Construction of linearly independent non-orthogonal AGP states

Dutta, Rishab; Chen, Guo P.; Henderson, Thomas M.; Scuseria, Gustavo E.

doi:10.1063/5.0045006

Construction of linearly independent non-orthogonal AGP states

Journal Article · Thu Mar 18 00:00:00 EDT 2021 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/5.0045006· OSTI ID:1774552

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Rice Univ., Houston, TX (United States); Rice University
Rice Univ., Houston, TX (United States)

We show how to construct a linearly independent set of antisymmetrized geminal power (AGP) states, which allows us to rewrite our recently introduced geminal replacement models as linear combinations of non-orthogonal AGPs. Furthermore, this greatly simplifies the evaluation of matrix elements and permits us to introduce an AGP-based selective configuration interaction method, which can reach arbitrary excitation levels relative to a reference AGP, balancing accuracy and cost as we see fit.

View Accepted Manuscript (DOE)

Research Organization:: Rice Univ., Houston, TX (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES); Welch Foundation

Grant/Contract Number:: SC0001474; SC0001474

OSTI ID:: 1774552

Journal Information:: Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 11 Vol. 154; ISSN 0021-9606

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

References (53)

Energy extrapolation in CI calculations Buenker, Robert J.; Peyerimhoff, Sigrid D. Theoretica Chimica Acta, Vol. 39, Issue 3 https://doi.org/10.1007/bf00555301	journal	October 1975
Complete multi-configuration self-consistent field theory Veillard, A.; Clementi, E. Theoretica Chimica Acta, Vol. 7, Issue 2 https://doi.org/10.1007/bf01151915	journal	January 1967
Nonunitary bogoliubov transformations and extension of Wick’s theorem Balian, R.; Brezin, E. Il Nuovo Cimento B Series 10, Vol. 64, Issue 1 https://doi.org/10.1007/bf02710281	journal	November 1969
On a simple configuration interaction method using non-orthogonal basis functions Urbán, L. Acta Physica Academiae Scientiarum Hungaricae, Vol. 27, Issue 1-4 https://doi.org/10.1007/bf03156772	journal	December 1969
Richardson-Gaudin geminal wavefunctions in a Slater determinant basis Fecteau, Charles-Émile; Berthiaume, Frédéric; Khalfoun, Meriem Journal of Mathematical Chemistry, Vol. 59, Issue 1 https://doi.org/10.1007/s10910-020-01197-0	journal	November 2020
Stability conditions and nuclear rotations in the Hartree-Fock theory Thouless, D. J. Nuclear Physics, Vol. 21 https://doi.org/10.1016/0029-5582(60)90048-1	journal	November 1960
Exact eigenstates of the pairing-force Hamiltonian Richardson, R. W.; Sherman, N. Nuclear Physics, Vol. 52 https://doi.org/10.1016/0029-5582(64)90687-x	journal	March 1964
A restricted class of exact eigenstates of the pairing-force Hamiltonian Richardson, R. W. Physics Letters, Vol. 3, Issue 6 https://doi.org/10.1016/0031-9163(63)90259-2	journal	February 1963
A size-consistent approach to strongly correlated systems using a generalized antisymmetrized product of nonorthogonal geminals Johnson, Paul A.; Ayers, Paul W.; Limacher, Peter A. Computational and Theoretical Chemistry, Vol. 1003 https://doi.org/10.1016/j.comptc.2012.09.030	journal	January 2013
Power sum decompositions of elementary symmetric polynomials Lee, Hwangrae Linear Algebra and its Applications, Vol. 492 https://doi.org/10.1016/j.laa.2015.11.018	journal	March 2016
Symmetry-projected Hartree–Fock–Bogoliubov equations Sheikh, Javid A.; Ring, Peter Nuclear Physics A, Vol. 665, Issue 1-2 https://doi.org/10.1016/s0375-9474(99)00424-8	journal	February 2000
Many – Body Methods in Chemistry and Physics Shavitt, Isaiah; Bartlett, Rodney J. https://doi.org/10.1017/CBO9780511596834	book	January 2009
Selected Configuration Interaction in a Basis of Cluster State Tensor Products Abraham, Vibin; Mayhall, Nicholas J. Journal of Chemical Theory and Computation, Vol. 16, Issue 10 https://doi.org/10.1021/acs.jctc.0c00141	journal	August 2020
Geminal Replacement Models Based on AGP Dutta, Rishab; Henderson, Thomas M.; Scuseria, Gustavo E. Journal of Chemical Theory and Computation https://doi.org/10.1021/acs.jctc.0c00807	journal	September 2020
A New Mean-Field Method Suitable for Strongly Correlated Electrons: Computationally Facile Antisymmetric Products of Nonorthogonal Geminals Limacher, Peter A.; Ayers, Paul W.; Johnson, Paul A. Journal of Chemical Theory and Computation, Vol. 9, Issue 3 https://doi.org/10.1021/ct300902c	journal	February 2013
