1
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Gałyńska M, de Moraes MMF, Tecmer P, Boguslawski K. Delving into the catalytic mechanism of molybdenum cofactors: a novel coupled cluster study. Phys Chem Chem Phys 2024; 26:18918-18929. [PMID: 38952220 DOI: 10.1039/d4cp01500b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/03/2024]
Abstract
In this work, we use modern electronic structure methods to model the catalytic mechanism of different variants of the molybdenum cofactor (Moco). We investigate the dependence of various Moco model systems on structural relaxation and the importance of environmental effects for five critical points along the reaction coordinate with the DMSO and NO3- substrates. Furthermore, we scrutinize the performance of various coupled-cluster approaches for modeling the relative energies along the investigated reaction paths, focusing on several pair coupled cluster doubles (pCCD) flavors and conventional coupled cluster approximations. Moreover, we elucidate the Mo-O bond formation using orbital-based quantum information measures, which highlight the flow of σM-O bond formation and σN/S-O bond breaking. Our study shows that pCCD-based models are a viable alternative to conventional methods and offer us unique insights into the bonding situation along a reaction coordinate. Finally, this work highlights the importance of environmental effects or changes in the core and, consequently, in the model itself to elucidate the change in activity of different Moco variants.
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Affiliation(s)
- Marta Gałyńska
- Institute of Physics, Faculty of Physics, Astronomy, and Informatics, Nicolaus Copernicus University in Toruń, Grudziądzka 5, 87-100 Toruń, Poland.
| | - Matheus Morato F de Moraes
- Institute of Physics, Faculty of Physics, Astronomy, and Informatics, Nicolaus Copernicus University in Toruń, Grudziądzka 5, 87-100 Toruń, Poland.
| | - Paweł Tecmer
- Institute of Physics, Faculty of Physics, Astronomy, and Informatics, Nicolaus Copernicus University in Toruń, Grudziądzka 5, 87-100 Toruń, Poland.
| | - Katharina Boguslawski
- Institute of Physics, Faculty of Physics, Astronomy, and Informatics, Nicolaus Copernicus University in Toruń, Grudziądzka 5, 87-100 Toruń, Poland.
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2
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Gałyńska M, Boguslawski K. Benchmarking Ionization Potentials from pCCD Tailored Coupled Cluster Models. J Chem Theory Comput 2024; 20:4182-4195. [PMID: 38752491 PMCID: PMC11137826 DOI: 10.1021/acs.jctc.4c00172] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/09/2024] [Revised: 05/04/2024] [Accepted: 05/07/2024] [Indexed: 05/29/2024]
Abstract
The ionization potential (IP) is an important parameter providing essential insights into the reactivity of chemical systems. IPs are also crucial for designing, optimizing, and understanding the functionality of modern technological devices. We recently showed that limiting the CC ansatz to the seniority-zero sector proves insufficient in predicting reliable and accurate ionization potentials within an IP equation-of-motion coupled-cluster formalism. Specifically, the absence of dynamical correlation in the seniority-zero pair coupled cluster doubles (pCCD) model led to unacceptably significant errors of approximately 1.5 eV. In this work, we aim to explore the impact of dynamical correlation and the choice of the molecular orbital basis (canonical vs localized) in CC-type methods targeting 230 ionized states in 70 molecules, comprising small organic molecules, medium-sized organic acceptors, and nucleobases. We focus on pCCD-based approaches as well as the conventional IP-EOM-CCD and IP-EOM-CCSD. Their performance is compared to the CCSD(T) or CCSDT equivalent and experimental reference data. Our statistical analysis reveals that all investigated frozen-pair coupled cluster methods exhibit similar performance, with differences in errors typically within chemical accuracy (1 kcal/mol or 0.05 eV). Notably, the effect of the molecular orbital basis, such as canonical Hartree-Fock or natural pCCD-optimized orbitals, on the IPs is marginal if dynamical correlation is accounted for. Our study suggests that triple excitations are crucial in achieving chemical accuracy in IPs when modeling electron detachment processes with pCCD-based methods.
