1951 lines
77 KiB
BibTeX
1951 lines
77 KiB
BibTeX
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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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author = {Sabre Kais and Craig Wenger and Qi Wei},
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date-added = {2020-11-27 20:54:34 +0100},
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date-modified = {2020-11-27 20:55:08 +0100},
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doi = {https://doi.org/10.1016/j.cplett.2006.03.035},
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journal = {Chem. Phys. Lett.},
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pages = {45 - 49},
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title = {Quantum criticality at the infinite complete basis set limit: A thermodynamic analog of the Yang and Lee theorem},
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volume = {423},
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year = {2006},
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Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0009261406003897},
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Bdsk-Url-2 = {https://doi.org/10.1016/j.cplett.2006.03.035}}
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@article{Goodson_2000b,
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author = {Goodson,David Z.},
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date-added = {2020-11-27 20:42:57 +0100},
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date-modified = {2020-11-27 20:43:12 +0100},
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doi = {10.1063/1.1318740},
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journal = {J. Chem. Phys.},
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pages = {6461-6464},
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title = {A summation procedure that improves the accuracy of the fourth-order Mo/ller--Plesset perturbation theory},
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volume = {113},
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year = {2000},
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Bdsk-Url-1 = {https://doi.org/10.1063/1.1318740}}
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@article{Pavlyukh_2017,
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author = {Y. Pavlyukh},
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date-added = {2020-11-25 22:26:26 +0100},
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date-modified = {2020-11-25 22:26:52 +0100},
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doi = {10.1038/s41598-017-00355-w},
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journal = {Sci. Rep.},
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pages = {504},
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title = {Pade resummation of many-body perturbation theory},
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volume = {7},
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year = {2017},
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Bdsk-Url-1 = {https://doi.org/10.1038/s41598-017-00355-w}}
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@article{Tarantino_2019,
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author = {Tarantino, Walter and Di Sabatino, Stefano},
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date-added = {2020-11-25 22:23:50 +0100},
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date-modified = {2020-11-25 22:24:04 +0100},
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doi = {10.1103/PhysRevB.99.075149},
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journal = {Phys. Rev. B},
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pages = {075149},
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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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volume = {99},
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year = {2019},
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Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.99.075149},
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Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevB.99.075149}}
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@article{Goodson_2000a,
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author = {Goodson,David Z.},
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date-added = {2020-11-25 10:05:02 +0100},
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date-modified = {2020-11-27 20:42:22 +0100},
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doi = {10.1063/1.481044},
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journal = {J. Chem. Phys.},
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pages = {4901-4909},
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title = {Convergent summation of M{\o}ller--Plesset perturbation theory},
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volume = {112},
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year = {2000},
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Bdsk-Url-1 = {https://doi.org/10.1063/1.481044}}
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@article{Loos_2013,
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author = {Loos, Pierre-Fran{\c c}ois},
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date-added = {2020-11-25 09:34:55 +0100},
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date-modified = {2020-11-25 09:35:07 +0100},
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doi = {10.1063/1.4790613},
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journal = {J. Chem. Phys.},
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pages = {064108},
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title = {High-Density Correlation Energy Expansion of the One-Dimensional Uniform Electron Gas},
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volume = {138},
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year = {2013},
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Bdsk-Url-1 = {https://dx.doi.org/10.1063/1.4790613}}
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@article{Gluzman_2020,
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author = {S. Gluzman},
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date-added = {2020-11-25 09:32:54 +0100},
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date-modified = {2020-11-25 09:33:54 +0100},
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doi = {10.3390/sym12101600},
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journal = {Symmetry},
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pages = {1600},
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title = {Pad\'e and Post-Pad\'e Approximations for Critical Phenomena},
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volume = {12},
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year = {2020},
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Bdsk-Url-1 = {https://doi.org/10.3390/sym12101600}}
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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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date-added = {2020-11-25 09:13:38 +0100},
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date-modified = {2020-11-25 09:14:27 +0100},
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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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Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/B9780128136515000097},
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Bdsk-Url-2 = {https://doi.org/10.1016/B978-0-12-813651-5.00009-7}}
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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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date-added = {2020-11-25 09:01:38 +0100},
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date-modified = {2020-11-25 09:03:36 +0100},
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doi = {10.1088/0022-3719/18/17/008},
