {2009}, - Bdsk-Url-1 = {https://doi.org/10.1021/jp908032x}} + bdsk-url-1 = {https://doi.org/10.1021/jp908032x}} @article{Miranda_2005, author = {Miranda, Katrina M.}, @@ -10083,7 +10084,7 @@ title = {The Chemistry of Nitroxyl ({{HNO}}) and Implications in Biology}, volume = {249}, year = {2005}, - Bdsk-Url-1 = {https://doi.org/10.1016/j.ccr.2004.08.010}} + bdsk-url-1 = {https://doi.org/10.1016/j.ccr.2004.08.010}} @article{Mirtschink_2013, author = {Mirtschink, Andr\'e and Seidl, Michael and {Gori-Giorgi}, Paola}, @@ -10099,7 +10100,7 @@ title = {Derivative {{Discontinuity}} in the {{Strong}}-{{Interaction Limit}} of {{Density}}-{{Functional Theory}}}, volume = {111}, year = {2013}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevLett.111.126402}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRevLett.111.126402}} @article{Mitas_1991, author = {Lubo{\v{s}} Mit{\'{a}}{\v{s}} and Eric L. Shirley and David M. Ceperley}, @@ -10115,8 +10116,8 @@ url = {https://doi.org/10.1063%2F1.460849}, volume = {95}, year = 1991, - Bdsk-Url-1 = {https://doi.org/10.1063%2F1.460849}, - Bdsk-Url-2 = {http://dx.doi.org/10.1063/1.460849}} + bdsk-url-1 = {https://doi.org/10.1063%2F1.460849}, + bdsk-url-2 = {http://dx.doi.org/10.1063/1.460849}} @inbook{Mitas_1993, author = {L. Mit\'a\v{s}}, @@ -10143,8 +10144,8 @@ url = {https://link.aps.org/doi/10.1103/PhysRevA.49.4411}, volume = {49}, year = {1994}, - Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevA.49.4411}, - Bdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevA.49.4411}} + bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevA.49.4411}, + bdsk-url-2 = {http://dx.doi.org/10.1103/PhysRevA.49.4411}} @article{Mitas_2006, author = {Mitas, Lubos}, @@ -10161,7 +10162,7 @@ title = {Structure of {{Fermion Nodes}} and {{Nodal Cells}}}, volume = {96}, year = {2006}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevLett.96.240402}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRevLett.96.240402}} @article{Mori-Sanchez_2008, author = {{Mori-S\'anchez}, Paula and Cohen, Aron J. and Yang, Weitao}, @@ -10177,7 +10178,7 @@ title = {Localization and {{Delocalization Errors}} in {{Density Functional Theory}} and {{Implications}} for {{Band}}-{{Gap Prediction}}}, volume = {100}, year = {2008}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevLett.100.146401}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRevLett.100.146401}} @article{Mori-Sanchez_2009, author = {{Mori-S\'anchez}, Paula and Cohen, Aron J. and Yang, Weitao}, @@ -10193,7 +10194,7 @@ title = {Discontinuous {{Nature}} of the {{Exchange}}-{{Correlation Functional}} in {{Strongly Correlated Systems}}}, volume = {102}, year = {2009}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevLett.102.066403}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRevLett.102.066403}} @article{Mori-Sanchez_2012, author = {{Mori-S\'anchez}, Paula and Cohen, Aron J. and Yang, Weitao}, @@ -10209,7 +10210,7 @@ title = {Failure of the Random-Phase-Approximation Correlation Energy}, volume = {85}, year = {2012}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevA.85.042507}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRevA.85.042507}} @article{Mori-Sanchez_2014, author = {{Mori-S\'anchez}, Paula and Cohen, Aron J.}, @@ -10225,7 +10226,7 @@ title = {The Derivative Discontinuity of the Exchange\textendash{}Correlation Functional}, volume = {16}, year = {2014}, - Bdsk-Url-1 = {https://doi.org/10.1039/C4CP01170H}} + bdsk-url-1 = {https://doi.org/10.1039/C4CP01170H}} @article{Mori-Sanchez_2018, abstract = {A stochastic minimization method for a real-space wave function, $\Psi$(r1, r2...rn), constrained to a chosen density, $\rho$(r), is developed. It enables the explicit calculation of the Levy constrained search, F[$\rho$] = min$\Psi\rightarrow\rho$\langle$\Psi$|T\^ + V\^ ee|$\Psi$\rangle, which gives the exact functional of density functional theory. This general method is illustrated in the evaluation of F[$\rho$] for densities in one dimension with a soft-Coulomb interaction. Additionally, procedures are given to determine the first and second functional derivatives, $\delta$F/$\delta\rho$(r) and $\delta$2F/[$\delta\rho$(r)$\delta\rho$(r${'}$)]. For a chosen external potential, v(r), the functional and its derivatives are used in minimizations over densities to give the exact energy, Ev, without needing to solve the Schr\"odinger equation.}, @@ -10243,7 +10244,7 @@ title = {Exact {{Density Functional Obtained}} via the {{Levy Constrained Search}}}, volume = {9}, year = {2018}, - Bdsk-Url-1 = {https://doi.org/10.1021/acs.jpclett.8b02332}} + bdsk-url-1 = {https://doi.org/10.1021/acs.jpclett.8b02332}} @article{Mosher_1973, author = {Mosher, Oren A. and Flicker, Wayne M. and Kuppermann, Aron}, @@ -10259,7 +10260,7 @@ title = {Electronic Spectroscopy of {\emph{S-trans}} 1,3-butadiene by Electron Impact}, volume = {59}, year = {1973}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.1680030}} + bdsk-url-1 = {https://doi.org/10.1063/1.1680030}} @article{Muller_2001, author = {M{\"u}ller, Thomas and Lischka, Hans}, @@ -10276,7 +10277,7 @@ url = {https://doi.org/10.1007/s002140100286}, volume = {106}, year = {2001}, - Bdsk-Url-1 = {https://doi.org/10.1007/s002140100286}} + bdsk-url-1 = {https://doi.org/10.1007/s002140100286}} @article{Nagy_1998, author = {Nagy, \'A}, @@ -10292,7 +10293,7 @@ title = {Optimized Potential Method for Ensembles of Excited States}, volume = {69}, year = {1998}, - Bdsk-Url-1 = {https://doi.org/10.1002/(SICI)1097-461X(1998)69:3%3C247::AID-QUA4%3E3.0.CO;2-V}} + bdsk-url-1 = {https://doi.org/10.1002/(SICI)1097-461X(1998)69:3%3C247::AID-QUA4%3E3.0.CO;2-V}} @article{Nagy_2001, abstract = {Recently an optimized potential method (OPM) has been derived for ensembles of excited states. Here an alternative OPM is proposed. The ensemble Kohn\textendash{}Sham potential in the generalized version of the Krieger\textendash{}Li\textendash{}Iafrate approximation to the OPM method is obtained.}, @@ -10310,7 +10311,7 @@ title = {An Alternative Optimized Potential Method for Ensembles of Excited States}, volume = {34}, year = {2001}, - Bdsk-Url-1 = {https://doi.org/10.1088/0953-4075/34/12/305}} + bdsk-url-1 = {https://doi.org/10.1088/0953-4075/34/12/305}} @article{Nagy_2005, author = {Nagy, \'A. and Liu, S. and Bartolloti, L.}, @@ -10327,7 +10328,7 @@ title = {Generalized Density Functional Theory for Degenerate States}, volume = {122}, year = {2005}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.1871933}} + bdsk-url-1 = {https://doi.org/10.1063/1.1871933}} @article{Nakano_1993a, author = {Nakano, Haruyuki}, @@ -10344,8 +10345,8 @@ url = {http://dx.doi.org/10.1016/0009-2614(93)89016-B}, volume = {207}, year = {1993}, - Bdsk-Url-1 = {http://dx.doi.org/10.1016/0009-2614(93)89016-B}, - Bdsk-Url-2 = {http://dx.doi.org/10.1016/0009-2614(93)89016-b}} + bdsk-url-1 = {http://dx.doi.org/10.1016/0009-2614(93)89016-B}, + bdsk-url-2 = {http://dx.doi.org/10.1016/0009-2614(93)89016-b}} @article{Nakano_1993b, author = {Nakano, Haruyuki}, @@ -10362,7 +10363,7 @@ url = {http://dx.doi.org/10.1063/1.465674}, volume = {99}, year = {1993}, - Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.465674}} + bdsk-url-1 = {http://dx.doi.org/10.1063/1.465674}} @article{Nakayama_1998, author = {Nakayama, Kenichi and Nakano, Haruyuki and Hirao, Kimihiko}, @@ -10378,7 +10379,7 @@ title = {Theoretical Study of the ???* Excited States of Linear Polyenes: {{The}} Energy Gap between {{11Bu}}+ and {{21Ag}}? States and Their Character}, volume = {66}, year = {1998}, - Bdsk-Url-1 = {https://doi.org/10.1002/(SICI)1097-461X(1998)66:2%3C157::AID-QUA7%3E3.0.CO;2-U}} + bdsk-url-1 = {https://doi.org/10.1002/(SICI)1097-461X(1998)66:2%3C157::AID-QUA7%3E3.0.CO;2-U}} @article{Nemec_2010, author = {Nemec, Norbert and Towler, Michael D. and Needs, R. J.}, @@ -10395,7 +10396,7 @@ url = {http://dx.doi.org/10.1063/1.3288054}, volume = {132}, year = {2010}, - Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.3288054}} + bdsk-url-1 = {http://dx.doi.org/10.1063/1.3288054}} @article{Nieto_2000, author = {Michael Martin Nieto}, @@ -10429,7 +10430,7 @@ url = {https://doi.org/10.1063/1.452353}, volume = {86}, year = {1987}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.452353}} + bdsk-url-1 = {https://doi.org/10.1063/1.452353}} @article{Nooijen_1999, author = {Nooijen, Marcel}, @@ -10445,7 +10446,7 @@ title = {Similarity Transformed Equation of Motion Coupled-Cluster Study of Excited States of Selected Azabenzenes}, volume = {55}, year = {1999}, - Bdsk-Url-1 = {https://doi.org/10.1016/S1386-1425(98)00261-3}} + bdsk-url-1 = {https://doi.org/10.1016/S1386-1425(98)00261-3}} @article{Nooijen_2000, author = {Nooijen, Marcel}, @@ -10462,7 +10463,7 @@ title = {Electronic {{Excitation Spectrum}} of {\emph{s}} -{{Tetrazine}}: {{An Extended}}-{{STEOM}}-{{CCSD Study}}}, volume = {104}, year = {2000}, - Bdsk-Url-1 = {https://doi.org/10.1021/jp993983z}} + bdsk-url-1 = {https://doi.org/10.1021/jp993983z}} @article{Noro_2000, author = {Noro, Takeshi and Sekiya, Masahiro and Koga, Toshikatsu and Matsuyama, Hisashi}, @@ -10479,7 +10480,7 @@ url = {http://dx.doi.org/10.1007/s002140000126}, volume = {104}, year = {2000}, - Bdsk-Url-1 = {http://dx.doi.org/10.1007/s002140000126}} + bdsk-url-1 = {http://dx.doi.org/10.1007/s002140000126}} @article{Ohtsuka_2017, author = {Ohtsuka, Yuhki and Hasegawa, Jun-ya}, @@ -10496,7 +10497,7 @@ url = {http://dx.doi.org/10.1063/1.4993214}, volume = {147}, year = {2017}, - Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.4993214}} + bdsk-url-1 = {http://dx.doi.org/10.1063/1.4993214}} @article{Oliveira_1988, author = {Oliveira, L. N. and Gross, E. K. U. and Kohn, W.}, @@ -10513,7 +10514,7 @@ title = {Density-Functional Theory for Ensembles of Fractionally Occupied States. {{II}}. {{Application}} to the {{He}} Atom}, volume = {37}, year = {1988}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevA.37.2821}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRevA.37.2821}} @article{Oliveira_1988a, author = {Oliveira, L. N. and Gross, E. K. U. and Kohn, W.}, @@ -10530,7 +10531,7 @@ title = {Density-Functional Theory for Ensembles of Fractionally Occupied States. {{II}}. {{Application}} to the {{He}} Atom}, volume = {37}, year = {1988}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevA.37.2821}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRevA.37.2821}} @book{Olivucci_2010, address = {Amsterdam; Boston (Mass.); Paris}, @@ -10557,7 +10558,7 @@ title = {Ab Initio Investigation of the Potential Energy Surfaces Involved in the Photophysics of S-Trans-1,3-Butadiene}, volume = {269}, year = {2001}, - Bdsk-Url-1 = {https://doi.org/10.1016/S0301-0104(01)00373-1}} + bdsk-url-1 = {https://doi.org/10.1016/S0301-0104(01)00373-1}} @article{Palczewski_2006, author = {Palczewski, Krzysztof}, @@ -10573,7 +10574,7 @@ title = {G {{Protein}}\textendash{{Coupled Receptor Rhodopsin}}}, volume = {75}, year = {2006}, - Bdsk-Url-1 = {https://doi.org/10.1146/annurev.biochem.75.103004.142743}} + bdsk-url-1 = {https://doi.org/10.1146/annurev.biochem.75.103004.142743}} @article{Palenikova_2008, author = {Jana P{\'a}len{\'\i}kov{\'a} and Michal Kraus and Pavel Neogr{\'a}dy and Vladimir Kell{\"o} and Miroslav Urban}, @@ -10588,7 +10589,7 @@ url = {https://doi.org/10.1080/00268970802454786}, volume = {106}, year = {2008}, - Bdsk-Url-1 = {https://doi.org/10.1080/00268970802454786}} + bdsk-url-1 = {https://doi.org/10.1080/00268970802454786}} @article{Palmer_1989, author = {Palmer, Michael H. and Walker, Isobel C.}, @@ -10604,7 +10605,7 @@ title = {The Electronic States of Benzene and the Azines. {{I}}. {{The}} Parent Compound Benzene. {{Correlation}} of Vacuum {{UV}} and Electron Scattering Data with Ab Initio {{CI}} Studies}, volume = {133}, year = {1989}, - Bdsk-Url-1 = {https://doi.org/10.1016/0301-0104(89)80104-1}} + bdsk-url-1 = {https://doi.org/10.1016/0301-0104(89)80104-1}} @article{Palmer_1991, author = {Palmer, Michael H. and Walker, Isobel C.}, @@ -10620,7 +10621,7 @@ title = {The Electronic States of the Azines. {{V}}. {{Pyridazine}}, Studied by {{VUV}} Absorption, near Threshold Electron Energy-Loss Spectroscopy and Ab Initio Multi-Reference Configuration Interaction Calculations}, volume = {157}, year = {1991}, - Bdsk-Url-1 = {https://doi.org/10.1016/0301-0104(91)87143-J}} + bdsk-url-1 = {https://doi.org/10.1016/0301-0104(91)87143-J}} @article{Palmer_1997, author = {Palmer, Michael H. and McNab, Hamish and Reed, David and Pollacchi, Anne and Walker, Isobel C. and Guest, Martyn F. and Siggel, Michele R.F.}, @@ -10636,7 +10637,7 @@ title = {The Molecular and Electronic States of 1,2,4,5-Tetrazine Studied by {{VUV}} Absorption, near-Threshold Electron Energy-Loss Spectroscopy and Ab Initio Multi-Reference Configuration Interaction Studies}, volume = {214}, year = {1997}, - Bdsk-Url-1 = {https://doi.org/10.1016/S0301-0104(96)00330-8}} + bdsk-url-1 = {https://doi.org/10.1016/S0301-0104(96)00330-8}} @book{ParrBook, address = {Clarendon Press}, @@ -10663,7 +10664,7 @@ title = {Calculation of Electronic Excited States of Molecules Using the {{Helmholtz}} Free-Energy Minimum Principle}, volume = {87}, year = {2013}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevA.87.062501}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRevA.87.062501}} @article{Pastorczak_2014, author = {Pastorczak, Ewa and Pernal, Katarzyna}, @@ -10680,7 +10681,7 @@ title = {Ensemble Density Variational Methods with Self- and Ghost-Interaction-Corrected Functionals}, volume = {140}, year = {2014}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.4866998}} + bdsk-url-1 = {https://doi.org/10.1063/1.4866998}} @article{Paterson_2006, author = {Paterson, Martin J. and Christiansen, Ove and Paw\l{}owski, Filip and J\o{}rgensen, Poul and H\"attig, Christof and Helgaker, Trygve and Sa\l{}ek, Pawe\l}, @@ -10696,7 +10697,7 @@ title = {Benchmarking Two-Photon Absorption with {{CC3}} Quadratic Response Theory, and Comparison with Density-Functional Response Theory}, volume = {124}, year = {2006}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.2163874}} + bdsk-url-1 = {https://doi.org/10.1063/1.2163874}} @article{Patil_2001, author = {S. H. Patil}, @@ -10733,7 +10734,7 @@ url = {http://dx.doi.org/10.1063/1.4981527}, volume = {146}, year = {2017}, - Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.4981527}} + bdsk-url-1 = {http://dx.doi.org/10.1063/1.4981527}} @article{Perarnau-Llobet_2015, author = {{Perarnau-Llobet}, Mart\'i and Hovhannisyan, Karen V. and Huber, Marcus and Skrzypczyk, Paul and Brunner, Nicolas and Ac\'in, Antonio}, @@ -10749,7 +10750,7 @@ title = {Extractable {{Work}} from {{Correlations}}}, volume = {5}, year = {2015}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevX.5.041011}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRevX.5.041011}} @article{Perdew_1985, author = {Perdew, John P. and Levy, Mel}, @@ -10767,7 +10768,7 @@ title = {Extrema of the Density Functional for the Energy: {{Excited}} States from the Ground-State Theory}, volume = {31}, year = {1985}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevB.31.6264}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRevB.31.6264}} @article{Petz_2011, author = {Petz, Ren{\'e} and L{\"u}chow, Arne}, @@ -10784,7 +10785,7 @@ url = {http://dx.doi.org/10.1002/cphc.201000942}, volume = {12}, year = {2011}, - Bdsk-Url-1 = {http://dx.doi.org/10.1002/cphc.201000942}} + bdsk-url-1 = {http://dx.doi.org/10.1002/cphc.201000942}} @article{Peyerimhoff_1970, author = {Peyerimhoff, Sigrid D. and Buenker, Robert J.}, @@ -10799,7 +10800,7 @@ title = {Comparison of the Molecular Structure and Spectra of Benzene and Borazine}, volume = {19}, year = {1970}, - Bdsk-Url-1 = {https://doi.org/10.1007/BF00527373}} + bdsk-url-1 = {https://doi.org/10.1007/BF00527373}} @article{Pincellt_1971, author = {Pincellt, U. and Cadioli, B. and David, D.J.}, @@ -10815,7 +10816,7 @@ title = {A Theoretical Study of the Electronic Structure and Conformation of Glyoxal}, volume = {9}, year = {1971}, - Bdsk-Url-1 = {https://doi.org/10.1016/0022-2860(71)85017-2}} + bdsk-url-1 = {https://doi.org/10.1016/0022-2860(71)85017-2}} @article{Pittalis_2006, author = {Pittalis, S. and Kurth, S. and Gross, E. K. U.}, @@ -10832,7 +10833,7 @@ title = {On the Degeneracy of Atomic States within Exact-Exchange (Spin-) Density Functional Theory}, volume = {125}, year = {2006}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.2338038}} + bdsk-url-1 = {https://doi.org/10.1063/1.2338038}} @article{Pittalis_2006a, author = {Pittalis, S. and Kurth, S. and Gross, E. K. U.}, @@ -10849,7 +10850,7 @@ title = {On the Degeneracy of Atomic States within Exact-Exchange (Spin-) Density Functional Theory}, volume = {125}, year = {2006}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.2338038}} + bdsk-url-1 = {https://doi.org/10.1063/1.2338038}} @article{Pittalis_2006b, author = {Pittalis, S. and Kurth, S. and Gross, E. K. U.}, @@ -10866,7 +10867,7 @@ title = {On the Degeneracy of Atomic States within Exact-Exchange (Spin-) Density Functional Theory}, volume = {125}, year = {2006}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.2338038}} + bdsk-url-1 = {https://doi.org/10.1063/1.2338038}} @article{Porter_2001, author = {Porter, A. R. and Towler, M. D. and Needs, R. J.}, @@ -10883,7 +10884,7 @@ title = {Excitons in Small Hydrogenated {{Si}} Clusters}, volume = {64}, year = {2001}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevB.64.035320}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRevB.64.035320}} @article{Porter_2001a, author = {Porter, A. R. and Al-Mushadani, O. K. and Towler, M. D. and Needs, R. J.}, @@ -10901,7 +10902,7 @@ title = {Electronic Excited-State Wave Functions for Quantum {{Monte Carlo}}: {{Application}} to Silane and Methane}, volume = {114}, year = {2001}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.1342765}} + bdsk-url-1 = {https://doi.org/10.1063/1.1342765}} @article{Povill_1992, author = {Povill, A. and Rubio, J. and Illas, F.