more refs

Manuscript/sfBSE.bib

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 %% This BibTeX bibliography file was created using BibDesk.
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-%% Created for Pierre-Francois Loos at 2020-12-06 14:37:50 +0100 
+%% Created for Pierre-Francois Loos at 2020-12-06 15:06:52 +0100 
 
 
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+@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. },
+	author = {Krylov, Anna I.},
+	date-added = {2020-12-06 15:06:47 +0100},
+	date-modified = {2020-12-06 15:06:52 +0100},
+	doi = {10.1146/annurev.physchem.59.032607.093602},
+	eprint = {https://doi.org/10.1146/annurev.physchem.59.032607.093602},
+	journal = {Annual Review of Physical Chemistry},
+	note = {PMID: 18173379},
+	number = {1},
+	pages = {433-462},
+	title = {Equation-of-Motion Coupled-Cluster Methods for Open-Shell and Electronically Excited Species: The Hitchhiker's Guide to Fock Space},
+	url = {https://doi.org/10.1146/annurev.physchem.59.032607.093602},
+	volume = {59},
+	year = {2008},
+	Bdsk-Url-1 = {https://doi.org/10.1146/annurev.physchem.59.032607.093602}}
+
+@article{Manohar_2008,
+	author = {Manohar,Prashant U. and Krylov,Anna I.},
+	date-added = {2020-12-06 15:04:49 +0100},
+	date-modified = {2020-12-06 15:04:56 +0100},
+	doi = {10.1063/1.3013087},
+	eprint = {https://doi.org/10.1063/1.3013087},
+	journal = {J. Chem. Phys.},
+	number = {19},
+	pages = {194105},
+	title = {A noniterative perturbative triples correction for the spin-flipping and spin-conserving equation-of-motion coupled-cluster methods with single and double substitutions},
+	url = {https://doi.org/10.1063/1.3013087},
+	volume = {129},
+	year = {2008},
+	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.},
+	date-added = {2020-12-06 15:04:33 +0100},
+	date-modified = {2020-12-06 15:04:44 +0100},
+	doi = {10.1021/jp0764079},
+	eprint = {https://doi.org/10.1021/jp0764079},
+	journal = {J. Phys. Chem. A},
+	note = {PMID: 18004832},
+	number = {50},
+	pages = {13264-13271},
+	title = {Performance of the Spin-Flip and Multireference Methods for Bond Breaking in Hydrocarbons:  A Benchmark Study},
+	url = {https://doi.org/10.1021/jp0764079},
+	volume = {111},
+	year = {2007},
+	Bdsk-Url-1 = {https://doi.org/10.1021/jp0764079}}
+
+@article{Wang_2005,
+	author = {Wang,Tao and Krylov,Anna I.},
+	date-added = {2020-12-06 15:04:15 +0100},
+	date-modified = {2020-12-06 15:04:28 +0100},
+	doi = {10.1063/1.2018645},
+	eprint = {https://doi.org/10.1063/1.2018645},
+	journal = {J. Chem. Phys.},
+	number = {10},
+	pages = {104304},
+	title = {The effect of substituents on electronic states' ordering in meta-xylylene diradicals: Qualitative insights from quantitative studies},
+	url = {https://doi.org/10.1063/1.2018645},
+	volume = {123},
+	year = {2005},
+	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.},
+	date-added = {2020-12-06 15:04:01 +0100},
+	date-modified = {2020-12-06 15:04:09 +0100},
+	doi = {10.1021/jacs.7b05197},
+	eprint = {https://doi.org/10.1021/jacs.7b05197},
+	journal = {J. Am. Chem. Soc.},
+	note = {PMID: 28732445},
+	number = {32},
+	pages = {11138-11148},
+	title = {Photoelectron Spectroscopy Study of Quinonimides},
+	url = {https://doi.org/10.1021/jacs.7b05197},
+	volume = {139},
+	year = {2017},
+	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.},
+	date-added = {2020-12-06 15:03:26 +0100},
+	date-modified = {2020-12-06 15:03:38 +0100},
+	doi = {10.1021/acs.jpca.7b10576},
+	eprint = {https://doi.org/10.1021/acs.jpca.7b10576},
+	journal = {J. Phys. Chem. A},
+	note = {PMID: 29227675},
+	number = {1},
+	pages = {420-430},
+	title = {An ab Initio Exploration of the Bergman Cyclization},
+	url = {https://doi.org/10.1021/acs.jpca.7b10576},
+	volume = {122},
+	year = {2018},
+	Bdsk-Url-1 = {https://doi.org/10.1021/acs.jpca.7b10576}}
+
+@article{Casanova_2012,
+	author = {Casanova,David},
+	date-added = {2020-12-06 15:03:14 +0100},
+	date-modified = {2020-12-06 15:03:22 +0100},
+	doi = {10.1063/1.4747341},
+	eprint = {https://doi.org/10.1063/1.4747341},
+	journal = {J. Chem. Phys.},
+	number = {8},
