1
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Dhawan D, Zgid D, Motta M. Quantum Algorithm for Imaginary-Time Green's Functions. J Chem Theory Comput 2024; 20:4629-4638. [PMID: 38761142 DOI: 10.1021/acs.jctc.4c00241] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/20/2024]
Abstract
Green's function methods lead to ab initio, systematically improvable simulations of molecules and materials while providing access to multiple experimentally observable properties such as the density of states and the spectral function. The calculation of the exact one-particle Green's function remains a significant challenge for classical computers and was attempted only on very small systems. Here, we present a hybrid quantum-classical algorithm to calculate the imaginary-time one-particle Green's function. The proposed algorithm combines the variational quantum eigensolver and the quantum subspace expansion methods to calculate Green's function in Lehmann's representation. We demonstrate the validity of this algorithm by simulating H2 and H4 on quantum simulators and on IBM's quantum devices.
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Affiliation(s)
- Diksha Dhawan
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24060, United States
| | - Dominika Zgid
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Mario Motta
- IBM Quantum, Almaden Research Center, San Jose, California 95120, United States
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2
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Liu Y, Meitei OR, Chin ZE, Dutt A, Tao M, Chuang IL, Van Voorhis T. Bootstrap Embedding on a Quantum Computer. J Chem Theory Comput 2023; 19:2230-2247. [PMID: 37001026 DOI: 10.1021/acs.jctc.3c00012] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/03/2023]
Abstract
We extend molecular bootstrap embedding to make it appropriate for implementation on a quantum computer. This enables solution of the electronic structure problem of a large molecule as an optimization problem for a composite Lagrangian governing fragments of the total system, in such a way that fragment solutions can harness the capabilities of quantum computers. By employing state-of-art quantum subroutines including the quantum SWAP test and quantum amplitude amplification, we show how a quadratic speedup can be obtained over the classical algorithm, in principle. Utilization of quantum computation also allows the algorithm to match─at little additional computational cost─full density matrices at fragment boundaries, instead of being limited to 1-RDMs. Current quantum computers are small, but quantum bootstrap embedding provides a potentially generalizable strategy for harnessing such small machines through quantum fragment matching.
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Affiliation(s)
- Yuan Liu
- Department of Physics, Co-Design Center for Quantum Advantage, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Oinam R. Meitei
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Zachary E. Chin
- Department of Physics, Co-Design Center for Quantum Advantage, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Arkopal Dutt
- Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Max Tao
- Department of Physics, Co-Design Center for Quantum Advantage, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Isaac L. Chuang
- Department of Physics, Co-Design Center for Quantum Advantage, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
- Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Troy Van Voorhis
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
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3
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Shee A, Yeh CN, Peng B, Kowalski K, Zgid D. Triple Excitations in Green's Function Coupled Cluster Solver for Studies of Strongly Correlated Systems in the Framework of Self-Energy Embedding Theory. J Phys Chem Lett 2023; 14:2416-2424. [PMID: 36856741 DOI: 10.1021/acs.jpclett.2c03616] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/18/2023]
Abstract
Embedding theories became important approaches used for accurate calculations of both molecules and solids. In these theories, a small chosen subset of orbitals is treated with an accurate method, called an impurity solver, capable of describing higher correlation effects. Ideally, such a chosen fragment should contain multiple orbitals responsible for the chemical and physical behavior of the compound. Handling a large number of chosen orbitals presents a very significant challenge for the current generation of solvers used in the physics and chemistry community. Here, we develop a Green's function coupled cluster singles doubles and triples (GFCCSDT) solver that can be used for a quantitative description in both molecules and solids. This solver allows us to treat orbital spaces that are inaccessible to other accurate solvers. At the same time, GFCCSDT maintains high accuracy of the resulting self-energy. Moreover, in conjunction with the GFCCSD solver, it allows us to test the systematic convergence of computational studies. Developing the CC family of solvers paves the road to fully systematic Green's function embedding calculations in solids. In this paper, we focus on the investigation of GFCCSDT self-energies for a strongly correlated problem of SrMnO3 solid. Subsequently, we apply this solver to solid MnO showing that an approximate variant of GFCCSDT is capable of yielding a high accuracy orbital resolved spectral function.