}, @@ -10930,7 +10931,7 @@ title = {Excitations and Benchmark Ensemble Density Functional Theory for Two Electrons}, volume = {140}, year = {2014}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.4872255}} + bdsk-url-1 = {https://doi.org/10.1063/1.4872255}} @article{Purvis_1982, author = {Purvis III, G. P. and Bartlett, R. J.}, @@ -10944,7 +10945,7 @@ url = {https://doi.org/10.1063/1.443164}, volume = {76}, year = {1982}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.443164}} + bdsk-url-1 = {https://doi.org/10.1063/1.443164}} @article{Purwanto_2009, author = {Purwanto, Wirawan and Zhang, Shiwei and Krakauer, Henry}, @@ -10962,7 +10963,7 @@ title = {Excited State Calculations Using Phaseless Auxiliary-Field Quantum {{Monte Carlo}}: {{Potential}} Energy Curves of Low-Lying {{C2}} Singlet States}, volume = {130}, year = {2009}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.3077920}} + bdsk-url-1 = {https://doi.org/10.1063/1.3077920}} @article{Purwanto_2009a, author = {Purwanto, Wirawan and Zhang, Shiwei and Krakauer, Henry}, @@ -10979,7 +10980,7 @@ title = {Excited State Calculations Using Phaseless Auxiliary-Field Quantum {{Monte Carlo}}: {{Potential}} Energy Curves of Low-Lying {{C2}} Singlet States}, volume = {130}, year = {2009}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.3077920}} + bdsk-url-1 = {https://doi.org/10.1063/1.3077920}} @article{Puzder_2002, author = {Puzder, Aaron and Williamson, A. J. and Grossman, Jeffrey C. and Galli, Giulia}, @@ -10996,7 +10997,7 @@ title = {Surface {{Chemistry}} of {{Silicon Nanoclusters}}}, volume = {88}, year = {2002}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevLett.88.097401}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRevLett.88.097401}} @article{Puzzarini_2014, author = {Puzzarini, Cristina and Penocchio, Emanuele and Biczysko, Malgorzata and Barone, Vincenzo}, @@ -11013,7 +11014,7 @@ title = {Molecular {{Structure}} and {{Spectroscopic Signatures}} of {{Acrolein}}: {{Theory Meets Experiment}}}, volume = {118}, year = {2014}, - Bdsk-Url-1 = {https://doi.org/10.1021/jp503672g}} + bdsk-url-1 = {https://doi.org/10.1021/jp503672g}} @misc{qmcchem, author = {A. Scemama and E. Giner and T. Applencourt and M. 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Malmqvist and L. {Serrano-Andres}}, @@ -11232,7 +11233,7 @@ title = {A Theoretical Study of the Electronic Spectrum of S-Tetrazine}, volume = {96}, year = {1999}, - Bdsk-Url-1 = {https://doi.org/10.1080/00268979909482997}} + bdsk-url-1 = {https://doi.org/10.1080/00268979909482997}} @article{Rubio_2008, author = {Mercedes Rubio and Luis Serrano-Andr{\'e}s and Manuela Merch{\'a}n}, @@ -11246,7 +11247,7 @@ url = {https://doi.org/10.1063/1.2837827}, volume = {128}, year = {2008}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.2837827}} + bdsk-url-1 = {https://doi.org/10.1063/1.2837827}} @article{Sagredo_2018, author = {Sagredo, Francisca and Burke, Kieron}, @@ -11263,7 +11264,7 @@ title = {Accurate Double Excitations from Ensemble Density Functional Calculations}, volume = {149}, year = {2018}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.5043411}} + bdsk-url-1 = {https://doi.org/10.1063/1.5043411}} @article{Saha_2006, author = {Saha, Biswajit and Ehara, Masahiro and Nakatsuji, Hiroshi}, @@ -11281,7 +11282,7 @@ title = {Singly and Doubly Excited States of Butadiene, Acrolein, and Glyoxal: {{Geometries}} and Electronic Spectra}, volume = {125}, year = {2006}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.2200344}} + bdsk-url-1 = {https://doi.org/10.1063/1.2200344}} @article{Santoro_2016, author = {Santoro, Fabrizio and Jacquemin, Denis}, @@ -11297,7 +11298,7 @@ url = {http://dx.doi.org/10.1002/wcms.1260}, volume = {6}, year = {2016}, - Bdsk-Url-1 = {http://dx.doi.org/10.1002/wcms.1260}} + bdsk-url-1 = {http://dx.doi.org/10.1002/wcms.1260}} @article{Scemama_2004, author = {Scemama, Anthony and Chaquin, Patrick and Caffarel, Michel}, @@ -11314,7 +11315,7 @@ url = {http://dx.doi.org/10.1063/1.1765098}, volume = {121}, year = {2004}, - Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.1765098}} + bdsk-url-1 = {http://dx.doi.org/10.1063/1.1765098}} @article{Scemama_2006a, author = {Scemama, Anthony and Leli{\`e}vre, Tony and Stoltz, Gabriel and Canc{\`e}s, Eric and Caffarel, Michel}, @@ -11331,7 +11332,7 @@ url = {http://dx.doi.org/10.1063/1.2354490}, volume = {125}, year = {2006}, - Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.2354490}} + bdsk-url-1 = {http://dx.doi.org/10.1063/1.2354490}} @article{Scemama_2006b, author = {Scemama, Anthony and Caffarel, Michel and Savin, Andreas}, @@ -11347,7 +11348,7 @@ url = {http://dx.doi.org/10.1002/jcc.20526}, volume = {28}, year = {2006}, - Bdsk-Url-1 = {http://dx.doi.org/10.1002/jcc.20526}} + bdsk-url-1 = {http://dx.doi.org/10.1002/jcc.20526}} @article{Scemama_2006c, author = {Scemama, Anthony and Filippi, Claudia}, @@ -11363,8 +11364,8 @@ url = {http://dx.doi.org/10.1103/PhysRevB.73.241101}, volume = {73}, year = {2006}, - Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevB.73.241101}, - Bdsk-Url-2 = {http://dx.doi.org/10.1103/physrevb.73.241101}} + bdsk-url-1 = {http://dx.doi.org/10.1103/PhysRevB.73.241101}, + bdsk-url-2 = {http://dx.doi.org/10.1103/physrevb.73.241101}} @article{Scemama_2011, author = {Scemama, Anthony and Caffarel, Michel and Chaudret, Robin and Piquemal, Jean-Philip}, @@ -11381,7 +11382,7 @@ url = {http://dx.doi.org/10.1021/ct1005938}, volume = {7}, year = {2011}, - Bdsk-Url-1 = {http://dx.doi.org/10.1021/ct1005938}} + bdsk-url-1 = {http://dx.doi.org/10.1021/ct1005938}} @article{Scemama_2013, author = {Scemama, Anthony and Caffarel, Michel and Oseret, Emmanuel and Jalby, William}, @@ -11398,7 +11399,7 @@ url = {http://dx.doi.org/10.1002/jcc.23216}, volume = {34}, year = {2013}, - Bdsk-Url-1 = {http://dx.doi.org/10.1002/jcc.23216}} + bdsk-url-1 = {http://dx.doi.org/10.1002/jcc.23216}} @article{Scemama_2014, author = {Scemama, A. and Applencourt, T. and Giner, E. and Caffarel, M.}, @@ -11415,7 +11416,7 @@ url = {http://dx.doi.org/10.1063/1.4903985}, volume = {141}, year = {2014}, - Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.4903985}} + bdsk-url-1 = {http://dx.doi.org/10.1063/1.4903985}} @article{Scemama_2016, author = {Scemama, Anthony and Applencourt, Thomas and Giner, Emmanuel and Caffarel, Michel}, @@ -11432,7 +11433,7 @@ url = {http://dx.doi.org/10.1002/jcc.24382}, volume = {37}, year = {2016}, - Bdsk-Url-1 = {http://dx.doi.org/10.1002/jcc.24382}} + bdsk-url-1 = {http://dx.doi.org/10.1002/jcc.24382}} @article{Scemama_2018, author = {A. 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Mehboob and Knecht, Stefan and Fromager, Emmanuel}, @@ -11706,7 +11707,7 @@ title = {Combining Linear Interpolation with Extrapolation Methods in Range-Separated Ensemble Density Functional Theory}, volume = {114}, year = {2016}, - Bdsk-Url-1 = {https://doi.org/10.1080/00268976.2015.1119902}} + bdsk-url-1 = {https://doi.org/10.1080/00268976.2015.1119902}} @article{Senjean_2018, author = {Senjean, Bruno and Fromager, Emmanuel}, @@ -11723,7 +11724,7 @@ title = {Unified Formulation of Fundamental and Optical Gap Problems in Density-Functional Theory for Ensembles}, volume = {98}, year = {2018}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevA.98.022513}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRevA.98.022513}} @article{Serrano-Andres_1993, author = {Serrano-Andr\'es, Luis and Merch\'an, Manuela and Nebot-Gil, Ignacio and Lindh, Roland and Roos, Bj\"orn O.}, @@ -11740,7 +11741,7 @@ title = {Towards an Accurate Molecular Orbital Theory for Excited States: {{Ethene}}, Butadiene, and Hexatriene}, volume = {98}, year = {1993}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.465071}} + bdsk-url-1 = {https://doi.org/10.1063/1.465071}} @article{Shakeshaft_2007, author = {Shakeshaft, Robin}, @@ -11756,7 +11757,7 @@ title = {Two-Photon Single and Double Ionization of Helium}, volume = {76}, year = {2007}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevA.76.063405}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRevA.76.063405}} @article{Sharma_2015b, author = {Sharma, Sandeep}, @@ -11772,7 +11773,7 @@ title = {A General Non-{{Abelian}} Density Matrix Renormalization Group Algorithm with Application to the {{C}} {\textsubscript{2}} Dimer}, volume = {142}, year = {2015}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.4905237}} + bdsk-url-1 = {https://doi.org/10.1063/1.4905237}} @article{Sharma_2017, author = {Sharma, Sandeep and Holmes, Adam A. and Jeanmairet, Guillaume and Alavi, Ali and Umrigar, C. J.}, @@ -11789,7 +11790,7 @@ url = {http://dx.doi.org/10.1021/acs.jctc.6b01028}, volume = {13}, year = {2017}, - Bdsk-Url-1 = {http://dx.doi.org/10.1021/acs.jctc.6b01028}} + bdsk-url-1 = {http://dx.doi.org/10.1021/acs.jctc.6b01028}} @article{Shea_2017, author = {Shea, Jacqueline A. R. and Neuscamman, Eric}, @@ -11805,7 +11806,7 @@ title = {Size {{Consistent Excited States}} via {{Algorithmic Transformations}} between {{Variational Principles}}}, volume = {13}, year = {2017}, - Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.7b00923}} + bdsk-url-1 = {https://doi.org/10.1021/acs.jctc.7b00923}} @article{Shea_2018, author = {Shea, Jacqueline A. R. and Neuscamman, Eric}, @@ -11823,7 +11824,7 @@ title = {Communication: {{A}} Mean Field Platform for Excited State Quantum Chemistry}, volume = {149}, year = {2018}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.5045056}} + bdsk-url-1 = {https://doi.org/10.1063/1.5045056}} @article{Shen_2009b, author = {Jun Shen and Shuhua Li}, @@ -11837,7 +11838,7 @@ url = {https://doi.org/10.1063/1.3256297}, volume = {131}, year = {2009}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.3256297}} + bdsk-url-1 = {https://doi.org/10.1063/1.3256297}} @article{Shi_2011, author = {Shi, Deheng and Zhang, Xiaoniu and Sun, Jinfeng and Zhu, Zunlue}, @@ -11853,7 +11854,7 @@ title = {{{MRCI}} Study on Spectroscopic and Molecular Properties of {{B}} {\textsuperscript{1}} {{$\Delta$}} {\textsubscript{g}} , , {{C}} {\textsuperscript{1}} {{$\Pi$}} {\textsubscript{g}} , , and 1 {\textsuperscript{1}} {{$\Delta$}} {\textsubscript{u}} Electronic States of the {{C}} {\textsubscript{2}} Radical}, volume = {109}, year = {2011}, - Bdsk-Url-1 = {https://doi.org/10.1080/00268976.2011.564593}} + bdsk-url-1 = {https://doi.org/10.1080/00268976.2011.564593}} @article{Shu_2017, author = {Shu, Yinan and Truhlar, Donald G.}, @@ -11869,7 +11870,7 @@ title = {Doubly {{Excited Character}} or {{Static Correlation}} of the {{Reference State}} in the {{Controversial}} 2 {\textsuperscript{1}} {{A}} {\textsubscript{g}} {{State}} of {\emph{Trans}} -{{Butadiene}}?}, volume = {139}, year = {2017}, - Bdsk-Url-1 = {https://doi.org/10.1021/jacs.7b06283}} + bdsk-url-1 = {https://doi.org/10.1021/jacs.7b06283}} @article{Siebbeles_2010, author = {Siebbeles, Laurens D. A.}, @@ -11887,7 +11888,7 @@ title = {Two Electrons from One Photon: {{Organic}} Solar Cells}, volume = {2}, year = {2010}, - Bdsk-Url-1 = {https://doi.org/10.1038/nchem.720}} + bdsk-url-1 = {https://doi.org/10.1038/nchem.720}} @article{Silva-Junior_2008, author = {Silva-Junior, M. R. and Schreiber, M. and Sauer, S. P. A. and Thiel, W.}, @@ -11925,7 +11926,7 @@ title = {Exact Thermal Density Functional Theory for a Model System: {{Correlation}} Components and Accuracy of the Zero-Temperature Exchange-Correlation Approximation}, volume = {93}, year = {2016}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevB.93.245131}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRevB.93.245131}} @article{Sobolewski_2003, author = {Sobolewski, Andrzej L. and Domcke, Wolfgang}, @@ -11941,7 +11942,7 @@ title = {Ab Initio Study of the Excited-State Coupled Electron\textendash{}Proton-Transfer Process in the 2-Aminopyridine Dimer}, volume = {294}, year = {2003}, - Bdsk-Url-1 = {https://doi.org/10.1016/S0301-0104(03)00388-4}} + bdsk-url-1 = {https://doi.org/10.1016/S0301-0104(03)00388-4}} @article{Sokolov_2016a, author = {Sokolov, Alexander Yu. and Chan, Garnet Kin-Lic}, @@ -11957,7 +11958,7 @@ title = {A Time-Dependent Formulation of Multi-Reference Perturbation Theory}, volume = {144}, year = {2016}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.4941606}} + bdsk-url-1 = {https://doi.org/10.1063/1.4941606}} @article{Sokolova_2000, author = {Sokolova, Svetlana and L{\"u}chow, Arne}, @@ -11974,8 +11975,8 @@ url = {http://dx.doi.org/10.1016/S0009-2614(00)00276-1}, volume = {320}, year = {2000}, - Bdsk-Url-1 = {http://dx.doi.org/10.1016/S0009-2614(00)00276-1}, - Bdsk-Url-2 = {http://dx.doi.org/10.1016/s0009-2614(00)00276-1}} + bdsk-url-1 = {http://dx.doi.org/10.1016/S0009-2614(00)00276-1}, + bdsk-url-2 = {http://dx.doi.org/10.1016/s0009-2614(00)00276-1}} @article{Starcke_2006, author = {Starcke, Jan Hendrik and Wormit, Michael and Schirmer, Jochen and Dreuw, Andreas}, @@ -11992,7 +11993,7 @@ title = {How Much Double Excitation Character Do the Lowest Excited States of Linear Polyenes Have?}, volume = {329}, year = {2006}, - Bdsk-Url-1 = {https://doi.org/10.1016/j.chemphys.2006.07.020}} + bdsk-url-1 = {https://doi.org/10.1016/j.chemphys.2006.07.020}} @article{Steinmann_2013, author = {Steinmann, Stephan N. and Yang, Weitao}, @@ -12009,7 +12010,7 @@ title = {Wave Function Methods for Fractional Electrons}, volume = {139}, year = {2013}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.4817849}} + bdsk-url-1 = {https://doi.org/10.1063/1.4817849}} @article{Stiefel_1996, author = {Stiefel, Edward I.}, @@ -12025,7 +12026,7 @@ title = {Transition Metal Sulfur Chemistry: Biological and Industrial Significance and Key Trends}, url = {http://dx.doi.org/10.1021/bk-1996-0653.ch001}, year = {1996}, - Bdsk-Url-1 = {http://dx.doi.org/10.1021/bk-1996-0653.ch001}} + bdsk-url-1 = {http://dx.doi.org/10.1021/bk-1996-0653.ch001}} @article{Stopkowicz_2015, author = {S. Stopkowicz and J. Gauss and K. K. Lange and E. I. Tellgren and T. Helgaker}, @@ -12050,7 +12051,7 @@ title = {A Revised {{MRCI}}-Algorithm Coupled to an Effective Valence-Shell {{Hamiltonian}}. {{II}}. {{Application}} to the Valence Excitations of Butadiene}, volume = {117}, year = {2002}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.1497678}} + bdsk-url-1 = {https://doi.org/10.1063/1.1497678}} @article{Su_2011, author = {Su, Peifeng and Wu, Jifang and Gu, Junjing and Wu, Wei and Shaik, Sason and Hiberty, Philippe C.}, @@ -12067,7 +12068,7 @@ title = {Bonding {{Conundrums}} in the {{C}} {\textsubscript{2}} {{Molecule}}: {{A Valence Bond Study}}}, volume = {7}, year = {2011}, - Bdsk-Url-1 = {https://doi.org/10.1021/ct100577v}} + bdsk-url-1 = {https://doi.org/10.1021/ct100577v}} @article{Sundstrom_2014, author = {Sundstrom, Eric J. and {Head-Gordon}, Martin}, @@ -12083,7 +12084,7 @@ title = {Non-Orthogonal Configuration Interaction for the Calculation of Multielectron Excited States}, volume = {140}, year = {2014}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.4868120}} + bdsk-url-1 = {https://doi.org/10.1063/1.4868120}} @book{SzaboBook, address = {New York}, @@ -12109,7 +12110,7 @@ title = {An {\emph{a}} {\emph{b}} {\emph{i}} {\emph{n}} {\emph{i}} {\emph{t}} {\emph{i}} {\emph{o}} Study of the Structure and Vibrational Spectra of Allyl and 1,4-pentadienyl Radicals}, volume = {93}, year = {1990}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.459189}} + bdsk-url-1 = {https://doi.org/10.1063/1.459189}} @article{Takahashi_1986, author = {Takahashi, M. and Paldus, J.}, @@ -12126,7 +12127,7 @@ title = {Time-dependent Coupled Cluster Approach: {{Excitation}} Energy Calculation Using an Orthogonally Spin-adapted Formalism}, volume = {85}, year = {1986}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.451241}} + bdsk-url-1 = {https://doi.org/10.1063/1.451241}} @article{Takano_2004, author = {Takano, Shuro and Yamamoto, Satoshi and Saito, Shuji}, @@ -12143,7 +12144,7 @@ url = {http://dx.doi.org/10.1016/j.jms.2004.01.003}, volume = {224}, year = {2004}, - Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.jms.2004.01.003}} + bdsk-url-1 = {http://dx.doi.org/10.1016/j.jms.2004.01.003}} @article{Tapavicza_2008, author = {Tapavicza, Enrico and Tavernelli, Ivano and Rothlisberger, Ursula and Filippi, Claudia and Casida, Mark E.}, @@ -12159,7 +12160,7 @@ title = {Mixed Time-Dependent Density-Functional Theory/Classical Trajectory Surface Hopping Study of Oxirane Photochemistry}, volume = {129}, year = {2008}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.2978380}} + bdsk-url-1 = {https://doi.org/10.1063/1.2978380}} @article{Tarte_1954, author = {Tarte, P.}, @@ -12185,7 +12186,7 @@ title = {A Long-Range-Corrected Time-Dependent Density Functional Theory}, volume = {120}, year = {2004}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.1688752}} + bdsk-url-1 = {https://doi.org/10.1063/1.1688752}} @article{Tellgren_2008, author = {E. I. Tellgren and A. Soncini and T. Helgaker}, @@ -12221,7 +12222,7 @@ title = {The Energy Density Functional Formalism for Excited States}, volume = {12}, year = {1979}, - Bdsk-Url-1 = {https://doi.org/10.1088/0022-3719/12/24/013}} + bdsk-url-1 = {https://doi.org/10.1088/0022-3719/12/24/013}} @article{Theophilou_1979a, abstract = {In this paper it is shown that the density can be used as the basic variable for calculating the properties of excited states. The correspondence is not between an eigenstate and its density, as is the case with the ground state, but between the subspace spanned by the number of lowest-energy eigenstates and the sum of their densities. An extension of the Hohenberg-Kohn-Sham theory for excited states has also been developed. The equations derived are similar in form to those for the ground-state density but the interpretation is different. The lowest-order approximation of the present theory coincides with Slater's `transition-state' theory.