author = {Motta, Mario and Genovese, Claudio and Ma, Fengjie and Cui, Zhi-Hao and Sawaya, Randy and Chan, Garnet Kin-Lic and Chepiga, Natalia and Helms, Phillip and Jim\'enez-Hoyos, Carlos and Millis, Andrew J. and Ray, Ushnish and Ronca, Enrico and Shi, Hao and Sorella, Sandro and Stoudenmire, Edwin M. and White, Steven R. and Zhang, Shiwei},
collaboration = {Simons Collaboration on the Many-Electron Problem},
date-added = {2022-03-09 10:53:47 +0100},
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doi = {10.1103/PhysRevX.10.031058},
issue = {3},
journal = {Phys. Rev. X},
month = {Sep},
numpages = {9},
pages = {031058},
publisher = {American Physical Society},
title = {Ground-State Properties of the Hydrogen Chain: Dimerization, Insulator-to-Metal Transition, and Magnetic Phases},
author = {Motta, Mario and Ceperley, David M and Chan, Garnet Kin-Lic and Gomez, John A and Gull, Emanuel and Guo, Sheng and Jim{\'e}nez-Hoyos, Carlos A and Lan, Tran Nguyen and Li, Jia and Ma, Fengjie and others},
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doi = {10.1103/PhysRevX.7.031059},
journal = {Phys. Rev. X},
number = {3},
pages = {031059},
title = {Towards the solution of the many-electron problem in real materials: Equation of state of the hydrogen chain with state-of-the-art many-body methods},
author = {Henderson, Thomas M. and Scuseria, Gustavo E. and Dukelsky, Jorge and Signoracci, Angelo and Duguet, Thomas},
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doi = {10.1103/PhysRevC.89.054305},
file = {/home/antoinem/Zotero/storage/NBW3DPNI/Henderson et al. - 2014 - Quasiparticle coupled cluster theory for pairing i.pdf;/home/antoinem/Zotero/storage/URGVY3VT/PhysRevC.89.html},
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publisher = {{American Physical Society}},
title = {Quasiparticle Coupled Cluster Theory for Pairing Interactions},
author = {Charles-{\'E}mile Fecteau and Samuel Cloutier and Jean-David Moisset, J{\'e}r{\'e}my Boulay and Patrick Bultinck and Alexandre Faribault and Paul A. Johnson},
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doi = {10.48550/arXiv.2202.12402},
eprint = {2202.12402},
primaryclass = {physics.chem-ph},
title = {Near-exact treatment of seniority-zero ground and excited states with a Richardson-Gaudin mean-field},
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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pages = {e1517},
title = {{{QUESTDB}}: a database of highly-accurate excitation energies for the electronic structure community},
year = {2021},
bdsk-url-1 = {https://doi.org/10.1002/wcms.1517}}
@article{Loos_2020,
author = {Loos, Pierre-Fran{\c c}ois and Scemama, Anthony and Boggio-Pasqua, Martial and Jacquemin, Denis},
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title = {Mountaineering Strategy to Excited States: Highly Accurate Energies and Benchmarks for Exotic Molecules and Radicals},
author = {Shepherd, James J. and Henderson, Thomas M. and Scuseria, Gustavo E.},
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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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pages = {094112},
publisher = {{American Institute of Physics}},
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},
volume = {144},
year = {2016},
bdsk-url-1 = {https://doi.org/10.1063/1.4942770}}
@article{Stein_2014,
author = {Stein, Tamar and Henderson, Thomas M. and Scuseria, Gustavo E.},
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doi = {10.1063/1.4880819},
file = {/home/antoinem/Zotero/storage/KI25I3H5/Stein et al. - 2014 - Seniority zero pair coupled cluster doubles theory.pdf},
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pages = {214113},
publisher = {{American Institute of Physics}},