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Affiliation(s)
- Avijit Shee
- Department of Chemistry, University of California, Berkeley, California 94720, United States
| | - Chia-Nan Yeh
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Bo Peng
- Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | - Karol Kowalski
- Pacific Northwest National Laboratory, Richland, Washington 99352, United States
| | - Dominika Zgid
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
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4
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Vorwerk C, Sheng N, Govoni M, Huang B, Galli G. Quantum embedding theories to simulate condensed systems on quantum computers. NATURE COMPUTATIONAL SCIENCE 2022; 2:424-432. [PMID: 38177872 DOI: 10.1038/s43588-022-00279-0] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2021] [Accepted: 06/14/2022] [Indexed: 01/06/2024]
Abstract
Quantum computers hold promise to improve the efficiency of quantum simulations of materials and to enable the investigation of systems and properties that are more complex than tractable at present on classical architectures. Here, we discuss computational frameworks to carry out electronic structure calculations of solids on noisy intermediate-scale quantum computers using embedding theories, and we give examples for a specific class of materials, that is, solid materials hosting spin defects. These are promising systems to build future quantum technologies, such as quantum computers, quantum sensors and quantum communication devices. Although quantum simulations on quantum architectures are in their infancy, promising results for realistic systems appear to be within reach.
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Affiliation(s)
- Christian Vorwerk
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, IL, USA
| | - Nan Sheng
- Department of Chemistry, University of Chicago, Chicago, IL, USA
| | - Marco Govoni
- Materials Science Division and Center for Molecular Engineering, Argonne National Laboratory, Lemont, IL, USA.
| | - Benchen Huang
- Department of Chemistry, University of Chicago, Chicago, IL, USA
| | - Giulia Galli
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, IL, USA.
- Department of Chemistry, University of Chicago, Chicago, IL, USA.
- Materials Science Division and Center for Molecular Engineering, Argonne National Laboratory, Lemont, IL, USA.
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5
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Sheng N, Vorwerk C, Govoni M, Galli G. Green's Function Formulation of Quantum Defect Embedding Theory. J Chem Theory Comput 2022; 18:3512-3522. [PMID: 35648660 DOI: 10.1021/acs.jctc.2c00240] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022]
Abstract
We present a Green's function formulation of the quantum defect embedding theory (QDET) where a double counting scheme is rigorously derived within the G0W0 approximation. We then show the robustness of our methodology by applying the theory with the newly derived scheme to several defects in diamond. Additionally, we discuss a strategy to obtain converged results as a function of the size and composition of the active space. Our results show that QDET is a promising approach to investigate strongly correlated states of defects in solids.
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Affiliation(s)
- Nan Sheng
- Department of Chemistry, University of Chicago, Chicago, Illinois 60637, United States
| | - Christian Vorwerk
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States
| | - Marco Govoni
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States.,Materials Science Division and Center for Molecular Engineering, Argonne National Laboratory, Lemont, Illinois 60439, United States
| | - Giulia Galli
- Department of Chemistry, University of Chicago, Chicago, Illinois 60637, United States.,Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States.,Materials Science Division and Center for Molecular Engineering, Argonne National Laboratory, Lemont, Illinois 60439, United States
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6
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Van Benschoten WZ, Shepherd JJ. Piecewise Interaction Picture Density Matrix Quantum Monte Carlo. J Chem Phys 2022; 156:184107. [DOI: 10.1063/5.0094290] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The density matrix quantum Monte Carlo (DMQMC) set of methods stochastically samples the exact $N$-body density matrix for interacting electrons at finite temperature. We introduce a simple modification to the interaction picture DMQMC method (IP-DMQMC) which overcomes the limitation of only sampling one inverse temperature point at a time, instead allowing for the sampling of a temperature range within a single calculation thereby reducing the computational cost. At the target inverse temperature, instead of ending the simulation, we incorporate a change of picture away from the interaction picture. The resulting equations of motion have piecewise functions and use the interaction picture in the first phase of a simulation, followed by the application of the Bloch equation once the target inverse temperature is reached. We find that the performance of this method is similar to or better than the DMQMC and IP-DMQMC algorithms in a variety of molecular test systems.
