fixing up references and other modifications
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Pierre-Francois Loos
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%% This BibTeX bibliography file was created using BibDesk.
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%% Created for Pierre-Francois Loos at 2022-03-06 22:50:10 +0100
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%% Created for Pierre-Francois Loos at 2022-03-07 20:27:55 +0100
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%% Saved with string encoding Unicode (UTF-8)
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@article{Veril_2021,
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author = {Micka{\"e}l V{\'e}ril and Anthony Scemama and Michel Caffarel and Filippo Lipparini and Martial Boggio-Pasqua and Denis Jacquemin and Pierre-Fran{\c c}ois Loos},
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date-added = {2022-03-07 20:24:41 +0100},
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date-modified = {2022-03-07 20:24:41 +0100},
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doi = {10.1002/wcms.1517},
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journal = {WIREs Comput. Mol. Sci.},
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pages = {e1517},
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title = {{{QUESTDB}}: a database of highly-accurate excitation energies for the electronic structure community},
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year = {2021},
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bdsk-url-1 = {https://doi.org/10.1002/wcms.1517}}
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@article{Loos_2020,
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author = {Loos, Pierre-Fran{\c c}ois and Scemama, Anthony and Boggio-Pasqua, Martial and Jacquemin, Denis},
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date-added = {2022-03-07 20:24:07 +0100},
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date-modified = {2022-03-07 20:24:10 +0100},
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||||
doi = {10.1021/acs.jctc.0c00227},
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||||
journal = {J. Chem. Theory Comput.},
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number = {6},
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||||
pages = {3720-3736},
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||||
title = {Mountaineering Strategy to Excited States: Highly Accurate Energies and Benchmarks for Exotic Molecules and Radicals},
|
||||
volume = {16},
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||||
year = {2020},
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||||
bdsk-url-1 = {https://doi.org/10.1021/acs.jctc.0c00227}}
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@article{Shepherd_2016,
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author = {Shepherd, James J. and Henderson, Thomas M. and Scuseria, Gustavo E.},
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date-added = {2022-03-07 20:15:57 +0100},
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||||
date-modified = {2022-03-07 20:15:57 +0100},
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||||
doi = {10.1063/1.4942770},
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file = {/home/antoinem/Zotero/storage/MTE8NM4A/Shepherd et al. - 2016 - Using full configuration interaction quantum Monte.pdf;/home/antoinem/Zotero/storage/MU5NRJNS/1.html},
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journal = {J. Chem. Phys.},
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||||
pages = {094112},
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publisher = {{American Institute of Physics}},
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||||
title = {Using Full Configuration Interaction Quantum {{Monte Carlo}} in a Seniority Zero Space to Investigate the Correlation Energy Equivalence of Pair Coupled Cluster Doubles and Doubly Occupied Configuration Interaction},
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volume = {144},
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||||
year = {2016},
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bdsk-url-1 = {https://doi.org/10.1063/1.4942770}}
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@article{Stein_2014,
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author = {Stein, Tamar and Henderson, Thomas M. and Scuseria, Gustavo E.},
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date-added = {2022-03-07 20:15:50 +0100},
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||||
date-modified = {2022-03-07 20:15:50 +0100},
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||||
doi = {10.1063/1.4880819},
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file = {/home/antoinem/Zotero/storage/KI25I3H5/Stein et al. - 2014 - Seniority zero pair coupled cluster doubles theory.pdf},
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journal = {J. Chem. Phys.},
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pages = {214113},
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publisher = {{American Institute of Physics}},
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title = {Seniority Zero Pair Coupled Cluster Doubles Theory},
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volume = {140},
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year = {2014},
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bdsk-url-1 = {https://doi.org/10.1063/1.4880819}}
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@article{Henderson_2015,
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author = {Henderson, Thomas M. and Bulik, Ireneusz W. and Scuseria, Gustavo E.},
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date-added = {2022-03-07 20:13:53 +0100},
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date-modified = {2022-03-07 20:13:53 +0100},
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||||
doi = {10.1063/1.4921986},
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||||
file = {/home/antoinem/Zotero/storage/YSB8DTFZ/Henderson et al. - 2015 - Pair extended coupled cluster doubles.pdf},
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journal = {J. Chem. Phys.},
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pages = {214116},
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publisher = {{American Institute of Physics}},
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title = {Pair Extended Coupled Cluster Doubles},
