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 = {Bytautas, Laimutis and Henderson, Thomas M. and {Jim{\'e}nez-Hoyos}, Carlos A. and Ellis, Jason K. and Scuseria, Gustavo E.},
date-added = {2021-01-06 09:31:37 +0100},
date-modified = {2021-01-06 09:31:37 +0100},
doi = {10.1063/1.3613706},
file = {/home/antoinem/Zotero/storage/IPX4UQJG/Bytautas et al. - 2011 - Seniority and orbital symmetry as tools for establ.pdf},
journal = {J. Chem. Phys.},
pages = {044119},
publisher = {{American Institute of Physics}},
title = {Seniority and Orbital Symmetry as Tools for Establishing a Full Configuration Interaction Hierarchy},
volume = {135},
year = {2011},
Bdsk-Url-1 = {https://doi.org/10.1063/1.3613706}}
@article{Damour_2021,
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.},
title = {{Configuration interaction wave functions: A seniority number approach}},
url = {http://dx.doi.org/10.1063/1.4882881},
volume = {140},
year = {2014}
}
@article{Raemdonck_2015,
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 },
title = {Polynomial scaling approximations and dynamic correlation corrections to doubly occupied configuration interaction wave functions},
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 Ŝ2 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 Ŝ2 and Ŝz. Energy and 〈Ŝ2〉 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},
series = {Theoretical and {{Mathematical Physics}}, {{The Nuclear Many}}-{{Body Problem}}},
title = {The {{Nuclear Many}}-{{Body Problem}}},
year = {1980}}
@article{Bytautas_2015,
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},
author = {Chen, Zhenhua and Zhou, Chen and Wu, Wei},
title = {Seniority Number in Valence Bond Theory},
journal = {Journal of Chemical Theory and Computation},
volume = {11},
number = {9},
pages = {4102-4108},
year = {2015},
doi = {10.1021/acs.jctc.5b00416},
note ={PMID: 26575906},
URL = {
https://doi.org/10.1021/acs.jctc.5b00416
},
eprint = {
https://doi.org/10.1021/acs.jctc.5b00416
}
}
@article{Bytautas_2018,
title = {Seniority based energy renormalization group (Ω-ERG) approach in quantum chemistry: Initial formulation and application to potential energy surfaces},
journal = {Computational and Theoretical Chemistry},
volume = {1141},
pages = {74-88},
year = {2018},
issn = {2210-271X},
doi = {https://doi.org/10.1016/j.comptc.2018.08.011},
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.}
}
@article{Henderson_2014,
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.},
archivePrefix = {arXiv},
arxivId = {1410.6529},
author = {Henderson, Thomas M. and Bulik, Ireneusz W. and Stein, Tamar and Scuseria, Gustavo E.},