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7
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Abstract
Quantum embedding schemes are a promising way to extend multireference computations to large molecules with strong correlation effects localized on a small number of atoms. This work introduces a second-order active-space embedding theory [ASET(2)] which improves upon mean-field frozen embedding by treating fragment-environment interactions via an approximate canonical transformation. The canonical transformation employed in ASET(2) is formulated using the driven similarity renormalization group. The ASET(2) scheme is benchmarked on the N═N bond dissociation in pentyldiazene, the S0 to S1 excitation in 1-octene, and the interaction energy of the O2-benzene complex. The ASET(2) explicit treatment of fragment-environment interactions beyond the mean-field level generally improves the accuracy of embedded computations, and it becomes necessary to achieve an accurate description of excitation energies of 1-octene and the singlet-triplet gap of the O2-benzene complex.
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Affiliation(s)
- Nan He
- Department of Chemistry and Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, United States
| | - Chenyang Li
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, China
| | - Francesco A Evangelista
- Department of Chemistry and Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, United States
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8
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Shee A, Yeh CN, Zgid D. Exploring Coupled Cluster Green's Function as a Method for Treating System and Environment in Green's Function Embedding Methods. J Chem Theory Comput 2022; 18:664-676. [PMID: 34989565 DOI: 10.1021/acs.jctc.1c00712] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Abstract
Within the self-energy embedding theory (SEET) framework, we study the coupled cluster Green's function (GFCC) method in two different contexts: as a method to treat either the system or the environment present in the embedding construction. Our study reveals that when GFCC is used to treat the environment we do not see improvement in total energies in comparison to the coupled cluster method itself. To rationalize this puzzling result, we analyze the performance of GFCC as an impurity solver with a series of transition metal oxides. These studies shed light on the strength and weaknesses of such a solver and demonstrate that such a solver gives very accurate results when the size of the impurity is small. We investigate if it is possible to achieve a systematic accuracy of the embedding solution when we increase the size of the impurity problem. We found that in such a case, the performance of the solver worsens, both in terms of finding the ground state solution of the impurity problem and the self-energies produced. We concluded that increasing the rank of GFCC solver is necessary to be able to enlarge impurity problems and achieve a reliable accuracy. We also have shown that natural orbitals from weakly correlated perturbative methods are better suited than symmetrized atomic orbitals (SAO) when the total energy of the system is the target quantity.
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Affiliation(s)
- Avijit Shee
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Chia-Nan Yeh
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Dominika Zgid
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
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9
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Ye HZ, Tran HK, Van Voorhis T. Accurate Electronic Excitation Energies in Full-Valence Active Space via Bootstrap Embedding. J Chem Theory Comput 2021; 17:3335-3347. [PMID: 33957050 DOI: 10.1021/acs.jctc.0c01221] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Fragment embedding has been widely used to circumvent the high computational scaling of using accurate electron correlation methods to describe the electronic ground states of molecules and materials. However, similar applications that utilize fragment embedding to treat electronic excited states are comparably less reported in the literature. The challenge here is twofold. First, most fragment embedding methods are most effective when the property of interest is local, but the change of the wave function upon excitation is nonlocal in general. Second, even for local excitations, an accurate estimate of, for example, the excitation energy can still be challenging owing to the need for a balanced treatment of both the ground and the excited states. In this work, we show that bootstrap embedding (BE), a fragment embedding method developed recently by our group, is promising toward describing general electronic excitations. Numerical simulations show that the excitation energies in full-valence active space (FVAS) can be well-estimated by BE to an error of ∼0.05 eV using relatively small fragments, for both local excitations and the excitations of some large dye molecules that exhibit strong charge-transfer characters. We hence anticipate BE to be a promising solution to accurately describing the excited states of large chemical systems.