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volume = {142},
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year = {2015},
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bdsk-url-1 = {https://doi.org/10.1063/1.4921986}}
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@article{Magoulas_2021,
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author = {Magoulas, Ilias and Gururangan, Karthik and Piecuch, Piotr and Deustua, J. Emiliano and Shen, Jun},
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date-added = {2022-03-06 22:49:34 +0100},
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@ -364,25 +430,27 @@
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@article{Knowles_1989,
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author = {Knowles, Peter J. and Handy, Nicholas C.},
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date-added = {2022-03-06 15:20:23 +0100},
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date-modified = {2022-03-06 15:20:23 +0100},
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file = {/Users/loos/Zotero/storage/XWJJMYAA/Knowles_1989.pdf},
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date-modified = {2022-03-07 20:10:37 +0100},
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doi = {10.1016/0010-4655(89)90033-7},
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journal = {Comput. Phys. Commun.},
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number = {1},
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pages = {75--83},
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title = {A Determinant Based Full Configuration Interaction Program},
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volume = {54},
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year = {1989}}
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year = {1989},
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bdsk-url-1 = {https://doi.org/10.1016/0010-4655(89)90033-7}}
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@article{Knowles_1984,
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author = {P. J. Knowles and N. C. Handy},
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date-added = {2022-03-06 15:20:23 +0100},
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date-modified = {2022-03-06 15:20:23 +0100},
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date-modified = {2022-03-07 20:10:12 +0100},
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doi = {10.1016/0009-2614(84)85513-X},
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journal = {Chem. Phys. Lett.},
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keywords = {correlation},
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pages = {315--321},
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title = {A new determinant-based full configuration interaction method},
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volume = {111},
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year = {1984}}
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year = {1984},
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bdsk-url-1 = {https://doi.org/10.1016/0009-2614(84)85513-X}}
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@article{Booth_2009,
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author = {Booth, George H. and Thom, Alex J. W. and Alavi, Ali},
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@ -498,55 +566,48 @@
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@article{Damour_2021,
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author = {Damour, Yann and V{\'{e}}ril, Micka{\"{e}}l and Kossoski, F{\'{a}}bris and Caffarel, Michel and Jacquemin, Denis and Scemama, Anthony and Loos, Pierre-Fran{\c{c}}ois},
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date-modified = {2022-03-07 20:17:03 +0100},
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doi = {10.1063/5.0065314},
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file = {:home/fabris/Downloads/5.0065314.pdf:pdf},
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issn = {0021-9606},
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journal = {The Journal of Chemical Physics},
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journal = {J. Chem. Phys.},
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number = {13},
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pages = {134104},
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publisher = {AIP Publishing, LLC},
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title = {{Accurate full configuration interaction correlation energy estimates for five- and six-membered rings}},
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url = {https://doi.org/10.1063/5.0065314},
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volume = {155},
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year = {2021},
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bdsk-url-1 = {https://doi.org/10.1063/5.0065314}}
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@article{Hollett_2022,
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@article{Elayan_2022,
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author = {Elayan,Ismael A and Gupta,Rishabh and Hollett,Joshua Wallace},
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date-modified = {2022-03-07 20:27:21 +0100},
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doi = {10.1063/5.0073227},
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eprint = {https://doi.org/10.1063/5.0073227},
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journal = {The Journal of Chemical Physics},
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number = {ja},
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pages = {null},
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title = {ΔNO and the complexities of electron correlation in simple hydrogen clusters},
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url = {https://doi.org/10.1063/5.0073227},
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volume = {0},
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year = {0},
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journal = {J. Chem. Phys.},
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pages = {094102},
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title = {{$\Delta$}NO and the complexities of electron correlation in simple hydrogen clusters},
