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Filip MA, Thom AJW. A hybrid stochastic configuration interaction-coupled cluster approach for multireference systems. J Chem Phys 2023; 158:2889005. [PMID: 37154279 DOI: 10.1063/5.0145767] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/07/2023] [Accepted: 04/19/2023] [Indexed: 05/10/2023] Open
Abstract
The development of multireference coupled cluster (MRCC) techniques has remained an open area of study in electronic structure theory for decades due to the inherent complexity of expressing a multiconfigurational wavefunction in the fundamentally single-reference coupled cluster framework. The recently developed multireference-coupled cluster Monte Carlo (mrCCMC) technique uses the formal simplicity of the Monte Carlo approach to Hilbert space quantum chemistry to avoid some of the complexities of conventional MRCC, but there is room for improvement in terms of accuracy and, particularly, computational cost. In this paper, we explore the potential of incorporating ideas from conventional MRCC-namely, the treatment of the strongly correlated space in a configuration interaction formalism-to the mrCCMC framework, leading to a series of methods with increasing relaxation of the reference space in the presence of external amplitudes. These techniques offer new balances of stability and cost against accuracy, as well as a means to better explore and better understand the structure of solutions to the mrCCMC equations.
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Affiliation(s)
- Maria-Andreea Filip
- Yusuf Hamied Department of Chemistry, University of Cambridge, Cambridge, United Kingdom
- Peterhouse, University of Cambridge, Cambridge, United Kingdom
| | - Alex J W Thom
- Yusuf Hamied Department of Chemistry, University of Cambridge, Cambridge, United Kingdom
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2
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Cruz JC, Garza J, Yanai T, Hirata S. Stochastic evaluation of four-component relativistic second-order many-body perturbation energies: A potentially quadratic-scaling correlation method. J Chem Phys 2022; 156:224102. [DOI: 10.1063/5.0091973] [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
A second-order many-body perturbation correction to the relativistic Dirac-Hartree-Fock energy is evaluated stochastically by integrating 13-dimensional products of four-component spinors and Coulomb potentials. The integration in the real space of electron coordinates is carried out by the Monte Carlo (MC) method with the Metropolis sampling, whereas the MC integration in the imaginary-time domain is performed by the inverse-CDF (cumulative distribution function) method. The computational cost to reach a given relative statistical error for spatially compact but heavy molecules is observed to be no worse than cubic and possibly quadratic with the number of electrons or basis functions. This is a vast improvement over the quintic scaling of the conventional, deterministic second-order many-body perturbation method. The algorithm is also easily and efficiently parallelized with demonstrated 92% strong scalability going from 64 to 4096 processors for a fixed job size.
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Affiliation(s)
- J. César Cruz
- Universidad Autónoma Metropolitana-Iztapalapa, Mexico
| | - Jorge Garza
- Departamento de Química, Universidad Autónoma Metropolitana-Iztapalapa, Mexico
| | - Takeshi Yanai
- Institute of Transformative Bio-Molecules, Nagoya University, Japan
| | - So Hirata
- Department of Chemistry, University of Illinois at Urbana-Champaign, United States of America
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3
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Ichibha T, Neufeld VA, Hongo K, Maezono R, Thom AJW. Making the most of data: Quantum Monte Carlo postanalysis revisited. Phys Rev E 2022; 105:045313. [PMID: 35590595 DOI: 10.1103/physreve.105.045313] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2021] [Accepted: 03/10/2022] [Indexed: 06/15/2023]
Abstract
In quantum Monte Carlo (QMC) methods, energy estimators are calculated as (functions of) statistical averages of quantities sampled during a calculation. Associated statistical errors of these averages are often estimated. This error estimation is not straightforward and there are several choices of the error estimation methods. We evaluate the performance of three methods (the Straatsma method, an autoregressive model, and a blocking analysis based on von Neumann's ratio test for randomness) for the energy time series given by three QMC methods [diffusion Monte Carlo, full configuration interaction Quantum Monte Carlo (FCIQMC), and coupled cluster Monte Carlo (CCMC)]. From these analyses, we describe a hybrid analysis method which provides reliable error estimates for a series of various lengths of FCIQMC and CCMC's time series. Equally important is the estimation of the appropriate start point of the equilibrated phase. We establish that a simple mean squared error rule method as described by White [K. P. White, Jr., Simulation 69(6), 323 (1997)10.1177/003754979706900601] can provide reasonable estimations.
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Affiliation(s)
- Tom Ichibha
- School of Information Science, JAIST, 1-1 Asahidai, Nomi, Ishikawa 923-1292, Japan
| | - Verena A Neufeld
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom and Department of Chemistry, Columbia University, New York, New York 10027, USA
| | - Kenta Hongo
- Research Center for Advanced Computing Infrastructure, JAIST, 1-1 Asahidai, Nomi, Ishikawa 923-1292, Japan
| | - Ryo Maezono
- School of Information Science, JAIST, 1-1 Asahidai, Nomi, Ishikawa 923-1292, Japan
| | - Alex J W Thom
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
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4
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Doran AE, Qiu DL, Hirata S. Monte Carlo MP2-F12 for Noncovalent Interactions: The C 60 Dimer. J Phys Chem A 2021; 125:7344-7351. [PMID: 34433271 DOI: 10.1021/acs.jpca.1c05021] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
A scalable stochastic algorithm is presented that can evaluate explicitly correlated (F12) second-order many-body perturbation (MP2) energies of weak, noncovalent, intermolecular interactions. It first transforms the formulas of the MP2 and F12 energy differences into a short sum of high-dimensional integrals of Green's functions in real space and imaginary time. These integrals are then evaluated by the Monte Carlo method augmented by parallel execution, redundant-walker convergence acceleration, direct-sampling autocorrelation elimination, and control-variate error reduction. By sharing electron-pair walkers across the supermolecule and its subsystems spanned by the joint basis set, the statistical uncertainty is reduced by one to 2 orders of magnitude in the MP2 binding energy corrected for the basis-set incompleteness and superposition errors. The method predicts the MP2-F12/aug-cc-pVDZ binding energy of 19.1 ± 4.0 kcal mol-1 for the C60 dimer at the center distance of 9.748 Å.