title = {Seniority Zero Pair Coupled Cluster Doubles Theory},
volume = {140},
year = {2014},
bdsk-url-1 = {https://doi.org/10.1063/1.4880819}}
@article{Henderson_2015,
author = {Henderson, Thomas M. and Bulik, Ireneusz W. and Scuseria, Gustavo E.},
author = {Lee, Seunghoon and Zhai, Huanchen and Sharma, Sandeep and Umrigar, C. J. and Chan, Garnet Kin-Lic},
date-added = {2022-03-06 22:47:21 +0100},
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doi = {10.1021/acs.jctc.1c00205},
journal = {J. Chem. Theory Comput.},
number = {6},
pages = {3414-3425},
title = {Externally Corrected CCSD with Renormalized Perturbative Triples (R-ecCCSD(T)) and the Density Matrix Renormalization Group and Selected Configuration Interaction External Sources},
author = {Fecteau,Charles-{\'E}mile and Fortin,Hubert and Cloutier,Samuel and Johnson,Paul A.},
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title = {Reduced density matrices of Richardson--Gaudin states in the Gaudin algebra basis},
volume = {153},
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bdsk-url-1 = {https://doi.org/10.1063/5.0027393}}
@article{Johnson_2020,
author = {Johnson,Paul A. and Fecteau,Charles-{\'E}mile and Berthiaume,Fr{\'e}d{\'e}ric and Cloutier,Samuel and Carrier,Laurie and Gratton,Marianne and Bultinck,Patrick and De Baerdemacker,Stijn and Van Neck,Dimitri and Limacher,Peter and Ayers,Paul W.},
date-added = {2022-03-06 20:16:57 +0100},
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doi = {10.1063/5.0022189},
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number = {10},
pages = {104110},
title = {Richardson--Gaudin mean-field for strong correlation in quantum chemistry},
volume = {153},
year = {2020},
bdsk-url-1 = {https://doi.org/10.1063/5.0022189}}
@article{Boguslawski_2016a,
author = {Boguslawski, Katharina and Tecmer, Pawe{\l} and Legeza, {\"O}rs},
date-added = {2022-03-06 20:16:11 +0100},
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doi = {10.1103/PhysRevB.94.155126},
file = {/home/antoinem/Zotero/storage/XLC79SPJ/Boguslawski et al. - 2016 - Analysis of two-orbital correlations in wave funct.pdf;/home/antoinem/Zotero/storage/5BTASXE6/PhysRevB.94.html;/home/antoinem/Zotero/storage/9IQSWNFY/PhysRevB.94.html},
journal = {Phys. Rev. B},
pages = {155126},
publisher = {{American Physical Society}},
title = {Analysis of Two-Orbital Correlations in Wave Functions Restricted to Electron-Pair States},
author = {Tecmer, Pawe{\l} and Boguslawski, Katharina and Johnson, Paul A. and Limacher, Peter A. and Chan, Matthew and Verstraelen, Toon and Ayers, Paul W.},
date-added = {2022-03-06 20:16:11 +0100},
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doi = {10.1021/jp502127v},
file = {/home/antoinem/Zotero/storage/Q2XDCYBY/Tecmer et al. - 2014 - Assessing the Accuracy of New Geminal-Based Approa.pdf;/home/antoinem/Zotero/storage/GNPWKYBS/jp502127v.html},
journal = {J. Phys. Chem. A},
pages = {9058--9068},
publisher = {{American Chemical Society}},
title = {Assessing the {{Accuracy}} of {{New Geminal}}-{{Based Approaches}}},
volume = {118},
year = {2014},
bdsk-url-1 = {https://doi.org/10.1021/jp502127v}}
@article{Boguslawski_2017a,
author = {Boguslawski, Katharina and Tecmer, Pawe{\l}},
date-added = {2022-03-06 20:16:11 +0100},
date-modified = {2022-03-06 20:16:11 +0100},
doi = {10.1021/acs.jctc.6b01134},
file = {/home/antoinem/Zotero/storage/QQLX55VV/Boguslawski and Tecmer - 2017 - Benchmark of Dynamic Electron Correlation Models f.pdf;/home/antoinem/Zotero/storage/FIW7UJXS/acs.jctc.html},
journal = {J. Chem. Theory Comput.},
pages = {5966--5983},
publisher = {{American Chemical Society}},
title = {Benchmark of {{Dynamic Electron Correlation Models}} for {{Seniority}}-{{Zero Wave Functions}} and {{Their Application}} to {{Thermochemistry}}},
