2670 lines
111 KiB
BibTeX
2670 lines
111 KiB
BibTeX
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abstract = {Summary This chapter contains sections titled: Introduction Formulation of the Correlation Problem Methods for Treating Electronic Correlation Recent Developments; Concluding Remarks},
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abstract = { The general theory of quantum mechanics is now almost complete, the imperfections that still remain being in connection with the exact fitting in of the theory with relativity ideas. These give rise to difficulties only when high-speed particles are involved, and are therefore of no importance in the consideration of atomic and molecular structure and ordinary chemical reactions, in which it is, indeed, usually sufficiently accurate if one neglects relativity variation of mass with velocity and assumes only Coulomb forces between the various electrons and atomic nuclei. The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble. It there fore becomes desirable that approximate practical methods of applying quantum mechanics should be developed, which can lead to an explanation of the main features of complex atomic systems without too much computation. Already before the arrival of quantum mechanics there existed a theory of atomic structure, based on Bohr's ideas of quantised orbits, which was fairly successful in a wide field. To get agreement with experiment it was found necessary to introduce the spin of the electron, giving a doubling in the number of orbits of an electron in an atom. With the help of this spin and Pauli's exclusion principle, a satisfactory theory of multiplet terms was obtained when one made the additional assumption that the electrons in an atom all set themselves with their spins parallel or antiparallel. If s denoted the magnitude of the resultant spin angular momentum, this s was combined vectorially with the resultant orbital angular momentum l to give a multiplet of multiplicity 2s + 1. The fact that one had to make this additional assumption was, however, a serious disadvantage, as no theoretical reasons to support it could be given. It seemed to show that there were large forces coupling the spin vectors of the electrons in an atom, much larger forces than could be accounted for as due to the interaction of the magnetic moments of the electrons. The position was thus that there was empirical evidence in favour of these large forces, but that their theoretical nature was quite unknown. },
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@article{Shanks_1955,
|
||
abstract = {This paper discusses a family of non-linear sequence-to-sequence transformations designated as ek, ekm, {\~e}k, and ed. A brief history of the transforms is related and a simple motivation for the transforms is given. Examples are given of the application of these transformations to divergent and slowly convergent sequences. In particular the examples include numerical series, the power series of rational and meromorphic functions, and a wide variety of sequences drawn from continued fractions, integral equations, geometry, fluid mechanics, and number theory. Theorems are proven which show the effectiveness of the transformations both in accelerating the convergence of (some) slowly convergent sequences and in inducing convergence in (some) divergent sequences. The essential unity of these two motives is stressed. Theorems are proven which show that these transforms often duplicate the results of well-known, but specialized techniques. These special algorithms include Newton's iterative process, Gauss's numerical integration, an identity of Euler, the Pad{\'e} Table, and Thiele's reciprocal differences. Difficulties which sometimes arise in the use of these transforms such as irregularity, non-uniform convergence to the wrong answer, and the ambiguity of multivalued functions are investigated. The concepts of antilimit and of the spectra of sequences are introduced and discussed. The contrast between discrete and continuous spectra and the consequent contrasting response of the corresponding sequences to the e1 transformation is indicated. The characteristic behaviour of a semiconvergent (asymptotic) sequence is elucidated by an analysis of its spectrum into convergent components of large amplitude and divergent components of small amplitude.},
|
||
author = {Shanks, Daniel},
|
||
date-added = {2020-12-02 20:05:53 +0100},
|
||
date-modified = {2020-12-02 21:46:29 +0100},
|
||
doi = {https://doi.org/10.1002/sapm19553411},
|
||
journal = {J. Math. Phys.},
|
||
number = {1-4},
|
||
pages = {1-42},
|
||
title = {Non-linear Transformations of Divergent and Slowly Convergent Sequences},
|
||
volume = {34},
|
||
year = {1955},
|
||
Bdsk-Url-1 = {https://onlinelibrary.wiley.com/doi/abs/10.1002/sapm19553411},
|
||
Bdsk-Url-2 = {https://doi.org/10.1002/sapm19553411}}
|
||
|
||
@article{DiSabatino_2015,
|
||
author = {Di Sabatino,S. and Berger,J. A. and Reining,L. and Romaniello,P.},
|
||
date-added = {2020-12-02 16:02:21 +0100},
|
||
date-modified = {2020-12-02 16:02:21 +0100},
|
||
doi = {10.1063/1.4926327},
|
||
journal = {J. Chem. Phys.},
|
||
number = {2},
|
||
pages = {024108},
|
||
title = {Reduced density-matrix functional theory: Correlation and spectroscopy},
|
||
volume = {143},
|
||
year = {2015},
|
||
Bdsk-Url-1 = {https://doi.org/10.1063/1.4926327}}
|
||
|
||
@article{Romaniello_2009,
|
||
author = {Romaniello, P. and Guyot, S. and Reining, L.},
|
||
date-added = {2020-12-02 16:01:08 +0100},
|
||
date-modified = {2020-12-02 16:01:18 +0100},
|
||
doi = {10.1063/1.3249965},
|
||
journal = {J. Chem. Phys.},
|
||
pages = {154111},
|
||
title = {The Self-Energy beyond {{GW}}: {{Local}} and Nonlocal Vertex Corrections},
|
||
volume = {131},
|
||
year = {2009},
|
||
Bdsk-Url-1 = {https://dx.doi.org/10.1063/1.3249965}}
|
||
|
||
@article{Tarantino_2017,
|
||
author = {Tarantino, Walter and Romaniello, Pina and Berger, J. A. and Reining, Lucia},
|
||
date-added = {2020-12-02 16:00:19 +0100},
|
||
date-modified = {2020-12-02 16:00:29 +0100},
|
||
doi = {10.1103/PhysRevB.96.045124},
|
||
journal = {Phys. Rev. B},
|
||
pages = {045124},
|
||
title = {Self-Consistent {{Dyson}} Equation and Self-Energy Functionals: {{An}} Analysis and Illustration on the Example of the {{Hubbard}} Atom},
|
||
volume = {96},
|
||
year = {2017},
|
||
Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevB.96.045124}}
|
||
|
||
@article{Romaniello_2012,
|
||
author = {Romaniello, Pina and Bechstedt, Friedhelm and Reining, Lucia},
|
||
date-added = {2020-12-02 15:59:28 +0100},