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Affiliation(s)
- Alexander E Doran
- Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
| | - David L Qiu
- Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
| | - So Hirata
- Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
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5
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Doran AE, Hirata S. Stochastic evaluation of fourth-order many-body perturbation energies. J Chem Phys 2021; 154:134114. [PMID: 33832241 DOI: 10.1063/5.0047798] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A scalable, stochastic algorithm evaluating the fourth-order many-body perturbation (MP4) correction to energy is proposed. Three hundred Goldstone diagrams representing the MP4 correction are computer generated and then converted into algebraic formulas expressed in terms of Green's functions in real space and imaginary time. They are evaluated by the direct (i.e., non-Markov, non-Metropolis) Monte Carlo (MC) integration accelerated by the redundant-walker and control-variate algorithms. The resulting MC-MP4 method is efficiently parallelized and is shown to display O(n5.3) size-dependence of cost, which is nearly two ranks lower than the O(n7) dependence of the deterministic MP4 algorithm. It evaluates the MP4/aug-cc-pVDZ energy for benzene, naphthalene, phenanthrene, and corannulene with the statistical uncertainty of 10 mEh (1.1% of the total basis-set correlation energy), 38 mEh (2.6%), 110 mEh (5.5%), and 280 mEh (9.0%), respectively, after about 109 MC steps.
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Affiliation(s)
- Alexander E Doran
- Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - So Hirata
- Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
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6
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Filip MA, Thom AJW. A stochastic approach to unitary coupled cluster. J Chem Phys 2020; 153:214106. [DOI: 10.1063/5.0026141] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
| | - Alex J. W. Thom
- Department of Chemistry, University of Cambridge, Cambridge, United Kingdom
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Doran AE, Hirata S. Convergence acceleration of Monte Carlo many-body perturbation methods by direct sampling. J Chem Phys 2020; 153:104112. [DOI: 10.1063/5.0020583] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Alexander E. Doran
- Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - So Hirata
- Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
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Doran AE, Hirata S. Convergence acceleration of Monte Carlo many-body perturbation methods by using many control variates. J Chem Phys 2020; 153:094108. [DOI: 10.1063/5.0020584] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022] Open
Affiliation(s)
- Alexander E. Doran
- Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - So Hirata
- Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
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Neufeld VA, Thom AJW. Accelerating Convergence in Fock Space Quantum Monte Carlo Methods. J Chem Theory Comput 2020; 16:1503-1510. [DOI: 10.1021/acs.jctc.9b01023] [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)
- 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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Gyevi-Nagy L, Kállay M, Nagy PR. Integral-Direct and Parallel Implementation of the CCSD(T) Method: Algorithmic Developments and Large-Scale Applications. J Chem Theory Comput 2019; 16:366-384. [DOI: 10.1021/acs.jctc.9b00957] [Citation(s) in RCA: 28] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Affiliation(s)
- László Gyevi-Nagy
- Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, P.O. Box 91, H-1521 Budapest, Hungary
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11
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Filip MA, Scott CJC, Thom AJW. Multireference Stochastic Coupled Cluster. J Chem Theory Comput 2019; 15:6625-6635. [DOI: 10.1021/acs.jctc.9b00741] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
| | | | - Alex J. W. Thom
- Department of Chemistry, University of Cambridge, Cambridge, U.K
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12
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Mihm TN, McIsaac AR, Shepherd JJ. An optimized twist angle to find the twist-averaged correlation energy applied to the uniform electron gas. J Chem Phys 2019; 150:191101. [PMID: 31117769 DOI: 10.1063/1.5091445] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2023] Open
Abstract
We explore an alternative to twist averaging in order to obtain more cost-effective and accurate extrapolations to the thermodynamic limit (TDL) for coupled cluster doubles (CCD) calculations. We seek a single twist angle to perform calculations at, instead of integrating over many random points or a grid. We introduce the concept of connectivity, a quantity derived from the nonzero four-index integrals in an MP2 calculation. This allows us to find a special twist angle that provides appropriate connectivity in the energy equation, which yields results comparable to full twist averaging. This special twist angle effectively makes the finite electron number CCD calculation represent the TDL more accurately, reducing the cost of twist-averaged CCD over Ns twist angles from Ns CCD calculations to Ns MP2 calculations plus one CCD calculation.
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Affiliation(s)
- Tina N Mihm
- Department of Chemistry, University of Iowa, Iowa City, Iowa 52242-1002, USA
| | - Alexandra R McIsaac
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - James J Shepherd
- Department of Chemistry, University of Iowa, Iowa City, Iowa 52242-1002, USA
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Pinski P, Neese F. Analytical gradient for the domain-based local pair natural orbital second order Møller-Plesset perturbation theory method (DLPNO-MP2). J Chem Phys 2019; 150:164102. [DOI: 10.1063/1.5086544] [Citation(s) in RCA: 23] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023] Open
Affiliation(s)
- Peter Pinski
- Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, 45470 Mülheim an der Ruhr, Germany
| | - Frank Neese
- Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, 45470 Mülheim an der Ruhr, Germany
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14
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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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15
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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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