+	pages = {084105},
+	title = {Avoided crossings, conical intersections, and low-lying excited states with a single reference method: The restricted active space spin-flip configuration interaction approach},
+	url = {https://doi.org/10.1063/1.4747341},
+	volume = {137},
+	year = {2012},
+	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},
+	date-added = {2020-12-06 15:02:57 +0100},
+	date-modified = {2020-12-06 15:03:06 +0100},
+	doi = {10.1063/1.4896372},
+	eprint = {https://doi.org/10.1063/1.4896372},
+	journal = {J. Chem. Phys.},
+	number = {12},
+	pages = {124122},
+	title = {Assessment of approximate computational methods for conical intersections and branching plane vectors in organic molecules},
+	url = {https://doi.org/10.1063/1.4896372},
+	volume = {141},
+	year = {2014},
+	Bdsk-Url-1 = {https://doi.org/10.1063/1.4896372}}
+
+@article{Lefrancois_2016,
+	author = {Lefrancois,Daniel and Rehn,Dirk R. and Dreuw,Andreas},
+	date-added = {2020-12-06 15:02:47 +0100},
+	date-modified = {2020-12-06 15:02:51 +0100},
+	doi = {10.1063/1.4961298},
+	eprint = {https://doi.org/10.1063/1.4961298},
+	journal = {The Journal of Chemical Physics},
+	number = {8},
+	pages = {084102},
+	title = {Accurate adiabatic singlet-triplet gaps in atoms and molecules employing the third-order spin-flip algebraic diagrammatic construction scheme for the polarization propagator},
+	url = {https://doi.org/10.1063/1.4961298},
+	volume = {145},
+	year = {2016},
+	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.},
+	author = {Zilvinas Rinkevicius and Hans {\AA}gren},
+	date-added = {2020-12-06 14:56:16 +0100},
+	date-modified = {2020-12-06 14:56:28 +0100},
+	doi = {https://doi.org/10.1016/j.cplett.2010.03.074},
+	issn = {0009-2614},
+	journal = {Chem. Phys. Lett.},
+	number = {4},
+	pages = {132 - 135},
+	title = {Spin-flip time dependent density functional theory for singlet--triplet splittings in σ,σ-biradicals},
+	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}}
+
+@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.},
+	author = {Ibeji, Collins U. and Ghosh, Debashree},
+	date-added = {2020-12-06 14:55:59 +0100},
+	date-modified = {2020-12-06 14:56:11 +0100},
+	doi = {10.1039/C5CP00214A},
+	issue = {15},
+	journal = {Phys. Chem. Chem. Phys.},
+	pages = {9849-9856},
+	publisher = {The Royal Society of Chemistry},
+	title = {Singlet--triplet gaps in polyacenes: a delicate balance between dynamic and static correlations investigated by spin--flip methods},
+	url = {http://dx.doi.org/10.1039/C5CP00214A},
+	volume = {17},
+	year = {2015},
+	Bdsk-Url-1 = {http://dx.doi.org/10.1039/C5CP00214A}}
+
+@article{Lefrancois_2015,
+	author = {Lefrancois,Daniel and Wormit,Michael and Dreuw,Andreas},
+	date-added = {2020-12-06 14:49:23 +0100},
+	date-modified = {2020-12-06 14:49:30 +0100},
+	doi = {10.1063/1.4931653},
+	eprint = {https://doi.org/10.1063/1.4931653},
+	journal = {J. Chem. Phys.},
+	number = {12},
+	pages = {124107},
+	title = {Adapting algebraic diagrammatic construction schemes for the polarization propagator to problems with multi-reference electronic ground states exploiting the spin-flip ansatz},
+	url = {https://doi.org/10.1063/1.4931653},
+	volume = {143},
+	year = {2015},
+	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.},
+	author = {Mato, Joani and Gordon, Mark S.},
+	date-added = {2020-12-06 14:49:12 +0100},
+	date-modified = {2020-12-06 14:49:18 +0100},
+	doi = {10.1039/C7CP06837A},
+	issue = {4},
+	journal = {Phys. Chem. Chem. Phys.},
+	pages = {2615-2626},
+	publisher = {The Royal Society of Chemistry},
+	title = {A general spin-complete spin-flip configuration interaction method},
+	url = {http://dx.doi.org/10.1039/C7CP06837A},
+	volume = {20},
+	year = {2018},
+	Bdsk-Url-1 = {http://dx.doi.org/10.1039/C7CP06837A}}
+
 @article{Levchenko_2004,
 	author = {Levchenko,Sergey V. and Krylov,Anna I.},
 	date-added = {2020-12-06 14:37:40 +0100},
@@ -371,7 +575,8 @@
 	pages = {205--226},
 	title = {Zur Theorie der Metalle},
 	volume = {71},
-	year = {1931}}
+	year = {1931},
+	Bdsk-Url-1 = {https://doi.org/10.1007/BF01341708}}
 