|
||
date-modified = {2020-12-02 15:59:40 +0100},
|
||
doi = {10.1103/PhysRevB.85.155131},
|
||
journal = {Phys. Rev. B},
|
||
pages = {155131},
|
||
title = {Beyond the {{GW}} Approximation: {{Combining}} Correlation Channels},
|
||
volume = {85},
|
||
year = {2012},
|
||
Bdsk-Url-1 = {https://dx.doi.org/10.1103/PhysRevB.85.155131}}
|
||
|
||
@article{Fromager_2020,
|
||
author = {Fromager, Emmanuel},
|
||
date-added = {2020-12-02 15:58:21 +0100},
|
||
date-modified = {2020-12-02 15:58:33 +0100},
|
||
doi = {10.1103/PhysRevLett.124.243001},
|
||
journal = {Phys. Rev. Lett.},
|
||
pages = {243001},
|
||
title = {Individual Correlations in Ensemble Density Functional Theory: State- and Density-Driven Decompositions without Additional Kohn-Sham Systems},
|
||
volume = {124},
|
||
year = {2020},
|
||
Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.124.243001},
|
||
Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevLett.124.243001}}
|
||
|
||
@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.},
|
||
author = {Deur, Killian and Mazouin, Laurent and Senjean, Bruno and Fromager, Emmanuel},
|
||
date-added = {2020-12-02 15:57:26 +0100},
|
||
date-modified = {2020-12-02 21:43:28 +0100},
|
||
doi = {10.1140/epjb/e2018-90124-7},
|
||
journal = {Eur. Phys. J. B},
|
||
pages = {162},
|
||
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}}
|
||
|
||
@article{Sagredo_2018,
|
||
author = {Sagredo, Francisca and Burke, Kieron},
|
||
date-added = {2020-12-02 15:56:44 +0100},
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||
date-modified = {2020-12-02 15:56:56 +0100},
|
||
doi = {10.1063/1.5043411},
|
||
journal = {J. Chem. Phys.},
|
||
pages = {134103},
|
||
title = {Accurate double excitations from ensemble density functional calculations},
|
||
volume = {149},
|
||
year = {2018},
|
||
Bdsk-Url-1 = {https://doi.org/10.1063/1.5043411}}
|
||
|
||
@article{Deur_2017,
|
||
author = {Deur, Killian and Mazouin, Laurent and Fromager, Emmanuel},
|
||
date-added = {2020-12-02 15:56:14 +0100},
|
||
date-modified = {2020-12-02 21:42:49 +0100},
|
||
doi = {10.1103/PhysRevB.95.035120},
|
||
journal = {Phys. Rev. B},
|
||
pages = {95.035120},
|
||
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}}
|
||
|
||
@article{Senjean_2018,
|
||
author = {Senjean, Bruno and Fromager, Emmanuel},
|
||
date-added = {2020-12-02 15:55:29 +0100},
|
||
date-modified = {2020-12-02 22:01:59 +0100},
|
||
doi = {10.1103/PhysRevA.98.022513},
|
||
journal = {Phys. Rev. A},
|
||
pages = {98.022513},
|
||
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}}
|
||
|
||
@article{Blase_2018,
|
||
author = {Blase, Xavier and Duchemin, Ivan and Jacquemin, Denis},
|
||
date-added = {2020-12-01 21:12:31 +0100},
|
||
date-modified = {2020-12-01 21:12:31 +0100},
|
||
doi = {10.1039/C7CS00049A},
|
||
journal = {Chem. Soc. Rev.},
|
||
pages = {1022-1043},
|
||
publisher = {The Royal Society of Chemistry},
|
||
title = {The Bethe--Salpeter equation in chemistry: relations with TD-DFT{,} applications and challenges},
|
||
volume = {47},
|
||
year = {2018},
|
||
Bdsk-Url-1 = {http://dx.doi.org/10.1039/C7CS00049A}}
|
||
|
||
@article{Blase_2020,
|
||
author = {X. Blase and I. Duchemin and D. Jacquemin and P. F. Loos},
|
||
date-added = {2020-12-01 21:12:31 +0100},
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||
date-modified = {2020-12-01 21:12:31 +0100},
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||
doi = {10.1021/acs.jpclett.0c01875},
|
||
journal = {J. Phys. Chem. Lett.},
|
||
pages = {7371},
|
||
title = {The Bethe-Salpeter Formalism: From Physics to Chemistry},
|
||
volume = {11},
|
||
year = {2020},
|
||
Bdsk-Url-1 = {https://doi.org/10.1021/acs.jpclett.0c01875}}
|
||
|
||
@article{Ghosh_2018,
|
||
author = {Ghosh, Soumen and Verma, Pragya and Cramer, Christopher J. and Gagliardi, Laura and Truhlar, Donald G.},
|
||
date-added = {2020-12-01 21:12:15 +0100},
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date-modified = {2020-12-01 21:12:15 +0100},
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||
doi = {10.1021/acs.chemrev.8b00193},
|
||
journal = {Chem. Rev.},
|
||
pages = {7249--7292},
|
||
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}}
|
||
|
||
@article{Adamo_2013,
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author = {Adamo, C. and Jacquemin, D.},
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||
date-added = {2020-12-01 21:11:58 +0100},
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date-modified = {2020-12-01 21:15:50 +0100},
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doi = {10.1039/C2CS35394F},
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||
journal = {Chem. Soc. Rev.},
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||
pages = {845--856},
|
||
title = {The Calculations of Excited-State Properties with Time-Dependent Density Functional Theory},
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||
volume = {42},
|
||
year = {2013},
|
||
Bdsk-Url-1 = {https://doi.org/10.1039/C2CS35394F}}
|
||
|
||
@article{Laurent_2013,
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||
author = {Laurent, Ad{\`e}le D. and Jacquemin, Denis},
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date-added = {2020-12-01 21:11:49 +0100},
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date-modified = {2020-12-01 21:15:13 +0100},
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doi = {10.1002/qua.24438},
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||
journal = {Int. J. Quantum Chem.},
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||
pages = {2019--2039},
|
||
title = {TD-DFT Benchmarks: A Review},
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||
volume = {113},
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year = {2013},
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||
Bdsk-Url-1 = {https://doi.org/10.1002/qua.24438}}
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@article{Gonzales_2012,
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author = {Gonz{\'a}lez, Leticia and Escudero, D. and Serrano-Andr\`es, L.},
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date-added = {2020-12-01 21:11:38 +0100},
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date-modified = {2020-12-01 21:11:38 +0100},
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||
doi = {10.1002/cphc.201100200},
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||
journal = {ChemPhysChem},
|
||
pages = {28--51},
|
||
title = {Progress and Challenges in the Calculation of Electronic Excited States},
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||
