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Dobrautz W, Sokolov IO, Liao K, Ríos PL, Rahm M, Alavi A, Tavernelli I. Toward Real Chemical Accuracy on Current Quantum Hardware Through the Transcorrelated Method. J Chem Theory Comput 2024; 20:4146-4160. [PMID: 38723159 PMCID: PMC11137825 DOI: 10.1021/acs.jctc.4c00070] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/19/2024] [Revised: 04/15/2024] [Accepted: 04/16/2024] [Indexed: 05/29/2024]
Abstract
Quantum computing is emerging as a new computational paradigm with the potential to transform several research fields including quantum chemistry. However, current hardware limitations (including limited coherence times, gate infidelities, and connectivity) hamper the implementation of most quantum algorithms and call for more noise-resilient solutions. We propose an explicitly correlated Ansatz based on the transcorrelated (TC) approach to target these major roadblocks directly. This method transfers, without any approximation, correlations from the wave function directly into the Hamiltonian, thus reducing the resources needed to achieve accurate results with noisy quantum devices. We show that the TC approach allows for shallower circuits and improves the convergence toward the complete basis set limit, providing energies within chemical accuracy to experiment with smaller basis sets and, thus, fewer qubits. We demonstrate our method by computing bond lengths, dissociation energies, and vibrational frequencies close to experimental results for the hydrogen dimer and lithium hydride using two and four qubits, respectively. To demonstrate our approach's current and near-term potential, we perform hardware experiments, where our results confirm that the TC method paves the way toward accurate quantum chemistry calculations already on today's quantum hardware.
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Affiliation(s)
- Werner Dobrautz
- Department
of Chemistry and Chemical Engineering, Chalmers
University of Technology, 41296 Gothenburg, Sweden
| | - Igor O. Sokolov
- IBM
Quantum, IBM Research Zurich, Säumerstrasse 4, 8803 Rüschlikon, Switzerland
| | - Ke Liao
- Max
Planck Institute for Solid State Research, Heisenbergstr. 1, 70569 Stuttgart, Germany
| | - Pablo López Ríos
- Max
Planck Institute for Solid State Research, Heisenbergstr. 1, 70569 Stuttgart, Germany
| | - Martin Rahm
- Department
of Chemistry and Chemical Engineering, Chalmers
University of Technology, 41296 Gothenburg, Sweden
| | - Ali Alavi
- Max
Planck Institute for Solid State Research, Heisenbergstr. 1, 70569 Stuttgart, Germany
- Yusuf
Hamied Department of Chemistry, University
of Cambridge, Lensfield
Road, Cambridge CB2 1EW, U.K.
| | - Ivano Tavernelli
- IBM
Quantum, IBM Research Zurich, Säumerstrasse 4, 8803 Rüschlikon, Switzerland
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2
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Kulahlioglu AH, Dreuw A. Dense-sparse quantum Monte Carlo algebraic diagrammatic construction and importance ranking. J Chem Phys 2024; 160:204111. [PMID: 38785284 DOI: 10.1063/5.0209137] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/19/2024] [Accepted: 05/07/2024] [Indexed: 05/25/2024] Open
Abstract
Quantum Monte Carlo Algebraic Diagrammatic Construction (QMCADC) has been proposed as a reformulation of the second-order ADC scheme for the polarization propagator within the projection quantum Monte Carlo formalism. Dense-sparse partitioning and importance ranking filtering strategies are now exploited to accelerate its convergence and to alleviate the sign problem inherent in such calculations. By splitting the configuration space into dense and sparse subsets, the corresponding projection operator is decomposed into four distinct blocks. Deterministic calculations handle the dense-to-dense and sparse-to-dense blocks, while the remaining blocks, dense-to-sparse and sparse-to-sparse, are stochastically evaluated. The dense set is efficiently stored in a fixed-size array, and the sparse set is represented through conventional floating random Monte Carlo walks. The stochastic projection is further refined through importance ranking criteria, enabling a reduction in the required number of walkers with a controllable bias. Our results demonstrate the integration of dense-sparse partitioning with importance ranking filtering to significantly enhance the efficiency of QMCADC, enabling large-scale molecular excited-state calculations. Furthermore, this novel approach maximizes the utilization of the sparsity of ADC(2), transforming QMCADC into a tailored framework for ADC calculations.
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Affiliation(s)
- Adem Halil Kulahlioglu
- Interdisciplinary Center for Scientific Computing, Ruprecht-Karls University, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
| | - Andreas Dreuw
- Interdisciplinary Center for Scientific Computing, Ruprecht-Karls University, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
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3
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Weser O, Alavi A, Manni GL. Exploiting Locality in Full Configuration Interaction Quantum Monte Carlo for Fast Excitation Generation. J Chem Theory Comput 2023; 19:9118-9135. [PMID: 38051202 PMCID: PMC10753814 DOI: 10.1021/acs.jctc.3c00546] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/24/2023] [Revised: 10/18/2023] [Accepted: 10/24/2023] [Indexed: 12/07/2023]
Abstract
In this paper, we propose an improved excitation generation algorithm for the full configuration interaction quantum Monte Carlo method, which is particularly effective in systems described by localized orbitals. The method is an extension of the precomputed heat-bath strategy of Holmes et al., with more effective sampling of double excitations and a novel approach for nonuniform sampling of single excitations. We demonstrate the effectiveness of the algorithm for a chain of 30 hydrogen atoms with atom-localized orbitals, a stack of benzene molecules, and an Fe(II)-porphyrin model complex, whereby we show an overall efficiency gain by a factor of two to four, as measured by variance reduction per wall-clock time.