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Affiliation(s)
- Hong-Zhou Ye
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Henry K Tran
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Troy Van Voorhis
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
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10
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Abstract
We present a Perspective on what the future holds for full configuration interaction (FCI) theory, with an emphasis on conceptual rather than technical details. Upon revisiting the early history of FCI, a number of its key contemporary approximations are compared on as equal a footing as possible, using a recent blind challenge on the benzene molecule as a testbed [Eriksen et al., J. Phys. Chem. Lett., 2020 11, 8922]. In the process, we review the scope of applications for which FCI continues to prove indispensable, and the required traits in terms of robustness, efficacy, and reliability its modern approximations must satisfy are discussed. We close by conveying a number of general observations on the merits offered by the state-of-the-art alongside some of the challenges still faced to this day. While the field has altogether seen immense progress over the years-the past decade, in particular-it remains clear that our community as a whole has a substantial way to go in enhancing the overall applicability of near-exact electronic structure theory for systems of general composition and increasing size.
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Affiliation(s)
- Janus J Eriksen
- School of Chemistry, University of Bristol, Cantock's Close, Bristol BS8 1TS, United Kingdom
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11
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Ye HZ, Tran HK, Van Voorhis T. Bootstrap Embedding For Large Molecular Systems. J Chem Theory Comput 2020; 16:5035-5046. [PMID: 32589842 DOI: 10.1021/acs.jctc.0c00438] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
Abstract
Recent developments in quantum embedding theories have provided attractive approaches to correlated calculations for large systems. In this work, we extend our previous work [J. Chem. Theory Comput. 2019, 15, 4497-4506; J. Phys. Chem. Lett. 2019, 10, 6368-6374] on bootstrap embedding (BE) to enable correlated ab initio calculations at the coupled cluster with singles and doubles (CCSD) level for large molecules. We introduce several new algorithmic developments that significantly reduce the computational cost of BE, while maintaining its accuracy. The resulting implementation scales as O(N3) for the integral transform and O(N) for the CCSD calculation. Numerical results on a series of conjugated molecules suggest that BE with reasonably sized fragments can recover more than 99.5% of the total correlation energy of a full CCSD calculation, while the required computational resources (time and storage) compare favorably to one popular local correlation scheme: domain localized pair natural orbital (DLPNO). The largest BE calculation in this work involves ∼2900 basis functions and can be performed on a single node with 16 CPU cores and 64 GB of memory in a few days. We anticipate that these developments represent an important step toward the application of BE to solve practical problems.
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Affiliation(s)
- Hong-Zhou Ye
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Henry K Tran
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Troy Van Voorhis
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
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12
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Dong X, Zgid D, Gull E, Strand HUR. Legendre-spectral Dyson equation solver with super-exponential convergence. J Chem Phys 2020; 152:134107. [DOI: 10.1063/5.0003145] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Xinyang Dong
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Dominika Zgid
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Emanuel Gull
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Hugo U. R. Strand
- Department of Physics, Chalmers University of Technology, SE-412 96 Gothenburg, Sweden
- Center for Computational Quantum Physics, The Flatiron Institute, New York, New York 10010, USA
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13
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He N, Evangelista FA. A zeroth-order active-space frozen-orbital embedding scheme for multireference calculations. J Chem Phys 2020; 152:094107. [PMID: 33480706 DOI: 10.1063/1.5142481] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022] Open
Abstract
Multireference computations of large-scale chemical systems are typically limited by the computational cost of quantum chemistry methods. In this work, we develop a zeroth-order active space embedding theory [ASET(0)], a simple and automatic approach for embedding any multireference dynamical correlation method based on a frozen-orbital treatment of the environment. ASET(0) is combined with the second-order multireference driven similarity renormalization group and tested on several benchmark problems, including the excitation energy of 1-octene and bond-breaking in ethane and pentyldiazene. Finally, we apply ASET(0) to study the singlet-triplet gap of p-benzyne and 9,10-anthracyne diradicals adsorbed on a NaCl surface. Our results show that despite its simplicity, ASET(0) is a powerful and sufficiently accurate embedding scheme applicable when the coupling between the fragment and the environment is in the weak to medium regime.