volume = {13},
|
||
year = {2012},
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||
Bdsk-Url-1 = {https://doi.org/10.1002/cphc.201100200}}
|
||
|
||
@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},
|
||
author = {Sneskov, Kristian and Christiansen, Ove},
|
||
date-added = {2020-12-01 21:11:24 +0100},
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date-modified = {2020-12-01 21:14:26 +0100},
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doi = {https://doi.org/10.1002/wcms.99},
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journal = {WIREs Comput. Mol. Sci.},
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||
pages = {566--584},
|
||
title = {Excited State Coupled Cluster Methods},
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||
volume = {2},
|
||
year = {2012},
|
||
Bdsk-Url-1 = {https://onlinelibrary.wiley.com/doi/abs/10.1002/wcms.99},
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Bdsk-Url-2 = {https://doi.org/10.1002/wcms.99}}
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@article{Krylov_2006,
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author = {Krylov, Anna I.},
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date-added = {2020-12-01 21:10:56 +0100},
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date-modified = {2020-12-01 21:14:02 +0100},
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doi = {10.1021/ar0402006},
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journal = {Acc. Chem. Res.},
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||
pages = {83-91},
|
||
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}}
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||
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@article{Dreuw_2005,
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author = {Dreuw, Andreas and Head-Gordon, Martin},
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date-added = {2020-12-01 21:10:39 +0100},
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date-modified = {2020-12-01 21:10:39 +0100},
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doi = {10.1021/cr0505627},
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file = {/Users/loos/Zotero/storage/WKGXAHGE/Dreuw_2005.pdf},
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issn = {0009-2665, 1520-6890},
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||
journal = {Chem. Rev.},
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||
language = {en},
|
||
pages = {4009--4037},
|
||
title = {Single-{{Reference}} Ab {{Initio Methods}} for the {{Calculation}} of {{Excited States}} of {{Large Molecules}}},
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||
volume = {105},
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||
year = {2005},
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||
Bdsk-Url-1 = {https://dx.doi.org/10.1021/cr0505627}}
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@article{Piecuch_2002,
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author = {Piotr Piecuch and Karol Kowalski and Ian S. O. Pimienta and Michael J. Mcguire},
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date-added = {2020-12-01 21:10:26 +0100},
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date-modified = {2020-12-01 21:13:27 +0100},
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doi = {10.1080/0144235021000053811},
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journal = {Int. Rev. Phys. Chem.},
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pages = {527-655},
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publisher = {Taylor & Francis},
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||
title = {Recent advances in electronic structure theory: Method of moments of coupled-cluster equations and renormalized coupled-cluster approaches},
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||
volume = {21},
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year = {2002},
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Bdsk-Url-1 = {https://doi.org/10.1080/0144235021000053811}}
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@book{AveryBook,
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address = {Dordrecht},
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author = {J. Avery},
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date-added = {2020-12-01 21:06:44 +0100},
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date-modified = {2020-12-01 21:06:44 +0100},
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publisher = {Kluwer Academic},
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title = {Hyperspherical harmonics: applications in quantum theory},
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year = {1989}}
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@book{CramerBook,
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author = {C. J. Cramer},
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date-added = {2020-12-01 21:06:44 +0100},
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date-modified = {2020-12-01 21:06:44 +0100},
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keywords = {qmech},
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||
publisher = {Wiley},
|
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title = {Essentials of Computational Chemistry: Theories and Models},
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year = {2004}}
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@book{FetterBook,
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author = {A. L. Fetter and J. D. Waleck},
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date-added = {2020-12-01 21:06:44 +0100},
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date-modified = {2020-12-01 21:06:44 +0100},
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publisher = {McGraw Hill, San Francisco},
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title = {Quantum Theory of Many Particle Systems},
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year = {1971}}
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@book{HerzbergBook,
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author = {K. P. Huber and G. Herzberg},
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date-added = {2020-12-01 21:06:44 +0100},
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date-modified = {2020-12-01 21:06:44 +0100},
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publisher = {van Nostrand Reinhold Company},
