1205 lines
45 KiB
BibTeX
1205 lines
45 KiB
BibTeX
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@article{Carrascal_2015,
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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},
|
||
date-modified = {2020-11-14 21:44:15 +0100},
|
||
doi = {10.1088/0953-8984/27/39/393001},
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||
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},
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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}}
|
||
|
||
@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},
|
||
date-added = {2020-11-14 21:44:15 +0100},
|
||
date-modified = {2020-11-14 21:44:15 +0100},
|
||
doi = {10.1140/epjb/e2018-90114-9},
|
||
journal = {Eur. Phys. J. B},
|
||
pages = {142},
|
||
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}}
|
||
|
||
@article{Surjan_2018,
|
||
author = {Surj{\'a}n,P{\'e}ter R. and Mih{\'a}lka,Zsuzsanna {\'E}. and Szabados,{\'A}gnes},
|
||
date-added = {2020-11-12 16:40:48 +0100},
|
||
date-modified = {2020-11-12 16:42:07 +0100},
|
||
doi = {10.1007/s00214-018-2372-3},
|
||
journal = {Theor. Chem. Acc.},
|
||
pages = {149},
|
||
title = {The inverse boundary value problem: application in many-body perturbation theory},
|
||
volume = {137},
|
||
year = {2018},
|
||
Bdsk-Url-1 = {https://doi.org/10.1063/1.5083191}}
|
||
|
||
@article{Pawlowski_2019a,
|
||
author = {Paw{\l}owski,Filip and Olsen,Jeppe and J{\o}rgensen,Poul},
|
||
date-added = {2020-11-12 15:24:23 +0100},
|
||
date-modified = {2020-11-12 15:33:57 +0100},
|
||
doi = {10.1063/1.5004037},
|
||
journal = {J. Chem. Phys.},
|
||
number = {13},
|
||
pages = {134108},
|
||
title = {Cluster perturbation theory. I. Theoretical foundation for a coupled cluster target state and ground-state energies},
|
||
volume = {150},
|
||
year = {2019},
|
||
Bdsk-Url-1 = {https://doi.org/10.1063/1.5004037}}
|
||
|
||
@article{Pawlowski_2019e,
|
||
author = {Paw{\l}owski,Filip and Olsen,Jeppe and J{\o}rgensen,Poul},
|
||
date-added = {2020-11-12 15:24:15 +0100},
|
||
date-modified = {2020-11-12 15:33:38 +0100},
|
||
doi = {10.1063/1.5053627},
|
||
journal = {J. Chem. Phys.},
|
||
number = {13},
|
||
pages = {134112},
|
||
title = {Cluster perturbation theory. V. Theoretical foundation for cluster linear target states},
|
||
url = {https://doi.org/10.1063/1.5053627},
|
||
volume = {150},
|
||
year = {2019},
|
||
Bdsk-Url-1 = {https://doi.org/10.1063/1.5053627}}
|
||
|
||
@article{Pawlowski_2019d,
|
||
author = {Paw{\l}owski,Filip and Olsen,Jeppe and J{\o}rgensen,Poul},
|
||
date-added = {2020-11-12 15:24:12 +0100},
|
||
date-modified = {2020-11-12 15:33:46 +0100},
|
||
doi = {10.1063/1.5053622},
|
||
journal = {J. Chem. Phys.},
|
||
number = {13},
|
||
pages = {134111},
|
||
title = {Cluster perturbation theory. IV. Convergence of cluster perturbation series for energies and molecular properties},
|
||
volume = {150},
|
||
year = {2019},
|
||
Bdsk-Url-1 = {https://doi.org/10.1063/1.5053622}}
|
||
|
||
@article{Pawlowski_2019c,
|
||
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},
|
||
date-added = {2020-11-12 15:24:07 +0100},
|
||
date-modified = {2020-11-12 15:33:50 +0100},
|
||
doi = {10.1063/1.5046935},
|
||
journal = {J. Chem. Phys.},
|
||
number = {13},
|
||
pages = {134110},
|
||
title = {Cluster perturbation theory. III. Perturbation series for coupled cluster singles and doubles excitation energies},
|
||
volume = {150},
|
||
year = {2019},
|
||
Bdsk-Url-1 = {https://doi.org/10.1063/1.5046935}}
|
||
|
||
@article{Pawlowski_2019b,
|
||
author = {Paw{\l}owski,Filip and Olsen,Jeppe and J{\o}rgensen,Poul},
|
||
date-added = {2020-11-12 15:24:02 +0100},
|
||
date-modified = {2020-11-12 15:33:53 +0100},
|
||
doi = {10.1063/1.5053167},
|
||
journal = {J. Chem. Phys.},
|
||
number = {13},
|
||
pages = {134109},
|
||
title = {Cluster perturbation theory. II. Excitation energies for a coupled cluster target state},
|
||
volume = {150},
|
||
year = {2019},
|
||
Bdsk-Url-1 = {https://doi.org/10.1063/1.5053167}}
|
||
|
||
@article{Leininger_2000,
|
||
author = {Leininger,Matthew L. and Allen,Wesley D. and Schaefer,Henry F. and Sherrill,C. David},
|
||
date-added = {2020-11-12 14:50:57 +0100},
|
||
date-modified = {2020-11-12 14:51:07 +0100},
|
||
doi = {10.1063/1.481764},
|
||
eprint = {https://doi.org/10.1063/1.481764},
|
||
journal = {The Journal of Chemical Physics},
|
||
number = {21},
|
||
pages = {9213-9222},
|
||
title = {Is Mo/ller--Plesset perturbation theory a convergent ab initio method?},
|
||
url = {https://doi.org/10.1063/1.481764},
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||
volume = {112},
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||
year = {2000},
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||
Bdsk-Url-1 = {https://doi.org/10.1063/1.481764}}
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||
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||
@article{Nesbet_1955,
|
||
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. },
|
||
author = {Nesbet, R. K. and Hartree, Douglas Rayner},
|
||
date-added = {2020-11-12 10:01:40 +0100},
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||
date-modified = {2020-11-12 10:02:40 +0100},
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||
doi = {10.1098/rspa.1955.0134},
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||
journal = {Proc. R. Soc. Lond. A},
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||
number = {1182},
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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},
|
||
Bdsk-Url-2 = {https://doi.org/10.1098/rspa.1955.0134}}
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||
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||
@article{Epstein_1926,
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||
author = {Epstein, Paul S.},
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||
date-added = {2020-11-12 10:00:50 +0100},
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||
date-modified = {2020-11-12 10:01:10 +0100},
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||