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volume = {156},
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year = {2022},
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bdsk-url-1 = {https://doi.org/10.1063/5.0073227}}
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@article{Alcoba_2014b,
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abstract = {This work deals with the configuration interaction method when an N-electron Hamiltonian is projected on Slater determinants which are classified according to their seniority number values. We study the spin features of the wave functions and the size of the matrices required to formulate states of any spin symmetry within this treatment. Correlation energies associated with the wave functions arising from the seniority-based configuration interaction procedure are determined for three types of molecular orbital basis: canonical molecular orbitals, natural orbitals, and the orbitals resulting from minimizing the expectation value of the N-electron seniority number operator. The performance of these bases is analyzed by means of numerical results obtained from selected N-electron systems of several spin symmetries. The comparison of the results highlights the efficiency of the molecular orbital basis which minimizes the mean value of the seniority number for a state, yielding energy values closer to those provided by the full configuration interaction procedure. {\textcopyright} 2014 AIP Publishing LLC.},
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author = {Alcoba, Diego R. and Torre, Alicia and Lain, Luis and Massaccesi, Gustavo E. and O{\~{n}}a, Ofelia B.},
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date-modified = {2022-03-07 20:25:42 +0100},
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doi = {10.1063/1.4882881},
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file = {:home/fabris/Downloads/1.4882881.pdf:pdf},
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issn = {00219606},
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journal = {Journal of Chemical Physics},
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journal = {J. Chem. Phys.},
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number = {23},
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pages = {234103},
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title = {{Configuration interaction wave functions: A seniority number approach}},
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url = {http://dx.doi.org/10.1063/1.4882881},
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volume = {140},
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year = {2014},
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bdsk-url-1 = {http://dx.doi.org/10.1063/1.4882881}}
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@article{Raemdonck_2015,
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author = {Van Raemdonck,Mario and Alcoba,Diego R. and Poelmans,Ward and De Baerdemacker,Stijn and Torre,Alicia and Lain,Luis and Massaccesi,Gustavo E. and Van Neck,Dimitri and Bultinck,Patrick},
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date-modified = {2022-03-07 20:19:45 +0100},
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doi = {10.1063/1.4930260},
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eprint = {https://doi.org/10.1063/1.4930260},
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journal = {The Journal of Chemical Physics},
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journal = {J. Chem. Phys.},
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number = {10},
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pages = {104106},
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title = {Polynomial scaling approximations and dynamic correlation corrections to doubly occupied configuration interaction wave functions},
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url = {https://doi.org/10.1063/1.4930260},
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volume = {143},
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year = {2015},
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bdsk-url-1 = {https://doi.org/10.1063/1.4930260}}
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@ -571,14 +632,12 @@
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@article{Alcoba_2014,
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abstract = {We present a configuration interaction method in which the Hamiltonian of an N-electron system is projected on Slater determinants selected according to the seniority-number criterion along with the traditional excitation-based procedure. This proposed method is especially useful to describe systems which exhibit dynamic (weak) correlation at determined geometric arrangements (where the excitation-based procedure is more suitable) but show static (strong) correlation at other arrangements (where the seniority-number technique is preferred). The hybrid method amends the shortcomings of both individual determinant selection procedures, yielding correct shapes of potential energy curves with results closer to those provided by the full configuration interaction method.},
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author = {Alcoba, Diego R. and Torre, Alicia and Lain, Luis and O{\~{n}}a, Ofelia B. and Capuzzi, Pablo and {Van Raemdonck}, Mario and Bultinck, Patrick and {Van Neck}, Dimitri},
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date-modified = {2022-03-07 20:11:21 +0100},
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doi = {10.1063/1.4904755},
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file = {:home/fabris/Downloads/1.4904755.pdf:pdf},
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issn = {0021-9606},
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journal = {The Journal of Chemical Physics},
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journal = {J. Chem. Phys.},
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number = {24},
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pages = {244118},
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title = {{A hybrid configuration interaction treatment based on seniority number and excitation schemes}},
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url = {http://dx.doi.org/10.1063/1.4904755},
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volume = {141},
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year = {2014},