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title = {Molecular Spectra and Molecular Structure: IV. Constants of diatomic molecules},
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year = {1979}}
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@book{JensenBook,
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address = {New York},
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author = {F. Jensen},
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date-added = {2020-12-01 21:06:44 +0100},
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date-modified = {2020-12-01 21:06:44 +0100},
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edition = {3rd},
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keywords = {qmech},
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publisher = {Wiley},
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title = {Introduction to Computational Chemistry},
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year = {2017}}
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@book{NISTbook,
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address = {New York},
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date-added = {2020-12-01 21:06:44 +0100},
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date-modified = {2020-12-01 21:06:44 +0100},
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editor = {F. W. J. Olver and D. W. Lozier and R. F. Boisvert and C. W. Clark},
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keywords = {maths},
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publisher = {Cambridge University Press},
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title = {NIST Handbook of Mathematical Functions},
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year = {2010}}
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@book{ParrBook,
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address = {Clarendon Press},
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author = {R. G. Parr and W. Yang},
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date-added = {2020-12-01 21:06:44 +0100},
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||
date-modified = {2020-12-01 21:06:44 +0100},
|
||
keywords = {dft; qmech},
|
||
publisher = {Oxford},
|
||
title = {Density-Functional Theory of Atoms and Molecules},
|
||
year = {1989}}
|
||
|
||
@book{ReiningBook,
|
||
author = {Martin, R.M. and Reining, L. and Ceperley, D.M.},
|
||
date-added = {2020-12-01 21:06:44 +0100},
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||
date-modified = {2020-12-01 21:06:44 +0100},
|
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isbn = {0521871506},
|
||
publisher = {Cambridge University Press},
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||
title = {Interacting Electrons: Theory and Computational Approaches},
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year = {2016}}
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@book{Schuck_Book,
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author = {P. Ring and P. Schuck},
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date-added = {2020-12-01 21:06:44 +0100},
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date-modified = {2020-12-01 21:06:44 +0100},
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||
publisher = {Springer},
|
||
title = {The Nuclear Many-Body Problem},
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year = {2004}}
|
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|
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@book{Stefanucci_2013,
|
||
abstract = {"The Green's function method is one of the most powerful and versatile formalisms in physics, and its nonequilibrium version has proved invaluable in many research fields. This book provides a unique, self-contained introduction to nonequilibrium many-body theory. Starting with basic quantum mechanics, the authors introduce the equilibrium and nonequilibrium Green's function formalisms within a unified framework called the contour formalism. The physical content of the contour Green's functions and the diagrammatic expansions are explained with a focus on the time-dependent aspect. Every result is derived step-by-step, critically discussed and then applied to different physical systems, ranging from molecules and nanostructures to metals and insulators. With an abundance of illustrative examples, this accessible book is ideal for graduate students and researchers who are interested in excited state properties of matter and nonequilibrium physics"--},
|
||
address = {Cambridge},
|
||
author = {Stefanucci, Gianluca and van Leeuwen, Robert},
|
||
date-added = {2020-12-01 21:06:44 +0100},
|
||
date-modified = {2020-12-01 21:06:44 +0100},
|
||
isbn = {978-0-521-76617-3},
|
||
keywords = {Many-body problem,Quantum theory,Green's functions,Mathematics,SCIENCE / Physics},
|
||
lccn = {QC174.17.G68 S74 2013},
|
||
publisher = {{Cambridge University Press}},
|
||
shorttitle = {Nonequilibrium Many-Body Theory of Quantum Systems},
|
||
title = {Nonequilibrium Many-Body Theory of Quantum Systems: A Modern Introduction},
|
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year = {2013}}
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@book{HelgakerBook,
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author = {T. Helgaker and P. J{\o}rgensen and J. Olsen},
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date-added = {2020-12-01 21:06:11 +0100},
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date-modified = {2020-12-01 21:06:17 +0100},
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title = {Invariance Property of the Brillouin-Wigner Perturbation Series},
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@article{Kais_2006,
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abstract = {Finite size scaling for calculations of the critical parameters of the few-body Schr{\"o}dinger equation is based on taking the number of elements in a complete basis set as the size of the system. We show in an analogy with Yang and Lee theorem, which states that singularities of the free energy at phase transitions occur only in the thermodynamic limit, that singularities in the ground state energy occur only in the infinite complete basis set limit. To illustrate this analogy in the complex-parameter space, we present calculations for Yukawa type potential, and a Coulomb type potential for two-electron atoms.},
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title = {Pade resummation of many-body perturbation theory},
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author = {Tarantino, Walter and Di Sabatino, Stefano},