Generalized Molecular Orbital Theory II Couty, Marc; Hall, Michael B. The Journal of Physical Chemistry A, Vol. 101, Issue 37 https://doi.org/10.1021/jp963953l	journal	September 1997
A new approach to density matrix functional theory Kollmar, Christian; Heß, Bernd A. The Journal of Chemical Physics, Vol. 119, Issue 9 https://doi.org/10.1063/1.1590635	journal	September 2003
Configuration Interaction Studies of Ground and Excited States of Polyatomic Molecules. I. The CI Formulation and Studies of Formaldehyde Whitten, J. L.; Hackmeyer, Melvyn The Journal of Chemical Physics, Vol. 51, Issue 12 https://doi.org/10.1063/1.1671985	journal	December 1969
Geminal Product Wavefunctions: A General Formalism Nicely, Vincent A.; Harrison, James F. The Journal of Chemical Physics, Vol. 54, Issue 10 https://doi.org/10.1063/1.1674685	journal	May 1971
Structure of Fermion Density Matrices. II. Antisymmetrized Geminal Powers Coleman, A. J. Journal of Mathematical Physics, Vol. 6, Issue 9 https://doi.org/10.1063/1.1704794	journal	September 1965
Reduced Density Matrices of Atoms and Molecules. I. The 2 Matrix of Double‐Occupancy, Configuration‐Interaction Wavefunctions for Singlet States Weinhold, Frank; Wilson, E. Bright The Journal of Chemical Physics, Vol. 46, Issue 7 https://doi.org/10.1063/1.1841109	journal	April 1967
Seniority and orbital symmetry as tools for establishing a full configuration interaction hierarchy Bytautas, Laimutis; Henderson, Thomas M.; Jiménez-Hoyos, Carlos A. The Journal of Chemical Physics, Vol. 135, Issue 4 https://doi.org/10.1063/1.3613706	journal	July 2011
Projected quasiparticle theory for molecular electronic structure Scuseria, Gustavo E.; Jiménez-Hoyos, Carlos A.; Henderson, Thomas M. The Journal of Chemical Physics, Vol. 135, Issue 12 https://doi.org/10.1063/1.3643338	journal	September 2011
Seniority zero pair coupled cluster doubles theory Stein, Tamar; Henderson, Thomas M.; Scuseria, Gustavo E. The Journal of Chemical Physics, Vol. 140, Issue 21 https://doi.org/10.1063/1.4880819	journal	June 2014
Seniority-based coupled cluster theory Henderson, Thomas M.; Bulik, Ireneusz W.; Stein, Tamar The Journal of Chemical Physics, Vol. 141, Issue 24 https://doi.org/10.1063/1.4904384	journal	December 2014
Pair extended coupled cluster doubles Henderson, Thomas M.; Bulik, Ireneusz W.; Scuseria, Gustavo E. The Journal of Chemical Physics, Vol. 142, Issue 21 https://doi.org/10.1063/1.4921986	journal	June 2015
Seniority number description of potential energy surfaces: Symmetric dissociation of water, N ₂ , C ₂ , and Be ₂ Bytautas, Laimutis; Scuseria, Gustavo E.; Ruedenberg, Klaus The Journal of Chemical Physics, Vol. 143, Issue 9 https://doi.org/10.1063/1.4929904	journal	September 2015
Polynomial scaling approximations and dynamic correlation corrections to doubly occupied configuration interaction wave functions Van Raemdonck, Mario; Alcoba, Diego R.; Poelmans, Ward The Journal of Chemical Physics, Vol. 143, Issue 10 https://doi.org/10.1063/1.4930260	journal	September 2015
Communication: Configuration interaction combined with spin-projection for strongly correlated molecular electronic structures Tsuchimochi, Takashi; Ten-no, Seiichiro The Journal of Chemical Physics, Vol. 144, Issue 1 https://doi.org/10.1063/1.4939585	journal	January 2016
Merging symmetry projection methods with coupled cluster theory: Lessons from the Lipkin model Hamiltonian Wahlen-Strothman, Jacob M.; Henderson, Thomas M.; Hermes, Matthew R. The Journal of Chemical Physics, Vol. 146, Issue 5 https://doi.org/10.1063/1.4974989	journal	February 2017
Projected coupled cluster theory Qiu, Yiheng; Henderson, Thomas M.; Zhao, Jinmo The Journal of Chemical Physics, Vol. 147, Issue 6 https://doi.org/10.1063/1.4991020	journal	August 2017
Projected coupled cluster theory: Optimization of cluster amplitudes in the presence of symmetry projection Qiu, Yiheng; Henderson, Thomas M.; Zhao, Jinmo The Journal of Chemical Physics, Vol. 149, Issue 16 https://doi.org/10.1063/1.5053605	journal	October 2018
Geminal-based configuration interaction Henderson, Thomas M.; Scuseria, Gustavo E. The Journal of Chemical Physics, Vol. 151, Issue 5 https://doi.org/10.1063/1.5116715	journal	August 2019