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Affiliation(s)
- Marta Gałyńska
- Institute of Physics, Faculty of Physics,
Astronomy, and Informatics, Nicolaus Copernicus
University in Toruń, Grudziadzka 5, 87-100 Toruń, Poland
| | - Katharina Boguslawski
- Institute of Physics, Faculty of Physics,
Astronomy, and Informatics, Nicolaus Copernicus
University in Toruń, Grudziadzka 5, 87-100 Toruń, Poland
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3
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Dutta R, Gao F, Khamoshi A, Henderson TM, Scuseria GE. Correlated pair ansatz with a binary tree structure. J Chem Phys 2024; 160:084113. [PMID: 38421064 DOI: 10.1063/5.0185375] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/30/2023] [Accepted: 02/02/2024] [Indexed: 03/02/2024] Open
Abstract
We develop an efficient algorithm to implement the recently introduced binary tree state (BTS) ansatz on a classical computer. BTS allows a simple approximation to permanents arising from the computationally intractable antisymmetric product of interacting geminals and respects size-consistency. We show how to compute BTS overlap and reduced density matrices efficiently. We also explore two routes for developing correlated BTS approaches: Jastrow coupled cluster on BTS and linear combinations of BT states. The resulting methods show great promise in benchmark applications to the reduced Bardeen-Cooper-Schrieffer Hamiltonian and the one-dimensional XXZ Heisenberg Hamiltonian.
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Affiliation(s)
- Rishab Dutta
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
| | - Fei Gao
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
| | - Armin Khamoshi
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
| | - Thomas M Henderson
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
| | - Gustavo E Scuseria
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
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4
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Johnson PA, DePrince AE. Single Reference Treatment of Strongly Correlated H 4 and H 10 Isomers with Richardson-Gaudin States. J Chem Theory Comput 2023; 19:8129-8146. [PMID: 37955440 DOI: 10.1021/acs.jctc.3c00807] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2023]
Abstract
Richardson-Gaudin (RG) states are employed as a variational wave function ansatz for strongly correlated isomers of H4 and H10. In each case, a single RG state describes the seniority-zero sector quite well. Simple natural orbital functionals offer a cheap and reasonable approximation of the outstanding weak correlation in the seniority-zero sector, while systematic improvement is achieved by performing a configuration interaction in terms of RG states.
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Affiliation(s)
| | - A Eugene DePrince
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, United States
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5
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Mamache S, Gałyńska M, Boguslawski K. Benchmarking ionization potentials using the simple pCCD model. Phys Chem Chem Phys 2023. [PMID: 37378457 DOI: 10.1039/d3cp01963b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/29/2023]
Abstract
The electron-detachment energy is measured by the ionization potential (IP). As a result, it is a fundamental, observable and important molecular electronic signature in photoelectron spectroscopy. A precise theoretical prediction of electron-detachment energies or ionization potentials is essential for organic optoelectronic systems like transistors, solar cells, or light-emitting diodes. In this work, we benchmark the performance of the recently presented IP variant of the equation-of-motion pair coupled cluster doubles (IP-EOM-pCCD) model to determine IPs. Specifically, the predicted ionization energies are compared to experimental results and higher-order coupled cluster theories based on statistically assessing 201 electron-detached states of 41 organic molecules for three different molecular orbital basis sets and two sets of particle-hole operators. While IP-EOM-pCCD features a reasonable spread and skewness of ionization energies, its mean error and standard deviation differ by up to 1.5 eV from reference data. Our study, thus, highlights the importance of dynamical correlation to reliably predict IPs from a pCCD reference function in small organic molecules.
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Affiliation(s)
- Saddem Mamache
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Toruń, Grudziadzka 5, 87-100 Toruń, Poland.
| | - Marta Gałyńska
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Toruń, Grudziadzka 5, 87-100 Toruń, Poland.
| | - Katharina Boguslawski
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Toruń, Grudziadzka 5, 87-100 Toruń, Poland.
