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Greene SM, Webber RJ, Smith JET, Weare J, Berkelbach TC. Full Configuration Interaction Excited-State Energies in Large Active Spaces from Subspace Iteration with Repeated Random Sparsification. J Chem Theory Comput 2022; 18:7218-7232. [PMID: 36345915 DOI: 10.1021/acs.jctc.2c00435] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Abstract
We present a stable and systematically improvable quantum Monte Carlo (QMC) approach to calculating excited-state energies, which we implement using our fast randomized iteration method for the full configuration interaction problem (FCI-FRI). Unlike previous excited-state quantum Monte Carlo methods, our approach, which is based on an asymmetric variant of subspace iteration, avoids the use of dot products of random vectors and instead relies upon trial vectors to maintain orthogonality and estimate eigenvalues. By leveraging recent advances, we apply our method to calculate ground- and excited-state energies of challenging molecular systems in large active spaces, including the carbon dimer with 8 electrons in 108 orbitals (8e,108o), an oxo-Mn(salen) transition metal complex (28e,28o), ozone (18e,87o), and butadiene (22e,82o). In the majority of these test cases, our approach yields total excited-state energies that agree with those from state-of-the-art methods─including heat-bath CI, the density matrix renormalization group approach, and FCIQMC─to within sub-milliHartree accuracy. In all cases, estimated excitation energies agree to within about 0.1 eV.
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Affiliation(s)
- Samuel M Greene
- Department of Chemistry, Columbia University, New York, New York10027, United States
| | - Robert J Webber
- Courant Institute of Mathematical Sciences, New York University, New York, New York10012, United States
| | - James E T Smith
- Center for Computational Quantum Physics, Flatiron Institute, New York, New York10010, United States
| | - Jonathan Weare
- Courant Institute of Mathematical Sciences, New York University, New York, New York10012, United States
| | - Timothy C Berkelbach
- Department of Chemistry, Columbia University, New York, New York10027, United States.,Center for Computational Quantum Physics, Flatiron Institute, New York, New York10010, United States
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Greene SM, Webber RJ, Weare J, Berkelbach TC. Improved Fast Randomized Iteration Approach to Full Configuration Interaction. J Chem Theory Comput 2020; 16:5572-5585. [DOI: 10.1021/acs.jctc.0c00437] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Samuel M. Greene
- Department of Chemistry, Columbia University, New York, New York 10027, United States
| | - Robert J. Webber
- Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, United States
| | - Jonathan Weare
- Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, United States
| | - Timothy C. Berkelbach
- Department of Chemistry, Columbia University, New York, New York 10027, United States
- Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, United States
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Greene SM, Webber RJ, Weare J, Berkelbach TC. Beyond Walkers in Stochastic Quantum Chemistry: Reducing Error Using Fast Randomized Iteration. J Chem Theory Comput 2019; 15:4834-4850. [DOI: 10.1021/acs.jctc.9b00422] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Samuel M. Greene
- Department of Chemistry and James Franck Institute, University of Chicago, Chicago, Illinois 60637, United States
| | - Robert J. Webber
- Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, United States
| | - Jonathan Weare
- Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, United States
| | - Timothy C. Berkelbach
- Department of Chemistry, Columbia University, New York, New York 10027, United States
- Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, United States
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Deustua JE, Yuwono SH, Shen J, Piecuch P. Accurate excited-state energetics by a combination of Monte Carlo sampling and equation-of-motion coupled-cluster computations. J Chem Phys 2019; 150:111101. [DOI: 10.1063/1.5090346] [Citation(s) in RCA: 22] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- J. Emiliano Deustua
- Department of Chemistry, Michigan State University, East Lansing, Michigan 48824, USA
| | - Stephen H. Yuwono
- Department of Chemistry, Michigan State University, East Lansing, Michigan 48824, USA
| | - Jun Shen
- Department of Chemistry, Michigan State University, East Lansing, Michigan 48824, USA
| | - Piotr Piecuch
- Department of Chemistry, Michigan State University, East Lansing, Michigan 48824, USA
- Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA
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Scott CJC, Di Remigio R, Crawford TD, Thom AJW. Diagrammatic Coupled Cluster Monte Carlo. J Phys Chem Lett 2019; 10:925-935. [PMID: 30724572 DOI: 10.1021/acs.jpclett.9b00067] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
We propose a modified coupled cluster Monte Carlo algorithm that stochastically samples connected terms within the truncated Baker-Campbell-Hausdorff expansion of the similarity-transformed Hamiltonian by construction of coupled cluster diagrams on the fly. Our new approach-diagCCMC-allows propagation to be performed using only the connected components of the similarity-transformed Hamiltonian, greatly reducing the memory cost associated with the stochastic solution of the coupled cluster equations. We show that for perfectly local, noninteracting systems diagCCMC is able to represent the coupled cluster wavefunction with a memory cost that scales linearly with system size. The favorable memory cost is observed with the only assumption of fixed stochastic granularity and is valid for arbitrary levels of coupled cluster theory. Significant reduction in memory cost is also shown to smoothly appear with dissociation of a finite chain of helium atoms. This approach is also shown not to break down in the presence of strong correlation through the example of a stretched nitrogen molecule. Our novel methodology moves the theoretical basis of coupled cluster Monte Carlo closer to deterministic approaches.