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title = {Diagonal Pad\'e approximant of the one-body Green's function: A study on Hubbard rings},
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author = {Loos, Pierre-Fran{\c c}ois},
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title = {High-Density Correlation Energy Expansion of the One-Dimensional Uniform Electron Gas},
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year = {2013},
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title = {Pad\'e and Post-Pad\'e Approximations for Critical Phenomena},
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year = {2020},
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@incollection{Goodson_2019,
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abstract = {The Schr{\"o}dinger equation for an atom or molecule includes parameters, such as bond lengths or nuclear charges, and the resulting energy eigenvalue can be treated as a function with the parameter values as continuous variables. Analysis of singular points of this function, at nonphysical parameter values, can explain and predict the success or failure of quantum chemical calculation methods. An introduction to the theory of singularities in functions of a complex variable is presented and examples of applications to quantum chemistry are described, including the calculation of molecular potential energy curves, the theoretical description of ionization, and the summation of perturbation theories.},
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author = {David Z. Goodson},
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booktitle = {Mathematical Physics in Theoretical Chemistry},
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doi = {https://doi.org/10.1016/B978-0-12-813651-5.00009-7},
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editor = {S.M. Blinder and J.E. House},
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isbn = {978-0-12-813651-5},
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keywords = {Singularities, Avoided crossings, Quadratic approximants, Molecular potential energy curves, Ionization, Finite-size scaling, Perturbation theory, Series summation},
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pages = {295 - 325},
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publisher = {Elsevier},
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series = {Developments in Physical {\&} Theoretical Chemistry},
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title = {Chapter 9 - Singularity analysis in quantum chemistry},
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year = {2019},
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@article{Mayer_1985,
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abstract = {The quadratic Pade method-a new method for calculating the local density of states in various physical systems-is introduced and discussed. The method is based upon the use of Hermite-Pade polynomials and it makes the calculation of densities of states a straightforward and relatively simple matter. Its advantages over other methods with similar generality and complexity are outlined and numerical results for various systems, which illustrate the virtues of the new method, are presented and discussed.},
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author = {I L Mayer and B Y Tong},
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journal = {J. Phys. C.: Solid State Phys.},
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pages = {3297--3318},
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title = {The quadratic Pade approximant method and its application for calculating densities of states},
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volume = {18},
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year = 1985,
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@book{BakerBook,
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author = {G. A. {Baker Jr.} and P. Graves-Morris},
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publisher = {Cambridge University Press},
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title = {Pad\'e Approximants},
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year = {1996}}
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@incollection{Pade_1892,
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author = {H. Pad\'e},
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editor = {Gauthier-Villars},
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pages = {3--93},
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publisher = {{\'E}ditions scientifiques et m{\'e}dicales Elsevier},
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title = {Sur la repr{\'e}sentation approch{\'e}e d'une fonction par des fractions rationnelles},
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volume = {9},
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year = {1892}}
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@article{Surjan_2000,
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author = {Surj{\'a}n,P. R. and Szabados,{\'A}.},
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title = {Optimized partitioning in perturbation theory: Comparison to related approaches},
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@article{Knowles_1988b,
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abstract = { An analysis of the `linear combination of atomic orbitals' approximation using the accurate molecular orbital equations shows that it does not lead to equations of the form usually assumed in the semi-empirical molecular orbital method. A new semi-empirical method is proposed, therefore, in terms of equivalent orbitals. The equations obtained, which do have the usual form, are applicable to a large class of molecules and do not involve the approximations that were thought necessary. In this method the ionization potentials are calculated by treating certain integrals as semi-empirical parameters. The value of these parameters is discussed in terms of the localization of equivalent orbitals and some approximate rules are suggested. As an illustration the ionization potentials of the paraffin series are considered and good agreement between the observed and calculated values is found. },
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author = {Hall, G. G. and Lennard-Jones, John Edward},
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@article{Burton_2018,
|
||