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6
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Khamoshi A, Dutta R, Scuseria GE. State Preparation of Antisymmetrized Geminal Power on a Quantum Computer without Number Projection. J Phys Chem A 2023; 127:4005-4014. [PMID: 37129503 DOI: 10.1021/acs.jpca.3c00525] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/03/2023]
Abstract
The antisymmetrized geminal power (AGP) is equivalent to the number projected Bardeen-Cooper-Schrieffer (PBCS) wave function. It is also an elementary symmetric polynomial (ESP) state. We generalize previous research on deterministically implementing the Dicke state to a state preparation algorithm for an ESP state, or equivalently AGP, on a quantum computer. Our method is deterministic and has polynomial cost, and it does not rely on number symmetry breaking and restoration. We also show that our circuit is equivalent to a disentangled unitary paired coupled cluster operator and a layer of unitary Jastrow operator acting on a single Slater determinant. The method presented herein highlights the ability of disentangled unitary coupled cluster to capture nontrivial entanglement properties that are hardly accessible with traditional Hartree-Fock based electronic structure methods.
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Affiliation(s)
- Armin Khamoshi
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, United States
| | - Rishab Dutta
- Department of Chemistry, Rice University, Houston, Texas 77005, United States
| | - Gustavo E Scuseria
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, United States
- Department of Chemistry, Rice University, Houston, Texas 77005, United States
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7
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Nowak A, Boguslawski K. A configuration interaction correction on top of pair coupled cluster doubles. Phys Chem Chem Phys 2023; 25:7289-7301. [PMID: 36810525 DOI: 10.1039/d2cp05171k] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023]
Abstract
Numerous numerical studies have shown that geminal-based methods are a promising direction to model strongly correlated systems with low computational costs. Several strategies have been introduced to capture the missing dynamical correlation effects, which typically exploit a posteriori corrections to account for correlation effects associated with broken-pair states or inter-geminal correlations. In this article, we scrutinize the accuracy of the pair coupled cluster doubles (pCCD) method extended by configuration interaction (CI) theory. Specifically, we benchmark various CI models, including, at most double excitations against selected CC corrections as well as conventional single-reference CC methods. A simple Davidson correction is also tested. The accuracy of the proposed pCCD-CI approaches is assessed for challenging small model systems such as the N2 and F2 dimers and various di- and triatomic actinide-containing compounds. In general, the proposed CI methods considerably improve spectroscopic constants compared to the conventional CCSD approach, provided a Davidson correction is included in the theoretical model. At the same time, their accuracy lies between those of the linearized frozen pCCD and frozen pCCD variants.
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Affiliation(s)
- Artur Nowak
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Toruń, Grudziadzka 5, 87-100 Toruń, Poland.
| | - Katharina Boguslawski
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Toruń, Grudziadzka 5, 87-100 Toruń, Poland.
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8
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Cassam-Chenaï P, Perez T, Accomasso D. 2D-block geminals: A non 1-orthogonal and non 0-seniority model with reduced computational complexity. J Chem Phys 2023; 158:074106. [PMID: 36813726 DOI: 10.1063/5.0133734] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/19/2023] Open
Abstract
We present a new geminal product wave function Ansatz where the geminals are not constrained to be strongly orthogonal or to be of seniority-zero. Instead, we introduce weaker orthogonality constraints between geminals that significantly lower the computational effort without sacrificing the indistinguishability of the electrons. That is to say, the electron pairs corresponding to the geminals are not fully distinguishable, and their product has yet to be antisymmetrized according to the Pauli principle to form a bona fide electronic wave function. Our geometrical constraints translate into simple equations involving the traces of products of our geminal matrices. In the simplest non-trivial model, a set of solutions is given by block-diagonal matrices where each block is 2 × 2 and consists of either a Pauli matrix or a normalized diagonal matrix multiplied by a complex parameter to be optimized. With this simplified Ansatz for geminals, the number of terms in the calculation of the matrix elements of quantum observables is considerably reduced. A proof of principle is reported and confirms that the Ansatz is more accurate than strongly orthogonal geminal products while remaining computationally affordable.