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Affiliation(s)
- Charles J C Scott
- Department of Chemistry , University of Cambridge , Cambridge CB2 1TN , United Kingdom
| | - Roberto Di Remigio
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry , University of Tromsø - The Arctic University of Norway , N-9037 Tromsø , Norway
- Department of Chemistry , Virginia Tech , Blacksburg , Virginia 24061 , United States
| | - T Daniel Crawford
- Department of Chemistry , Virginia Tech , Blacksburg , Virginia 24061 , United States
| | - Alex J W Thom
- Department of Chemistry , University of Cambridge , Cambridge CB2 1TN , United Kingdom
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Spencer JS, Blunt NS, Choi S, Etrych J, Filip MA, Foulkes WMC, Franklin RST, Handley WJ, Malone FD, Neufeld VA, Di Remigio R, Rogers TW, Scott CJC, Shepherd JJ, Vigor WA, Weston J, Xu R, Thom AJW. The HANDE-QMC Project: Open-Source Stochastic Quantum Chemistry from the Ground State Up. J Chem Theory Comput 2019; 15:1728-1742. [DOI: 10.1021/acs.jctc.8b01217] [Citation(s) in RCA: 28] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- James S. Spencer
- Department of Physics, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom
- Department of Materials, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom
| | - Nick S. Blunt
- University Chemical Laboratory, Lensfield Road, Cambridge CB2 1EW, United Kingdom
- St. John’s College, St. John’s Street, Cambridge, CB2 1TP, United Kingdom
| | - Seonghoon Choi
- University Chemical Laboratory, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Jiří Etrych
- University Chemical Laboratory, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Maria-Andreea Filip
- University Chemical Laboratory, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - W. M. C. Foulkes
- Department of Physics, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom
- Department of Physics, University of Illinois at Urbana−Champaign, Urbana, Illinois 61801, United States
| | - Ruth S. T. Franklin
- University Chemical Laboratory, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Will J. Handley
- Astrophysics Group, Cavendish Laboratory, Cambridge, CB3 OHE, United Kingdom
- Kavli Institute for Cosmology, Madingley Road, Cambridge, CB3 0HA, United Kingdom
- Gonville & Caius College, Trinity Street, Cambridge, CB2 1TA, United Kingdom
| | - Fionn D. Malone
- Department of Physics, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom
- Quantum Simulations Group, Lawrence Livermore National Laboratory, Livermore, California 94550, United States
| | - Verena A. Neufeld
- University Chemical Laboratory, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Roberto Di Remigio
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Tromsø—The Arctic University of Norway, N-9037 Tromsø, Norway
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Thomas W. Rogers
- Department of Physics, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom
| | - Charles J. C. Scott
- University Chemical Laboratory, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | | | - William A. Vigor
- Department of Chemistry, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom
| | - Joseph Weston
- Department of Physics, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom
| | - RuQing Xu
- Department of Modern Physics, University of Science and Technology, Hefei, Anhui 230026, China
| | - Alex J. W. Thom
- University Chemical Laboratory, Lensfield Road, Cambridge CB2 1EW, United Kingdom
- Department of Chemistry, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom
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Neufeld VA, Thom AJW. Exciting Determinants in Quantum Monte Carlo: Loading the Dice with Fast, Low-Memory Weights. J Chem Theory Comput 2018; 15:127-140. [DOI: 10.1021/acs.jctc.8b00844] [Citation(s) in RCA: 20] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Verena A. Neufeld
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Alex J. W. Thom
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
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Deustua JE, Shen J, Piecuch P. Converging High-Level Coupled-Cluster Energetics by Monte Carlo Sampling and Moment Expansions. PHYSICAL REVIEW LETTERS 2017; 119:223003. [PMID: 29286766 DOI: 10.1103/physrevlett.119.223003] [Citation(s) in RCA: 55] [Impact Index Per Article: 7.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/31/2017] [Indexed: 06/07/2023]
Abstract
We propose a new approach to the determination of accurate electronic energies that are equivalent to the results of high-level coupled-cluster (CC) calculations. The approach is based on merging the CC(P;Q) formalism, which corrects energies obtained with an arbitrary truncation in the cluster operator, with the stochastic configuration interaction and CC ideas. The advantages of the proposed methodology are illustrated by molecular examples, where the goal is to recover the energetics obtained in the CC calculations with a full treatment of singly, doubly, and triply excited clusters.
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Affiliation(s)
- J Emiliano Deustua
- Department of Chemistry, Michigan State University, East Lansing, Michigan 48824, USA
| | - Jun Shen
- Department of Chemistry, Michigan State University, East Lansing, Michigan 48824, USA
| | - Piotr Piecuch
- Department of Chemistry, Michigan State University, East Lansing, Michigan 48824, USA
- Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA
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Scott CJC, Thom AJW. Stochastic coupled cluster theory: Efficient sampling of the coupled cluster expansion. J Chem Phys 2017; 147:124105. [DOI: 10.1063/1.4991795] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
| | - Alex J. W. Thom
- Department of Chemistry, University of Cambridge, Cambridge, United Kingdom
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