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Affiliation(s)
- Nan He
- Department of Chemistry, Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, USA
| | - Francesco A Evangelista
- Department of Chemistry, Cherry Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, USA
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14
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Bauman NP, Peng B, Kowalski K. Coupled Cluster Green's function formulations based on the effective Hamiltonians. Mol Phys 2020. [DOI: 10.1080/00268976.2020.1725669] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
Affiliation(s)
- Nicholas P. Bauman
- William R. Wiley Environmental Molecular Sciences Laboratory, Battelle, Pacific Northwest National Laboratory, Richland, WA, USA
| | - Bo Peng
- Advanced Computing, Mathematics, and Data Division, Battelle, Pacific Northwest National Laboratory, Richland, WA, USA
| | - Karol Kowalski
- William R. Wiley Environmental Molecular Sciences Laboratory, Battelle, Pacific Northwest National Laboratory, Richland, WA, USA
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15
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Veccham SP, Lee J, Head-Gordon M. Making many-body interactions nearly pairwise additive: The polarized many-body expansion approach. J Chem Phys 2019; 151:194101. [DOI: 10.1063/1.5125802] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023] Open
Affiliation(s)
- Srimukh Prasad Veccham
- Department of Chemistry, University of California, Berkeley, California 94720 USA, and Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Joonho Lee
- Department of Chemistry, University of California, Berkeley, California 94720 USA, and Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Martin Head-Gordon
- Department of Chemistry, University of California, Berkeley, California 94720 USA, and Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
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16
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Abstract
Recent developments in quantum embedding have offered an attractive approach to describing electron correlation in molecules. However, previous methods such as density matrix embedding theory (DMET) require rigid partitioning of the system into fragments, which creates significant ambiguity for molecules. Bootstrap embedding (BE) is more flexible because it allows overlapping fragments, but when done on an orbital-by-orbital basis, BE introduces ambiguity in defining the connectivity of the orbitals. In this Letter, we present an atom-based fragment definition that significantly augments BE's performance in molecules. The resulting method, which we term atom-based BE, is very effective at recovering valence electron correlation in moderate-sized bases and delivers near-chemical-accuracy results using extrapolation. We anticipate atom-based BE may lead to a low-scaling and highly accurate approach to electron correlation in large molecules.
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Affiliation(s)
- Hong-Zhou Ye
- Department of Chemistry , Massachusetts Institute of Technology , Cambridge , Massachusetts 02139 , United States
| | - Troy Van Voorhis
- Department of Chemistry , Massachusetts Institute of Technology , Cambridge , Massachusetts 02139 , United States
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17
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Shee A, Zgid D. Coupled Cluster as an Impurity Solver for Green’s Function Embedding Methods. J Chem Theory Comput 2019; 15:6010-6024. [DOI: 10.1021/acs.jctc.9b00603] [Citation(s) in RCA: 25] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Avijit Shee
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Dominika Zgid
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
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18
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Tran LN, Shea JAR, Neuscamman E. Tracking Excited States in Wave Function Optimization Using Density Matrices and Variational Principles. J Chem Theory Comput 2019; 15:4790-4803. [DOI: 10.1021/acs.jctc.9b00351] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Lan Nguyen Tran
- Department of Chemistry, University of California, Berkeley, California 94720, United States
- Ho Chi Minh City Institute of Physics, VAST, Ho Chi Minh City 700000, Vietnam
| | - Jacqueline A. R. Shea
- Department of Chemistry, University of California, Berkeley, California 94720, United States
| | - Eric Neuscamman
- Department of Chemistry, University of California, Berkeley, California 94720, United States
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
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19
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Abstract
![]()
Fragment
embedding is one way to circumvent the high computational
scaling of accurate electron correlation methods. The challenge of
applying fragment embedding to molecular systems primarily lies in
the strong entanglement and correlation that prevent accurate fragmentation
across chemical bonds. Recently, Schmidt decomposition has been shown
effective for embedding fragments that are strongly coupled to a bath
in several model systems. In this work, we extend a recently developed
quantum embedding scheme, bootstrap embedding (BE), to molecular systems.
The resulting method utilizes the matching conditions naturally arising
from using overlapping fragments to optimize the embedding. Numerical
simulation suggests that the accuracy of the embedding improves rapidly
with fragment size for small molecules, whereas larger fragments that
include orbitals from different atoms may be needed for larger molecules.