abstract = {We explore the existence and behavior of holomorphic restricted Hartree-Fock (h-RHF) solutions for two-electron problems. Through algebraic geometry, the exact number of solutions with n basis functions is rigorously identified as 1/2(3n - 1), proving that states must exist for all molecular geometries. A detailed study on the h-RHF states of HZ (STO3G) then demonstrates both the conservation of holomorphic solutions as geometry or atomic charges are varied and the emergence of complex h-RHF solutions at coalescence points. Using catastrophe theory, the nature of these coalescence points is described, highlighting the influence of molecular symmetry. The h-RHF states of HHeH2+ and HHeH (STO-3G) are then compared, illustrating the isomorphism between systems with two electrons and two electron holes. Finally, we explore the h-RHF states of ethene (STO-3G) by considering the $\pi$ electrons as a two-electron problem and employ NOCI to identify a crossing of the lowest energy singlet and triplet states at the perpendicular geometry.},
|
||
author = {Burton, Hugh G. A. and Gross, Mark and Thom, Alex J. W.},
|
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date-added = {2020-11-18 21:16:36 +0100},
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date-modified = {2020-11-18 21:16:36 +0100},
|
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doi = {10.1021/acs.jctc.7b00980},
|
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file = {/Users/loos/Zotero/storage/E9FNMAU8/Burton et al. - 2018 - Holomorphic Hartree--Fock Theory The Nature of Two.pdf},
|
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issn = {1549-9618, 1549-9626},
|
||
journal = {J. Chem. Theory Comput.},
|
||
month = feb,
|
||
number = {2},
|
||
pages = {607-618},
|
||
shorttitle = {Holomorphic {{Hartree}}\textendash{{Fock Theory}}},
|
||
title = {Holomorphic {{Hartree}}\textendash{{Fock Theory}}: {{The Nature}} of {{Two}}-{{Electron Problems}}},
|
||
volume = {14},
|
||
year = {2018},
|
||
Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.7b00980}}
|
||
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||
@article{Burton_2016,
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author = {H. G. A. Burton and A. J. W. Thom},
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date-added = {2020-11-18 21:16:36 +0100},
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date-modified = {2020-11-18 21:16:36 +0100},
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doi = {10.1021/acs.jctc.5b01005},
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journal = {J. Chem. Theory Comput.},
|
||
pages = {167},
|
||
title = {Holomorphic {Hartree--Fock} Theory: An Inherently Multireference Approach},
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volume = {12},
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||
year = {2016},
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||
Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.5b01005}}
|
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@article{Carrascal_2015,
|
||
abstract = {This review explains the relationship between density functional theory and strongly correlated models using the simplest possible example, the two-site Hubbard model. The relationship to traditional quantum chemistry is included. Even in this elementary example, where the exact ground-state energy and site occupations can be found analytically, there is much to be explained in terms of the underlying logic and aims of density functional theory. Although the usual solution is analytic, the density functional is given only implicitly. We overcome this difficulty using the Levy\textendash{}Lieb construction to create a parametrization of the exact function with negligible errors. The symmetric case is most commonly studied, but we find a rich variation in behavior by including asymmetry, as strong correlation physics vies with charge-transfer effects. We explore the behavior of the gap and the many-body Green's function, demonstrating the `failure' of the Kohn\textendash{}Sham (KS) method to reproduce the fundamental gap. We perform benchmark calculations of the occupation and components of the KS potentials, the correlation kinetic energies, and the adiabatic connection. We test several approximate functionals (restricted and unrestricted Hartree\textendash{}Fock and Bethe ansatz local density approximation) to show their successes and limitations. We also discuss and illustrate the concept of the derivative discontinuity. Useful appendices include analytic expressions for density functional energy components, several limits of the exact functional (weak- and strong-coupling, symmetric and asymmetric), various adiabatic connection results, proofs of exact conditions for this model, and the origin of the Hubbard model from a minimal basis model for stretched H2.},
|
||
author = {Carrascal, D J and Ferrer, J and Smith, J C and Burke, K},
|
||
date-added = {2020-11-14 21:44:15 +0100},
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date-modified = {2020-11-14 21:44:15 +0100},
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||
doi = {10.1088/0953-8984/27/39/393001},
|
||
file = {/Users/loos/Zotero/storage/LRMWNYEQ/Carrascal et al. - 2015 - The Hubbard dimer a density functional case study.pdf},
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||
issn = {0953-8984, 1361-648X},
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||
journal = {J. Phys. Condens. Matter},
|
||
language = {en},
|
||
month = oct,
|
||
number = {39},
|
||
pages = {393001},
|
||
shorttitle = {The {{Hubbard}} Dimer},
|
||
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}}
|
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|
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@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.},
|
||
author = {Carrascal, Diego J. and Ferrer, Jaime and Maitra, Neepa and Burke, Kieron},
|
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date-added = {2020-11-14 21:44:15 +0100},
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date-modified = {2020-11-14 21:44:15 +0100},
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doi = {10.1140/epjb/e2018-90114-9},
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journal = {Eur. Phys. J. B},
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pages = {142},
|
||
title = {Linear Response Time-Dependent Density Functional Theory of the {{Hubbard}} Dimer},
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||
volume = {91},
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year = {2018},