}, @@ -12239,7 +12240,7 @@ title = {The Energy Density Functional Formalism for Excited States}, volume = {12}, year = {1979}, - Bdsk-Url-1 = {https://doi.org/10.1088/0022-3719/12/24/013}} + bdsk-url-1 = {https://doi.org/10.1088/0022-3719/12/24/013}} @article{Theophilou_2018, author = {Theophilou, Andreas K.}, @@ -12256,7 +12257,7 @@ title = {A Novel Density Functional Theory for Atoms, Molecules, and Solids}, volume = {149}, year = {2018}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.5038262}} + bdsk-url-1 = {https://doi.org/10.1063/1.5038262}} @article{Tognetti_2016, author = {Tognetti, Vincent and Loos, Pierre-Fran{\c c}ois}, @@ -12273,7 +12274,7 @@ title = {Natural Occupation Numbers in Two-Electron Quantum Rings}, volume = {144}, year = {2016}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.4940919}} + bdsk-url-1 = {https://doi.org/10.1063/1.4940919}} @article{Toulouse_2007, author = {Toulouse, Julien and Umrigar, C. J.}, @@ -12290,7 +12291,7 @@ url = {http://dx.doi.org/10.1063/1.2437215}, volume = {126}, year = {2007}, - Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.2437215}} + bdsk-url-1 = {http://dx.doi.org/10.1063/1.2437215}} @article{Toulouse_2008, author = {Toulouse, Julien and Umrigar, C. J.}, @@ -12306,7 +12307,7 @@ title = {Full Optimization of {{Jastrow}}\textendash{{Slater}} Wave Functions with Application to the First-Row Atoms and Homonuclear Diatomic Molecules}, volume = {128}, year = {2008}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.2908237}} + bdsk-url-1 = {https://doi.org/10.1063/1.2908237}} @article{Trail_2015, author = {J. R. Trail and R. J. Needs}, @@ -12320,8 +12321,8 @@ url = {https://doi.org/10.1063/1.4907589}, volume = {142}, year = {2015}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.4907589}, - Bdsk-Url-2 = {http://dx.doi.org/10.1063/1.4907589}} + bdsk-url-1 = {https://doi.org/10.1063/1.4907589}, + bdsk-url-2 = {http://dx.doi.org/10.1063/1.4907589}} @article{Troyer_2005, author = {M. Troyer and U.-J. Wiese}, @@ -12347,7 +12348,7 @@ url = {http://dx.doi.org/10.1063/1.4955109}, volume = {145}, year = {2016}, - Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.4955109}} + bdsk-url-1 = {http://dx.doi.org/10.1063/1.4955109}} @article{Tuna_2015, author = {Tuna, Deniz and Lefrancois, Daniel and Wola\'nski, \L{}ukasz and Gozem, Samer and Schapiro, Igor and Andruni\'ow, Tadeusz and Dreuw, Andreas and Olivucci, Massimo}, @@ -12363,7 +12364,7 @@ title = {Assessment of {{Approximate Coupled}}-{{Cluster}} and {{Algebraic}}-{{Diagrammatic}}-{{Construction Methods}} for {{Ground}}- and {{Excited}}-{{State Reaction Paths}} and the {{Conical}}-{{Intersection Seam}} of a {{Retinal}}-{{Chromophore Model}}}, volume = {11}, year = {2015}, - Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.5b00022}} + bdsk-url-1 = {https://doi.org/10.1021/acs.jctc.5b00022}} @book{UllrichBook, address = {New York}, @@ -12401,8 +12402,8 @@ url = {http://dx.doi.org/10.1103/PhysRevLett.94.150201}, volume = {94}, year = {2005}, - Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevLett.94.150201}, - Bdsk-Url-2 = {http://dx.doi.org/10.1103/physrevlett.94.150201}} + bdsk-url-1 = {http://dx.doi.org/10.1103/PhysRevLett.94.150201}, + bdsk-url-2 = {http://dx.doi.org/10.1103/physrevlett.94.150201}} @article{Umrigar_2007, author = {Umrigar, C. J. and Toulouse, Julien and Filippi, Claudia and Sorella, S. and Hennig, R. G.}, @@ -12419,8 +12420,8 @@ url = {http://dx.doi.org/10.1103/PhysRevLett.98.110201}, volume = {98}, year = {2007}, - Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevLett.98.110201}, - Bdsk-Url-2 = {http://dx.doi.org/10.1103/physrevlett.98.110201}} + bdsk-url-1 = {http://dx.doi.org/10.1103/PhysRevLett.98.110201}, + bdsk-url-2 = {http://dx.doi.org/10.1103/physrevlett.98.110201}} @article{Valone_1980, author = {Valone, Steven M.}, @@ -12437,7 +12438,7 @@ title = {A One-to-one Mapping between One-particle Densities and Some {\emph{n}} -particle Ensembles}, volume = {73}, year = {1980}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.440656}} + bdsk-url-1 = {https://doi.org/10.1063/1.440656}} @article{VanderLugt_1969, author = {{Van der Lugt}, W. Th. A. M. and Oosterhoff, Luitzen J.}, @@ -12453,7 +12454,7 @@ title = {Symmetry Control and Photoinduced Reactions}, volume = {91}, year = {1969}, - Bdsk-Url-1 = {https://doi.org/10.1021/ja01050a019}} + bdsk-url-1 = {https://doi.org/10.1021/ja01050a019}} @article{vanFaassen_2002, author = {{van Faassen}, M. and {de Boeij}, P. L. and {van Leeuwen}, R. and Berger, J. A. and Snijders, J. G.}, @@ -12469,7 +12470,7 @@ title = {Ultranonlocality in {{Time}}-{{Dependent Current}}-{{Density}}-{{Functional Theory}}: {{Application}} to {{Conjugated Polymers}}}, volume = {88}, year = {2002}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevLett.88.186401}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRevLett.88.186401}} @article{Vanzini_2018, abstract = {The spectral potential is the dynamical generalization of the Kohn\textendash{}Sham potential. It targets, in principle exactly, the spectral function in addition to the electronic density. Here we examine the spectral potential in one of the simplest solvable models exhibiting a non-trivial interplay between electron-electron interaction and inhomogeneity, namely the asymmetric Hubbard dimer. We discuss a general strategy to introduce approximations, which consists in calculating the spectral potential in the homogeneous limit (here represented by the symmetric Hubbard dimer) and importing it in the real inhomogeneous system through a suitable ``connector''. The comparison of different levels of approximation to the spectral potential with the exact solution of the asymmetric Hubbard dimer gives insights about the advantages and the difficulties of this connector strategy for applications in real materials.}, @@ -12487,7 +12488,7 @@ title = {Spectroscopy of the {{Hubbard}} Dimer: The Spectral Potential}, volume = {91}, year = {2018}, - Bdsk-Url-1 = {https://doi.org/10.1140/epjb/e2018-90277-3}} + bdsk-url-1 = {https://doi.org/10.1140/epjb/e2018-90277-3}} @article{Varandas_2008, author = {Varandas, A. J. C.}, @@ -12504,7 +12505,7 @@ title = {Extrapolation to the Complete-Basis-Set Limit and the Implications of Avoided Crossings: {{The X $\Sigma$1g}}+, {{B $\Delta$1g}}, and {{B}}${'}$ {{$\Sigma$1g}}+ States of {{C2}}}, volume = {129}, year = {2008}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.3036115}} + bdsk-url-1 = {https://doi.org/10.1063/1.3036115}} @article{Vosko_1980, author = {Vosko, S. H. and Wilk, L. and Nusair, M.}, @@ -12516,7 +12517,7 @@ title = {Accurate Spin-Dependent Electron Liquid Correlation Energies for Local Spin Density Calculations: A Critical Analysis}, volume = {58}, year = {1980}, - Bdsk-Url-1 = {https://dx.doi.org/10.1139/p80-159}} + bdsk-url-1 = {https://dx.doi.org/10.1139/p80-159}} @article{Vuckovic_2016, abstract = {The construction of density-functional approximations is explored by modeling the adiabatic connection locally, using energy densities defined in terms of the electrostatic potential of the exchange-correlation hole. These local models are more amenable to the construction of size-consistent approximations than their global counterparts. In this work we use accurate input local ingredients to assess the accuracy of a range of local interpolation models against accurate exchange-correlation energy densities. The importance of the strictly correlated electrons (SCE) functional describing the strong coupling limit is emphasized, enabling the corresponding interpolated functionals to treat strong correlation effects. In addition to exploring the performance of such models numerically for the helium and beryllium isoelectronic series and the dissociation of the hydrogen molecule, an approximate analytic model is presented for the initial slope of the local adiabatic connection. Comparisons are made with approaches based on global models, and prospects for future approximations based on the local adiabatic connection are discussed.}, @@ -12534,7 +12535,7 @@ title = {Exchange\textendash{{Correlation Functionals}} via {{Local Interpolation}} along the {{Adiabatic Connection}}}, volume = {12}, year = {2016}, - Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.6b00177}} + bdsk-url-1 = {https://doi.org/10.1021/acs.jctc.6b00177}} @article{Vuckovic_2017, abstract = {From a simplified version of the mathematical structure of the strong coupling limit of the exact exchange-correlation functional, we construct an approximation for the electronic repulsion energy at physical coupling strength, which is fully nonlocal. This functional is self-interaction free and yields energy densities within the definition of the electrostatic potential of the exchange-correlation hole that are locally accurate and have the correct asymptotic behavior. The model is able to capture strong correlation effects that arise from chemical bond dissociation, without relying on error cancellation. These features, which are usually missed by standard density functional theory (DFT) functionals, are captured by the highly nonlocal structure, which goes beyond the ``Jacob's ladder'' framework for functional construction, by using integrals of the density as the key ingredient. Possible routes for obtaining the full exchange-correlation functional by recovering the missing kinetic component of the correlation energy are also implemented and discussed.}, @@ -12552,7 +12553,7 @@ title = {Simple {{Fully Nonlocal Density Functionals}} for {{Electronic Repulsion Energy}}}, volume = {8}, year = {2017}, - Bdsk-Url-1 = {https://doi.org/10.1021/acs.jpclett.7b01113}} + bdsk-url-1 = {https://doi.org/10.1021/acs.jpclett.7b01113}} @article{Vuckovic_2017a, author = {Vuckovic, Stefan and Levy, Mel and {Gori-Giorgi}, Paola}, @@ -12569,7 +12570,7 @@ title = {Augmented Potential, Energy Densities, and Virial Relations in the Weak- and Strong-Interaction Limits of {{DFT}}}, volume = {147}, year = {2017}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.4997311}} + bdsk-url-1 = {https://doi.org/10.1063/1.4997311}} @article{Vuckovic_2018, abstract = {Approximate exchange-correlation functionals built by modeling in a nonlinear way the adiabatic connection (AC) integrand of density functional theory have many attractive features, being virtually parameter-free and satisfying different exact properties, but they also have a fundamental flaw: they violate the size-consistency condition, crucial to evaluate interaction energies of molecular systems. We show that size consistency in the AC-based functionals can be restored in a very simple way at no extra computational cost. Results on a large set of benchmark molecular interaction energies show that functionals based on the interaction strength interpolation approximations are significantly more accurate than second-order perturbation theory.}, @@ -12587,7 +12588,7 @@ title = {Restoring {{Size Consistency}} of {{Approximate Functionals Constructed}} from the {{Adiabatic Connection}}}, volume = {9}, year = {2018}, - Bdsk-Url-1 = {https://doi.org/10.1021/acs.jpclett.8b01054}} + bdsk-url-1 = {https://doi.org/10.1021/acs.jpclett.8b01054}} @article{Wagner_2003, author = {Wagner, Lucas and Mit\'a\v{s}, Lubos}, @@ -12604,8 +12605,8 @@ url = {http://dx.doi.org/10.1016/S0009-2614(03)00128-3}, volume = {370}, year = {2003}, - Bdsk-Url-1 = {http://dx.doi.org/10.1016/S0009-2614(03)00128-3}, - Bdsk-Url-2 = {http://dx.doi.org/10.1016/s0009-2614(03)00128-3}} + bdsk-url-1 = {http://dx.doi.org/10.1016/S0009-2614(03)00128-3}, + bdsk-url-2 = {http://dx.doi.org/10.1016/s0009-2614(03)00128-3}} @article{Wagner_2007, author = {Wagner, Lucas K. and Mit\'a\v{s}, Lubos}, @@ -12622,7 +12623,7 @@ url = {http://dx.doi.org/10.1063/1.2428294}, volume = {126}, year = {2007}, - Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.2428294}} + bdsk-url-1 = {http://dx.doi.org/10.1063/1.2428294}} @article{Wagner_2013, author = {Wagner, Lucas K.}, @@ -12639,7 +12640,7 @@ url = {http://dx.doi.org/10.1002/qua.24526}, volume = {114}, year = {2013}, - Bdsk-Url-1 = {http://dx.doi.org/10.1002/qua.24526}} + bdsk-url-1 = {http://dx.doi.org/10.1002/qua.24526}} @article{Wang_2004, author = {Wang, Fan and Ziegler, Tom}, @@ -12654,7 +12655,7 @@ title = {Time-Dependent Density Functional Theory Based on a Noncollinear Formulation of the Exchange-Correlation Potential}, volume = {121}, year = {2004}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.1821494}} + bdsk-url-1 = {https://doi.org/10.1063/1.1821494}} @article{Wang_2006, author = {Wang, Fan and Ziegler, Tom}, @@ -12669,7 +12670,7 @@ title = {Use of Noncollinear Exchange-Correlation Potentials in Multiplet Resolutions by Time-Dependent Density Functional Theory}, volume = {106}, year = {2006}, - Bdsk-Url-1 = {https://doi.org/10.1002/qua.21050}} + bdsk-url-1 = {https://doi.org/10.1002/qua.21050}} @article{Wang_2011, author = {Wang, Li and Huang, Dao-ling and Zhen, Jun-feng and Zhang, Qun and Chen, Yang}, @@ -12686,7 +12687,7 @@ url = {http://dx.doi.org/10.1088/1674-0068/24/01/1-3}, volume = {24}, year = {2011}, - Bdsk-Url-1 = {http://dx.doi.org/10.1088/1674-0068/24/01/1-3}} + bdsk-url-1 = {http://dx.doi.org/10.1088/1674-0068/24/01/1-3}} @article{Wanko_2005, author = {Wanko, M. and Hoffmann, M. and Strodel, P. and Koslowski, A. and Thiel, W. and Neese, F. and Frauenheim, T. and Elstner, M.}, @@ -12703,7 +12704,7 @@ title = {Calculating {{Absorption Shifts}} for {{Retinal Proteins}}: {{Computational Challenges}}}, volume = {109}, year = {2005}, - Bdsk-Url-1 = {https://doi.org/10.1021/jp0463060}} + bdsk-url-1 = {https://doi.org/10.1021/jp0463060}} @article{Watson_2012, author = {Watson, Mark A. and Chan, Garnet Kin-Lic}, @@ -12716,7 +12717,7 @@ title = {Excited States of Butadiene to Chemical Accuracy: Reconciling Theory and Experiment}, volume = {8}, year = {2012}, - Bdsk-Url-1 = {http://dx.doi.org/10.1021/ct300591z}} + bdsk-url-1 = {http://dx.doi.org/10.1021/ct300591z}} @article{Watts_1996, author = {Watts, John D. and Gwaltney, Steven R. and Bartlett, Rodney J.}, @@ -12732,7 +12733,7 @@ title = {Coupled-cluster Calculations of the Excitation Energies of Ethylene, Butadiene, and Cyclopentadiene}, volume = {105}, year = {1996}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.471988}} + bdsk-url-1 = {https://doi.org/10.1063/1.471988}} @article{Weber_1999, author = {Weber, Peter and Reimers, Jeffrey R.}, @@ -12748,7 +12749,7 @@ title = {Ab {{Initio}} and {{Density Functional Calculations}} of the {{Energies}} of the {{Singlet}} and {{Triplet Valence Excited States}} of {{Pyrazine}}}, volume = {103}, year = {1999}, - Bdsk-Url-1 = {https://doi.org/10.1021/jp991403s}} + bdsk-url-1 = {https://doi.org/10.1021/jp991403s}} @article{Whitten_1969, author = {Whitten, J. L. and Hackmeyer, Melvyn}, @@ -12765,7 +12766,7 @@ url = {http://dx.doi.org/10.1063/1.1671985}, volume = {51}, year = {1969}, - Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.1671985}} + bdsk-url-1 = {http://dx.doi.org/10.1063/1.1671985}} @article{Wiberg_1998, author = {Wiberg, K. B. and Stratmann, R. E. and Frisch, M. J.}, @@ -12801,7 +12802,7 @@ title = {A Theoretical Study of the Excited States of the Nitroxyl Radical ({{HNO}}) via the Equations of Motion Method}, volume = {30}, year = {1975}, - Bdsk-Url-1 = {https://doi.org/10.1016/0009-2614(75)80039-X}} + bdsk-url-1 = {https://doi.org/10.1016/0009-2614(75)80039-X}} @article{Williamson_2002, author = {Williamson, Andrew J. and Grossman, Jeffrey C. and Hood, Randolph Q. and Puzder, Aaron and Galli, Giulia}, @@ -12819,7 +12820,7 @@ title = {Quantum {{Monte Carlo Calculations}} of {{Nanostructure Optical Gaps}}: {{Application}} to {{Silicon Quantum Dots}}}, volume = {89}, year = {2002}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevLett.89.196803}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRevLett.89.196803}} @article{Williamson_2002a, author = {Williamson, Andrew J. and Grossman, Jeffrey C. and Hood, Randolph Q. and Puzder, Aaron and Galli, Giulia}, @@ -12837,7 +12838,7 @@ title = {Quantum {{Monte Carlo Calculations}} of {{Nanostructure Optical Gaps}}: {{Application}} to {{Silicon Quantum Dots}}}, volume = {89}, year = {2002}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevLett.89.196803}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRevLett.89.196803}} @article{Witek_2003, author = {Witek, Henryk A. and Nakano, Haruyuki and Hirao, Kimihiko}, @@ -12853,7 +12854,7 @@ title = {Multireference Perturbation Theory with Optimized Partitioning. {{II}}. {{Applications}} to Molecular Systems}, volume = {24}, year = {2003}, - Bdsk-Url-1 = {https://doi.org/10.1002/jcc.10311}} + bdsk-url-1 = {https://doi.org/10.1002/jcc.10311}} @article{Woodcock_2002, author = {Woodcock, H. Lee and Schaefer, Henry F. and Schreiner, Peter R.}, @@ -12871,7 +12872,7 @@ title = {Problematic {{Energy Differences}} between {{Cumulenes}} and {{Poly}}-Ynes: {{Does This Point}} to a {{Systematic Improvement}} of {{Density Functional Theory}}?}, volume = {106}, year = {2002}, - Bdsk-Url-1 = {https://doi.org/10.1021/jp0212895}} + bdsk-url-1 = {https://doi.org/10.1021/jp0212895}} @article{Wouters_2014, author = {Wouters, Sebastian and Poelmans, Ward and Ayers, Paul W. and Van Neck, Dimitri}, @@ -12888,7 +12889,7 @@ title = {{{CheMPS2}}: {{A}} Free Open-Source Spin-Adapted Implementation of the Density Matrix Renormalization Group for Ab Initio Quantum Chemistry}, volume = {185}, year = {2014}, - Bdsk-Url-1 = {https://doi.org/10.1016/j.cpc.2014.01.019}} + bdsk-url-1 = {https://doi.org/10.1016/j.cpc.2014.01.019}} @article{Wu_2007, author = {Wu, Z. J. and Wang, M. Y. and Su, Z. M.