BE scales linearly with system size (apart from an integral transform)
and hence can potentially be useful for large-scale calculations.
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Affiliation(s)
- Hong-Zhou Ye
- Department of Chemistry , Massachusetts Institute of Technology , Cambridge , Massachusetts 02139 , United States
| | - Nathan D Ricke
- Department of Chemistry , Massachusetts Institute of Technology , Cambridge , Massachusetts 02139 , United States
| | - Henry K Tran
- Department of Chemistry , Massachusetts Institute of Technology , Cambridge , Massachusetts 02139 , United States
| | - Troy Van Voorhis
- Department of Chemistry , Massachusetts Institute of Technology , Cambridge , Massachusetts 02139 , United States
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20
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Teke NK, Pavošević F, Peng C, Valeev EF. Explicitly correlated renormalized second-order Green’s function for accurate ionization potentials of closed-shell molecules. J Chem Phys 2019; 150:214103. [DOI: 10.1063/1.5090983] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Nakul K. Teke
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, USA
| | - Fabijan Pavošević
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, USA
| | - Chong Peng
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, USA
| | - Edward F. Valeev
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, USA
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21
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Peng B, Van Beeumen R, Williams-Young DB, Kowalski K, Yang C. Approximate Green's Function Coupled Cluster Method Employing Effective Dimension Reduction. J Chem Theory Comput 2019; 15:3185-3196. [PMID: 30951302 DOI: 10.1021/acs.jctc.9b00172] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The Green's function coupled cluster (GFCC) method, originally proposed in the early 1990s, is a powerful many-body tool for computing and analyzing the electronic structure of molecular and periodic systems, especially when electrons of the system are strongly correlated. However, in order for the GFCC to become a method that may be routinely used in the electronic structure calculations, robust numerical techniques and approximations must be employed to reduce its extremely high computational overhead. In our recent studies, it has been demonstrated that the GFCC equations can be solved directly in the frequency domain using iterative linear solvers, which can be easily distributed in a massively parallel environment. In the present work, we demonstrate a successful application of model-order-reduction (MOR) techniques in the GFCC framework. Briefly speaking, for a frequency regime of interest that requires high-resolution descriptions of spectral function, instead of solving the GFCC linear equation of full dimension for every single frequency point of interest, an efficiently solvable linear system model of a reduced dimension may be built upon projecting the original GFCC linear system onto a subspace. From this reduced order model is obtained a reasonable approximation to the full dimensional GFCC linear equations in both interpolative and extrapolative spectral regions. Here, we show that the subspace can be properly constructed in an iterative manner from the auxiliary vectors of the GFCC linear equations at some selected frequencies within the spectral region of interest. During the iterations, the quality of the subspace, as well as the linear system model, can be systematically improved. The method is tested in this work in terms of the efficiency and accuracy of computing spectral functions for some typical molecular systems such as carbon monoxide, 1,3-butadiene, benzene, and adenine. To reach the same level of accuracy as that of the original GFCC method, the application of MOR in the GFCC method is able to significantly lower the original computational cost for the aforementioned molecules in designated frequency regimes. As a byproduct, the reduced order model obtained by this method is found to provide a high-quality initial guess, which improves the convergence rate for the existing iterative linear solver.