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Bdsk-Url-1 = {https://doi.org/10.1140/epjb/e2018-90114-9}}
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@article{Surjan_2018,
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author = {Surj{\'a}n,P{\'e}ter R. and Mih{\'a}lka,Zsuzsanna {\'E}. and Szabados,{\'A}gnes},
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doi = {10.1007/s00214-018-2372-3},
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journal = {Theor. Chem. Acc.},
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pages = {149},
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title = {The inverse boundary value problem: application in many-body perturbation theory},
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volume = {137},
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year = {2018},
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Bdsk-Url-1 = {https://doi.org/10.1063/1.5083191}}
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@article{Pawlowski_2019a,
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author = {Paw{\l}owski,Filip and Olsen,Jeppe and J{\o}rgensen,Poul},
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date-added = {2020-11-12 15:24:23 +0100},
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date-modified = {2020-11-12 15:33:57 +0100},
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doi = {10.1063/1.5004037},
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number = {13},
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pages = {134108},
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title = {Cluster perturbation theory. I. Theoretical foundation for a coupled cluster target state and ground-state energies},
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volume = {150},
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year = {2019},
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Bdsk-Url-1 = {https://doi.org/10.1063/1.5004037}}
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@article{Pawlowski_2019e,
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author = {Paw{\l}owski,Filip and Olsen,Jeppe and J{\o}rgensen,Poul},
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date-added = {2020-11-12 15:24:15 +0100},
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date-modified = {2020-11-12 15:33:38 +0100},
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doi = {10.1063/1.5053627},
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journal = {J. Chem. Phys.},
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number = {13},
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pages = {134112},
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title = {Cluster perturbation theory. V. Theoretical foundation for cluster linear target states},
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url = {https://doi.org/10.1063/1.5053627},
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volume = {150},
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year = {2019},
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Bdsk-Url-1 = {https://doi.org/10.1063/1.5053627}}
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@article{Pawlowski_2019d,
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author = {Paw{\l}owski,Filip and Olsen,Jeppe and J{\o}rgensen,Poul},
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date-added = {2020-11-12 15:24:12 +0100},
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date-modified = {2020-11-12 15:33:46 +0100},
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doi = {10.1063/1.5053622},
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journal = {J. Chem. Phys.},
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number = {13},
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pages = {134111},
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title = {Cluster perturbation theory. IV. Convergence of cluster perturbation series for energies and molecular properties},
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volume = {150},
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year = {2019},
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Bdsk-Url-1 = {https://doi.org/10.1063/1.5053622}}
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@article{Pawlowski_2019c,
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author = {Baudin,Pablo and Paw{\l}owski,Filip and Bykov,Dmytro and Liakh,Dmitry and Kristensen,Kasper and Olsen,Jeppe and J{\o}rgensen,Poul},
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date-added = {2020-11-12 15:24:07 +0100},
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journal = {J. Chem. Phys.},
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number = {13},
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pages = {134110},
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title = {Cluster perturbation theory. III. Perturbation series for coupled cluster singles and doubles excitation energies},
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volume = {150},
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year = {2019},
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Bdsk-Url-1 = {https://doi.org/10.1063/1.5046935}}
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@article{Pawlowski_2019b,
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author = {Paw{\l}owski,Filip and Olsen,Jeppe and J{\o}rgensen,Poul},
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date-added = {2020-11-12 15:24:02 +0100},
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number = {13},
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pages = {134109},
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title = {Cluster perturbation theory. II. Excitation energies for a coupled cluster target state},
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volume = {150},
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year = {2019},
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Bdsk-Url-1 = {https://doi.org/10.1063/1.5053167}}
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@article{Leininger_2000,
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author = {Leininger,Matthew L. and Allen,Wesley D. and Schaefer,Henry F. and Sherrill,C. David},
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title = {Is Mo/ller--Plesset perturbation theory a convergent ab initio method?},
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Bdsk-Url-1 = {https://doi.org/10.1063/1.481764}}
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@article{Nesbet_1955,