}, @@ -12905,7 +12906,7 @@ url = {http://dx.doi.org/10.1002/jcc.20603}, volume = {28}, year = {2007}, - Bdsk-Url-1 = {http://dx.doi.org/10.1002/jcc.20603}} + bdsk-url-1 = {http://dx.doi.org/10.1002/jcc.20603}} @article{Xiao_2016, author = {Xiao, Suo and Li, Xiaopeng and Sun, Weiwei and Guan, Baoqin and Wang, Yong}, @@ -12921,7 +12922,7 @@ url = {http://dx.doi.org/10.1016/j.cej.2016.05.068}, volume = {306}, year = {2016}, - Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.cej.2016.05.068}} + bdsk-url-1 = {http://dx.doi.org/10.1016/j.cej.2016.05.068}} @article{Xu_2013, abstract = {We present a new approach to calculating potential energy surfaces for photochemical reactions by combining self-consistent-field calculations for single-reference ground and excited states with symmetrycorrected spin-flip Tamm-Dancoff approximation calculations for multireference electronic states. The method is illustrated by an application with the M05-2X exchange-correlation functional to cis-trans isomerization of the penta-2,4-dieniminium cation, which is a model (with three conjugated double bonds) of the protonated Schiff base of retinal. We find good agreement with multireference configuration interaction-plus-quadruples (MRCISD+Q) wave function calculations along three key paths in the strong-interaction region of the ground and first excited singlet states.}, @@ -12939,7 +12940,7 @@ title = {Combined {{Self}}-{{Consistent}}-{{Field}} and {{Spin}}-{{Flip Tamm}}\textendash{{Dancoff Density Functional Approach}} to {{Potential Energy Surfaces}} for {{Photochemistry}}}, volume = {4}, year = {2013}, - Bdsk-Url-1 = {https://doi.org/10.1021/jz301935x}} + bdsk-url-1 = {https://doi.org/10.1021/jz301935x}} @article{Yanai_2004, author = {Yanai, Takeshi and Tew, David P and Handy, Nicholas C}, @@ -12955,7 +12956,7 @@ title = {A New Hybrid Exchange\textendash{}Correlation Functional Using the {{Coulomb}}-Attenuating Method ({{CAM}}-{{B3LYP}})}, volume = {393}, year = {2004}, - Bdsk-Url-1 = {https://doi.org/10.1016/j.cplett.2004.06.011}} + bdsk-url-1 = {https://doi.org/10.1016/j.cplett.2004.06.011}} @article{Yang_2013a, author = {Yang, Weitao and {Mori-S\'anchez}, Paula and Cohen, Aron J.}, @@ -12972,7 +12973,7 @@ title = {Extension of Many-Body Theory and Approximate Density Functionals to Fractional Charges and Fractional Spins}, volume = {139}, year = {2013}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.4817183}} + bdsk-url-1 = {https://doi.org/10.1063/1.4817183}} @article{Yang_2014, author = {Yang, Zeng-Hui and Trail, John R. and {Pribram-Jones}, Aurora and Burke, Kieron and Needs, Richard J. and Ullrich, Carsten A.}, @@ -12989,7 +12990,7 @@ title = {Exact and Approximate {{Kohn}}-{{Sham}} Potentials in Ensemble Density-Functional Theory}, volume = {90}, year = {2014}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevA.90.042501}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRevA.90.042501}} @article{Yang_2017, author = {Yang, Zeng-Hui and {Pribram-Jones}, Aurora and Burke, Kieron and Ullrich, Carsten A.}, @@ -13006,7 +13007,7 @@ title = {Direct {{Extraction}} of {{Excitation Energies}} from {{Ensemble Density}}-{{Functional Theory}}}, volume = {119}, year = {2017}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevLett.119.033003}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRevLett.119.033003}} @article{Zhang_1996, author = {Zhang, Nan and Hayase, Takasuke and Kawamata, Hiroshi and Nakao, Kojiro and Nakajima, Atsushi and Kaya, Koji}, @@ -13023,7 +13024,7 @@ url = {http://dx.doi.org/10.1063/1.471048}, volume = {104}, year = {1996}, - Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.471048}} + bdsk-url-1 = {http://dx.doi.org/10.1063/1.471048}} @article{Zhao_2011, author = {Zhao, Yan and Loos, Pierre-Fran{\c c}ois and Gill, Peter M. W.}, @@ -13039,7 +13040,7 @@ title = {Correlation Energy of Anisotropic Quantum Dots}, volume = {84}, year = {2011}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevA.84.032513}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRevA.84.032513}} @article{Zhao_2016, author = {Zhao, Luning and Neuscamman, Eric}, @@ -13055,7 +13056,7 @@ title = {Equation of {{Motion Theory}} for {{Excited States}} in {{Variational Monte Carlo}} and the {{Jastrow Antisymmetric Geminal Power}} in {{Hilbert Space}}}, volume = {12}, year = {2016}, - Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.6b00480}} + bdsk-url-1 = {https://doi.org/10.1021/acs.jctc.6b00480}} @article{Zhou_2017, author = {Zhou, Xiaojun and Wang, Fan}, @@ -13071,7 +13072,7 @@ url = {http://dx.doi.org/10.1002/jcc.24750}, volume = {38}, year = {2017}, - Bdsk-Url-1 = {http://dx.doi.org/10.1002/jcc.24750}} + bdsk-url-1 = {http://dx.doi.org/10.1002/jcc.24750}} @article{Zimmerman_2009, author = {Zimmerman, Paul M. and Toulouse, Julien and Zhang, Zhiyong and Musgrave, Charles B. and Umrigar, C. J.}, @@ -13088,7 +13089,7 @@ title = {Excited States of Methylene from Quantum {{Monte Carlo}}}, volume = {131}, year = {2009}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.3220671}} + bdsk-url-1 = {https://doi.org/10.1063/1.3220671}} @article{Zimmerman_2011, author = {Zimmerman, Paul M. and Bell, Franziska and Casanova, David and {Head-Gordon}, Martin}, @@ -13105,7 +13106,7 @@ title = {Mechanism for {{Singlet Fission}} in {{Pentacene}} and {{Tetracene}}: {{From Single Exciton}} to {{Two Triplets}}}, volume = {133}, year = {2011}, - Bdsk-Url-1 = {https://doi.org/10.1021/ja208431r}} + bdsk-url-1 = {https://doi.org/10.1021/ja208431r}} @article{Zimmerman_2013, author = {Zimmerman, Paul M. and Musgrave, Charles B. and {Head-Gordon}, Martin}, @@ -13121,7 +13122,7 @@ title = {A {{Correlated Electron View}} of {{Singlet Fission}}}, volume = {46}, year = {2013}, - Bdsk-Url-1 = {https://doi.org/10.1021/ar3001734}} + bdsk-url-1 = {https://doi.org/10.1021/ar3001734}} @article{Zimmerman_2017, author = {Zimmerman, Paul M.}, @@ -13138,7 +13139,7 @@ url = {http://dx.doi.org/10.1063/1.4977727}, volume = {146}, year = {2017}, - Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.4977727}} + bdsk-url-1 = {http://dx.doi.org/10.1063/1.4977727}} @article{Zulfikri_2016, author = {Zulfikri, Habiburrahman and Amovilli, Claudio and Filippi, Claudia}, @@ -13154,7 +13155,7 @@ title = {Multiple-{{Resonance Local Wave Functions}} for {{Accurate Excited States}} in {{Quantum Monte Carlo}}}, volume = {12}, year = {2016}, - Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.5b01077}} + bdsk-url-1 = {https://doi.org/10.1021/acs.jctc.5b01077}} @article{Tozer_1998, author = {Tozer, David J. and Handy, Nicholas C.}, @@ -13171,7 +13172,7 @@ title = {Improving Virtual {{Kohn}}\textendash{{Sham}} Orbitals and Eigenvalues: {{Application}} to Excitation Energies and Static Polarizabilities}, volume = {109}, year = {1998}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.477711}} + bdsk-url-1 = {https://doi.org/10.1063/1.477711}} @article{Tozer_1999, author = {Tozer, David J. and Amos, Roger D. and Handy, Nicholas C. and Roos, Bjorn O. and {Serrano-Andres}, Luis}, @@ -13187,7 +13188,7 @@ title = {Does Density Functional Theory Contribute to the Understanding of Excited States of Unsaturated Organic Compounds?}, volume = {97}, year = {1999}, - Bdsk-Url-1 = {https://doi.org/10.1080/00268979909482888}} + bdsk-url-1 = {https://doi.org/10.1080/00268979909482888}} @article{Tozer_2000, author = {Tozer, David J. and Handy, Nicholas C.}, @@ -13199,7 +13200,7 @@ title = {On the Determination of Excitation Energies Using Density Functional Theory}, volume = {2}, year = {2000}, - Bdsk-Url-1 = {https://doi.org/10.1039/a910321j}} + bdsk-url-1 = {https://doi.org/10.1039/a910321j}} @article{Tozer_2003, author = {Tozer, David J.}, @@ -13215,7 +13216,7 @@ title = {Relationship between Long-Range Charge-Transfer Excitation Energy Error and Integer Discontinuity in {{Kohn}}\textendash{{Sham}} Theory}, volume = {119}, year = {2003}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.1633756}} + bdsk-url-1 = {https://doi.org/10.1063/1.1633756}} @article{Levine_2006, author = {Levine, Benjamin G. and Ko, Chaehyuk and Quenneville, Jason and Martinez, Todd J.}, @@ -13228,7 +13229,7 @@ title = {Conical Intersections and Double Excitations in Time-Dependent Density Functional Theory}, volume = {104}, year = {2006}, - Bdsk-Url-1 = {https://doi.org/10.1080/00268970500417762}} + bdsk-url-1 = {https://doi.org/10.1080/00268970500417762}} @article{Kohn_1965, author = {W. Kohn and L. J. Sham}, @@ -13240,7 +13241,7 @@ title = {Self-Consistent Equations Including Exchange and Correlation Effects}, volume = {140}, year = {1965}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRev.140.A1133}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRev.140.A1133}} @article{Angeli_2001, author = {Angeli, C. and Cimiraglia, R. and Evangelisti, S. and Leininger, T. and Malrieu, J.-P.}, @@ -13256,7 +13257,7 @@ title = {Introduction of {\emph{n}} -Electron Valence States for Multireference Perturbation Theory}, volume = {114}, year = {2001}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.1361246}} + bdsk-url-1 = {https://doi.org/10.1063/1.1361246}} @inbook{Roos_1996, author = {Roos, B. O. and Andersson, K. and Fulscher, M. P. and Malmqvist, P.-A. and {Serrano-Andr\'es}, L.}, @@ -13281,7 +13282,7 @@ title = {Second-Order Perturbation Theory With a CASSCF Reference Function}, volume = {94}, year = {1990}, - Bdsk-Url-1 = {http://dx.doi.org/10.1021/j100377a012}} + bdsk-url-1 = {http://dx.doi.org/10.1021/j100377a012}} @article{Andersson_1992, author = {Andersson, Kerstin and Malmqvist, Per-Ake and Roos, Bj{\"o}rn O.}, @@ -13294,8 +13295,8 @@ title = {Second-Order Perturbation Theory With a Complete Active Space Self-Consistent Field Reference Function}, volume = {96}, year = {1992}, - Bdsk-Url-1 = {http://scitation.aip.org/content/aip/journal/jcp/96/2/10.1063/1.462209}, - Bdsk-Url-2 = {http://dx.doi.org/10.1063/1.462209}} + bdsk-url-1 = {http://scitation.aip.org/content/aip/journal/jcp/96/2/10.1063/1.462209}, + bdsk-url-2 = {http://dx.doi.org/10.1063/1.462209}} @article{Roca-Sanjuan_2006, author = {Daniel {Roca-Sanjuan} and Mercedes Rubio and Manuela Merchan and Luis {Serrano-Andres}}, @@ -13307,7 +13308,7 @@ title = {Ab Initio Determination of The Ionization Potentials of {{DNA}} And {{RNA}} Nucleobases}, volume = {125}, year = {2006}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.2336217}} + bdsk-url-1 = {https://doi.org/10.1063/1.2336217}} @article{Govoni_2018, author = {Marco Govoni and Giulia Galli}, @@ -13319,7 +13320,7 @@ title = {GW100: Comparison of Methods and Accuracy of Results Obtained with the WEST Code}, volume = {14}, year = {2018}, - Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.7b00952}} + bdsk-url-1 = {https://doi.org/10.1021/acs.jctc.7b00952}} @article{Adler_2007, author = {T. B. Adler and G. Knizia and H.-J. Werner}, @@ -13342,7 +13343,7 @@ title = {Understanding and Reducing Errors in Density Functional Calculations}, volume = {111}, year = {2013}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevLett.111.073003}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRevLett.111.073003}} @article{Tew_2007, author = {D. P. Tew and W. Klopper and C. Neiss and C. Hattig}, @@ -13354,7 +13355,7 @@ title = {Quintuple-{{$\zeta$}} Quality Coupled-Cluster Correlation Energies With Triple-{{$\zeta$}} Basis Sets}, volume = {9}, year = {2007}, - Bdsk-Url-1 = {https://doi.org/10.1039/b617230j}} + bdsk-url-1 = {https://doi.org/10.1039/b617230j}} @article{GinTewGarAla-JCTC-18, author = {Giner, Emmanuel and Tew, David P. and Garniron, Yann and Alavi, Ali}, @@ -13370,7 +13371,7 @@ url = {https://doi.org/10.1021/acs.jctc.8b00591}, volume = {14}, year = {2018}, - Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.8b00591}} + bdsk-url-1 = {https://doi.org/10.1021/acs.jctc.8b00591}} @article{Hattig_2012, author = {C. Hattig and W. Klopper and A. Kohn and D. P. Tew}, @@ -13382,7 +13383,7 @@ title = {Explicitly Correlated Electrons in Molecules}, volume = {112}, year = {2012}, - Bdsk-Url-1 = {https://doi.org/10.1021/cr200168z}} + bdsk-url-1 = {https://doi.org/10.1021/cr200168z}} @article{Kesharwani_2018, author = {M. K. Kesharwani and N. Sylvetsky and A. Kohn and D. P. Tew and Jan M. L. Martin}, @@ -13394,7 +13395,7 @@ title = {Do CCSD And Approximate CCSD-F12 Variants Converge To The Same Basis Set Limits? The Case Of Atomization Energies And Approximate Ccsd-F12 Variants Converge To The Same Basis Set Limits? The Case Of Atomization Energies}, volume = {149}, year = {2018}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.5048665}} + bdsk-url-1 = {https://doi.org/10.1063/1.5048665}} @article{BooCleAlaTew-JCP-2012, author = {G. H. Booth and D. Cleland and A. Alavi and D. P. Tew}, @@ -13406,7 +13407,7 @@ title = {An Explicitly Correlated Approach To Basis Set Incompleteness In Full Configuration Interaction Quantum Monte Carlo}, volume = {137}, year = {2012}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.4762445}} + bdsk-url-1 = {https://doi.org/10.1063/1.4762445}} @article{Tew08, author = {D. P. Tew}, @@ -13428,7 +13429,7 @@ title = {Perspective: Explicitly Correlated Electronic Structure Theory For Complex Systems}, volume = {146}, year = {2017}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.4976974}} + bdsk-url-1 = {https://doi.org/10.1063/1.4976974}} @article{Tenno_2012b, author = {S. Ten-no}, @@ -13553,7 +13554,7 @@ title = {Range-Separated Multideterminant Density-Functional Theory With A Short-Range Correlation Functional Of The On-Top Pair Density}, volume = {150}, year = {2019}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.5082638}} + bdsk-url-1 = {https://doi.org/10.1063/1.5082638}} @article{Lieb_1983, author = {E. H. Lieb}, @@ -13605,7 +13606,7 @@ title = {Hybrid and Constrained Resolution-of-Identity Techniques for Coulomb Integrals}, volume = {13}, year = {2017}, - Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.6b01215}} + bdsk-url-1 = {https://doi.org/10.1021/acs.jctc.6b01215}} @article{Rojas_1995, author = {H. N. Rojas and R. W. Godby and R. J. Needs}, @@ -13617,7 +13618,7 @@ title = {Space-Time Method for Ab Initio Calculations of Self-Energies and Dielectric Response Functions of Solids}, volume = {74}, year = {1995}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevLett.74.1827}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRevLett.74.1827}} @article{Weigend_2003a, author = {Weigend, Florian and Furche, Filipp and Ahlrichs, Reinhart}, @@ -13629,7 +13630,7 @@ title = {Gaussian basis sets of quadruple zeta valence quality for atoms H-Kr}, volume = {119}, year = {2003}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.1627293}} + bdsk-url-1 = {https://doi.org/10.1063/1.1627293}} @article{Weigend_2005a, author = {Weigend, Florian and Ahlrichs, Reinhart}, @@ -13641,7 +13642,7 @@ title = {Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: Design and assessment of accuracy}, volume = {7}, year = {2005}, - Bdsk-Url-1 = {https://doi.org/10.1039/b508541a}} + bdsk-url-1 = {https://doi.org/10.1039/b508541a}} @article{Jacquemin_2016, author = {D. Jacquemin and I. Duchemin and X. Blase}, @@ -13653,7 +13654,7 @@ title = {Assessment Of The Convergence Of Partially Self-Consistent {{BSE/GW}} Calculations}, volume = {114}, year = {2016}, - Bdsk-Url-1 = {https://doi.org/10.1080/00268976.2015.1119901}} + bdsk-url-1 = {https://doi.org/10.1080/00268976.2015.1119901}} @article{Marini_2009, author = {Andrea Marini and Conor Hogan and Myrta Gruning and Daniele Varsano}, @@ -13665,7 +13666,7 @@ title = {Yambo: An Ab Initio Tool For Excited State Calculations}, volume = {180}, year = {2009}, - Bdsk-Url-1 = {https://doi.org/10.1016/j.cpc.2009.02.003}} + bdsk-url-1 = {https://doi.org/10.1016/j.cpc.2009.02.003}} @article{Deslippe_2012, author = {Jack Deslippe and Georgy Samsonidze and David A. Strubbe and Manish Jain and Marvin L. Cohen and Steven G. Louie}, @@ -13677,7 +13678,7 @@ title = {BerkeleyGW: A Massively Parallel Computer Package for the Calculation of the Quasiparticle and Optical Properties of Materials and Nanostructures}, volume = {183}, year = {2012}, - Bdsk-Url-1 = {https://doi.org/10.1016/j.cpc.2011.12.006}} + bdsk-url-1 = {https://doi.org/10.1016/j.cpc.2011.12.006}} @article{Lewis_2019a, author = {Alan M. Lewis and Timothy C. Berkelbach}, @@ -13689,7 +13690,7 @@ title = {Vertex Corrections to the Polarizability Do Not Improve the GW Approximation for the Ionization Potential of Molecules}, volume = {15}, year = {2019}, - Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.8b00995}} + bdsk-url-1 = {https://doi.org/10.1021/acs.jctc.8b00995}} @article{Krause_2015, author = {K. Krause and M. E. Harding and W. Klopper}, @@ -13712,7 +13713,7 @@ title = {Explicitly Correlated Renormalized Second-Order Green's Function For Accurate Ionization Potentials Of Closed-Shell Molecules}, volume = {150}, year = {2019}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.5090983}} + bdsk-url-1 = {https://doi.org/10.1063/1.5090983}} @article{Johnson_2018, author = {C. M. Johnson and A. E. Doran and S. L. Ten-no and S. Hirata}, @@ -13724,7 +13725,7 @@ title = {Monte Carlo Explicitly Correlated Many-Body Green's Function Theory}, volume = {149}, year = {2018}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.5054610}} + bdsk-url-1 = {https://doi.org/10.1063/1.5054610}} @article{Lee_2018a, author = {J. Lee and M. Head-Gordon}, @@ -13735,7 +13736,7 @@ 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}} + 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}}, @@ -13747,7 +13748,7 @@ 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}} + bdsk-url-1 = {https://doi.org/10.1016/0009-2614(86)80461-4}} @article{Li_2014, author = {Li, Zhendong and Suo, Bingbing and Liu, Wenjian}, @@ -13765,7 +13766,7 @@ 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}} + 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.}, @@ -13782,7 +13783,7 @@ 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}} + bdsk-url-1 = {https://doi.org/10.1063/1.4906941}} @article{Zhang_2015, author = {Zhang, Xing and Herbert, John M.}, @@ -13800,7 +13801,7 @@ 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}} + bdsk-url-1 = {https://doi.org/10.1063/1.4907376}} @article{DiSabatino_2015, author = {Di Sabatino,S. and Berger,J. A. and Reining,L. and Romaniello,P.