 @article{Adamo_2013,
 	author = {Adamo, C. and Jacquemin, D.},
@@ -13089,6 +13294,7 @@
 	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}}
 
 @article{Wetherell_2018,

Manuscript/sfBSE.tex

@@ -47,7 +47,7 @@ The fact that none of these methods is successful in every chemical scenario has
 Like adiabatic time-dependent density-functional theory (TD-DFT), \cite{Runge_1984,Casida_1995,Petersilka_1996} the Bethe-Salpeter equation (BSE) formalism within the static approximation \cite{Salpeter_1951,Strinati_1988} is plagued by the lack of double (and higher) excitations, which are, for example, ubiquitous in conjugated molecules like polyenes. \cite{Maitra_2004,Cave_2004,Saha_2006,Watson_2012,Shu_2017,Barca_2018a,Barca_2018b,Loos_2019}
 
 One way to access double excitations is via the spin-flip formalism established by Krylov in 2001, \cite{Krylov_2001a,Krylov_2001b,Krylov_2002} with earlier attempts by Bethe, \cite{Bethe_1931} as well as Shibuya and McKoy. \cite{Shibuya_1970}
-Nowadays, spin-flip techniques are widely available for many types of methods such as equation-of-motion coupled cluster (EOM-CC), \cite{} configuration interaction (CI), \cite{} TD-DFT, \cite{} and others \cite{} with successful applications in bond breaking processes, \cite{} radical chemistry, \cite{} and the photochemistry of conical intersections \cite{} to mention a few. 
+Nowadays, spin-flip techniques are widely available for many types of methods such as equation-of-motion coupled cluster (EOM-CC), \cite{Krylov_2001a} configuration interaction (CI), \cite{Krylov_2001b} TD-DFT, \cite{Shao_2003,Wang_2004,Li_2011a,Bernard_2012,Zhang_2015} and others \cite{Krylov_2002,Levchenko_2004,Manohar_2008,Casanova_2008,Casanova_2009a,Casanova_2009b,Mayhall_2014a,Mayhall_2014b,Bell_2013,Dutta_2013,Mayhall_2014c,Lefrancois_2015,Mato_2018} with successful applications in bond breaking processes, \cite{Golubeva_2007} radical chemistry, \cite{Slipchenko_2002,Wang_2005,Slipchenko_2003,Rinkevicius_2010,Ibeji_2015,Hossain_2017,Orms_2018,Luxon_2018} and the photochemistry of conical intersections \cite{Casanova_2012,Gozem_2013,Nikiforov_2014,Lefrancois_2016} to mention a few. 
 We refer the interested reader to Refs.~\onlinecite{Krylov_2006,Krylov_2008,Casanova_2020} for a more detailed review of spin-flip methods.
 
 The idea behind the spin-flip formalism is quite simple: instead of starting the calculation  from the singlet ground state, one can start from the lowest triplet state.