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Affiliation(s)
- Bo Peng
- William R. Wiley Environmental Molecular Sciences Laboratory, Battelle , Pacific Northwest National Laboratory , K8-91, P.O. Box 999, Richland , Washington 99352 , United States
| | - Roel Van Beeumen
- Computational Research Division , Lawrence Berkeley National Laboratory , Berkeley , California 94720 , United States
| | - David B Williams-Young
- Computational Research Division , Lawrence Berkeley National Laboratory , Berkeley , California 94720 , United States
| | - Karol Kowalski
- William R. Wiley Environmental Molecular Sciences Laboratory, Battelle , Pacific Northwest National Laboratory , K8-91, P.O. Box 999, Richland , Washington 99352 , United States
| | - Chao Yang
- Computational Research Division , Lawrence Berkeley National Laboratory , Berkeley , California 94720 , United States
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22
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Rusakov AA, Iskakov S, Tran LN, Zgid D. Self-Energy Embedding Theory (SEET) for Periodic Systems. J Chem Theory Comput 2018; 15:229-240. [DOI: 10.1021/acs.jctc.8b00927] [Citation(s) in RCA: 35] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Alexander A. Rusakov
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Sergei Iskakov
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Lan Nguyen Tran
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, United States
- Ho Chi Minh City Institute of Physics, Vietnam Academy of Science and Technology (VAST), Ho Chi Minh City 70000, Vietnam
| | - Dominika Zgid
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
- Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, United States
- Center for Computational Quantum Physics, The Flatiron Institute, New York, New York 10010, United States
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23
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Peng B, Kowalski K. Green's function coupled cluster formulations utilizing extended inner excitations. J Chem Phys 2018; 149:214102. [PMID: 30525725 DOI: 10.1063/1.5046529] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In this paper, we analyze new approximations of the Green's function coupled cluster (GFCC) method where locations of poles are improved by extending the excitation level of inner auxiliary operators. These new GFCC approximations can be categorized as the GFCC-i(n, m) method, where the excitation level of the inner auxiliary operators (m) used to describe the ionization potential and electron affinity effects in the N - 1 and N + 1 particle spaces is higher than the excitation level (n) used to correlate the ground-state coupled cluster wave function for the N-electron system. Furthermore, we reveal the so-called "n + 1" rule in this category [or the GFCC-i(n, n + 1) method], which states that in order to maintain size-extensivity of the Green's function matrix elements, the excitation level of inner auxiliary operators X p (ω) and Y q (ω) cannot exceed n + 1. We also discuss the role of the moments of coupled cluster equations that in a natural way assures these properties. Our implementation in the present study is focused on the first approximation in this GFCC category, i.e., the GFCC-i(2,3) method. As our first practice, we use the GFCC-i(2,3) method to compute the spectral functions for the N2 and CO molecules in the inner and outer valence regimes. In comparison with the Green's function coupled cluster singles, doubles results, the computed spectral functions from the GFCC-i(2,3) method exhibit better agreement with the experimental results and other theoretical results, particularly in terms of providing higher resolution of satellite peaks and more accurate relative positions of these satellite peaks with respect to the main peak positions.
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Affiliation(s)
- Bo Peng
- William R. Wiley Environmental Molecular Sciences Laboratory, Battelle, Pacific Northwest National Laboratory, K8-91, P.O. Box 999, Richland, Washington 99352, USA
| | - Karol Kowalski
- William R. Wiley Environmental Molecular Sciences Laboratory, Battelle, Pacific Northwest National Laboratory, K8-91, P.O. Box 999, Richland, Washington 99352, USA
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24
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Mühlbach AH, Reiher M. Quantum system partitioning at the single-particle level. J Chem Phys 2018; 149:184104. [DOI: 10.1063/1.5055942] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Adrian H. Mühlbach
- Laboratorium für Physikalische Chemie, ETH Zürich, Vladimir-Prelog-Weg 2, CH-8093 Zürich, Switzerland
| | - Markus Reiher
- Laboratorium für Physikalische Chemie, ETH Zürich, Vladimir-Prelog-Weg 2, CH-8093 Zürich, Switzerland
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25
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Eriksen JJ, Gauss J. Many-Body Expanded Full Configuration Interaction. I. Weakly Correlated Regime. J Chem Theory Comput 2018; 14:5180-5191. [DOI: 10.1021/acs.jctc.8b00680] [Citation(s) in RCA: 40] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Janus J. Eriksen
- Institut für Physikalische Chemie, Johannes Gutenberg-Universität Mainz, Duesbergweg 10-14, 55128 Mainz, Germany
| | - Jürgen Gauss
- Institut für Physikalische Chemie, Johannes Gutenberg-Universität Mainz, Duesbergweg 10-14, 55128 Mainz, Germany
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26
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Abstract
We present a new theoretical approach, unrestricted self-energy embedding theory (USEET), that is a Green's function embedding theory used to study problems in which an open, embedded system exchanges electrons with the environment. USEET has a high potential to be used in studies of strongly correlated systems with an odd number of electrons and open shell systems such as transition metal complexes important in inorganic chemistry. In this paper, we show that USEET results agree very well with common quantum chemistry methods while avoiding typical bottlenecks present in these methods.