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Affiliation(s)
| | - Thomas Perez
- Université Côte d'Azur, LJAD, UMR 7351, 06100 Nice, France
| | - Davide Accomasso
- Dipartimento di Chimica e Chimica Industriale, Universita' di Pisa, via Moruzzi 13, 56124 Pisa, Italy
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9
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Faribault A, Dimo C, Moisset JD, Johnson PA. Reduced density matrices/static correlation functions of Richardson–Gaudin states without rapidities. J Chem Phys 2022; 157:214104. [DOI: 10.1063/5.0123911] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/02/2022] Open
Abstract
Seniority-zero geminal wavefunctions are known to capture bond-breaking correlation. Among this class of wavefunctions, Richardson–Gaudin states stand out as they are eigenvectors of a model Hamiltonian. This provides a clear physical picture, clean expressions for reduced density matrix (RDM) elements, and systematic improvement (with a complete set of eigenvectors). Known expressions for the RDM elements require the computation of rapidities, which are obtained by first solving for the so-called eigenvalue based variables (EBV) and then root-finding a Lagrange interpolation polynomial. In this paper, we obtain expressions for the RDM elements directly in terms of the EBV. The final expressions can be computed at the same cost as the rapidity expressions. Therefore, except, in particular, circumstances, it is entirely unnecessary to compute rapidities at all. The RDM elements require numerically inverting a matrix, and while this is usually undesirable, we demonstrate that it is stable, except when there is degeneracy in the single-particle energies. In such cases, a different construction would be required.
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Affiliation(s)
| | - Claude Dimo
- Physics Department and Research Center OPTIMAS, Technische Universität Kaiserslautern, 67663 Kaiserslautern, Germany
| | | | - Paul A. Johnson
- Département de Chimie, Université Laval, Québec, Québec G1V 0A6, Canada
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10
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Tecmer P, Boguslawski K. Geminal-based electronic structure methods in quantum chemistry. Toward a geminal model chemistry. Phys Chem Chem Phys 2022; 24:23026-23048. [PMID: 36149376 DOI: 10.1039/d2cp02528k] [Citation(s) in RCA: 18] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
In this review, we discuss the recent progress in developing geminal-based theories for challenging problems in quantum chemistry. Specifically, we focus on the antisymmetrized geminal power, generalized valence bond, antisymmetrized product of strongly orthogonal geminals, singlet-type orthogonal geminals, the antisymmetric product of 1-reference orbital geminal, also known as the pair coupled cluster doubles ansatz, and geminals constructed from Richardson-Gaudin states. Furthermore, we review various corrections to account for the missing dynamical correlation effects in geminal models and possible extensions to target electronically excited states and open-shell species. Finally, we discuss some numerical examples and present-day challenges for geminal-based models, including a quantitative and qualitative analysis of wave functions, and software availability.
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Affiliation(s)
- Paweł Tecmer
- Institute of Physics, Faculty of Physics, Astronomy, and Informatics, Nicolaus Copernicus University in Toruń, Grudziądzka 5, 87-100 Toruń, Poland.
| | - Katharina Boguslawski
- Institute of Physics, Faculty of Physics, Astronomy, and Informatics, Nicolaus Copernicus University in Toruń, Grudziądzka 5, 87-100 Toruń, Poland.
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11
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Moisset JD, Fecteau CÉ, Johnson PA. Density matrices of seniority-zero geminal wavefunctions. J Chem Phys 2022; 156:214110. [DOI: 10.1063/5.0088602] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022] Open
Abstract
Scalar products and density matrix elements of closed-shell pair geminal wavefunctions are evaluated directly in terms of the pair amplitudes, resulting in an analog of Wick’s theorem for fermions or bosons. This expression is, in general, intractable, but it is shown how it becomes feasible in three distinct ways for Richardson–Gaudin (RG) states, the antisymmetrized geminal power, and the antisymmetrized product of strongly orthogonal geminals. Dissociation curves for hydrogen chains are computed with off-shell RG states and the antisymmetrized product of interacting geminals. Both are near exact, suggesting that the incorrect results observed with ground state RG states (a local maximum rather than smooth dissociation) may be fixable using a different RG state.