}, @@ -13811,7 +13812,7 @@ title = {Reduced density-matrix functional theory: Correlation and spectroscopy}, volume = {143}, year = {2015}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.4926327}} + bdsk-url-1 = {https://doi.org/10.1063/1.4926327}} @article{Langre_2018, author = {M. F. Lange and T. C. Berkelbach}, @@ -13837,7 +13838,7 @@ title = {Unphysical Divergences in Response Theory}, volume = {145}, year = {2016}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.4963749}} + bdsk-url-1 = {https://doi.org/10.1063/1.4963749}} @article{Becke_1993a, author = {A. D. Becke}, @@ -13849,7 +13850,7 @@ title = {Density-Functional Thermochemistry. III. The Role of Exact Exchange}, volume = {98}, year = {1993}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.464913}} + bdsk-url-1 = {https://doi.org/10.1063/1.464913}} @article{Perdew_1996, author = {J. P. Perdew and K. Burke and M. Ernzerhof}, @@ -13861,7 +13862,7 @@ title = {Generalized Gradient Approximation Made Simple}, volume = {77}, year = {1996}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevLett.77.3865}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRevLett.77.3865}} @article{Gill_1994, author = {P. M. W. Gill}, @@ -13873,7 +13874,7 @@ title = {Molecular Integrals Over Gaussian Basis Functions}, volume = {25}, year = {1994}, - Bdsk-Url-1 = {https://doi.org/10.1016/S0065-3276(08)60019-2}} + bdsk-url-1 = {https://doi.org/10.1016/S0065-3276(08)60019-2}} @article{Pavlyukh_2017, author = {Y. Pavlyukh}, @@ -13885,7 +13886,7 @@ title = {Pade resummation of many-body perturbation theory}, volume = {7}, year = {2017}, - Bdsk-Url-1 = {https://doi.org/10.1038/s41598-017-00355-w}} + bdsk-url-1 = {https://doi.org/10.1038/s41598-017-00355-w}} @book{HerzbergBook, author = {K. P. Huber and G. Herzberg}, @@ -13905,7 +13906,7 @@ 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}} + bdsk-url-1 = {https://doi.org/10.1063/1.1651060}} @article{Curtiss_1991, author = {Curtiss, Larry A. and Raghavachari, Krishnan and Trucks, Gary W. and Pople, John A.}, @@ -13921,7 +13922,7 @@ 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}} + bdsk-url-1 = {https://doi.org/10.1063/1.460205}} @article{Silva-Junior_2010, author = {Silva-Junior, Mario R. and Schreiber, Marko and Sauer, Stephan P. A. and Thiel, Walter}, @@ -13938,7 +13939,7 @@ 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}} + 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}, @@ -13955,7 +13956,7 @@ 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}} + 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.}, @@ -13972,7 +13973,7 @@ 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}} + 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}, @@ -13989,7 +13990,7 @@ 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}} + 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}, @@ -14006,7 +14007,7 @@ 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}} + 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}, @@ -14023,7 +14024,7 @@ 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}} + 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}, @@ -14039,7 +14040,7 @@ 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}} + 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}, @@ -14055,7 +14056,7 @@ title = {Local {{Hamiltonians}} for Quantitative {{Green}}'s Function Embedding Methods}, volume = {141}, year = {2014}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.4901432}} + bdsk-url-1 = {https://doi.org/10.1063/1.4901432}} @book{FetterBook, author = {A. L. Fetter and J. D. Waleck}, @@ -14081,8 +14082,8 @@ 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}} + 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}, @@ -14098,8 +14099,8 @@ title = {Random-Phase Approximation and Its Applications in Computational Chemistry and Materials Science}, volume = {47}, year = {2012}, - Bdsk-File-1 = {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}, - Bdsk-Url-1 = {https://dx.doi.org/10.1007/s10853-012-6570-4}} + bdsk-file-1 = {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}, + 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.}, @@ -14115,7 +14116,7 @@ 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}} + bdsk-url-1 = {https://dx.doi.org/10.1103/PhysRevB.97.121102}} @article{Aryasetiawan_2012, author = {Aryasetiawan, F. and Sakuma, R. and Karlsson, K.}, @@ -14131,7 +14132,7 @@ title = {G {{W}} Approximation with Self-Screening Correction}, volume = {85}, year = {2012}, - Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevB.85.035106}} + bdsk-url-1 = {https://dx.doi.org/10.1103/PhysRevB.85.035106}} @article{Phillips_2014, author = {Phillips, Jordan J. and Zgid, Dominika}, @@ -14148,7 +14149,7 @@ 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}} + 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}, @@ -14164,7 +14165,7 @@ 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}} + bdsk-url-1 = {https://dx.doi.org/10.1063/1.4921259}} @article{Rusakov_2016, author = {Rusakov, Alexander A. and Zgid, Dominika}, @@ -14180,7 +14181,7 @@ 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}} + 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"--}, @@ -14209,7 +14210,7 @@ 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}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRevB.54.8411}} @article{Casida_1989, author = {Casida, Mark E. and Chong, Delano P.}, @@ -14223,7 +14224,7 @@ 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}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRevA.40.4837}} @article{Casida_1991, author = {Casida, Mark E. and Chong, Delano P.}, @@ -14238,7 +14239,7 @@ 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}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRevA.44.5773}} @article{Casida_1991a, author = {Casida, Mark E. and Chong, Delano P.}, @@ -14252,7 +14253,7 @@ 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}} + 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}, @@ -14269,7 +14270,7 @@ 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}} + 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.}, @@ -14309,7 +14310,7 @@ 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}} + bdsk-url-1 = {https://dx.doi.org/10.1016/0009-2614(80)80396-4}} @article{Pulay_1982, author = {Pulay, P.}, @@ -14324,7 +14325,7 @@ title = {{{ImprovedSCF}} Convergence Acceleration}, volume = {3}, year = {1982}, - Bdsk-Url-1 = {https://dx.doi.org/10.1002/jcc.540030413}} + 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}, @@ -14339,7 +14340,7 @@ 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}} + bdsk-url-1 = {https://dx.doi.org/10.1088/1367-2630/16/11/113025}} @incollection{Hedin_1970, author = {Hedin, Lars and Lundqvist, Stig}, @@ -14354,7 +14355,7 @@ 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}} + bdsk-url-1 = {https://dx.doi.org/10.1016/S0081-1947(08)60615-3}} @article{Hybertsen_1985a, author = {Hybertsen, Mark S. and Louie, Steven G.}, @@ -14371,7 +14372,7 @@ 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}} + bdsk-url-1 = {https://dx.doi.org/10.1103/PhysRevLett.55.1418}} @article{Klein_1961, author = {Klein, Abraham}, @@ -14387,7 +14388,7 @@ 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}} + 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.}, @@ -14403,7 +14404,7 @@ 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}} + bdsk-url-1 = {https://dx.doi.org/10.1103/PhysRevLett.81.1662}} @article{Galitskii_1958, author = {V. Galitskii and A. Migdal}, @@ -14429,7 +14430,7 @@ 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}} + bdsk-url-1 = {https://dx.doi.org/10.1103/PhysRevA.75.062506}} @article{Onida_2002, author = {G. Onida and L. Reining and A. Rubio and}, @@ -14441,7 +14442,7 @@ 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}} + bdsk-url-1 = {https://doi.org/10.1103/RevModPhys.74.601}} @article{Aryasetiawan_1998, author = {F. Aryasetiawan and O. Gunnarsson}, @@ -14453,7 +14454,7 @@ title = {The GW Method}, volume = {61}, year = {1998}, - Bdsk-Url-1 = {https://doi.org/10.1088/0034-4885/61/3/002}} + bdsk-url-1 = {https://doi.org/10.1088/0034-4885/61/3/002}} @article{Ambrosek_2010, author = {Ambrosek, David and Loos, Pierre-Fran{\c c}ois and Assfeld, Xavier and Daniel, Chantal}, @@ -14470,7 +14471,7 @@ 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}} + bdsk-url-1 = {https://dx.doi.org/10.1016/j.jinorgbio.2010.04.002}} @article{Dumont_2008, author = {Dumont, {\'E}lise and Loos, Pierre-Fran{\c c}ois and Assfeld, Xavier}, @@ -14487,7 +14488,7 @@ 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}} + 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}, @@ -14504,7 +14505,7 @@ 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}} + bdsk-url-1 = {https://dx.doi.org/10.1021/jp806465e}} @article{Loos_2015, author = {Loos, Pierre-Fran{\c c}ois and Ball, Caleb J. and Gill, Peter M. W.}, @@ -14520,7 +14521,7 @@ title = {Chemistry in One Dimension}, volume = {17}, year = {2015}, - Bdsk-Url-1 = {https://dx.doi.org/10.1039/C4CP03571B}} + bdsk-url-1 = {https://dx.doi.org/10.1039/C4CP03571B}} @article{Almbladh_1999, author = {Almbladh, C.-O. and Barth, U. Von and Leeuwen, R. Van}, @@ -14555,7 +14556,7 @@ 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}} + 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}, @@ -14570,7 +14571,7 @@ 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}} + 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}, @@ -14585,7 +14586,7 @@ 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}} + bdsk-url-1 = {https://dx.doi.org/10.1088/1367-2630/16/11/119601}} @article{Blase_2016, author = {Blase, Xavier and Boulanger, Paul and Bruneval, Fabien and Fernandez-Serra, Marivi and Duchemin, Ivan}, @@ -14600,7 +14601,7 @@ 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}} + bdsk-url-1 = {https://dx.doi.org/10.1063/1.4940139}} @article{Bruneval_2009, author = {Bruneval, Fabien}, @@ -14614,7 +14615,7 @@ 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}} + bdsk-url-1 = {https://dx.doi.org/10.1103/PhysRevLett.103.176403}} @article{Bruneval_2012, author = {Bruneval, Fabien}, @@ -14629,7 +14630,7 @@ 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}} + bdsk-url-1 = {https://dx.doi.org/10.1063/1.4718428}} @article{Bruneval_2013, author = {Bruneval, Fabien and Marques, Miguel A. L.}, @@ -14644,7 +14645,7 @@ 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}} + bdsk-url-1 = {https://dx.doi.org/10.1021/ct300835h}} @article{Bruneval_2016a, author = {Bruneval, Fabien}, @@ -14659,7 +14660,7 @@ 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}} + 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.}, @@ -14676,7 +14677,7 @@ 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}} + 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}, @@ -14693,7 +14694,7 @@ 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}} + bdsk-url-1 = {https://dx.doi.org/10.1103/PhysRevB.88.075105}} @phdthesis{Caruso_2013b, author = {Caruso, Fabio}, @@ -14716,7 +14717,7 @@ title = {Electron Propagator Theory}, volume = {74}, year = {2017}, - Bdsk-Url-1 = {https://dx.doi.org/10.1016/bs.aiq.2016.05.001}} + 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}, @@ -14732,7 +14733,7 @@ title = {Variational Energy Functionals Tested on Atoms}, volume = {69}, year = {2004}, - Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevB.69.195102}} + bdsk-url-1 = {https://dx.doi.org/10.1103/PhysRevB.69.195102}} @article{Dahlen_2004a, author = {Dahlen, Nils Erik and {von Barth}, Ulf}, @@ -14747,7 +14748,7 @@ 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}} + 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}, @@ -14761,7 +14762,7 @@ 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}} + bdsk-url-1 = {https://dx.doi.org/10.1002/qua.20306}} @article{Dahlen_2005, author = {Dahlen, Nils Erik and {van Leeuwen}, Robert}, @@ -14776,7 +14777,7 @@ 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}} + bdsk-url-1 = {https://dx.doi.org/10.1063/1.1884965}} @article{Danovich_2011, author = {Danovich, David}, @@ -14792,7 +14793,7 @@ 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}} + bdsk-url-1 = {https://dx.doi.org/10.1002/wcms.38}} @article{Dreuw_2015, author = {Dreuw, Andreas and Wormit, Michael}, @@ -14807,7 +14808,7 @@ 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}} + bdsk-url-1 = {https://dx.doi.org/10.1002/wcms.1206}} @phdthesis{vanFaassen_2005, author = {{van Faassen}, Meta}, @@ -14832,7 +14833,7 @@ 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}} + bdsk-url-1 = {https://dx.doi.org/10.1103/PhysRevLett.93.126406}} @book{March_1999, address = {London}, @@ -14858,7 +14859,7 @@ 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}} + 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.}, @@ -14874,7 +14875,7 @@ title = {Quasiparticle {{Self}}-{{Consistent G W Theory}}}, volume = {96}, year = {2006}, - Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevLett.96.226402}} + bdsk-url-1 = {https://dx.doi.org/10.1103/PhysRevLett.96.226402}} @article{Hattig_2002, author = {H{\"a}ttig, Christof and Hald, Kasper}, @@ -14888,7 +14889,7 @@ 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}} + bdsk-url-1 = {https://dx.doi.org/10.1039/b110847f}} @article{Ismail-Beigi_2010, author = {Ismail-Beigi, Sohrab}, @@ -14903,7 +14904,7 @@ 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}} + bdsk-url-1 = {https://dx.doi.org/10.1103/PhysRevB.81.195126}} @article{LaflammeJanssen_2015, author = {Laflamme Janssen, Jonathan and Rousseau, Bruno and C{\^o}t{\'e}, Michel}, @@ -14917,7 +14918,7 @@ 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}} + 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.}, @@ -14933,7 +14934,7 @@ 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}} + 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.}, @@ -14948,7 +14949,7 @@ 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}} + 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.}, @@ -14963,7 +14964,7 @@ 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}} + bdsk-url-1 = {https://dx.doi.org/10.1063/1.4983126}} @article{Ren_2013, author = {Ren, Xinguo and Rinke, Patrick and Scuseria, Gustavo E. and Scheffler, Matthias}, @@ -14980,7 +14981,7 @@ 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}} + 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}, @@ -14995,7 +14996,7 @@ title = {Accurate {{Quasiparticle Spectra}} from the {{T}}-{{Matrix Self}}-{{Energy}} and the {{Particle}}\textendash{}{{Particle Random Phase Approximation}}}, volume = {8}, year = {2017}, - Bdsk-Url-1 = {https://dx.doi.org/10.1021/acs.jpclett.7b01275}} + bdsk-url-1 = {https://dx.doi.org/10.1021/acs.jpclett.7b01275}} @article{Zhukov_2005, author = {Zhukov, V. P. and Chulkov, E. V. and Echenique, P. M.}, @@ -15009,7 +15010,7 @@ 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}} + 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}, @@ -15024,7 +15025,7 @@ title = {Stochastic {{GW Calculations}} for {{Molecules}}}, volume = {13}, year = {2017}, - Bdsk-Url-1 = {https://dx.doi.org/10.1021/acs.jctc.7b00770}} + bdsk-url-1 = {https://dx.doi.org/10.1021/acs.jctc.7b00770}} @article{Sun_2004, author = {Sun, Ping and Kotliar, Gabriel}, @@ -15038,7 +15039,7 @@ title = {Many-{{Body Approximation Scheme}} beyond {{GW}}}, volume = {92}, year = {2004}, - Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevLett.92.196402}} + 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}, @@ -15053,7 +15054,7 @@ 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}} + 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}, @@ -15068,7 +15069,7 @@ title = {Stochastic Evaluation of Second-Order {{Dyson}} Self-Energies}, volume = {138}, year = {2013}, - Bdsk-Url-1 = {https://dx.doi.org/10.1063/1.4801862}} + bdsk-url-1 = {https://dx.doi.org/10.1063/1.4801862}} @article{Leng_2016, author = {Leng, Xia and Jin, Fan and Wei, Min and Ma, Yuchen}, @@ -15083,7 +15084,7 @@ 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}} + bdsk-url-1 = {https://dx.doi.org/10.1002/wcms.1265}} @article{Ke_2011, author = {Ke, San-Huang}, @@ -15100,7 +15101,7 @@ 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}} + 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.}, @@ -15136,7 +15137,7 @@ title = {Fully Self-Consistent {{G W}} and Quasiparticle Self-Consistent {{G W}} for Molecules}, volume = {89}, year = {2014}, - Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevB.89.155417}} + bdsk-url-1 = {https://dx.doi.org/10.1103/PhysRevB.89.155417}} @article{Ku_2002, author = {Ku, Wei and Eguiluz, Adolfo G.}, @@ -15153,7 +15154,7 @@ title = {Band-{{Gap Problem}} in {{Semiconductors Revisited}}: {{Effects}} of {{Core States}} and {{Many}}-{{Body Self}}-{{Consistency}}}, volume = {89}, year = {2002}, - Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevLett.89.126401}} + bdsk-url-1 = {https://dx.doi.org/10.1103/PhysRevLett.89.126401}} @article{Lani_2012, author = {Lani, Giovanna and Romaniello, Pina and Reining, Lucia}, @@ -15168,7 +15169,7 @@ title = {Approximations for Many-Body {{Green}}'s Functions: Insights from the Fundamental Equations}, volume = {14}, year = {2012}, - Bdsk-Url-1 = {https://dx.doi.org/10.1088/1367-2630/14/1/013056}} + bdsk-url-1 = {https://dx.doi.org/10.1088/1367-2630/14/1/013056}} @article{Li_2017, author = {Li, Jing and Holzmann, Markus and Duchemin, Ivan and Blase, Xavier and Olevano, Valerio}, @@ -15184,7 +15185,7 @@ title = {Helium {{Atom Excitations}} by the {{G W}} and {{Bethe}}-{{Salpeter Many}}-{{Body Formalism}}}, volume = {118}, year = {2017}, - Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevLett.118.163001}} + bdsk-url-1 = {https://dx.doi.org/10.1103/PhysRevLett.118.163001}} @article{Maebashi_2011, author = {Maebashi, Hideaki and Takada, Yasutami}, @@ -15200,7 +15201,7 @@ title = {Analysis of Exact Vertex Function for Improving on the {{GW $\Gamma$}} Scheme for First-Principles Calculation of Electron Self-Energy}, volume = {84}, year = {2011}, - Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevB.84.245134}} + bdsk-url-1 = {https://dx.doi.org/10.1103/PhysRevB.84.245134}} @article{Mahan_1989, author = {Mahan, G. D. and Sernelius, B. E.