file = {/home/antoinem/Zotero/storage/YLPA4GNY/Boguslawski - 2017 - Erratum ``Targeting excited states in all-trans po.pdf;/home/antoinem/Zotero/storage/7MJG68RQ/1.html},
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pages = {139901},
publisher = {{American Institute of Physics}},
title = {Erratum: ``{{Targeting}} Excited States in All-Trans Polyenes with Electron-Pair States'' [{{J}}. {{Chem}}. {{Phys}}. 145, 234105 (2016)]},
volume = {147},
year = {2017},
bdsk-url-1 = {https://doi.org/10.1063/1.5006124}}
@article{Boguslawski_2014b,
author = {Boguslawski, Katharina and Tecmer, Pawe{\l} and Bultinck, Patrick and De Baerdemacker, Stijn and Van Neck, Dimitri and Ayers, Paul W.},
date-added = {2022-03-06 20:16:11 +0100},
date-modified = {2022-03-06 20:16:11 +0100},
doi = {10.1021/ct500759q},
file = {/home/antoinem/Zotero/storage/S2ZFWFVC/Boguslawski et al. - 2014 - Nonvariational Orbital Optimization Techniques for.pdf;/home/antoinem/Zotero/storage/Z26HYNRT/ct500759q.html},
journal = {J. Chem. Theory Comput.},
pages = {4873--4882},
publisher = {{American Chemical Society}},
title = {Nonvariational {{Orbital Optimization Techniques}} for the {{AP1roG Wave Function}}},
volume = {10},
year = {2014},
bdsk-url-1 = {https://doi.org/10.1021/ct500759q}}
@article{Boguslawski_2019,
author = {Boguslawski, Katharina},
date-added = {2022-03-06 20:16:11 +0100},
date-modified = {2022-03-06 20:16:11 +0100},
doi = {10.1021/acs.jctc.8b01053},
file = {/home/antoinem/Zotero/storage/9P2GLQNQ/Boguslawski - 2019 - Targeting Doubly Excited States with Equation of M.pdf;/home/antoinem/Zotero/storage/Q7RN4NWG/acs.jctc.html},
journal = {J. Chem. Theory Comput.},
pages = {18--24},
publisher = {{American Chemical Society}},
title = {Targeting {{Doubly Excited States}} with {{Equation}} of {{Motion Coupled Cluster Theory Restricted}} to {{Double Excitations}}},
file = {/home/antoinem/Zotero/storage/KHBWEYJD/Boguslawski - 2016 - Targeting excited states in all-trans polyenes wit.pdf;/home/antoinem/Zotero/storage/3APDNSK4/1.html},
journal = {J. Chem. Phys.},
pages = {234105},
publisher = {{American Institute of Physics}},
title = {Targeting Excited States in All-Trans Polyenes with Electron-Pair States},
volume = {145},
year = {2016},
bdsk-url-1 = {https://doi.org/10.1063/1.4972053}}
@article{Limacher_2013,
author = {Limacher, Peter A. and Ayers, Paul W. and Johnson, Paul A. and De Baerdemacker, Stijn and Van Neck, Dimitri and Bultinck, Patrick},
date-added = {2022-03-06 20:15:46 +0100},
date-modified = {2022-03-06 20:15:46 +0100},
doi = {10.1021/ct300902c},
file = {/home/antoinem/Zotero/storage/DC5HMNVA/Limacher et al. - 2013 - A New Mean-Field Method Suitable for Strongly Corr.pdf;/home/antoinem/Zotero/storage/GMVQZCGN/ct300902c.html},
journal = {J. Chem. Theory Comput.},
pages = {1394--1401},
publisher = {{American Chemical Society}},
title = {A {{New Mean}}-{{Field Method Suitable}} for {{Strongly Correlated Electrons}}: {{Computationally Facile Antisymmetric Products}} of {{Nonorthogonal Geminals}}},
volume = {9},
year = {2013},
bdsk-url-1 = {https://doi.org/10.1021/ct300902c}}
@article{Wouters_2014,
author = {Wouters, Sebastian and Poelmans, Ward and Ayers, Paul W. and Van Neck, Dimitri},
date-added = {2022-03-06 20:15:46 +0100},
date-modified = {2022-03-06 20:15:46 +0100},
doi = {10.1016/j.cpc.2014.01.019},
issn = {00104655},
journal = {Computer Physics Communications},
month = jun,
number = {6},
pages = {1501-1514},
shorttitle = {{{CheMPS2}}},
title = {{{CheMPS2}}: {{A}} Free Open-Source Spin-Adapted Implementation of the Density Matrix Renormalization Group for Ab Initio Quantum Chemistry},
author = {Boguslawski, Katharina and Ayers, Paul W.},
date-added = {2022-03-06 20:15:46 +0100},