Efficient evaluation of AGP reduced density matrices Khamoshi, Armin; Henderson, Thomas M.; Scuseria, Gustavo E. The Journal of Chemical Physics, Vol. 151, Issue 18 https://doi.org/10.1063/1.5127850	journal	November 2019
Correlating the antisymmetrized geminal power wave function Henderson, Thomas M.; Scuseria, Gustavo E. The Journal of Chemical Physics, Vol. 153, Issue 8 https://doi.org/10.1063/5.0021144	journal	August 2020
Richardson–Gaudin mean-field for strong correlation in quantum chemistry Johnson, Paul A.; Fecteau, Charles-Émile; Berthiaume, Frédéric The Journal of Chemical Physics, Vol. 153, Issue 10 https://doi.org/10.1063/5.0022189	journal	September 2020
Reduced density matrices of Richardson–Gaudin states in the Gaudin algebra basis Fecteau, Charles-Émile; Fortin, Hubert; Cloutier, Samuel The Journal of Chemical Physics, Vol. 153, Issue 16 https://doi.org/10.1063/5.0027393	journal	October 2020
Exploring non-linear correlators on AGP Khamoshi, Armin; Chen, Guo P.; Henderson, Thomas M. The Journal of Chemical Physics, Vol. 154, Issue 7 https://doi.org/10.1063/5.0039618	journal	February 2021
Sums of Like Powers of Multivariate Linear Forms Fischer, Ismor Mathematics Magazine, Vol. 67, Issue 1 https://doi.org/10.1080/0025570x.1994.11996185	journal	February 1994
Symmetry broken and restored coupled-cluster theory: I. Rotational symmetry and angular momentum Duguet, T. Journal of Physics G: Nuclear and Particle Physics, Vol. 42, Issue 2 https://doi.org/10.1088/0954-3899/42/2/025107	journal	December 2014
Correlating AGP on a quantum computer Khamoshi, Armin; Evangelista, Francesco A.; Scuseria, Gustavo E. Quantum Science and Technology, Vol. 6, Issue 1 https://doi.org/10.1088/2058-9565/abc1bb	journal	November 2020
Configuration interaction with antisymmetrized geminal powers Uemura, Wataru; Kasamatsu, Shusuke; Sugino, Osamu Physical Review A, Vol. 91, Issue 6 https://doi.org/10.1103/physreva.91.062504	journal	June 2015
Antisymmetrized geminal powers with larger chemical basis sets Uemura, Wataru; Nakajima, Takahito Physical Review A, Vol. 99, Issue 1 https://doi.org/10.1103/physreva.99.012519	journal	January 2019
Polynomial similarity transformation theory: A smooth interpolation between coupled cluster doubles and projected BCS applied to the reduced BCS Hamiltonian Degroote, Matthias; Henderson, Thomas M.; Zhao, Jinmo Physical Review B, Vol. 93, Issue 12 https://doi.org/10.1103/physrevb.93.125124	journal	March 2016
Sign of the overlap of Hartree-Fock-Bogoliubov wave functions Robledo, L. M. Physical Review C, Vol. 79, Issue 2 https://doi.org/10.1103/physrevc.79.021302	journal	February 2009
Quasiparticle coupled cluster theory for pairing interactions Henderson, Thomas M.; Scuseria, Gustavo E.; Dukelsky, Jorge Physical Review C, Vol. 89, Issue 5 https://doi.org/10.1103/physrevc.89.054305	journal	May 2014
Particle-number projected Bogoliubov-coupled-cluster theory: Application to the pairing Hamiltonian Qiu, Y.; Henderson, T. M.; Duguet, T. Physical Review C, Vol. 99, Issue 4 https://doi.org/10.1103/physrevc.99.044301	journal	April 2019
Concept of Off-Diagonal Long-Range Order and the Quantum Phases of Liquid He and of Superconductors Yang, C. N. Reviews of Modern Physics, Vol. 34, Issue 4 https://doi.org/10.1103/revmodphys.34.694	journal	October 1962
Structure of Fermion Density Matrices Coleman, A. J. Reviews of Modern Physics, Vol. 35, Issue 3 https://doi.org/10.1103/revmodphys.35.668	journal	July 1963
Colloquium : Exactly solvable Richardson-Gaudin models for many-body quantum systems Dukelsky, J.; Pittel, S.; Sierra, G. Reviews of Modern Physics, Vol. 76, Issue 3 https://doi.org/10.1103/revmodphys.76.643	journal	August 2004
Computing Characteristic Polynomials from Eigenvalues Rehman, Rizwana; Ipsen, Ilse C. F. SIAM Journal on Matrix Analysis and Applications, Vol. 32, Issue 1 https://doi.org/10.1137/100788392	journal	January 2011
Computing Elementary Symmetric Functions and Their Derivatives: A Didactic Baker, Frank B.; Harwell, Michael R. Applied Psychological Measurement, Vol. 20, Issue 2 https://doi.org/10.1177/014662169602000206	journal	June 1996
On the Theory of Automorphic Functions of a Matrix Variable I-Geometrical Basis Hua, Loo-Keng American Journal of Mathematics, Vol. 66, Issue 3 https://doi.org/10.2307/2371910	journal	July 1944

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