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bdsk-url-1 = {http://dx.doi.org/10.1063/1.4904755}}
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@ -596,27 +655,24 @@
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@article{Bytautas_2015,
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abstract = {The present study further explores the concept of the seniority number ($\Omega$) by examining different configuration interaction (CI) truncation strategies in generating compact wave functions in a systematic way. While the role of $\Omega$ in addressing static (strong) correlation problem has been addressed in numerous previous studies, the usefulness of seniority number in describing weak (dynamic) correlation has not been investigated in a systematic way. Thus, the overall objective in the present work is to investigate the role of $\Omega$ in addressing also dynamic electron correlation in addition to the static correlation. Two systematic CI truncation strategies are compared beyond minimal basis sets and full valence active spaces. One approach is based on the seniority number (defined as the total number of singly occupied orbitals in a determinant) and another is based on an excitation-level limitation. In addition, molecular orbitals are energy-optimized using multiconfigurational-self-consistent-field procedure for all these wave functions. The test cases include the symmetric dissociation of water (6-31G), N2 (6-31G), C2 (6-31G), and Be2 (cc-pVTZ). We find that the potential energy profile for H2O dissociation can be reasonably well described using only the $\Omega$ = 0 sector of the CI wave function. For the Be2 case, we show that the full CI potential energy curve (cc-pVTZ) is almost exactly reproduced using either $\Omega$-based (including configurations having up to $\Omega$ = 2 in the virtual-orbital-space) or excitation-based (up to single-plus-double-substitutions) selection methods, both out of a full-valence-reference function. Finally, in dissociation cases of N2 and C2, we shall also consider novel hybrid wave functions obtained by a union of a set of CI configurations representing the full valence space and a set of CI configurations where seniority-number restriction is imposed for a complete set (full-valence-space and virtual) of correlated molecular orbitals, simultaneously. We discuss the usefulness of the seniority number concept in addressing both static and dynamic electron correlation problems along dissociation paths.},
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author = {Bytautas, Laimutis and Scuseria, Gustavo E. and Ruedenberg, Klaus},
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date-modified = {2022-03-07 20:12:47 +0100},
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doi = {10.1063/1.4929904},
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file = {:home/fabris/Downloads/1.4929904.pdf:pdf},
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issn = {00219606},
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journal = {Journal of Chemical Physics},
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journal = {J. Chem. Phys.},
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number = {9},
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pages = {094105},
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title = {{Seniority number description of potential energy surfaces: Symmetric dissociation of water, N2, C2, and Be2}},
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url = {http://dx.doi.org/10.1063/1.4929904},
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volume = {143},
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year = {2015},
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bdsk-url-1 = {http://dx.doi.org/10.1063/1.4929904}}
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@article{Chen_2015,
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author = {Chen, Zhenhua and Zhou, Chen and Wu, Wei},
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date-modified = {2022-03-07 20:16:41 +0100},
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doi = {10.1021/acs.jctc.5b00416},
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eprint = {https://doi.org/10.1021/acs.jctc.5b00416},
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journal = {Journal of Chemical Theory and Computation},
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note = {PMID: 26575906},
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journal = {J. Chem. Theory Comput.},
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number = {9},
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pages = {4102-4108},
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title = {Seniority Number in Valence Bond Theory},
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url = {https://doi.org/10.1021/acs.jctc.5b00416},
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volume = {11},
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year = {2015},
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bdsk-url-1 = {https://doi.org/10.1021/acs.jctc.5b00416}}
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@ -624,12 +680,11 @@
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@article{Bytautas_2018,
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abstract = {This investigation combines the concept of the seniority number Ω (defined as the total number of singly occupied orbitals in a determinant) with the energy renormalization group (ERG) approach to obtain the lowest-energy electronic states on molecular potential energy surfaces. The proposed Ω-ERG method uses Slater determinants that are ordered according to seniority number Ω in ascending order. In the Ω-ERG procedure, the active system consists of M (N-electron) states and K additional complement (N-electron) states (complement-system). Among the M states in the active system the lowest-energy m states represent target states of interest (target-states), thus m ≤ M. The environment consists of Full Configuration Interaction (FCI) determinants that represent a reservoir from which the complement-states K are being selected. The goal of the Ω-ERG procedure is to obtain lowest-energy target states m of FCI quality in an iterative way at a reduced computational cost. In general, the convergence rate of Ω-ERG energies towards FCI values depends on m and M, thus, the notation Ω-ERG(m, M) is used. It is found that the Ω-ERG(m, M) method can be very effective for calculating lowest-energy m (ground and excited) target states when a sufficiently large number of sweeps is used. We find that the fastest convergence is observed when M > m. The performance of the Ω-ERG(m, M) procedure in describing strongly correlated molecular systems has been illustrated by examining bond-breaking processes in N2, H8, H2O and C2. The present, proof-of-principle study yields encouraging results for calculating multiple electronic states on potential energy surfaces with near Full CI quality.},