date-modified = {2022-03-06 20:15:46 +0100},
doi = {10.1021/acs.jctc.5b00776},
file = {/home/antoinem/Zotero/storage/X9BZXVSJ/Boguslawski and Ayers - 2015 - Linearized Coupled Cluster Correction on the Antis.pdf;/home/antoinem/Zotero/storage/JYCLDH9E/acs.jctc.html},
journal = {J. Chem. Theory Comput.},
pages = {5252--5261},
publisher = {{American Chemical Society}},
title = {Linearized {{Coupled Cluster Correction}} on the {{Antisymmetric Product}} of 1-{{Reference Orbital Geminals}}},
author = {Boguslawski, Katharina and Tecmer, Pawe{\l} and Limacher, Peter A. and Johnson, Paul A. and Ayers, Paul W. and Bultinck, Patrick and De Baerdemacker, Stijn and Van Neck, Dimitri},
date-added = {2022-03-06 20:15:46 +0100},
date-modified = {2022-03-06 20:15:46 +0100},
doi = {10.1063/1.4880820},
file = {/home/antoinem/Zotero/storage/BVAZILSS/Boguslawski et al. - 2014 - Projected seniority-two orbital optimization of th.pdf;/home/antoinem/Zotero/storage/LA6SD7AH/1.html},
journal = {J. Chem. Phys.},
pages = {214114},
publisher = {{American Institute of Physics}},
title = {Projected Seniority-Two Orbital Optimization of the Antisymmetric Product of One-Reference Orbital Geminal},
volume = {140},
year = {2014},
bdsk-url-1 = {https://doi.org/10.1063/1.4880820}}
@article{Limacher_2014a,
author = {Limacher, Peter and W. Ayers, Paul and A. Johnson, Paul and Baerdemacker, Stijn De and Van Neck, Dimitri and Bultinck, Patrick},
date-added = {2022-03-06 20:15:46 +0100},
date-modified = {2022-03-06 20:15:46 +0100},
doi = {10.1039/C3CP53301H},
file = {/home/antoinem/Zotero/storage/2KIWXTMG/A. Limacher et al. - 2014 - Simple and inexpensive perturbative correction sch.pdf;/home/antoinem/Zotero/storage/G2AM79JD/A. Limacher et al. - 2014 - Simple and inexpensive perturbative correction sch.pdf;/home/antoinem/Zotero/storage/2IG32UHQ/c3cp53301h.html;/home/antoinem/Zotero/storage/HWN8YQEX/c3cp53301h.html},
journal = {Phys. Chem. Chem. Phys.},
pages = {5061--5065},
publisher = {{Royal Society of Chemistry}},
title = {Simple and Inexpensive Perturbative Correction Schemes for Antisymmetric Products of Nonorthogonal Geminals},
abstract = {We discuss some strategies for extending recent geminal-based methods to open-shells by replacing the geminal-creation operators with more general composite boson creation operators, and even creation operators that mix fermionic and bosonic components. We also discuss the utility of symmetry-breaking and restoration, but using a projective (not a variational) approach. Both strategies---either together or separately---give a pathway for extending geminals-based methods to open shells, while retaining the computational efficiency and conceptual simplicity of existing geminal product wavefunctions.},
author = {Paul A. Johnson and Peter A. Limacher and Taewon D. Kim and Michael Richer and Ram{\'o}n Alain Miranda-Quintana and Farnaz Heidar-Zadeh and Paul W. Ayers and Patrick Bultinck and Stijn {De Baerdemacker} and Dimitri {Van Neck}},
date-added = {2022-03-06 20:15:46 +0100},
date-modified = {2022-03-06 20:15:46 +0100},
doi = {https://doi.org/10.1016/j.comptc.2017.05.010},
journal = {Comput. Theor. Chem.},
pages = {207-219},
title = {Strategies for extending geminal-based wavefunctions: Open shells and beyond},
author = {Limacher, Peter A. and Kim, Taewon D. and Ayers, Paul W. and Johnson, Paul A. and Baerdemacker, Stijn De and Neck, Dimitri Van and Bultinck, Patrick},
date-added = {2022-03-06 20:15:46 +0100},
date-modified = {2022-03-06 20:15:46 +0100},
doi = {10.1080/00268976.2013.874600},
file = {/home/antoinem/Zotero/storage/QK9XACGM/Limacher et al. - 2014 - The influence of orbital rotation on the energy of.pdf;/home/antoinem/Zotero/storage/RB83UH42/00268976.2013.html},