}, @@ -15225,7 +15226,7 @@ title = {Quasidegenerate Second-Order Perturbation Corrections to Single-Excitation Configuration Interaction}, volume = {96}, year = {1999}, - Bdsk-Url-1 = {https://dx.doi.org/10.1080/00268979909482996}} + bdsk-url-1 = {https://dx.doi.org/10.1080/00268979909482996}} @article{Hedin_1965, author = {Hedin, Lars}, @@ -15238,7 +15239,7 @@ title = {New Method for Calculating the One-Particle {{Green}}'s Function with Application to the Electron-Gas Problem}, volume = {139}, year = {1965}, - Bdsk-Url-1 = {https://doi.org/10.1103/PhysRev.139.A796}} + bdsk-url-1 = {https://doi.org/10.1103/PhysRev.139.A796}} @article{Ohnishi_2016, author = {Ohnishi, Yu-ya and Ten-no, Seiichiro}, @@ -15255,7 +15256,7 @@ title = {Explicitly Correlated Frequency-Independent Second-Order Green's Function for Accurate Ionization Energies}, volume = {37}, year = {2016}, - Bdsk-Url-1 = {https://dx.doi.org/10.1002/jcc.24468}} + bdsk-url-1 = {https://dx.doi.org/10.1002/jcc.24468}} @article{Hellgren_2015, author = {Hellgren, Maria and Caruso, Fabio and Rohr, Daniel R. and Ren, Xinguo and Rubio, Angel and Scheffler, Matthias and Rinke, Patrick}, @@ -15271,7 +15272,7 @@ title = {Static Correlation and Electron Localization in Molecular Dimers from the Self-Consistent {{RPA}} and {{G W}} Approximation}, volume = {91}, year = {2015}, - Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevB.91.165110}} + bdsk-url-1 = {https://dx.doi.org/10.1103/PhysRevB.91.165110}} @article{Steinbeck_2000, author = {Steinbeck, L. and Rubio, A. and Reining, L. and Torrent, M. and White, I. D. and Godby, R. W.}, @@ -15307,7 +15308,7 @@ title = {General-{{Order Many}}-{{Body Green}}'s {{Function Method}}}, volume = {11}, year = {2015}, - Bdsk-Url-1 = {https://dx.doi.org/10.1021/acs.jctc.5b00005}} + bdsk-url-1 = {https://dx.doi.org/10.1021/acs.jctc.5b00005}} @article{Hirata_2017, author = {Hirata, So and Doran, Alexander E. and Knowles, Peter J. and Ortiz, J. V.}, @@ -15323,7 +15324,7 @@ 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}} + bdsk-url-1 = {https://dx.doi.org/10.1063/1.4994837}} @article{vanSetten_2018, author = {{van Setten}, Michiel J. and Costa, Ramon and Vi{\~n}es, Francesc and Illas, Francesc}, @@ -15338,7 +15339,7 @@ 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}} + 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}, @@ -15352,7 +15353,7 @@ 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}} + 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}, @@ -15367,7 +15368,7 @@ 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}} + 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.}, @@ -15383,7 +15384,7 @@ 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}} + bdsk-url-1 = {https://dx.doi.org/10.1021/ct300648t}} @article{Trofimov_2002, author = {Trofimov, A. B. and Stelter, G. and Schirmer, J.}, @@ -15399,7 +15400,7 @@ 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}} + bdsk-url-1 = {https://dx.doi.org/10.1063/1.1504708}} @article{Trofimov_2005, author = {Trofimov, A. B. and Schirmer, J.}, @@ -15414,7 +15415,7 @@ 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}} + 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.}, @@ -15429,7 +15430,7 @@ 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}} + 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}, @@ -15443,7 +15444,7 @@ 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}} + bdsk-url-1 = {https://dx.doi.org/10.1103/PhysRevB.79.201104}} @article{Tiago_2006, author = {Tiago, Murilo L. and Chelikowsky, James R.}, @@ -15457,7 +15458,7 @@ 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}} + bdsk-url-1 = {https://dx.doi.org/10.1103/PhysRevB.73.205334}} @article{Ou_2016, author = {Ou, Qi and Subotnik, Joseph E.}, @@ -15473,7 +15474,7 @@ 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}} + bdsk-url-1 = {https://dx.doi.org/10.1021/acs.jpca.6b03294}} @article{Ou_2018, author = {Ou, Qi and Subotnik, Joseph E.}, @@ -15489,7 +15490,7 @@ 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}} + bdsk-url-1 = {https://dx.doi.org/10.1021/acs.jctc.7b00246}} @article{Romaniello_2009, author = {Romaniello, P. and Guyot, S. and Reining, L.}, @@ -15505,7 +15506,7 @@ 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}} + bdsk-url-1 = {https://dx.doi.org/10.1063/1.3249965}} @article{Tarantino_2017, author = {Tarantino, Walter and Romaniello, Pina and Berger, J. A. and Reining, Lucia}, @@ -15522,7 +15523,7 @@ 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}} + bdsk-url-1 = {https://dx.doi.org/10.1103/PhysRevB.96.045124}} @article{Takada_2001, author = {Takada, Yasutami}, @@ -15536,7 +15537,7 @@ 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}} + 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.}, @@ -15548,7 +15549,7 @@ title = {Many-Body Properties of a Spherical Two-Dimensional Electron Gas}, volume = {65}, year = {2002}, - Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevB.65.195418}} + bdsk-url-1 = {https://dx.doi.org/10.1103/PhysRevB.65.195418}} @article{Tempere_2007, author = {Tempere, J and Silvera, I and Devreese, J}, @@ -15560,7 +15561,7 @@ title = {Multielectron Bubbles in Helium as a Paradigm for Studying Electrons on Surfaces with Curvature}, volume = {62}, year = {2007}, - Bdsk-Url-1 = {https://dx.doi.org/10.1016/j.surfrep.2007.03.001}} + bdsk-url-1 = {https://dx.doi.org/10.1016/j.surfrep.2007.03.001}} @article{Holm_1998, author = {Holm, Bengt and {von Barth}, Ulf}, @@ -15596,7 +15597,7 @@ title = {Analytic Evaluation of the Electronic Self-Energy in the {{G W}} Approximation for Two Electrons on a Sphere}, volume = {87}, year = {2013}, - Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevB.87.075104}} + bdsk-url-1 = {https://dx.doi.org/10.1103/PhysRevB.87.075104}} @article{Schirmer_1983, author = {Schirmer, J. and Cederbaum, L. S. and Walter, O.}, @@ -15621,7 +15622,7 @@ title = {Intermediate State Representation Approach to Physical Properties of Electronically Excited Molecules}, volume = {120}, year = {2004}, - Bdsk-Url-1 = {https://dx.doi.org/10.1063/1.1752875}} + bdsk-url-1 = {https://dx.doi.org/10.1063/1.1752875}} @article{vanSetten_2015, author = {{van Setten}, Michiel J. and Caruso, Fabio and Sharifzadeh, Sahar and Ren, Xinguo and Scheffler, Matthias and Liu, Fang and Lischner, Johannes and Lin, Lin and Deslippe, Jack R. and Louie, Steven G. and Yang, Chao and Weigend, Florian and Neaton, Jeffrey B. and Evers, Ferdinand and Rinke, Patrick}, @@ -15638,7 +15639,7 @@ title = {{{{\emph{GW}}}} 100: {{Benchmarking}} {{{\emph{G}}}}{\textsubscript{0}}{{{\emph{W}}}}{\textsubscript{0}} for {{Molecular Systems}}}, volume = {11}, year = {2015}, - Bdsk-Url-1 = {https://dx.doi.org/10.1021/acs.jctc.5b00453}} + bdsk-url-1 = {https://dx.doi.org/10.1021/acs.jctc.5b00453}} @article{Holleboom_1990, author = {Holleboom, L. J. and Snijders, J. G.}, @@ -15653,7 +15654,7 @@ title = {A Comparison between the {{Mo}}/Ller\textendash{}{{Plesset}} and {{Green}}'s Function Perturbative Approaches to the Calculation of the Correlation Energy in the Many-electron Problem}, volume = {93}, year = {1990}, - Bdsk-Url-1 = {https://dx.doi.org/10.1063/1.459578}} + bdsk-url-1 = {https://dx.doi.org/10.1063/1.459578}} @article{Stan_2006, author = {Stan, A and Dahlen, N. E and van Leeuwen, R.}, @@ -15667,7 +15668,7 @@ title = {Fully Self-Consistent {{{\emph{GW}}}} Calculations for Atoms and Molecules}, volume = {76}, year = {2006}, - Bdsk-Url-1 = {https://dx.doi.org/10.1209/epl/i2006-10266-6}} + bdsk-url-1 = {https://dx.doi.org/10.1209/epl/i2006-10266-6}} @article{Ren_2015, author = {Ren, Xinguo and Marom, Noa and Caruso, Fabio and Scheffler, Matthias and Rinke, Patrick}, @@ -15684,7 +15685,7 @@ title = {Beyond the {{G W}} Approximation: {{A}} Second-Order Screened Exchange Correction}, volume = {92}, year = {2015}, - Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevB.92.081104}} + bdsk-url-1 = {https://dx.doi.org/10.1103/PhysRevB.92.081104}} @article{Neuhauser_2014, author = {Neuhauser, Daniel and Gao, Yi and Arntsen, Christopher and Karshenas, Cyrus and Rabani, Eran and Baer, Roi}, @@ -15699,7 +15700,7 @@ title = {Breaking the {{Theoretical Scaling Limit}} for {{Predicting Quasiparticle Energies}}: {{The Stochastic G W Approach}}}, volume = {113}, year = {2014}, - Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevLett.113.076402}} + bdsk-url-1 = {https://dx.doi.org/10.1103/PhysRevLett.113.076402}} @article{Neuhauser_2017, author = {Neuhauser, Daniel and Baer, Roi and Zgid, Dominika}, @@ -15714,7 +15715,7 @@ title = {Stochastic {{Self}}-{{Consistent Second}}-{{Order Green}}'s {{Function Method}} for {{Correlation Energies}} of {{Large Electronic Systems}}}, volume = {13}, year = {2017}, - Bdsk-Url-1 = {https://dx.doi.org/10.1021/acs.jctc.7b00792}} + bdsk-url-1 = {https://dx.doi.org/10.1021/acs.jctc.7b00792}} @article{Ortiz_2013, author = {Ortiz, Joseph Vincent}, @@ -15730,7 +15731,7 @@ 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}} + 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.}, @@ -15744,7 +15745,7 @@ 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}} + 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.}, @@ -15760,7 +15761,7 @@ 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}} + 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}, @@ -15775,7 +15776,7 @@ 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}} + 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}, @@ -15787,7 +15788,7 @@ 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}} + 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}, @@ -15810,7 +15811,7 @@ 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}} + 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.}, @@ -15824,7 +15825,7 @@ 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}} + 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.}, @@ -15839,8 +15840,8 @@ 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}} + 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.}, @@ -15853,7 +15854,7 @@ 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}} + 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.}, @@ -15868,8 +15869,8 @@ 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}} + bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.119.056402}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRevLett.119.056402}} @article{Albrecht_1998, author = {Albrecht, Stefan and Reining, Lucia and Del Sole, Rodolfo and Onida, Giovanni}, @@ -15884,8 +15885,8 @@ url = {https://link.aps.org/doi/10.1103/PhysRevLett.80.4510}, volume = {80}, year = {1998}, - Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.80.4510}, - Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevLett.80.4510}} + bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.80.4510}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRevLett.80.4510}} @article{vanderHorst_1999, author = {van der Horst, J.-W. and Bobbert, P. A. and Michels, M. A. J. and Brocks, G. and Kelly, P. J.}, @@ -15900,8 +15901,8 @@ url = {https://link.aps.org/doi/10.1103/PhysRevLett.83.4413}, volume = {83}, year = {1999}, - Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.83.4413}, - Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevLett.83.4413}} + bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.83.4413}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRevLett.83.4413}} @article{Tiago_2003, author = {Tiago, Murilo L. and Northrup, John E. and Louie, Steven G.}, @@ -15917,8 +15918,8 @@ url = {https://link.aps.org/doi/10.1103/PhysRevB.67.115212}, volume = {67}, year = {2003}, - Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.67.115212}, - Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevB.67.115212}} + bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.67.115212}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRevB.67.115212}} @article{Tiago_2008, author = {Tiago, Murilo L. and Kent,P. R. C. and Hood,Randolph Q. and Reboredo,Fernando A.}, @@ -15930,7 +15931,7 @@ title = {Neutral and charged excitations in carbon fullerenes from first-principles many-body theories}, volume = {129}, year = {2008}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.2973627}} + bdsk-url-1 = {https://doi.org/10.1063/1.2973627}} @article{Sai_2008, author = {Sai, Na and Tiago, Murilo L. and Chelikowsky, James R. and Reboredo, Fernando A.}, @@ -15945,8 +15946,8 @@ title = {Optical spectra and exchange-correlation effects in molecular crystals}, volume = {77}, year = {2008}, - Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.77.161306}, - Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevB.77.161306}} + bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.77.161306}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRevB.77.161306}} @article{Palumno_2009, author = {Palummo,Maurizia and Hogan,Conor and Sottile,Francesco and Bagal\'{a},Paolo and Rubio,Angel}, @@ -15958,7 +15959,7 @@ title = {Ab Initio Electronic and Optical Spectra of Free-Base Porphyrins: The Role of Electronic Correlation}, volume = {131}, year = {2009}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.3204938}} + bdsk-url-1 = {https://doi.org/10.1063/1.3204938}} @article{Rocca_2010, author = {Rocca,Dario and Lu,Deyu and Galli,Giulia}, @@ -15970,7 +15971,7 @@ title = {Ab Initio Calculations of Optical Absorption Spectra: Solution of the Bethe--Salpeter Equation Within Density Matrix Perturbation Theory}, volume = {133}, year = {2010}, - Bdsk-Url-1 = {https://doi.org/10.1063/1.3494540}} + bdsk-url-1 = {https://doi.org/10.1063/1.3494540}} @article{Sharifzadeh_2012, author = {Sharifzadeh, Sahar and Biller, Ariel and Kronik, Leeor and Neaton, Jeffrey B.}, @@ -15986,8 +15987,8 @@ url = {https://link.aps.org/doi/10.1103/PhysRevB.85.125307}, volume = {85}, year = {2012}, - Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.85.125307}, - Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevB.85.125307}} + bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.85.125307}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRevB.85.125307}} @article{Cudazzo_2012, author = {Cudazzo, Pierluigi and Gatti, Matteo and Rubio, Angel}, @@ -16003,8 +16004,8 @@ url = {https://link.aps.org/doi/10.1103/PhysRevB.86.195307}, volume = {86}, year = {2012}, - Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.86.195307}, - Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevB.86.195307}} + bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.86.195307}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRevB.86.195307}} @article{Hirose_2015, author = {Hirose, Daichi and Noguchi, Yoshifumi and Sugino, Osamu}, @@ -16020,8 +16021,8 @@ url = {https://link.aps.org/doi/10.1103/PhysRevB.91.205111}, volume = {91}, year = {2015}, - Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.91.205111}, - Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevB.91.205111}} + bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.91.205111}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRevB.91.205111}} @article{Ziaei_2017, author = {Ziaei, Vafa and Bredow, Thomas}, @@ -16036,8 +16037,8 @@ title = {Simple many-body based screening mixing ansatz for improvement of $GW$/Bethe-Salpeter equation excitation energies of molecular systems}, volume = {96}, year = {2017}, - Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.96.195115}, - Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevB.96.195115}} + bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.96.195115}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRevB.96.195115}} @article{Cocchi_2015, author = {Cocchi, Caterina and Draxl, Claudia}, @@ -16053,8 +16054,8 @@ url = {https://link.aps.org/doi/10.1103/PhysRevB.92.205105}, volume = {92}, year = {2015}, - Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.92.205105}, - Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevB.92.205105}} + bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.92.205105}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRevB.92.205105}} @article{Abramson_2017, author = {Refaely-Abramson, Sivan and da Jornada, Felipe H. and Louie, Steven G. and Neaton, Jeffrey B.}, @@ -16069,8 +16070,8 @@ url = {https://link.aps.org/doi/10.1103/PhysRevLett.119.267401}, volume = {119}, year = {2017}, - Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.119.267401}, - Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevLett.119.267401}} + bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.119.267401}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRevLett.119.267401}} @article{Lastra_2011, author = {Garcia-Lastra, J. M. and Thygesen, K. S.}, @@ -16086,8 +16087,8 @@ url = {https://link.aps.org/doi/10.1103/PhysRevLett.106.187402}, volume = {106}, year = {2011}, - Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.106.187402}, - Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevLett.106.187402}} + bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.106.187402}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRevLett.106.187402}} @article{Baumeier_2012b, author = {Baumeier, Bj\"{o}rn and Andrienko, Denis and Ma, Yuchen and Rohlfing, Michael}, @@ -16098,7 +16099,7 @@ title = {Excited States of Dicyanovinyl-Substituted Oligothiophenes from Many-Body Green's Functions Theory}, volume = {8}, year = {2012}, - Bdsk-Url-1 = {https://doi.org/10.1021/ct300311x}} + bdsk-url-1 = {https://doi.org/10.1021/ct300311x}} @article{Duchemin_2012, author = {Duchemin, I. and Deutsch, T. and Blase, X.}, @@ -16113,8 +16114,8 @@ url = {https://link.aps.org/doi/10.1103/PhysRevLett.109.167801}, volume = {109}, year = {2012}, - Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.109.167801}, - Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevLett.109.167801}} + bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.109.167801}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRevLett.109.167801}} @article{Rangel_2016, author = {Rangel, Tonatiuh and Hamed, Samia M. and Bruneval, Fabien and Neaton, Jeffrey B.