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author = {Laimutis Bytautas and Jorge Dukelsky},
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date-modified = {2022-03-07 20:26:54 +0100},
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doi = {https://doi.org/10.1016/j.comptc.2018.08.011},
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issn = {2210-271X},
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journal = {Computational and Theoretical Chemistry},
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journal = {Comput. Theor. Chem.},
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pages = {74-88},
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title = {Seniority based energy renormalization group (Ω-ERG) approach in quantum chemistry: Initial formulation and application to potential energy surfaces},
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url = {https://www.sciencedirect.com/science/article/pii/S2210271X18304651},
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title = {Seniority based energy renormalization group ({$\Omega$}-ERG) approach in quantum chemistry: Initial formulation and application to potential energy surfaces},
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volume = {1141},
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year = {2018},
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bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S2210271X18304651},
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@ -637,19 +692,14 @@
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@article{Henderson_2014,
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abstract = {Doubly occupied configuration interaction (DOCI) with optimized orbitals often accurately describes strong correlations while working in a Hilbert space much smaller than that needed for full configuration interaction. However, the scaling of such calculations remains combinatorial with system size. Pair coupled cluster doubles (pCCD) is very successful in reproducing DOCI energetically, but can do so with low polynomial scaling (N3, disregarding the two-electron integral transformation from atomic to molecular orbitals). We show here several examples illustrating the success of pCCD in reproducing both the DOCI energy and wave function and show how this success frequently comes about. What DOCI and pCCD lack are an effective treatment of dynamic correlations, which we here add by including higher-seniority cluster amplitudes which are excluded from pCCD. This frozen pair coupled cluster approach is comparable in cost to traditional closed-shell coupled cluster methods with results that are competitive for weakly correlated systems and often superior for the description of strongly correlated systems.},
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archiveprefix = {arXiv},
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arxivid = {1410.6529},
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author = {Henderson, Thomas M. and Bulik, Ireneusz W. and Stein, Tamar and Scuseria, Gustavo E.},
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date-modified = {2022-03-07 20:13:27 +0100},
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doi = {10.1063/1.4904384},
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eprint = {1410.6529},
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file = {:home/fabris/.local/share/data/Mendeley Ltd./Mendeley Desktop/Downloaded/Henderson et al. - 2014 - Seniority-based coupled cluster theory.pdf:pdf},
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issn = {0021-9606},
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journal = {The Journal of Chemical Physics},
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journal = {J. Chem. Phys.},
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month = {dec},
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number = {24},
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pages = {244104},
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title = {{Seniority-based coupled cluster theory}},
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url = {http://aip.scitation.org/doi/10.1063/1.4904384},
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volume = {141},
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year = {2014},
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bdsk-url-1 = {http://aip.scitation.org/doi/10.1063/1.4904384},
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@ -689,19 +739,14 @@
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bdsk-url-1 = {https://doi.org/10.1007/BF01151915}}
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@article{Loos_2018,
|
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abstract = {Striving to define very accurate vertical transition energies, we perform both high-level coupled cluster (CC) calculations (up to CCSDTQP) and selected configuration interaction (sCI) calculations (up to several millions of determinants) for 18 small compounds (water, hydrogen sulfide, ammonia, hydrogen chloride, dinitrogen, carbon monoxide, acetylene, ethylene, formaldehyde, methanimine, thioformaldehyde, acetaldehyde, cyclopropene, diazomethane, formamide, ketene, nitrosomethane, and the smallest streptocyanine). By systematically increasing the order of the CC expansion, the number of determinants in the CI expansion as well as the size of the one-electron basis set, we have been able to reach near full CI (FCI) quality transition energies. These calculations are carried out on CC3/aug-cc-pVTZ geometries, using a series of increasingly large atomic basis sets systematically including diffuse functions. In this way, we define a list of 110 transition energies for states of various characters (valence, Rydberg, n → $\pi$∗, $\pi$ → $\pi$ ∗, singlet, triplet, etc.) to be used as references for further calculations. Benchmark transition energies are provided at the aug-cc-pVTZ level as well as with additional basis set corrections, in order to obtain results close to the complete basis set limit. These reference data are used to benchmark a series of 12 excited-state wave function methods accounting for double and triple contributions, namely ADC(2), ADC(3), CIS(D), CIS(D∞), CC2, STEOM-CCSD, CCSD, CCSDR(3), CCSDT-3, CC3, CCSDT., and CCSDTQ. It turns out that CCSDTQ yields a negligible difference with the extrapolated CI values with a mean absolute error as small as 0.01 eV, whereas the coupled cluster approaches including iterative triples are also very accurate (mean absolute error of 0.03 eV). Consequently, CCSDT-3 and CC3 can be used to define reliable benchmarks. This observation does not hold for ADC(3) that delivers quite large errors for this set of small compounds, with a clear tendency to overcorrect its second-order version, ADC(2). Finally, we discuss the possibility to use basis set extrapolation approaches so as to tackle more easily larger compounds.},