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Affiliation(s)
| | | | - Paul A. Johnson
- Département de Chimie, Université Laval, Québec, Québec G1V 0A6, Canada
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12
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Fecteau CÉ, Cloutier S, Moisset JD, Boulay J, Bultinck P, Faribault A, Johnson PA. Near-exact treatment of seniority-zero ground and excited states with a Richardson-Gaudin mean-field. J Chem Phys 2022; 156:194103. [PMID: 35597662 DOI: 10.1063/5.0091338] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Eigenvectors of the reduced Bardeen-Cooper-Schrieffer (BCS) Hamiltonian, Richardson-Gaudin (RG) states, are used as a variational wavefunction ansatz for strongly correlated electronic systems. These states are geminal products whose coefficients are solutions of non-linear equations. Previous results showed an un-physical apparent avoided crossing in ground state dissociation curves for hydrogen chains. In this paper, it is shown that each seniority-zero state of the molecular Coulomb Hamiltonian corresponds directly to an RG state. However, the seniority-zero ground state does not correspond to the ground state of a reduced BCS Hamiltonian. The difficulty is in choosing the correct RG state. The systems studied showed a clear choice, and we expect that it should always be possible to reason physically which state to choose.
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Affiliation(s)
- Charles-Émile Fecteau
- Département de chimie, Université Laval, 1045 Avenue de la Médecine, bureau 1220, Québec, Québec G1V 0A6, Canada
| | - Samuel Cloutier
- Département de chimie, Université Laval, 1045 Avenue de la Médecine, bureau 1220, Québec, Québec G1V 0A6, Canada
| | - Jean-David Moisset
- Département de chimie, Université Laval, 1045 Avenue de la Médecine, bureau 1220, Québec, Québec G1V 0A6, Canada
| | - Jérémy Boulay
- Département de chimie, Université Laval, 1045 Avenue de la Médecine, bureau 1220, Québec, Québec G1V 0A6, Canada
| | - Patrick Bultinck
- Ghent Quantum Chemistry Group, Department of Chemistry, Ghent University, Krijgslaan 281 S3, B-9000 Ghent, Belgium
| | | | - Paul A Johnson
- Département de chimie, Université Laval, 1045 Avenue de la Médecine, bureau 1220, Québec, Québec G1V 0A6, Canada
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13
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Sørensen LK. On the size consistency problem for anti-symmetrised geminal power wave function ansatz. Mol Phys 2022. [DOI: 10.1080/00268976.2022.2049385] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
Affiliation(s)
- L. K. Sørensen
- Department of Theoretical Chemistry and Biology, School of Engineering Sciences in Chemistry, Biotechnology and Health, Royal Institute of Technology, Stockholm, SE, Sweden
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14
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Fragmentation of Identical and Distinguishable Bosons’ Pairs and Natural Geminals of a Trapped Bosonic Mixture. ATOMS 2021. [DOI: 10.3390/atoms9040092] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022] Open
Abstract
In a mixture of two kinds of identical bosons, there are two types of pairs: identical bosons’ pairs, of either species, and pairs of distinguishable bosons. In the present work, the fragmentation of pairs in a trapped mixture of Bose–Einstein condensates is investigated using a solvable model, the symmetric harmonic-interaction model for mixtures. The natural geminals for pairs made of identical or distinguishable bosons are explicitly contracted by diagonalizing the intra-species and inter-species reduced two-particle density matrices, respectively. Properties of pairs’ fragmentation in the mixture are discussed, the role of the mixture’s center-of-mass and relative center-of-mass coordinates is elucidated, and a generalization to higher-order reduced density matrices is made. As a complementary result, the exact Schmidt decomposition of the wave function of the bosonic mixture is constructed. The entanglement between the two species is governed by the coupling of their individual center-of-mass coordinates, and it does not vanish at the limit of an infinite number of particles where any finite-order intra-species and inter-species reduced density matrix per particle is 100% condensed. Implications are briefly discussed.