}, @@ -16126,7 +16127,7 @@ title = {Evaluating the GW Approximation with CCSD(T) for Charged Excitations Across the Oligoacenes}, volume = {12}, year = {2016}, - Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.6b00163}} + bdsk-url-1 = {https://doi.org/10.1021/acs.jctc.6b00163}} @article{Faber_2015, author = {Faber, C. and Boulanger, P. and Attaccalite, C. and Cannuccia, E. and Duchemin, I. and Deutsch, T. and Blase, X.}, @@ -16142,8 +16143,8 @@ url = {https://link.aps.org/doi/10.1103/PhysRevB.91.155109}, volume = {91}, year = {2015}, - Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.91.155109}, - Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevB.91.155109}} + bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.91.155109}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRevB.91.155109}} @article{Montserrat_2016, author = {Monserrat, Bartomeu}, @@ -16159,8 +16160,8 @@ url = {https://link.aps.org/doi/10.1103/PhysRevB.93.100301}, volume = {93}, year = {2016}, - Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.93.100301}, - Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevB.93.100301}} + bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.93.100301}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRevB.93.100301}} @article{Zhenglu_2019, author = {Li, Zhenglu and Antonius, Gabriel and Wu, Meng and da Jornada, Felipe H. and Louie, Steven G.}, @@ -16175,8 +16176,8 @@ url = {https://link.aps.org/doi/10.1103/PhysRevLett.122.186402}, volume = {122}, year = {2019}, - Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.122.186402}, - Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevLett.122.186402}} + bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.122.186402}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRevLett.122.186402}} @article{Maggio_2016, author = {Maggio, Emanuele and Kresse, Georg}, @@ -16191,8 +16192,8 @@ url = {https://link.aps.org/doi/10.1103/PhysRevB.93.235113}, volume = {93}, year = {2016}, - Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.93.235113}, - Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevB.93.235113}} + bdsk-url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.93.235113}, + bdsk-url-2 = {https://doi.org/10.1103/PhysRevB.93.235113}} @article{Boulanger_2014, author = {Boulanger, Paul and Jacquemin, Denis and Duchemin, Ivan and Blase, Xavier}, @@ -16203,4 +16204,4 @@ title = {Fast and Accurate Electronic Excitations in Cyanines with the Many-Body Bethe-Salpeter Approach}, volume = {10}, year = {2014}, - Bdsk-Url-1 = {https://doi.org/10.1021/ct401101u}} + bdsk-url-1 = {https://doi.org/10.1021/ct401101u}} diff --git a/TrUEGs.tex b/TrUEGs.tex index 0ccefb8..ff43166 100644 --- a/TrUEGs.tex +++ b/TrUEGs.tex @@ -30,6 +30,9 @@ \newcommand{\LCPQ}{Laboratoire de Chimie et Physique Quantiques (UMR 5626), Universit\'e de Toulouse, CNRS, UPS, France} \newcommand{\VRIJE}{Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modelling, FEW, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands} +% COUPLING CONSTANT: +\newcommand{\cc}{{\color{blue} \mu}} + \begin{document} \title{Transient Uniform Electron Gases} @@ -37,8 +40,8 @@ \author{Pierre-Fran\c{c}ois \surname{Loos}} \email{loos@irsamc.ups-tlse.fr} \affiliation{\LCPQ} -\author{Paola \surname{Gori-Giorgi}} -\affiliation{\VRIJE} +%\author{Paola \surname{Gori-Giorgi}} +%\affiliation{\VRIJE} \author{Michael \surname{Seidl}} \affiliation{\VRIJE} @@ -48,9 +51,9 @@ % \includegraphics[width=\linewidth]{TOC} %\end{wrapfigure} The uniform electron gas (UEG), a hypothetical system with finite homogenous electron density composed by an infinite number of electrons in a box of infinite volume, is the practical pillar of density-functional theory (DFT) and the foundation of the most acclaimed approximation of DFT, the local-density approximation (LDA). -In the last thirty years, the knowledge of analytical parametrizations of the infinite UEG (IUEG) exchange-correlation energy has allowed researchers to perform millions of approximate electronic structure calculations for atoms, molecules, and solids. +In the last thirty years, the knowledge of analytical parametrizations of the infinite UEG (IUEG) exchange-correlation energy has allowed researchers to perform countless of approximate electronic structure calculations for atoms, molecules, and solids. Recently, it has been shown that the traditional concept of the IUEG is not the unique example of UEGs, and systems, in their lowest-energy state, consisting of electrons that are confined to the surface of a sphere provide a new family of UEGs with more customizable properties. -Here, we show that, some of the excited states associated with these systems can be classified as transient UEGs (TUEGs) as their electron density is only homogenous for very specific values of the radius of the sphere. +Here, we show that, some of the excited states associated with these systems can be classified as transient UEGs (TUEGs) as their electron density is only homogenous for very specific values of the radius of the sphere even though the electronic wave function is not rotationally invariant. Concrete examples are provided in the case of two-electron systems. \end{abstract} @@ -68,81 +71,137 @@ One can also access excited states via the time-dependent version of DFT. \cite{ As commonly done, the LDA can be refined by adding up new ingredients, such as the gradient of the density $\nabla \rho$ [which defines the generalized gradient approximation (GGA)], \cite{Perdew_1986,Becke_1988,Lee_1988,Perdew_1996} the kinetic energy density $\tau$ (meta-GGA), \cite{Becke_1988b,Sun_2015} exact Hartree-Fock (HF) exchange (yielding the so-called hybrid functionals), \cite{Becke_1993a,Becke_1993b,Adamo_1999} and others. Each of these quantities defines a new rung of the well-known Jacob ladder of DFT \cite{Perdew_2001} that is supposed to bring electronic structure theory calculations from the evil Hartree world to the chemical accuracy heaven. -The UEG, also known as jellium in some context, \cite{Loos_2016} is a hypothetical infinite substance where an infinite number of electrons ``bathe'' in a (uniform) positively charged jelly of infinite volume. \cite{ParrBook,Loos_2016} -It is can be ``created`` via a \textit{gedanken} experiment by pouring electrons in an expandable box while keeping the ratio $\rho = n/V$ of the number of electrons $n$ and the volume of the box $V$ constant. -In the so-called thermodynamic limit where both $n$ and $V$ goes to infinity but $\rho$ remains finite, the electron density eventually becomes homogeneous. -In the following, this paradigm is named the infinite UEG (IUEG) for obvious reasons. +The UEG, also known as jellium in some context, \cite{Loos_2016} is a hypothetical infinite substance where an infinite number of electrons ``bathe'' in a (uniform) positively charged jelly of infinite volume. \cite{ParrBook,Loos_2016} It can be "created" via a \textit{gedanken} experiment by pouring electrons in an expandable box while keeping the ratio $\rho = N/V$ of the number of electrons $N$ and the volume of the box $V$ constant. In the so-called thermodynamic limit where both $N$ and $V$ goes to infinity but $\rho$ remains finite, the electron density eventually becomes homogeneous. In the following, this paradigm is named the infinite UEG (IUEG) for obvious reasons. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Finite uniform electron gases} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Recently, it has been shown that one can create finite UEGs (FUEGs) by placing a finite number of electrons onto the surface of a sphere of radius $R$. \cite{Tempere_2002,Tempere_2007,Seidl_2007,Loos_2009a,Loos_2009c,Loos_2010e,Loos_2011b,Gill_2012,Loos_2018b} Of course, FUEGs only appear for well-defined electron numbers and electronic states. \cite{Rogers_2016,Rogers_2017} -In particular, the spin-unpolarized ground state of $n$ electrons on a sphere has a homogeneous density for $n = 2(L+1)^2$ (where $L \in \mathbb{N}$) for any $R$ values, and this holds also within the HF approximation. \cite{Loos_2011b} +In particular, the spin-unpolarized ground state of $N$ electrons on a sphere has a homogeneous density for $N = 2(\ell_{\rm max}+1)^2$ (where $\ell_{\rm max} \in \mathbb{N}$) for any $R$ values, and this holds also within the HF approximation. \cite{Loos_2011b} This property comes from the addition theorem of the spherical harmonics \cite{NISTbook} $Y_{\ell m}(\bm{\Omega})$ (which are the spatial orbitals of the system in this particular case): \begin{equation} - \sum_{\ell=0}^L \sum_{m=-\ell}^{+\ell} Y_{\ell m}^*(\bm{\Omega}) Y_{\ell m}(\bm{\Omega}) = \frac{(L+1)^2}{2\pi^2} + \label{eq:ellMax} + \sum_{\ell=0}^{\ell_{\rm max}} \sum_{m=-\ell}^{+\ell} Y_{\ell m}^*(\bm{\Omega}) Y_{\ell m}(\bm{\Omega}) = \frac{(\ell_{\rm max}+1)^2}{2\pi^2} \end{equation} where $\bm{\Omega}=(\theta,\phi)$ gathers the polar and azimuthal angles, respectively. -Thanks to this amazing property, these FUEGs have be employed to construct alternative LDA functionals for both KS-DFT \cite{Loos_2014b,Loos_2017a} and ensemble DFT. \cite{Loos_2020g,Marut_2020} -Besides, hints of the equivalence of the FUEG and IUEG models have been found in the thermodynamic limit, \ie, when $L \to \infty$. \cite{Bowick_2002,Loos_2011b} +Thanks to this key property, these FUEGs have be employed to construct alternative LDA functionals for both KS-DFT \cite{Loos_2014b,Loos_2017a} and ensemble DFT. \cite{Loos_2020g,Marut_2020} +Besides, hints of the equivalence of the FUEG and IUEG models have been found in the thermodynamic limit, \ie, when $\ell_{\rm max} \to \infty$. \cite{Bowick_2002,Loos_2011b} -The two-electron case (\ie, $L = 0$) is of particular interest \cite{Seidl_2007,Loos_2009a,Loos_2018b} as it has been shown to be extremely useful for testing electronic structure methods \cite{Seidl_2007,Loos_2009a,Pedersen_2010,Loos_2012c,Schindlmayr_2013,Sun_2016,Loos_2018b} and is, furthermore, exactly solvable for a countably infinite set of $R$ values. \cite{Loos_2009c,Loos_2010e,Loos_2012} -In this case, the many-body Hamiltonian is simply +The case with $N=2$ electrons ($\ell_{\rm max} = 0$) is of particular interest \cite{Seidl_2007,Loos_2009a,Loos_2018b} as it has been shown to be extremely useful for testing electronic structure methods \cite{Mitas_2006,Seidl_2007,Loos_2009a,Pedersen_2010,Loos_2012c,Schindlmayr_2013,Loos_2015b,Sun_2016,Loos_2018b} and is, furthermore, exactly solvable for a countably infinite set of $R$ values. \cite{Loos_2009c,Loos_2010e,Loos_2012} +In this case, the many-body hamiltonian reads \begin{equation} \label{eq:H} - \Hat{H} = - \frac{\nabla_1^2 + \nabla_2^2}{2} + \frac{1}{r_{12}} + \Hat{H} = \frac{\hat{\ell}_1^2 + \hat{\ell}_2^2}{2m\,R^2} + \lambda\,\frac{e^2}{r_{12}}. \end{equation} -where $r_{12} = \abs{\bm{r}_1 - \bm{r}_2}$ is the interelectronic distance, \ie, the electrons interact Coulombically \textit{through} the sphere. +The squares $\hat{\ell}_n^2=-\hbar^2\hat{A}_n$ of the (orbital) angular momentum operators are essentially the angular parts $\hat{A}_n$ of the Laplacian, +\begin{equation} +\hat{A} = \frac1{\sin\theta}\,\frac{\partial}{\partial\theta}\,\sin\theta\,\frac{\partial}{\partial\theta} + \;+\;\frac1{\sin^2\theta}\,\frac{\partial^2}{\partial\phi^2}, +\end{equation} +while $r_{12}$ is the \textit{spatial distance} between the two electrons, \ie, the electrons interact Coulombically \textit{through} the sphere, +\begin{equation} +r_{12} = R \sqrt{2(1 - \cos\gamma)} \equiv r_{12}(\gamma). +\end{equation} +Here, $\gamma=\gamma(\Omega_1,\Omega_2)$ is the angle between the two electrons on the sphere +(viewed from the spherical center), +\begin{equation} + \label{eq:cosGamma} +\cos\gamma = \cos \theta_1 \cos \theta_2 + \sin \theta_1 \sin \theta_2 \cos(\phi_1 - \phi_2). +\end{equation} +In Eq.~\eqref{eq:H}, we have introduced a coupling constant $\lambda$ which in the real universe (where the electrons, each with charge $-e$, \textit{repel} each other) has the value $\lambda=1$. However, in addition to this realistic situation, we here also wish to consider cases with $\lambda\ne1$, including the non-interacting case $\lambda=0$. In particular, we shall consider the interesting case $\lambda<0$ when the electrons \textit{attract} each other. + +In atomic units ($m=e^2=\hbar=1$) where $R$ is given in units of the bohr radius $a_0=0.529$\AA, our hamiltonian reads +\begin{equation} + \label{eq:H2} + \Hat{H} = \frac1{R^2}\left\{ - \frac{\hat{A}_1+\hat{A}_2}2 \; + \; \cc \cdot \frac{1}{\sqrt{2(1 - \cos\gamma)}} \right\}, +\end{equation} +with an effective coupling constant, +\begin{equation} + \label{eq:cc} +\cc = \lambda R. +\end{equation} +Obviously, different interaction strengths $\lambda\ne0$ at a fixed radius $R>0$ are equivalent to different radii $R\ne0$ at +a fixed interaction strength $\lambda>0$ (where a negative sign of $R$ has no geometric meaning but simply describes attractive +electrons): Just as in the infinite UEG, the limit of high (low) density corresponds to the limit of weak (strong) interaction. + Following Breit, \cite{Breit_1930} one can write the total electronic wave function as \begin{equation} -\label{eq:Phi} - \Phi (\bm{x}_1,\bm{x}_2) - = \Xi(s_1,s_2) \chi (\bm{r}_1,\bm{r}_2) \Psi(r_{12}) +\label{eq:PhiOLD} + \Phi(\bm{x}_1,\bm{x}_2) = \Xi(s_1,s_2) \, \chi(\Omega_1,\Omega_2) \, \Psi(\gamma) \end{equation} -where $\Xi$, $\chi$ and $\Psi$ are the spin, angular and interelectronic wave functions, respectively, and $\bm{x}_i = (s_i,\bm{r}_i)$ is a composite coordinate gathering the spin coordinate $s_i$ and the spatial coordinate $\bm{r}_i$ associated with the $i$th electron. -The singlet and triplet wave functions read \cite{BetheBook} +where $\Xi$, $\chi$ and $\Psi$ are the spin, the non-interacting angular and the interelectronic angular wave functions, respectively, and $\bm{x}_i = (s_i,\Omega_i)$ is a composite coordinate gathering the spin coordinate $s_i$ and the spatial (angular) coordinate $\Omega_i$ associated with the $i$th electron. + +In the non-interacting limit $\lambda=\cc=0$, we have $\Psi(\gamma)=1$. In cases with finite interaction, $\cc\ne0$, this interelectronic wavefunction $\Psi(\gamma)=\Psi_{\cc}(\gamma)$, depending on the value of $\cc$, is either known analytically {\color{red} (Ref.?)} or must be computed numerically. + +The singlet and triplet spin wave functions read \cite{BetheBook} \begin{subequations} \begin{align} ^1\Xi(s_1,s_2) & - = \frac{1}{\sqrt{2}} \qty[ \alpha(s_1) \beta(s_2) - \beta(s_1) \alpha(s_2) ] \\ + = \frac{1}{\sqrt{2}} \, \Big[ \alpha(s_1) \beta(s_2) - \beta(s_1) \alpha(s_2) \Big] \\ ^3\Xi(s_1,s_2) & = \begin{cases} \alpha(s_1) \alpha(s_2), \\ - \frac{1}{\sqrt{2}} \qty[ \alpha(s_1) \beta(s_2) + \beta(s_1) \alpha(s_2) ] \\ + \frac{1}{\sqrt{2}} \, \Big[ \alpha(s_1) \beta(s_2) + \beta(s_1) \alpha(s_2) \Big] \\ \beta(s_1) \beta(s_2). \end{cases} \end{align} \end{subequations} +Since the factor $\Psi(\gamma)$ in Eq.~\eqref{eq:PhiOLD} is symmetrical (upon swapping the coordinates of the two electrons), see Eq.~\eqref{eq:cosGamma}, the symmetry of the non-interacting angular wave functions $\chi(\Omega_1,\Omega_2)$ must be opposite to the one of the spin factor $\Xi(s_1,s_2)$. Consequently (as in the helium atom), the ground-state is a singlet, +\begin{equation} + \label{eq:spin_1S} + \chi_{^1S} (\Omega_1,\Omega_2) = Y_{00}(\Omega_1)Y_{00}(\Omega_2) = \frac1{4\pi} +\end{equation} +(in the usual notation $^{2S+1}L$ with the quantum number $L$ of total orbital angular momentum +$\hat{\bm{L}}=\hat{\bm{\ell}}_1+\hat{\bm{\ell}}_2$ of the two electrons). +Similarly, for the $^3P$ and $^1P$ two-electron states, the angular non-interacting wave functions are \cite{Breit_1930,Seidl_2007,Loos_2009a,Loos_2009c,Loos_2010e} +\begin{subequations} +\begin{align} + \label{eq:spin_3P} + \chi_{^3P} (\Omega_1,\Omega_2) & = \frac1{\sqrt{2}}\,\Big[Y_{10}(\Omega_1)Y_{00}(\Omega_2)-Y_{00}(\Omega_1)Y_{10}(\Omega_2)\Big] + \nonumber\\ + & = \frac{1}{4\pi}\sqrt{\frac32}\,\Big(\cos \theta_1 - \cos \theta_2\Big), + \\ + \label{eq:spin_1P} + \chi_{^1P} (\Omega_1,\Omega_2) & = \frac1{\sqrt{2}}\,\Big[Y_{10}(\Omega_1)Y_{00}(\Omega_2)+Y_{00}(\Omega_1)Y_{10}(\Omega_2)\Big] + \nonumber\\ + & = \frac{1}{4\pi}\sqrt{\frac32}\,\Big(\cos \theta_1 + \cos \theta_2\Big). +\end{align} +\end{subequations} -After integration over the spin coordinates, the total electronic density is, by definition, \cite{DavidsonBook} +By definition, \cite{DavidsonBook} the total electronic density (as a function of the solid angle $\Omega$ on the sphere) is given by the integral \begin{equation} \label{eq:rho} - \rho(\bm{r}_1) = 2 \int \chi (\bm{r}_1,\bm{r}_2)^2 \Psi(r_{12})^2 d\bm{r}_2 + \rho(\Omega_1) = 2 \int \chi (\Omega_1,\Omega_2)^2 \Psi(\gamma)^2 d\Omega_2 +% \rho(\bm{r}_1) = 2 \int \chi (\bm{r}_1,\bm{r}_2)^2 \Psi(r_{12})^2 d\bm{r}_2 \end{equation} -and, following Seidl, \cite{Seidl_2007} one can decompose the square of the (totally symmetric) interelectronic wave function over the complete basis set composed by the Legendre polynomials +(in the notation $d\Omega_2=\sin\theta_2\,d\theta_2\,d\phi_2$), where we have already integrated over the spin coordinates. + +$\bullet$ For the singlet ground state, we have $\chi_{^1S} (\Omega_1,\Omega_2) = \frac{1}{4\pi}$, see Eq.