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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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Bdsk-Url-1 = {https://doi.org/10.1088%2F0022-3719%2F18%2F17%2F008},
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Bdsk-Url-2 = {https://doi.org/10.1088/0022-3719/18/17/008}}
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@book{BakerBook,
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author = {G. A. {Baker Jr.} and P. Graves-Morris},
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date-added = {2020-11-25 08:58:42 +0100},
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date-modified = {2020-11-25 08:59:33 +0100},
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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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booktitle = {Annales scientifiques de l'{\'E}.N.S.},
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date-added = {2020-11-25 08:48:36 +0100},
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date-modified = {2020-11-25 08:56:44 +0100},
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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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date-added = {2020-11-25 08:29:04 +0100},
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date-modified = {2020-11-25 09:15:28 +0100},
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doi = {10.1063/1.481006},
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journal = {J. Chem. Phys.},
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number = {10},
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pages = {4438-4446},
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title = {Optimized partitioning in perturbation theory: Comparison to related approaches},
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volume = {112},
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year = {2000},
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Bdsk-Url-1 = {https://doi.org/10.1063/1.481006}}
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@article{Tsuchimochi_2019,
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author = {Takashi Tsuchimochi and Seiichiro L. Ten-no},
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doi = {10.1021/acs.jctc.9b00897},
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journal = {J. Chem. Theory Comput.},
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pages = {6688},
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title = {Second-order perturbation theory with spin-symmetry-projected Hartree--Fock},
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volume = {15},
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year = {2019},
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Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.9b00897}}
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@article{Tsuchimochi_2014,
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author = {Takashi Tsuchimochi and Troy {Van Voorhis}},
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doi = {10.1063/1.4898804},
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journal = {J. Chem. Phys.},
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pages = {164117},
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title = {Extended {M\oller--Plesset} perturbation theory for dynamical and static correlations},
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volume = {141},
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year = {2014},
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Bdsk-Url-1 = {https://doi.org/10.1063/1.4898804}}
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@article{Knowles_1988a,
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author = {Peter J. Knowles and Nicholas C. Handy},
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doi = {10.1021/j100322a018},
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journal = {J. Phys. Chem.},
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pages = {3097},
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title = {Convergence of projected unrestricted {Hartree--Fock M\oller--Plesset} series},
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volume = {92},
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year = {1988},
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Bdsk-Url-1 = {https://doi.org/10.1021/j100322a018}}
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@article{Knowles_1988b,
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author = {Peter J. Knowles and Nicholas C. Handy},
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doi = {10.1063/1.454397},
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journal = {J. Chem. Phys.},
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pages = {6991},
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title = {Projected unrestricted {M\oller--Plesset} second-order energies},
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volume = {88},
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year = {1988},
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Bdsk-Url-1 = {https://doi.org/10.1063/1.454397}}
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@article{Schlegel_1986,
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author = {H. Bernhard Schlegel},
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doi = {10.1063/1.450026},
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journal = {J. Chem. Phys.},
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pages = {4530},
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title = {Potential energy curves using unrestricted {M\oller--Plesset} perturbation theory with spin annihilation},
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volume = {84},
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year = {1986},
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Bdsk-Url-1 = {https://doi.org/10.1063/1.450026}}
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@article{Schlegel_1988,
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author = {H. Bernhard Schlegel},
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doi = {10.1021/j100322a014},
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journal = {J. Phys. Chem.},
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pages = {3075},
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title = {{M\oller--Plesset} perturbation theory with spin projection},
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volume = {91},
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year = {1988},
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Bdsk-Url-1 = {https://doi.org/10.1021/j100322a014}}
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@article{Gill_1988a,
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author = {P. M. W. Gill and M. W. Wong and R. H. Nobes and L. Radom},
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doi = {10.1016/0009-2614(88)80328-2},
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journal = {Chem. Phys. Lett.},
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pages = {541},
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title = {How well can {RMP4} theory treat homolytic fragmentations?},
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volume = {148},
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year = {1988},
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Bdsk-Url-1 = {https://doi.org/10.1016/0009-2614(88)80328-2}}
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@article{Nobes_1987,
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author = {R. H. Nobes and J. A. Pople and L. Radom and N. C. Handy and P. J. Knowles},
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doi = {10.1016/0009-2614(87)80545-6},
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journal = {Chem. Phys. Lett.},
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pages = {481},