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15
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Blunt NS. Fixed- and Partial-Node Approximations in Slater Determinant Space for Molecules. J Chem Theory Comput 2021; 17:6092-6104. [PMID: 34549947 DOI: 10.1021/acs.jctc.1c00500] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We present a study of fixed- and partial-node approximations in Slater determinant basis sets, using full configuration interaction quantum Monte Carlo (FCIQMC) to perform sampling. Walker annihilation in the FCIQMC method allows partial-node simulations to be performed, relaxing the nodal constraint to converge to the FCI solution. This is applied to ab initio molecular systems, using symmetry-projected Jastrow mean-field wave functions for complete active space (CAS) problems. Convergence and the sign problem within the partial-node approximation are studied, which is shown to eventually be limited in its use due to the large walker populations required. However, the fixed-node approximation results in an accurate and practical method. We apply these approaches to various molecular systems and active spaces, including ferrocene and acenes. This also provides a test of symmetry-projected Jastrow mean-field wave functions in variational Monte Carlo for a new set of problems. For trans-polyacetylene molecules and acenes, we find that the time to perform a constant number of fixed-node FCIQMC iterations scales as O(N1.44) and O(N1.75), respectively, resulting in an efficient method for CAS-based problems that can be applied accurately to large active spaces.
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Affiliation(s)
- Nick S Blunt
- Yusuf Hamied Department of Chemistry, Lensfield Road, Cambridge CB2 1EW, U.K.,St John's College, St John's Street, Cambridge CB2 1TP, U.K
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16
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Marie A, Kossoski F, Loos PF. Variational coupled cluster for ground and excited states. J Chem Phys 2021; 155:104105. [PMID: 34525834 DOI: 10.1063/5.0060698] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In single-reference coupled-cluster (CC) methods, one has to solve a set of non-linear polynomial equations in order to determine the so-called amplitudes that are then used to compute the energy and other properties. Although it is of common practice to converge to the (lowest-energy) ground-state solution, it is also possible, thanks to tailored algorithms, to access higher-energy roots of these equations that may or may not correspond to genuine excited states. Here, we explore the structure of the energy landscape of variational CC and we compare it with its (projected) traditional version in the case where the excitation operator is restricted to paired double excitations (pCCD). By investigating two model systems (the symmetric stretching of the linear H4 molecule and the continuous deformation of the square H4 molecule into a rectangular arrangement) in the presence of weak and strong correlations, the performance of variational pCCD (VpCCD) and traditional pCCD is gauged against their configuration interaction (CI) equivalent, known as doubly occupied CI, for reference Slater determinants made of ground- or excited-state Hartree-Fock orbitals or state-specific orbitals optimized directly at the VpCCD level. The influence of spatial symmetry breaking is also investigated.
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Affiliation(s)
- Antoine Marie
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse, France
| | - Fábris Kossoski
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse, France
| | - Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse, France
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17
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Johnson PA, Fortin H, Cloutier S, Fecteau CÉ. Transition density matrices of Richardson-Gaudin states. J Chem Phys 2021; 154:124125. [PMID: 33810647 DOI: 10.1063/5.0041051] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Recently, ground state eigenvectors of the reduced Bardeen-Cooper-Schrieffer (BCS) Hamiltonian, Richardson-Gaudin (RG) states, have been employed as a wavefunction ansatz for strong correlation. This wavefunction physically represents a mean-field of pairs of electrons (geminals) with a constant pairing strength. To move beyond the mean-field, one must develop the wavefunction on the basis of all the RG states. This requires both practical expressions for transition density matrices and an idea of which states are most important in the expansion. In this contribution, we present expressions for the transition density matrix elements and calculate them numerically for half-filled picket-fence models (reduced BCS models with constant energy spacing). There are no Slater-Condon rules for RG states, though an analog of the aufbau principle proves to be useful in choosing which states are important.