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Affiliation(s)
- Lan Nguyen Tran
- Department of Chemistry , University of Michigan , Ann Arbor , Michigan 48109 , United States
- Department of Physics , University of Michigan , Ann Arbor , Michigan 48109 , United States
- Ho Chi Minh City Institute of Physics, VAST , Ho Chi Minh City 70000 , Vietnam
| | - Sergei Iskakov
- Department of Physics , University of Michigan , Ann Arbor , Michigan 48109 , United States
| | - Dominika Zgid
- Department of Chemistry , University of Michigan , Ann Arbor , Michigan 48109 , United States
- Center for Computational Quantum Physics , The Flatiron Institute , New York , New York 10010 , United States
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27
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Neuhauser D, Baer R, Zgid D. Stochastic Self-Consistent Second-Order Green’s Function Method for Correlation Energies of Large Electronic Systems. J Chem Theory Comput 2017; 13:5396-5403. [DOI: 10.1021/acs.jctc.7b00792] [Citation(s) in RCA: 35] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Daniel Neuhauser
- Department
of Chemistry and Biochemistry, University of California at Los Angeles, Los Angeles, California 90095, United States
| | - Roi Baer
- Fritz
Haber Center for Molecular Dynamics, Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
| | - Dominika Zgid
- Department
of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
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28
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Kananenka AA, Zgid D. Combining Density Functional Theory and Green’s Function Theory: Range-Separated, Nonlocal, Dynamic, and Orbital-Dependent Hybrid Functional. J Chem Theory Comput 2017; 13:5317-5331. [DOI: 10.1021/acs.jctc.7b00701] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Alexei A. Kananenka
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Dominika Zgid
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
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29
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Pavošević F, Peng C, Ortiz JV, Valeev EF. Communication: Explicitly correlated formalism for second-order single-particle Green’s function. J Chem Phys 2017; 147:121101. [DOI: 10.1063/1.5000916] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022] Open
Affiliation(s)
- Fabijan Pavošević
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, USA
| | - Chong Peng
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, USA
| | - J. V. Ortiz
- Department of Chemistry and Biochemistry, Auburn University, Auburn, Alabama 36849-5312, USA
| | - Edward F. Valeev
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, USA
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30
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Eriksen JJ, Lipparini F, Gauss J. Virtual Orbital Many-Body Expansions: A Possible Route towards the Full Configuration Interaction Limit. J Phys Chem Lett 2017; 8:4633-4639. [PMID: 28892390 DOI: 10.1021/acs.jpclett.7b02075] [Citation(s) in RCA: 49] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
It is demonstrated how full configuration interaction (FCI) results in extended basis sets may be obtained to within sub-kJ/mol accuracy by decomposing the energy in terms of many-body expansions in the virtual orbitals of the molecular system at hand. This extension of the FCI application range lends itself to two unique features of the current approach, namely, that the total energy calculation can be performed entirely within considerably reduced orbital subspaces and may be so by means of embarrassingly parallel programming. Facilitated by a rigorous and methodical screening protocol and further aided by expansion points different from the Hartree-Fock solution, all-electron numerical results are reported for H2O in polarized core-valence basis sets ranging from double-ζ (10 e, 28 o) to quadruple-ζ (10 e, 144 o) quality.
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Affiliation(s)
- Janus J Eriksen
- Institut für Physikalische Chemie, Johannes Gutenberg-Universität Mainz , D-55128 Mainz, Germany
| | - Filippo Lipparini
- Institut für Physikalische Chemie, Johannes Gutenberg-Universität Mainz , D-55128 Mainz, Germany
| | - Jürgen Gauss
- Institut für Physikalische Chemie, Johannes Gutenberg-Universität Mainz , D-55128 Mainz, Germany
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