|
||||
archivePrefix = {arXiv},
|
||||
arxivId = {1807.02045},
|
||||
author = {Loos, Pierre Fran{\c{c}}ois and Scemama, Anthony and Blondel, Aymeric and Garniron, Yann and Caffarel, Michel and Jacquemin, Denis},
|
||||
doi = {10.1021/acs.jctc.8b00406},
|
||||
eprint = {1807.02045},
|
||||
issn = {15499626},
|
||||
journal = {Journal of Chemical Theory and Computation},
|
||||
number = {8},
|
||||
pages = {4360--4379},
|
||||
pmid = {29966098},
|
||||
title = {{A Mountaineering Strategy to Excited States: Highly Accurate Reference Energies and Benchmarks}},
|
||||
volume = {14},
|
||||
year = {2018}
|
||||
}
|
||||
|
||||
abstract = {Striving to define very accurate vertical transition energies, we perform both high-level coupled cluster (CC) calculations (up to CCSDTQP) and selected configuration interaction (sCI) calculations (up to several millions of determinants) for 18 small compounds (water, hydrogen sulfide, ammonia, hydrogen chloride, dinitrogen, carbon monoxide, acetylene, ethylene, formaldehyde, methanimine, thioformaldehyde, acetaldehyde, cyclopropene, diazomethane, formamide, ketene, nitrosomethane, and the smallest streptocyanine). By systematically increasing the order of the CC expansion, the number of determinants in the CI expansion as well as the size of the one-electron basis set, we have been able to reach near full CI (FCI) quality transition energies. These calculations are carried out on CC3/aug-cc-pVTZ geometries, using a series of increasingly large atomic basis sets systematically including diffuse functions. In this way, we define a list of 110 transition energies for states of various characters (valence, Rydberg, n → $\pi$∗, $\pi$ → $\pi$ ∗, singlet, triplet, etc.) to be used as references for further calculations. Benchmark transition energies are provided at the aug-cc-pVTZ level as well as with additional basis set corrections, in order to obtain results close to the complete basis set limit. These reference data are used to benchmark a series of 12 excited-state wave function methods accounting for double and triple contributions, namely ADC(2), ADC(3), CIS(D), CIS(D∞), CC2, STEOM-CCSD, CCSD, CCSDR(3), CCSDT-3, CC3, CCSDT., and CCSDTQ. It turns out that CCSDTQ yields a negligible difference with the extrapolated CI values with a mean absolute error as small as 0.01 eV, whereas the coupled cluster approaches including iterative triples are also very accurate (mean absolute error of 0.03 eV). Consequently, CCSDT-3 and CC3 can be used to define reliable benchmarks. This observation does not hold for ADC(3) that delivers quite large errors for this set of small compounds, with a clear tendency to overcorrect its second-order version, ADC(2). Finally, we discuss the possibility to use basis set extrapolation approaches so as to tackle more easily larger compounds.},
|
||||
author = {Loos, Pierre Fran{\c{c}}ois and Scemama, Anthony and Blondel, Aymeric and Garniron, Yann and Caffarel, Michel and Jacquemin, Denis},
|
||||
date-modified = {2022-03-07 20:19:10 +0100},
|
||||
doi = {10.1021/acs.jctc.8b00406},
|
||||
journal = {J. Chem. Theory Comput.},
|
||||
number = {8},
|
||||
pages = {4360--4379},
|
||||
title = {{A Mountaineering Strategy to Excited States: Highly Accurate Reference Energies and Benchmarks}},
|
||||
volume = {14},
|
||||
year = {2018},
|
||||
bdsk-url-1 = {https://doi.org/10.1021/acs.jctc.8b00406}}
|
||||
|
||||
@ -1,8 +1,8 @@
|
||||
\documentclass[aip,jcp,reprint,noshowkeys,superscriptaddress]{revtex4-1}
|
||||
\usepackage{graphicx,dcolumn,bm,xcolor,microtype,multirow,amscd,amsmath,amssymb,amsfonts,physics,wrapfig,txfonts,siunitx}
|
||||
\usepackage[version=4]{mhchem}
|
||||
%\usepackage{natbib}
|
||||
%\bibliographystyle{achemso}
|
||||
\usepackage{natbib}
|
||||
\bibliographystyle{achemso}
|
||||
|
||||
\newcommand{\fk}[1]{\textcolor{blue}{#1}}
|
||||
|
||||
@ -112,7 +112,7 @@ which has been shown to be particularly effective at catching static correlation
|
||||
while higher sectors tend to contribute progressively less. \cite{Bytautas_2011,Bytautas_2015,Alcoba_2014b,Alcoba_2014}
|
||||
However, already at the sCI0 level, $\Ndet$ scales exponentially with $\Nbas$, since excitations of all excitation degrees are included.
|
||||
Therefore, despite the encouraging successes of seniority-based CI methods, their unfavorable computational scaling restricts applications to very small systems.
|
||||
Besides CI, other methods that exploit the concept of seniority number have been pursued. \cite{Limacher_2013,Limacher_2014,Tecmer_2014,Boguslawski_2014a,Boguslawski_2015,Boguslawski_2014b,Boguslawski_2014c,Johnson_2017,Fecteau_2020,Johnson_2020,Henderson_2014,Chen_2015,Bytautas_2018}
|
||||
Besides CI, other methods that exploit the concept of seniority number have been pursued. \cite{Limacher_2013,Limacher_2014,Tecmer_2014,Boguslawski_2014a,Boguslawski_2015,Boguslawski_2014b,Boguslawski_2014c,Johnson_2017,Fecteau_2020,Johnson_2020,Henderson_2014,Stein_2014,Henderson_2015,Chen_2015,Shepherd_2016,Bytautas_2018}
|
||||
|
||||
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
@ -206,7 +206,7 @@ We have calculated the potential energy curves (PECs) for the dissociation of si
|
||||
which display a variable number of bond breaking.
|
||||
For the latter two molecules, we considered linearly arranged with equally spaced hydrogen atoms, and computed PECs along the symmetric dissociation coordinate.
|
||||
For ethylene, we considered the \ce{C=C} double bond breaking, while freezing the remaining internal coordinates.
|
||||
Its equilibrium geometry was taken from Ref.~\cite{Loos_2018} and is reproduced in the \SupInf.