journal = {Mol. Phys.},
pages = {853--862},
publisher = {{Taylor \& Francis}},
title = {The Influence of Orbital Rotation on the Energy of Closed-Shell Wavefunctions},
author = {Emmanuel Giner and Anthony Scemama and Michel Caffarel},
date-added = {2021-01-06 09:31:37 +0100},
date-modified = {2021-01-06 09:31:37 +0100},
doi = {10.1063/1.4905528},
issn = {1089-7690},
journal = {J. Chem. Phys.},
month = {Jan},
number = {4},
pages = {044115},
publisher = {AIP Publishing},
title = {Fixed-node diffusion Monte Carlo potential energy curve of the fluorine molecule F2 using selected configuration interaction trial wavefunctions},
author = {Y. Garniron and K. Gasperich and T. Applencourt and A. Benali and A. Fert{\'e} and J. Paquier and B. Pradines and R. Assaraf and P. Reinhardt and J. Toulouse and P. Barbaresco and N. Renon and G. David and J. P. Malrieu and M. V{\'e}ril and M. Caffarel and P. F. Loos and E. Giner and A. Scemama},
date-added = {2021-01-06 09:31:37 +0100},
date-modified = {2021-01-06 09:31:37 +0100},
doi = {10.1021/acs.jctc.9b00176},
journal = {J. Chem. Theory Comput.},
pages = {3591},
title = {Quantum Package 2.0: a open-source determinant-driven suite of programs},
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},
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.},
author = {Alcoba, Diego R. and Torre, Alicia and Lain, Luis and Massaccesi, Gustavo E. and O{\~{n}}a, Ofelia B.},
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},
abstract = {In this work we project the Hamiltonian of an N-electron system onto a set of N-electron determinants cataloged by their seniority numbers and their excitation levels with respect to a reference determinant. We show that, in open-shell systems, the diagonalization of the N-electron Hamiltonian matrix leads to eigenstates of the operator {\^S}2 when the excitation levels are counted in terms of spatial orbitals instead of spin-orbitals. Our proposal is based on the commutation relations between the N-electron operators seniority number and spatial excitation level, as well as between these operators and the spin operators {\^S}2 and {\^S}z. Energy and 〈{\^S}2〉 expectation values of molecular systems obtained from our procedure are compared with those arising from the standard hybrid configuration interaction methods based on seniority numbers and spin-orbital-excitation levels. We analyze the behavior of these methods, evaluating their computational costs and establishing their usefulness.},
author = {Alcoba, Diego R. and Torre, Alicia and Lain, Luis and O{\~{n}}a, Ofelia B. and Massaccesi, Gustavo E. and Capuzzi, Pablo},
keywords = {Configuration interaction methodology,Excitation level operators,Excitation levels in N-electron determinants,Hybrid methods in CI treatments,Seniority number of N-electron determinants,Seniority number operators,Spin contamination of wave functions},
pages = {315--332},
publisher = {Elsevier Inc.},
title = {{Hybrid Treatments Based on Determinant Seniority Numbers and Spatial Excitation Levels in the Configuration Interaction Framework}},
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.},
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},
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.},
author = {Bytautas, Laimutis and Scuseria, Gustavo E. and Ruedenberg, Klaus},
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.},
title = {Seniority based energy renormalization group ({$\Omega$}-ERG) approach in quantum chemistry: Initial formulation and application to potential energy surfaces},
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.},
author = {Henderson, Thomas M. and Bulik, Ireneusz W. and Stein, Tamar and Scuseria, Gustavo E.},
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}},