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title = {Slow convergence of the {M\oller--Plesset} perturbation series: the dissociation energy of hydrogen cyanide and the electron affinity of the cyano radical},
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volume = {138},
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year = {1987},
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Bdsk-Url-1 = {https://doi.org/10.1016/0009-2614(87)80545-6}}
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@article{Laidig_1987,
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author = {William D. Laidig and Paul Saxe and Rodney J. Bartlett},
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doi = {10.1063/1.452291},
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journal = {J. Chem. Phys.},
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pages = {887},
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title = {The description of \ce{N2} and \ce{F2} potential energy surfaces using multireference coupled cluster theory},
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volume = {86},
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year = {1987},
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Bdsk-Url-1 = {https://doi.org/10.1063/1.452291}}
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@article{Bartlett_1975,
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author = {R. J. Bartlett and D. M. Silver},
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doi = {10.1063/1.430878},
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journal = {J. Chem. Phys.},
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pages = {3258},
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title = {Many-body perturbation theory applied to electron pair correlation energies. I. Closed-shell first-row diatomic hydrides},
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volume = {62},
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year = {1975},
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Bdsk-Url-1 = {https://doi.org/10.1063/1.430878}}
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@article{Krishnan_1980,
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author = {R. Krishnan and M. J. Frisch and J. A. Pople},
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doi = {10.1063/1.439657},
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journal = {J. Chem. Phys.},
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pages = {4244},
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title = {Contribution of triple substitutions to the electron correlation energy in fourth order perturbation theory},
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volume = {72},
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year = {1980},
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Bdsk-Url-1 = {https://doi.org/10.1063/1.439657}}
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@article{Pople_1978,
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author = {J. A. Pople and R. Krishnan and H. B. Schlegel and J. S. Binkley},
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doi = {10.1002/qua.560140503},
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journal = {Int. J. Quantum Chem.},
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pages = {545},
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title = {Electron correlation theories and their application to the study of simple reaction potential surfaces},
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volume = {14},
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year = {1978},
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Bdsk-Url-1 = {https://doi.org/10.1002/qua.560140503}}
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@article{Pople_1976,
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author = {John A. Pople and Stephen Binkley and Rolf Seeger},
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doi = {10.1002/qua.560100802},
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journal = {Int. J. Quantum Chem. Symp.},
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pages = {1},
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title = {Theoretical models incorporating electron correlation},
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volume = {10},
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year = {1976},
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Bdsk-Url-1 = {https://doi.org/10.1002/qua.560100802}}
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@article{Knowles_1985,
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author = {P. J. Knowles and K. Somasundram and N. C. Handy and K. Hirao},
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doi = {10.1016/0009-2614(85)85002-8},
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journal = {Chem. Phys. Lett.},
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pages = {8},
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title = {The Calculation of High-Order Energies in the Many-Body Perturbation Theory Series},
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volume = {113},
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year = {1985},
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Bdsk-Url-1 = {https://doi.org/10.1016/0009-2614(85)85002-8}}
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@article{Laidig_1985,
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author = {William D. Laidig and George Fitzgerald and Rodney J. Bartlett},
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doi = {10.1016/0009-2614(85)80934-9},
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journal = {Chem. Phys. Lett.},
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pages = {151},
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title = {Is Fifth-Order MBPT Enough?},
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volume = {113},
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year = {1985},
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Bdsk-Url-1 = {https://doi.org/10.1016/0009-2614(85)80934-9}}
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@article{Hall_1951,
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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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date-added = {2020-11-24 09:45:15 +0100},
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date-modified = {2020-11-24 09:45:50 +0100},
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doi = {10.1098/rspa.1951.0048},
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journal = {Proc. R. Soc. Lond. A},
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pages = {541-552},
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title = {The molecular orbital theory of chemical valency VIII. A method of calculating ionization potentials},
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volume = {205},
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year = {1951},
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Bdsk-Url-1 = {https://royalsocietypublishing.org/doi/abs/10.1098/rspa.1951.0048},
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Bdsk-Url-2 = {https://doi.org/10.1098/rspa.1951.0048}}
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@article{Roothaan_1951,
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author = {Roothaan, C. C. J.},
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date-added = {2020-11-24 09:43:57 +0100},
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date-modified = {2020-11-24 09:44:09 +0100},
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doi = {10.1103/RevModPhys.23.69},
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||
journal = {Rev. Mod. Phys.},
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pages = {69--89},
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title = {New Developments in Molecular Orbital Theory},
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||
volume = {23},
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year = {1951},