doi = {10.1103/PhysRev.28.695},
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||
issue = {4},
|
||
journal = {Phys. Rev.},
|
||
month = {Oct},
|
||
numpages = {0},
|
||
pages = {695--710},
|
||
publisher = {American Physical Society},
|
||
title = {The Stark Effect from the Point of View of Schroedinger's Quantum Theory},
|
||
url = {https://link.aps.org/doi/10.1103/PhysRev.28.695},
|
||
volume = {28},
|
||
year = {1926},
|
||
Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRev.28.695},
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||
Bdsk-Url-2 = {https://doi.org/10.1103/PhysRev.28.695}}
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||
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||
@article{Gill_1994,
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||
author = {P. M. W. Gill},
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||
date-added = {2020-11-12 09:57:40 +0100},
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||
date-modified = {2020-11-12 09:57:40 +0100},
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||
doi = {10.1016/S0065-3276(08)60019-2},
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||
journal = {Adv. Quantum Chem.},
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||
pages = {141--205},
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title = {Molecular Integrals Over Gaussian Basis Functions},
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volume = {25},
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year = {1994},
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Bdsk-Url-1 = {https://doi.org/10.1016/S0065-3276(08)60019-2}}
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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.},
|
||
date-added = {2020-11-12 09:31:14 +0100},
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||
date-modified = {2020-11-12 09:33:15 +0100},
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||
doi = {10.1063/1.4978898},
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||
journal = {J. Chem. Phys.},
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||
number = {12},
|
||
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}}
|
||
|
||
@article{Mihalka_2019,
|
||
author = {Mih{\'a}lka,Zsuzsanna {\'E}. and Szabados,{\'A}gnes and Surj{\'a}n,P{\'e}ter R.},
|
||
date-added = {2020-11-12 09:29:42 +0100},
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||
date-modified = {2020-11-12 09:33:07 +0100},
|
||
doi = {10.1063/1.5083191},
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||
journal = {J. Chem. Phys.},
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||
number = {3},
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||
pages = {031101},
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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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||
year = {2019},
|
||
Bdsk-Url-1 = {https://doi.org/10.1063/1.5083191}}
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||
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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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||
date-added = {2020-11-12 09:28:43 +0100},
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||
date-modified = {2020-11-12 09:30:45 +0100},
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||
doi = {10.1103/PhysRevA.96.062106},
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||
issue = {6},
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||
journal = {Phys. Rev. A},
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||
month = {Dec},
|
||
numpages = {5},
|
||
pages = {062106},
|
||
publisher = {American Physical Society},
|
||
title = {Analytic-continuation approach to the resummation of divergent series in Rayleigh-Schr\"odinger perturbation theory},
|
||
url = {https://link.aps.org/doi/10.1103/PhysRevA.96.062106},
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||
volume = {96},
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||
year = {2017},
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||
Bdsk-Url-1 = {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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date-added = {2020-11-12 09:14:42 +0100},
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doi = {10.1088/1751-8113/44/43/435303},
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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},
|
||
publisher = {{IOP} Publishing},
|
||
title = {Slow non-Hermitian cycling: exact solutions and the Stokes phenomenon},
|
||
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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Bdsk-Url-2 = {https://doi.org/10.1088/1751-8113/44/43/435303}}
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@book{BenderPTBook,
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author = {C. M. Bender},
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publisher = {World Scientific},
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title = {{{\cal PT}}-Symmetry in Quantum and Classical Physics},
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year = {2019}}
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@article{Benda_2018,
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author = {Zsuzsanna Benda and Thomas-C. Jagau},
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pages = {6978--6984},
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title = {Locating Exceptional Points on Multidimensional Complex-Valued Potential Energy Surfaces},
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volume = {9},
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year = {2018},
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Bdsk-Url-1 = {https://doi.org/10.1021/acs.jpclett.8b03228}}
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@book{BenderBook,
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author = {C. M. Bender and S. A. Orszag},
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date-added = {2020-07-28 09:59:40 +0200},