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abstract = { A systematic method is developed for estimating or calculating corrections for configuration interaction in atomic, molecular and nuclear wave-function calculations. Solutions of the Hartree-Fock equations for a single Slater determinant or approximate Hartree-Fock solutions obtained by Roothaan's iterative procedure have special properties which are used to simplify the matrix of the many-particle Hamiltonian. A restricted self-consistent field method is proposed for treating states of low symmetry. This method avoids the off-diagonal Lagrange multipliers encountered in previous methods and is adapted to configuration interaction calculations. },
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author = {Nesbet, R. K. and Hartree, Douglas Rayner},
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doi = {10.1098/rspa.1955.0134},
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pages = {312-321},
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title = {Configuration interaction in orbital theories},
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volume = {230},
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year = {1955},
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Bdsk-Url-1 = {https://royalsocietypublishing.org/doi/abs/10.1098/rspa.1955.0134},
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Bdsk-Url-2 = {https://doi.org/10.1098/rspa.1955.0134}}
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@article{Epstein_1926,
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author = {Epstein, Paul S.},
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numpages = {0},
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pages = {695--710},
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publisher = {American Physical Society},
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title = {The Stark Effect from the Point of View of Schroedinger's Quantum Theory},
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url = {https://link.aps.org/doi/10.1103/PhysRev.28.695},
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volume = {28},
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year = {1926},
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Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRev.28.695},
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@article{Gill_1994,
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@article{Mihalka_2017b,
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author = {Mih{\'a}lka,Zsuzsanna {\'E}. and Szabados,{\'A}gnes and Surj{\'a}n,P{\'e}ter R.},
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pages = {124121},
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title = {Effect of partitioning on the convergence properties of the Rayleigh-Schr{\"o}dinger perturbation series},
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volume = {146},
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year = {2017},
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Bdsk-Url-1 = {https://doi.org/10.1063/1.4978898}}
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@article{Mihalka_2019,
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author = {Mih{\'a}lka,Zsuzsanna {\'E}. and Szabados,{\'A}gnes and Surj{\'a}n,P{\'e}ter R.},
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title = {Application of the Cauchy integral formula as a tool of analytic continuation for the resummation of divergent perturbation series},
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volume = {150},
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Bdsk-Url-1 = {https://doi.org/10.1063/1.5083191}}
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@article{Mihalka_2017a,
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author = {Mih\'alka, Zsuzsanna \'E. and Surj\'an, P\'eter R.},
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month = {Dec},
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numpages = {5},
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pages = {062106},
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publisher = {American Physical Society},
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title = {Analytic-continuation approach to the resummation of divergent series in Rayleigh-Schr\"odinger perturbation theory},
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url = {https://link.aps.org/doi/10.1103/PhysRevA.96.062106},
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Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevA.96.062106}}
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@article{Berry_2011,
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abstract = {For non-Hermitian Hamiltonians with an isolated degeneracy (`exceptional point'), a model for cycling around loops that enclose or exclude the degeneracy is solved exactly in terms of Bessel functions. Floquet solutions, returning exactly to their initial states (up to a constant) are found, as well as exact expressions for the adiabatic multipliers when the evolving states are represented as a superposition of eigenstates of the instantaneous Hamiltonian. Adiabatically (i.e. for slow cycles), the multipliers of exponentially subdominant eigenstates can vary wildly, unlike those driven by Hermitian operators, which change little. These variations are explained as an example of the Stokes phenomenon of asymptotics. Improved (superadiabatic) approximations tame the variations of the multipliers but do not eliminate them.},
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author = {M V Berry and R Uzdin},
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journal = {J. Phys. A Math. Theor.},
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month = {oct},
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number = {43},
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pages = {435303},
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publisher = {{IOP} Publishing},
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title = {Slow non-Hermitian cycling: exact solutions and the Stokes phenomenon},
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url = {https://doi.org/10.1088%2F1751-8113%2F44%2F43%2F435303},
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volume = {44},
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year = 2011,
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Bdsk-Url-1 = {https://doi.org/10.1088%2F1751-8113%2F44%2F43%2F435303},
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