|
||||
Its equilibrium geometry was taken from Ref.~\onlinecite{Loos_2018} and is reproduced in the \SupInf.
|
||||
Due to the (multiple) bond breaking, these are challenging systems for electronic structure methods,
|
||||
being often considered when assessing novel methodologies.
|
||||
We evaluated the convergence of four observables: the non-parallelity error (NPE), the distance error, the vibrational frequencies, and the equilibrium geometries.
|
||||
@ -220,7 +220,7 @@ From the PECs, we have also extracted the vibrational frequencies and equilibriu
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
|
||||
The hCI method was implemented in {\QP} via a straightforward adaptation of the
|
||||
\textit{configuration interaction using a perturbative selection made iteratively} (CIPSI) algorithm \cite{Huron_1973,Giner_2013,Giner_2015,Garniron_2018},
|
||||
\textit{configuration interaction using a perturbative selection made iteratively} (CIPSI) algorithm, \cite{Huron_1973,Giner_2013,Giner_2015,Garniron_2018}
|
||||
by allowing only for determinants having a given maximum hierarchy $h$.
|
||||
The excitation-based CI, seniority-based CI, and FCI calculations presented here were also performed with the CIPSI algorithm implemented in {\QP}. \cite{Garniron_2019}
|
||||
In practice, we consider the CI energy to be converged when the second-order perturbation correction lies below \SI{0.01}{\milli\hartree}, \cite{Garniron_2018}
|
||||
@ -229,8 +229,6 @@ Nevertheless, we decided to present the results as functions of the formal numbe
|
||||
which are not related to the particular algorithmic choices of the CIPSI calculations.
|
||||
All CI calculations were performed for the cc-pVDZ basis set and with frozen core orbitals.
|
||||
For the \ce{HF} molecule we have also tested basis set effects, by considered the cc-pVTZ and cc-pVQZ basis sets.
|
||||
\titou{Geometries? SI?}
|
||||
\fk{Only the geometry of ethylene has to be given. I added it to the Sup. Info.}
|
||||
\titou{T2: I think it might be worth mentioning that the determinant-driven framework of {\QP} allows to include any arbitrary set of determinants.
|
||||
This would also justify why we are focusing on the number of determinants instead of the actual scaling of the method.
|
||||
I think this is a important point because the CISD Hilbert space has a size proportional to $N^4$ but the cost associated with solving the CISD equations scales as $N^6$... Actually, it follows the same rules as CC: CISD scales as $N^6$, CISDT as $N^8$, CISDTQ as $N^{10}$, etc.
|
||||
@ -242,7 +240,7 @@ However, the selected nature of the CIPSI algorithm means that the actual number
|
||||
The CI calculations were performed with both canonical HF orbitals and optimized orbitals.
|
||||
In the latter case, the energy is obtained variationally in the CI space and in the orbital parameter space, hence an orbital-optimized CI (oo-CI) method.
|
||||
We employed the algorithm described elsewhere \cite{Damour_2021} and also implemented in {\QP} for optimizing the orbitals within a CI wave function.
|
||||
In order to avoid converging to a saddle point solution, we employed a similar strategy as recently described in Ref.~\cite{Hollett_2022}.
|
||||
In order to avoid converging to a saddle point solution, we employed a similar strategy as recently described in Ref.~\onlinecite{Elayan_2022}.
|
||||
Namely, whenever the eigenvalue of the orbital rotation Hessian is negative and the corresponding gradient component $g_i$ lies below a given threshold $g_0$,
|
||||
then this gradient component is replaced by $g_0 \abs{g_i}/g_i$.
|
||||
While we cannot ensure that the obtained solutions are global minima in the orbital parameter space, we verified that in all stationary solutions surveyed here
|
||||
@ -277,8 +275,6 @@ This is observed for single bond breaking (\ce{HF} and \ce{F2}) as well as the m
|
||||
For \ce{H8}, hCI and excitation-based CI perform similarly.
|
||||
The convergence with respect to $\Ndet$ is slower in the latter, more challenging cases, irrespective of the class of CI methods, as would be expected.
|
||||
But more importantly, the superiority of the hCI methods appears to be highlighted in the multiple bond break systems (compare ethylene and \ce{N2} with \ce{HF} and \ce{F2} in Fig.~\ref{fig:plot_stat}).
|
||||
\titou{T2: Would it be a good idea to write the \ce{HF} molecule as \ce{FH}?}
|
||||
\fk{Don't think so. I included ``molecule'' after HF whenever one could have understood Hartree-Fock instead.}
|
||||
|
||||
%%% FIG 2 %%%
|
||||
\begin{figure}[h!]