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Affiliation(s)
- Paul A Johnson
- Département de Chimie, Université Laval, Québec, Québec G1V 0A6, Canada
| | - Hubert Fortin
- Département de Chimie, Université Laval, Québec, Québec G1V 0A6, Canada
| | - Samuel Cloutier
- Département de Chimie, Université Laval, Québec, Québec G1V 0A6, Canada
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18
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Dutta R, Chen GP, Henderson TM, Scuseria GE. Construction of linearly independent non-orthogonal AGP states. J Chem Phys 2021; 154:114112. [DOI: 10.1063/5.0045006] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Rishab Dutta
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
| | - Guo P. Chen
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
| | - Thomas M. Henderson
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
| | - Gustavo E. Scuseria
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
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Khamoshi A, Chen GP, Henderson TM, Scuseria GE. Exploring non-linear correlators on AGP. J Chem Phys 2021; 154:074113. [DOI: 10.1063/5.0039618] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Armin Khamoshi
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA
| | - Guo P. Chen
- Department of Chemistry, Rice University, Houston, Texas 77005-1892, USA
| | - Thomas M. Henderson
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA
- Department of Chemistry, Rice University, Houston, Texas 77005-1892, USA
| | - Gustavo E. Scuseria
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA
- Department of Chemistry, Rice University, Houston, Texas 77005-1892, USA
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Fecteau CÉ, Fortin H, Cloutier S, Johnson PA. Reduced density matrices of Richardson-Gaudin states in the Gaudin algebra basis. J Chem Phys 2020; 153:164117. [PMID: 33138426 DOI: 10.1063/5.0027393] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022] Open
Abstract
Eigenvectors of the reduced Bardeen-Cooper-Schrieffer Hamiltonian have recently been employed as a variational wavefunction ansatz in quantum chemistry. This wavefunction is a mean-field of pairs of electrons (geminals). In this contribution, we report optimal expressions for their reduced density matrices in both the original physical basis and the basis of the Richardson-Gaudin pairs. Physical basis expressions were originally reported by Gorohovsky and Bettelheim [Phys. Rev. B 84, 224503 (2011)]. In each case, the expressions scale like O(N4), with the most expensive step being the solution of linear equations. Analytic gradients are also reported in the physical basis. These expressions are an important step toward practical mean-field methods to treat strongly correlated electrons.
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Affiliation(s)
| | - Hubert Fortin
- Département de chimie, Université Laval, Québec, Québec G1V 0A6, Canada
| | - Samuel Cloutier
- Département de chimie, Université Laval, Québec, Québec G1V 0A6, Canada
| | - Paul A Johnson
- Département de chimie, Université Laval, Québec, Québec G1V 0A6, Canada
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21
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Harsha G, Henderson TM, Scuseria GE. Wave function methods for canonical ensemble thermal averages in correlated many-fermion systems. J Chem Phys 2020; 153:124115. [DOI: 10.1063/5.0022702] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Gaurav Harsha
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
| | - Thomas M. Henderson
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
| | - Gustavo E. Scuseria
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
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Dutta R, Henderson TM, Scuseria GE. Geminal Replacement Models Based on AGP. J Chem Theory Comput 2020; 16:6358-6367. [DOI: 10.1021/acs.jctc.0c00807] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Rishab Dutta
- Department of Chemistry, Rice University, Houston, Texas 77005, United States
| | - Thomas M. Henderson
- Department of Chemistry, Rice University, Houston, Texas 77005, United States
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, United States
| | - Gustavo E. Scuseria
- Department of Chemistry, Rice University, Houston, Texas 77005, United States
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, United States
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23
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Henderson TM, Scuseria GE. Correlating the antisymmetrized geminal power wave function. J Chem Phys 2020; 153:084111. [DOI: 10.1063/5.0021144] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Thomas M. Henderson
- Department of Chemistry, Rice University, Houston, Texas 77005-1892, USA
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA
| | - Gustavo E. Scuseria
- Department of Chemistry, Rice University, Houston, Texas 77005-1892, USA
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA
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24
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Khamoshi A, Henderson TM, Scuseria GE. Efficient evaluation of AGP reduced density matrices. J Chem Phys 2019; 151:184103. [DOI: 10.1063/1.5127850] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Armin Khamoshi
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA
| | - Thomas M. Henderson
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA
- Department of Chemistry, Rice University, Houston, Texas 77005-1892, USA
| | - Gustavo E. Scuseria
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA
- Department of Chemistry, Rice University, Houston, Texas 77005-1892, USA
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