~\eqref{eq:spin_1S}. Consequently, \begin{equation} - \Psi(r_{12})^2 = \sum_{\ell=0}^{\infty} c_{\ell} P_{\ell}(\cos \gamma) +\rho_{^1S}(\Omega_1) = \frac{2}{(4\pi)^2} \int \Psi(\gamma)^2 d\Omega_2 . \end{equation} -where +Obviously, this integral cannot depend on $\Omega_1$, implying that the ground state of two electrons on the surface of a sphere has a uniform density, \begin{equation} - c_{\ell} = \frac{2\ell+1}{2} \int_0^\pi P_{\ell}(\cos \gamma) \Psi(r_{12})^2 \sin \gamma d\gamma +\rho_{^1S}(\Omega) = \frac{2}{4\pi}, % 2/(4\pi R^2), \end{equation} -and the interelectronic angle $\gamma$ is defined as $r_{12} = R \sqrt{2 - 2 \cos \gamma}$ or, equivalently, $\cos \gamma = \cos \theta_1 \cos \theta_2 + \sin \theta_1 \sin \theta_2 \cos(\phi_1 - \phi_2)$. -For the singlet ground state, we have $\chi_{^1S} (\bm{r}_1,\bm{r}_2) = 1$, and taking advantage of the addition theorem of the Legendre polynomials, \cite{NISTbook} \ie, -\begin{equation} - P_{\ell}(\cos \gamma) = \frac{4\pi}{2\ell+1} \sum_{m=-\ell}^{+\ell} Y_{\ell m}^*(\bm{\Omega}_1) Y_{\ell m}(\bm{\Omega}_2) -\end{equation} -and the orthonormality of the spherical harmonics, one finds that $c_\ell = 0$ for $\ell > 0$, demonstrating that the ground state of two electrons on a surface of a sphere has a uniform density $\rho_{^1S}(\bm{r}) = 2/(4\pi R^2)$ for any $R$ values. -This result is also true for any excited states with $^1S$ symmetry. -For the other electronic states corresponding to higher total angular momentum, such as the lowest singlet and triplet $P$ states, \cite{Loos_2010e} the electron density is, in general, inhomogeneous, except in the very unlikely conditions discussed below. \cite{Seidl_2007} +for any value $\cc \in {\mathbb{R}}$ of the interaction constant. This result is also true for any excited states with $^1S$ symmetry. + +$\bullet$ For the other electronic states corresponding to higher total orbital angular momentum $L$, such as the lowest singlet and triplet $P$ states, \cite{Loos_2010e} the electron density is typically nonuniform, except in the very unlikely conditions discussed in the following section. \cite{Seidl_2007} {\color{green} +%We wish to point out that nonuniform densities are not in contradiction with the form of our hamiltonian $\hat{H}$ in Eq.~\eqref{eq:H} +We wish to point out that nonuniform densities do not contradict the form of our hamiltonian $\hat{H}$ in Eq.~\eqref{eq:H} +although $\hat{H}$ has no preferred direction in space. +{\color{red} Ref.?} +} + +%Remark: Discuss the question of having no preferred direction in space! %%% FIG 1 %%% \begin{figure} \includegraphics[width=\linewidth]{3P} \caption{ $c_0 - 2 c_1/3 + c_2/5$ as a function of the radius of the sphere $R$ for various states of $^3P$ symmetry. - The root associated to each state (which corresponds to the value of $R$ for which the electron density is uniform) is located by a marker. + The zero associated with each state (which corresponds to the value of $R$ for which the electron density is uniform) is located by a marker. \label{fig:3P}} \end{figure} %%% %%% %%% %%% @@ -150,56 +209,47 @@ For the other electronic states corresponding to higher total angular momentum, %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Transient uniform electron gases} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -As evidenced by Eq.~\eqref{eq:rho}, both the angular and interelectronic wave functions contribute to the electron density and a subtle interplay between these two quantities may result in a uniform density. -To illustrate this, let us consider explicit examples. +As evidenced by Eq.~\eqref{eq:rho}, the electron density $\rho(\Omega)$ on the spherical surface is affected by both the non-interacting angular wave function $\chi(\Omega_1,\Omega_2)$ and the interelectronic one, $\Psi(\gamma)$. For particular values of $\cc$, a subtle interplay between these two quantities may result in a uniform density $\rho(\Omega)=\frac{2}{4\pi}$ as we shall illustrate now explicitly for the example of the $^3P$ and $^1P$ two-electron states. -For the $^3P$ and $^1P$ two-electron states, the angular wave functions are \cite{Breit_1930,Seidl_2007,Loos_2009a,Loos_2009c,Loos_2010e} -\begin{subequations} -\begin{align} - \label{eq:spin_3P} - \chi_{^3P} (\bm{r}_1,\bm{r}_2) & = \cos \theta_1 - \cos \theta_2 - \\ - \label{eq:spin_1P} - \chi_{^1P} (\bm{r}_1,\bm{r}_2) & = \cos \theta_1 + \cos \theta_2 -\end{align} -\end{subequations} -After a lengthy derivation, the square of $\chi$ can be expanded in terms of spherical harmonics, and, after integration over the coordinates of the second electron, it yields +To evaluate the integral of Eq.~\eqref{eq:rho} in the general case, we follow Ref.\cite{Seidl_2007} and decompose the square of the interelectronic wave function over the complete basis set composed by the Legendre polynomials $P_{\ell}(x)$, +\begin{equation} + \label{eq:expansion_c} + \Psi(\gamma)^2 = \sum_{\ell=0}^{\infty} c_{\ell} P_{\ell}(\cos \gamma). +\end{equation} +Using this expression along with the angular functions \eqref{eq:spin_3P} and \eqref{eq:spin_1P} for the $^3P$ and $^1P$ two-electron states (expressing their squares in terms of the $Y_{\ell m}(\Omega)$ and taking advantage of the general properties of spherical harmonics and Legendre polynomials), we find from Eq.~\eqref{eq:rho} the densities \begin{subequations} \begin{align} \label{eq:3P} - \rho_{^3P}(\bm{r}) & = - \qty(c_0 - \frac{c_2}{5}) Y_{00}(\bm{\Omega})^2 - + \qty(c_0 - \frac{2 c_1}{3} + \frac{c_2}{5}) Y_{10}(\bm{\Omega})^2 + \rho_{^3P}(\Omega) & = + \qty(c_0 - \frac{c_2}{5}) Y_{00}(\Omega)^2 + + \qty(c_0 - \frac{2 c_1}{3} + \frac{c_2}{5}) Y_{10}(\Omega)^2 \\ \label{eq:1P} - \rho_{^1P}(\bm{r}) & = - \qty(c_0 - \frac{c_2}{5}) Y_{00}(\bm{\Omega})^2 - + \qty(c_0 + \frac{2 c_1}{3} + \frac{c_2}{5}) Y_{10}(\bm{\Omega})^2 + \rho_{^1P}(\Omega) & = + \qty(c_0 - \frac{c_2}{5}) Y_{00}(\Omega)^2 + + \qty(c_0 + \frac{2 c_1}{3} + \frac{c_2}{5}) Y_{10}(\Omega)^2 \end{align} \end{subequations} -As readily seen from these expressions and remembering that $Y_{00}(\bm{\Omega})^2 = 1/(4\pi)$, the electron density is uniform if and only if the component associated with $Y_{10}(\bm{\Omega})^2$ vanishes, \ie, +Since $Y_{00}(\bm{\Omega})^2 = \frac1{4\pi}$, these densities are uniform if and only if the component associated with $Y_{10}(\bm{\Omega})^2$ vanishes, \begin{equation} \label{eq:condition} - c_0 \mp \frac{2 c_1}{3} + \frac{c_2}{5} = 0 + c_0 \mp \frac{2 c_1}{3} + \frac{c_2}{5} = 0. +\end{equation} +From our numerical wave functions $\Psi(\gamma)$, the coefficients $c_{\ell}$ of the expansion \eqref{eq:expansion_c} can be extracted via +\begin{equation} + c_{\ell} = \frac{2\ell+1}{2} \int_0^\pi P_{\ell}(\cos \gamma) \Psi(\gamma)^2 \sin \gamma d\gamma. \end{equation} -For each (ground or excited) $^3P$ states, there exists one and only one value of the radius, $R_\text{UEG}$, for which Eq.~\eqref{eq:condition} is fulfilled, and it can be computed numerically with great precision thanks to explicitly correlated calculations. \cite{Loos_2009a} -Figure \ref{fig:3P} shows the behavior of $c_0 - 2 c_1/3 + c_2/5$ as a function of $R$ for the $^3P$ ground state and its first and second excited states. -As one can see, $R_\text{UEG}$ is negative (which corresponds to an attractive ``electron'' pair \cite{Seidl_2007,Seidl_2010} or exciton \cite{Pedersen_2010,Loos_2012c}) and gets larger (in absolute value) for excited states. -Because this model has an inhomogeneous electron density except for a unique $R$ value, we name these ``ephemeral'' systems as transient UEGs (TUEGs). -Note that this feature was first discovered by Seidl in Appendix A of Ref.~\onlinecite{Seidl_2007}. -He also provided an estimate $R_\text{UEG} \approx \SI{-5.3}{\bohr}$ for the $^3P$ ground state, a rather good estimate that we refine here to $R_\text{UEG} \approx \SI{-5.32527}{\bohr}$. +For each (ground or excited) $^3P$ states, there exists one and only one value of the "radius" $\cc$ in Eq.~\eqref{eq:cc}, $\cc=\cc_\text{UEG}<0$, for which these coefficients satisfy Eq.~\eqref{eq:condition}. $\cc_\text{UEG}$ can be computed numerically with great precision thanks to explicitly correlated calculations. \cite{Loos_2009a} Figure \ref{fig:3P} shows the behavior of $c_0 - 2 c_1/3 + c_2/5$ as a function of $\cc$ for the $^3P$ ground state and its first and second excited states. As one can see, $\cc_\text{UEG}$ is negative (which corresponds to an attractive ``electron'' pair \cite{Seidl_2007,Seidl_2010} or exciton \cite{Pedersen_2010,Loos_2012c}) and gets larger (in absolute value) for excited states. +Because this model has a nonuniform electron density except for a unique $\cc$ value, we name these ``ephemeral'' systems as transient UEGs (TUEGs). Note that this feature was first discovered in Appendix A of Ref.~\onlinecite{Seidl_2007}. There, also an estimate $\cc_\text{UEG} \approx -5.3$ was provided for the $^3P$ ground state, a rather good estimate that we refine here to $\cc_\text{UEG} \approx -5.32527$. -For the $^1P$ states, the condition $c_0 + 2 c_1/3 + c_2/5 = 0$ [see Eq.~\eqref{eq:condition}] cannot be fulfilled and, hence, these states never exhibit uniform densities. -This further highlights the subtle balance that must be accomplished between the spin and spatial parts of the wave function [see Eq.~\eqref{eq:rho}] and this can help us rationalizing why the $^3P$ states are TUEGs. +For the $^1P$ states, the condition $c_0 + 2 c_1/3 + c_2/5 = 0$ [see Eq.~\eqref{eq:condition}] cannot be fulfilled and, hence, these states never exhibit uniform densities. This further highlights the subtle balance that must be accomplished +between the non-interacting and the interelectronic (angular) parts (denoted here $\chi$ and $\Psi$, respectively) of the wave function +[see Eq.~\eqref{eq:rho}] and this can help us rationalizing why the $^3P$ states are TUEGs. -The $^3P$ spin wave function, $\chi_{^3P}$, defined in Eq.~\eqref{eq:spin_3P} has the natural tendency to pull apart same-spin electrons in accordance with the Pauli exclusion principle, creating in the process a so-called Fermi hole. \cite{Boyd_1974,Giner_2016a} -The same physical effect can be obtained by increasing the value of $R$ (\ie, $R \gg 0$). -In such a case, the two electrons localize (or ``crystallize'') on opposite side of the sphere to minimize their repsulsion and they form a Wigner crystal. \cite{Wigner_1934} -Oppositely, when $R \ll 0$, the two electrons are attracted to each other to form a pair of tightly bound electrons that freely move on the sphere. \cite{Seidl_2007,Seidl_2010} -For certain $R$ values, the attractive effect stemming from the spatial part of the wave function exactly compensates the Pauli exclusion principle originating from the spin part of the wave function to make the total electron density uniform, hence producing TUEGs. -In higher-energy excited states, the same-spin electrons are further away as compared to the ground state due to the larger number of nodes in the excited-state wave functions. -Therefore, the magnitude of the attractive effect has to be larger to compensate it, which corresponds to more negative values of $R$. +The $^3P$ non-interacting angular wave function, $\chi_{^3P}$, defined in Eq.~\eqref{eq:spin_3P} has the natural tendency to pull apart same-spin electrons in accordance with the Pauli exclusion principle, creating in the process a so-called Fermi hole. \cite{Boyd_1974,Giner_2016a} +The same physical effect can, independently, result from repulsion: In the case $\cc \gg 0$, two strongly repulsive electrons localize (or ``crystallize'') on opposite sides of the sphere to minimize their repulsion and they form a Wigner crystal. \cite{Wigner_1934} +Oppositely, when $\cc \ll 0$, the two electrons are strongly attracted to each other, forming a tightly bound pair that moves freely on the sphere. \cite{Seidl_2007,Seidl_2010} For certain values $\cc<0$, the attractive force seems to exactly compensate the "repulsive" effect of the Pauli exclusion principle, thus making the total electron density uniform, hence producing TUEGs. In higher-energy excited states, the same-spin electrons are further away as compared to the ground state due to the larger number of nodes in the excited-state wave functions. Therefore, a compensating attraction must be larger, corresponding to stronger negative values of $\cc$. %%% FIG 2 %%% \begin{figure} @@ -211,29 +261,31 @@ Therefore, the magnitude of the attractive effect has to be larger to compensate %%% %%% %%% %%% For the IUEG and FUEGs, the density is uniform independently of the level of theory, \ie, the system has homogeneous density within the exact theory or any approximate methods (such as the HF approximation) unless the spin and/or spatial symmetry is broken. \cite{Fukutome_1981,Stuber_2003,VignaleBook} -However, the value of $R_\text{UEG}$ is, \textit{a priori}, highly dependent on the level of theory for TUEGs. -Indeed, it is very unlikely that the exact theory and the HF approximation provide the same value of $R_\text{UEG}$ as the uniformity stems from the competition between Fermi effects originating from the antisymmetric nature of the wave function (which are well described at the HF level) and correlation effects (which are absent, by definition, at the HF level). -Actually, it is even possible for a system to be a TUEG within the exact treatment and being non-uniform for all $R$ values at the HF level. -It seems to be the case for the present two-electron system. +For TUEGs, however, the value of $\cc_\text{UEG}$ is, \textit{a priori}, highly dependent on the level of theory. +Indeed, it is very unlikely that the exact theory and the HF approximation provide the same value of $\cc_\text{UEG}$ as the uniformity stems from the competition between Fermi effects originating from the antisymmetric nature of the wave function (which are well described at the HF level) and correlation effects (which, by definition, are absent at the HF level). Actually, it is even possible for a system to be a TUEG within the exact treatment and being non-uniform for all $\cc$ values at the HF level. This seems to be the case for the present two-electron system. -Expanding the two HF orbitals of the $^3P$ ground state in a basis of zonal harmonics $Y_{\ell}(\theta) \equiv Y_{\ell 0}(\theta,\phi)$, we have not found any $R$ values for which the HF electron density, $\rho^\text{HF}(\theta)$, is uniform. -However, at $R \approx \SI{-7}{\bohr}$, $\rho^\text{HF}$ is \textit{locally} uniform around $\theta = \pi/2$ (\ie, in the $xy$ plane), as shown in Fig.~\ref{fig:HF}. -We believe that this outcome is a direct consequence of the single-determinant nature of the HF approximation which can only include, by definition, one of the three equivalent $sp$ configurations (\ie, $sp_x$, $sp_y$, and $sp_z$). -The fact that this phenomenon appears at larger (absolute) $R$ values in the HF approximation is not surprising as, contrary to the repulsive regime (\ie, $R > 0$) where the electrons are too close to each other at the HF level (compared to the exact picture), \cite{Gori-Giorgi_2008,Pearson_2009} in the attractive regime (\ie, $R < 0$) they are too far away from each other. -This implies that the interaction strength has to be greater (which is equivalent to a larger absolute value of $R$) to overcome this drawback. \cite{Seidl_2010,Burton_2019a,Marie_2020} +Expanding the two HF orbitals of the $^3P$ ground state in a basis of zonal harmonics $Y_{\ell}(\theta) \equiv Y_{\ell 0}(\theta,\phi)$, we have not found any $\cc$ values for which the HF electron density, +\begin{equation} +\tilde{\rho}^\text{HF}(\theta) = \sin\theta\cdot\int_0^{2\pi}d\phi\,\rho^\text{HF}(\Omega), +\end{equation} +is uniform. +At $\cc \approx -7$, however, $\tilde{\rho}^\text{HF}(\theta)$ is \textit{locally} uniform around $\theta = \frac{\pi}{2}$ +(\ie, in a belt closely above and below the $xy$ plane), as shown in Fig.~\ref{fig:HF}. We believe that this outcome is a direct consequence of the single-determinant nature of the HF approximation which, by definition, can only include one of the three equivalent $sp$ configurations (\ie, $sp_x$, $sp_y$, and $sp_z$). The fact that this phenomenon appears at larger (absolute) $\cc$ values in the HF approximation is not surprising as, contrary to the repulsive regime (\ie, $\cc > 0$) where the electrons are too close to each other at the HF level (compared to the exact picture), \cite{Gori-Giorgi_2008,Pearson_2009} in the attractive regime (\ie, $\cc < 0$) they are too far away from each other. This implies that the interaction strength has to be greater (which is equivalent to a larger absolute value of $\cc$) to overcome this drawback. \cite{Seidl_2010,Burton_2019a,Marie_2020} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Concluding remarks} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Here, we have introduced the concept of transient UEGs (TUEGs), a novel family of electron gases that exhibit, in very particular conditions, homogenous densities. Using the electrons-on-a-sphere model, we have presented an example of such TUEGs created thanks to the competing effects of the Pauli exclusion principle and the creation of an attractive electron pair. -TUEGs with larger number of electrons certainly exists and we hope to investigate these in the future. +TUEGs with larger number of electrons certainly exist and we hope to investigate these in the future. As a final remark, we would like to mention that a very similar analysis can be easily performed for higher-dimensional systems where TUEGs can likely be obtained for different values of the radius of the $D$-dimensional sphere. \cite{Loos_2011b} The three-dimensional version where electrons are confined to the surface of a 3-sphere (or glome) could be of particular interest, especially in the context of the development of new exchange-correlation functionals within DFT.\cite{Sun_2015,Agboola_2015,Loos_2017a} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section*{Acknowledgements} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +{\color{green} The authors thank Paola Gori-Giorgi for pointing out the uniform density case of Ref.~\onlinecite{Seidl_2007}.} +%Stimulating discussions with Mike Seidl are also acknowledged. This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (Grant agreement No.~863481). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%