|
||||
@ -318,7 +314,7 @@ and the performance of seniority-based CI is much poorer (due to the slow recove
|
||||
|
||||
%\subsection{Equilibrium geometries and vibrational frequencies}
|
||||
|
||||
In Fig.~\ref{fig:xe} and \ref{fig:freq}, we present the convergence of the equilibrium geometries and vibrational frequencies, respectively,
|
||||
In Figs.~\ref{fig:xe} and \ref{fig:freq}, we present the convergence of the equilibrium geometries and vibrational frequencies, respectively,
|
||||
as functions of $\Ndet$, for the three classes of CI methods.
|
||||
For the equilibrium geometries, hCI performs slightly better overall than excitation-based CI.
|
||||
A more significant advantage of hCI can be seen for the vibrational frequencies.
|
||||
@ -378,7 +374,7 @@ Based on the present oo-CI results, hCI still has the upper hand when compared w
|
||||
Orbital optimization usually reduces the NPE for seniority-based CI (in this case we only considered oo-DOCI) as well.
|
||||
The gain is specially noticeable for \ce{H4} and \ce{H8} (where the orbitals become symmetry-broken \cite{}),
|
||||
and much less so for \ce{HF}, ethylene, and \ce{N2} (where the orbitals remain symmetry-preserving).
|
||||
This is in line with what has been observed before for \ce{N2} \cite{Bytautas_2011}.
|
||||
This is in line with what has been observed before for \ce{N2}. \cite{Bytautas_2011}
|
||||
For \ce{F2}, we found that orbital optimization actually increases the NPE (though by a small amount),
|
||||
due to the larger energy lowering at the Franck-Condon region than at dissociation.
|
||||
These results suggest that, when bond breaking involves one site, orbital optimization at the DOCI level does not have such an important role,
|
||||
@ -426,8 +422,8 @@ The superiority of hCI methods is more noticeable for the non-parallelity and di
|
||||
The comparison to seniority-based CI is less trivial.
|
||||
DOCI (the first level of seniority-based CI) often provides even lower NPEs for a similar $\Ndet$, but it falls short in describing the other properties investigated here.
|
||||
If higher accuracy is desired, than the convergence is faster with hCI (and also excitation-based CI) than seniority-based CI, at least for HF orbitals.
|
||||
Finally, the exponential scaling of seniority-based CI in practice precludes this approach for larger systems and larger basis sets,
|
||||
while the favorable polynomial scaling and encouraging performance of hCI as an alternative.
|
||||
Finally, the exponential scaling of seniority-based CI in practice precludes this approach for larger systems and basis sets,
|
||||
while the favorable polynomial scaling and encouraging performance of hCI is an alternative.
|
||||
|
||||
We found surprisingly good results for the first level of hCI (hCI1) and the orbital optimized version of CIS (oo-CIS), two methods with very favorable computational scaling.
|
||||
In particular, oo-CIS correctly describes single bond breaking.
|
||||
@ -436,14 +432,14 @@ We hope to report on generalizations to excited states in the future.
|
||||
%For the challenging cases of \ce{H4} and \ce{H8}, hCI and excitation-based CI perform similarly.
|
||||
An important conclusion is that orbital optimization at the CI level is not necessarily a recommended strategy,
|
||||
given the overall modest improvement in convergence when compared to results with canonical HF orbitals.
|
||||
One should bear in mind that optimizing the orbitals is always accompanied with well-known challenges (several solutions, convergence issues)
|
||||
and may imply in a significant computational burden (associated with the calculations of the orbital gradient and Hessian, and the many iterations that are often required),
|
||||
One should bear in mind that optimizing the orbitals is always accompanied with well-known challenges (several solutions, convergence issues, etc)
|
||||
and may imply a significant computational burden (associated with the calculations of the orbital gradient and Hessian, and the many iterations that are often required),
|
||||
specially for larger CI spaces.
|
||||
In this sense, stepping up in the CI hierarchy might be a more straightforward and possibly a cheaper alternative than optimizing the orbitals.
|
||||
One interesting possibility to explore is to first optimize the orbitals at a lower level of CI, and then to employ this set of orbitals at a higher level of CI.
|
||||
|
||||
The hCI pathway presented here offers several interesting possibilities to pursue.
|
||||
One could generalize and adapt hCI for excited states and open-shell systems,
|
||||
One could generalize and adapt hCI for excited states \cite{Veril_2021} and open-shell systems, \cite{Loos_2020}
|
||||
develop coupled-cluster methods based on an analogous excitation-seniority truncation of the excitation operator, \cite{Aroeira_2021,Magoulas_2021,Lee_2021}
|
||||
and explore the accuracy of hCI trial wave functions for quantum Monte Carlo simulations. \cite{Dash_2019,Dash_2021,Cuzzocrea_2022}
|
||||
|
||||
|
||||
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