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date-modified = {2020-07-28 09:59:40 +0200},
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publisher = {Springer},
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title = {Advanced Mathematical Methods for Scientists and Engineers: Asymptotics Methods and Perturbation Theory},
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year = {1978}}
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@article{Gill_1986,
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author = {Gill, Peter M. W. and Radom, Leo},
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date = {1986-11-28},
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doi = {10.1016/0009-2614(86)80686-8},
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journal = {Chem. Phys. Lett.},
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title = {Deceptive convergence in {M{\o}ller-Plesset} perturbation energies},
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Bdsk-Url-1 = {https://doi.org/10.1016/0009-2614(86)80686-8}}
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@article{Gill_1988,
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author = {Gill, Peter M. W. and Pople, John A. and Radom, Leo and Nobes, Ross H.},
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pages = {7307--7314},
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title = {Why does unrestricted {M{\o}ller-Plesset} perturbation theory converge so slowly for spin‐contaminated wave functions?},
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year = {1988},
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Bdsk-Url-1 = {https://doi.org/10.1063/1.455312}}
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@article{Sergeev_2005,
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author = {Sergeev, Alexey V. and Goodson, David Z. and Wheeler, Steven E. and Allen, Wesley D.},
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title = {On the nature of the {M{\o}ller-Plesset} critical point},
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Bdsk-Url-1 = {https://doi.org/10.1063/1.1991854}}
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@article{Sergeev_2006,
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author = {Sergeev, Alexey V. and Goodson, David Z.},
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title = {Singularities of {M{\o}ller-Plesset} energy functions},
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year = {2006},
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Bdsk-Url-1 = {https://doi.org/10.1063/1.2173989}}
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@article{Stillinger_2000,
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author = {Stillinger, Frank H.},
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date = {2000-05-31},
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date-modified = {2020-08-22 22:14:50 +0200},
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doi = {10.1063/1.481608},
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journal = {J. Chem. Phys.},
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number = {22},
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pages = {9711--9715},
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title = {{M{\o}ller-Plesset} convergence issues in computational quantum chemistry},
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Bdsk-Url-1 = {https://doi.org/10.1063/1.481608}}
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@article{Olsen_1996,
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author = {Olsen, Jeppe and Christiansen, Ove and Koch, Henrik and J{\o}rgensen, Poul},
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doi = {10.1063/1.472352},
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journal = {J. Chem. Phys.},
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pages = {5082--5090},
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title = {Surprising cases of divergent behavior in {M{\o}ller-Plesset} perturbation theory},
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volume = {105},
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year = {1996},
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||
Bdsk-Url-1 = {https://doi.org/10.1063/1.472352}}
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||
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||
@article{Olsen_2000,
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author = {Olsen, Jeppe and J{\o}rgensen, Poul and Helgaker, Trygve and Christiansen, Ove},
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date-modified = {2020-11-12 09:19:09 +0100},
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doi = {10.1063/1.481611},
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journal = {J. Chem. Phys.},
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pages = {9736--9748},
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title = {Divergence in {M{\o}ller-Plesset} theory: {A} simple explanation based on a two-state model},
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author = {Cejnar, Pavel and Heinze, Stefan and Jolie, Jan},
|
||
year = {2003},
|
||
volume = {68},
|
||
pages = {034326},
|
||
publisher = {{American Physical Society}},
|
||
doi = {10.1103/PhysRevC.68.034326},
|
||
journal = {Phys. Rev. C}}
|
||
|
||
@article{Cejnar_2000,
|
||
title = {Quantum Phase Transitions Studied within the Interacting Boson Model},
|
||
author = {Cejnar, Pavel and Jolie, Jan},
|
||
year = {2000},
|
||
volume = {61},
|
||
pages = {6237--6247},
|
||
publisher = {{American Physical Society}},
|
||
doi = {10.1103/PhysRevE.61.6237},
|
||
journal = {Phys. Rev. E}}
|
||
|
||
@article{Cejnar_2007a,
|
||
title = {Phase Structure of Interacting Boson Models in Arbitrary Dimension},
|
||
author = {Cejnar, Pavel and Iachello, Francesco},
|
||
year = {2007},
|
||
volume = {40},
|
||
pages = {581--595},
|
||
publisher = {{IOP Publishing}},
|
||
doi = {10.1088/1751-8113/40/4/001},
|
||
journal = {J. Phys. A: Math. Theor.}}
|
||
|
||
|
||
|
||
|