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Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/RevModPhys.23.69},
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Bdsk-Url-2 = {https://doi.org/10.1103/RevModPhys.23.69}}
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@article{Slater_1951,
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author = {Slater, J. C.},
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date-added = {2020-11-24 09:42:40 +0100},
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date-modified = {2020-11-24 09:42:58 +0100},
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||
doi = {10.1103/PhysRev.82.538},
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journal = {Phys. Rev.},
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pages = {538--541},
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title = {Magnetic Effects and the Hartree-Fock Equation},
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volume = {82},
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year = {1951},
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Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRev.82.538},
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Bdsk-Url-2 = {https://doi.org/10.1103/PhysRev.82.538}}
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@article{Loos_2019d,
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author = {P. F. Loos and B. Pradines and A. Scemama and J. Toulouse and E. Giner},
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date-added = {2020-11-23 11:07:32 +0100},
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date-modified = {2020-11-23 11:07:32 +0100},
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doi = {10.1021/acs.jpclett.9b01176},
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journal = {J. Phys. Chem. Lett.},
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||
pages = {2931--2937},
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||
title = {A Density-Based Basis-Set Correction for Wave Function Theory},
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volume = {10},
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year = {2019},
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Bdsk-Url-1 = {https://doi.org/10.1021/acs.jctc.8b01103}}
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@article{Giner_2019,
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||
author = {E. Giner and A. Scemama and J. Toulouse and P. F. Loos},
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date-added = {2020-11-23 11:04:23 +0100},
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date-modified = {2020-11-23 11:04:23 +0100},
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||
journal = {J. Chem. Phys.},
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pages = {144118},
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title = {Chemically Accurate Excitation Energies With Small Basis Sets},
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volume = {151},
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year = {2019}}
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@article{Loos_2020a,
|
||
author = {P. F. Loos and A. Scemama and D. Jacquemin},
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abstract = {A study is made of the general Hartree---Fock (GHF) method, in which the basic spin-orbitals may be mixtures of functions having α and β spins. The existence of the solutions to the GHF equations has been proven by Lieb and Simon, and the nature of the various types of solutions has been group theoretically classified by Fukutome. Some numerical applications using Gaussian bases are carried out for some simple systems: the beryllium and carbon atoms and the BH molecule. Some GHF solutions of the general Fukutome-type ``torsional spin density waves'' (TSDW) were found.},
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author = {Istv{\'a}n Mayer and Per-Olov L{\"o}wdin},
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title = {Some comments on the general Hartree---Fock method},
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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.},
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author = {Burton, Hugh G. A. and Gross, Mark and Thom, Alex J. W.},
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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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journal = {J. Chem. Theory Comput.},
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month = feb,
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number = {2},
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pages = {607-618},
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shorttitle = {Holomorphic {{Hartree}}\textendash{{Fock Theory}}},
|
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title = {Holomorphic {{Hartree}}\textendash{{Fock Theory}}: {{The Nature}} of {{Two}}-{{Electron Problems}}},
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volume = {14},
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year = {2018},
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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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title = {Holomorphic {Hartree--Fock} Theory: An Inherently Multireference Approach},
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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.},
|
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author = {Carrascal, D J and Ferrer, J and Smith, J C and Burke, K},
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date-added = {2020-11-14 21:44:15 +0100},
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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},
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month = oct,
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number = {39},
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pages = {393001},
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shorttitle = {The {{Hubbard}} Dimer},
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title = {The {{Hubbard}} Dimer: A Density Functional Case Study of a Many-Body Problem},
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volume = {27},
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year = {2015},
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Bdsk-Url-1 = {https://doi.org/10.1088/0953-8984/27/39/393001}}
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@article{Carrascal_2018,
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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.},
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author = {Carrascal, Diego J. and Ferrer, Jaime and Maitra, Neepa and Burke, Kieron},
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doi = {10.1140/epjb/e2018-90114-9},
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pages = {142},
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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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@article{Pawlowski_2019a,
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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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author = {Paw{\l}owski,Filip and Olsen,Jeppe and J{\o}rgensen,Poul},
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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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@article{Pawlowski_2019b,
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author = {Paw{\l}owski,Filip and Olsen,Jeppe and J{\o}rgensen,Poul},
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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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title = {Analytic-continuation approach to the resummation of divergent series in Rayleigh-Schr\"odinger perturbation theory},
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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 = {Cejnar, Pavel and Iachello, Francesco},
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