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Affiliation(s)
- Oskar Weser
- Max-Planck-Institute
for Solid State Research, Stuttgart 70569, Germany
| | - Ali Alavi
- Max-Planck-Institute
for Solid State Research, Stuttgart 70569, Germany
- Yusuf
Hamied Department of Chemistry, University
of Cambridge, Lensfield
Road, Cambridge CB2 1EW, U.K.
| | - Giovanni Li Manni
- Max-Planck-Institute
for Solid State Research, Stuttgart 70569, Germany
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4
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Li Manni G, Fdez. Galván I, Alavi A, Aleotti F, Aquilante F, Autschbach J, Avagliano D, Baiardi A, Bao JJ, Battaglia S, Birnoschi L, Blanco-González A, Bokarev SI, Broer R, Cacciari R, Calio PB, Carlson RK, Carvalho Couto R, Cerdán L, Chibotaru LF, Chilton NF, Church JR, Conti I, Coriani S, Cuéllar-Zuquin J, Daoud RE, Dattani N, Decleva P, de Graaf C, Delcey M, De Vico L, Dobrautz W, Dong SS, Feng R, Ferré N, Filatov(Gulak) M, Gagliardi L, Garavelli M, González L, Guan Y, Guo M, Hennefarth MR, Hermes MR, Hoyer CE, Huix-Rotllant M, Jaiswal VK, Kaiser A, Kaliakin DS, Khamesian M, King DS, Kochetov V, Krośnicki M, Kumaar AA, Larsson ED, Lehtola S, Lepetit MB, Lischka H, López Ríos P, Lundberg M, Ma D, Mai S, Marquetand P, Merritt ICD, Montorsi F, Mörchen M, Nenov A, Nguyen VHA, Nishimoto Y, Oakley MS, Olivucci M, Oppel M, Padula D, Pandharkar R, Phung QM, Plasser F, Raggi G, Rebolini E, Reiher M, Rivalta I, Roca-Sanjuán D, Romig T, Safari AA, Sánchez-Mansilla A, Sand AM, Schapiro I, Scott TR, Segarra-Martí J, Segatta F, Sergentu DC, Sharma P, Shepard R, Shu Y, Staab JK, Straatsma TP, Sørensen LK, Tenorio BNC, Truhlar DG, Ungur L, Vacher M, Veryazov V, Voß TA, Weser O, Wu D, Yang X, Yarkony D, Zhou C, Zobel JP, Lindh R. The OpenMolcas Web: A Community-Driven Approach to Advancing Computational Chemistry. J Chem Theory Comput 2023; 19:6933-6991. [PMID: 37216210 PMCID: PMC10601490 DOI: 10.1021/acs.jctc.3c00182] [Citation(s) in RCA: 42] [Impact Index Per Article: 42.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/13/2023] [Indexed: 05/24/2023]
Abstract
The developments of the open-source OpenMolcas chemistry software environment since spring 2020 are described, with a focus on novel functionalities accessible in the stable branch of the package or via interfaces with other packages. These developments span a wide range of topics in computational chemistry and are presented in thematic sections: electronic structure theory, electronic spectroscopy simulations, analytic gradients and molecular structure optimizations, ab initio molecular dynamics, and other new features. This report offers an overview of the chemical phenomena and processes OpenMolcas can address, while showing that OpenMolcas is an attractive platform for state-of-the-art atomistic computer simulations.
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Affiliation(s)
- Giovanni Li Manni
- Electronic
Structure Theory Department, Max Planck
Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany
| | - Ignacio Fdez. Galván
- Department
of Chemistry − BMC, Uppsala University, P.O. Box 576, SE-75123 Uppsala, Sweden
| | - Ali Alavi
- Electronic
Structure Theory Department, Max Planck
Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany
- Yusuf Hamied
Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Flavia Aleotti
- Department
of Industrial Chemistry “Toso Montanari”, University of Bologna, 40136 Bologna, Italy
| | - Francesco Aquilante
- Theory and
Simulation of Materials (THEOS) and National Centre for Computational
Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Jochen Autschbach
- Department
of Chemistry, University at Buffalo, State
University of New York, Buffalo, New York 14260-3000, United States
| | - Davide Avagliano
- Department
of Industrial Chemistry “Toso Montanari”, University of Bologna, 40136 Bologna, Italy
| | - Alberto Baiardi
- ETH Zurich, Laboratory for Physical Chemistry, Vladimir-Prelog-Weg 2, 8093 Zurich, Switzerland
| | - Jie J. Bao
- Department
of Chemistry, Chemical Theory Center, and Minnesota Supercomputing
Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, United
States
| | - Stefano Battaglia
- Department
of Chemistry − BMC, Uppsala University, P.O. Box 576, SE-75123 Uppsala, Sweden
| | - Letitia Birnoschi
- The Department
of Chemistry, The University of Manchester, M13 9PL, Manchester, U.K.
| | - Alejandro Blanco-González
- Chemistry
Department, Bowling Green State University, Overmann Hall, Bowling Green, Ohio 43403, United States
| | - Sergey I. Bokarev
- Institut
für Physik, Universität Rostock, Albert-Einstein-Str. 23-24, 18059 Rostock, Germany
- Chemistry
Department, School of Natural Sciences, Technical University of Munich, Lichtenbergstr. 4, 85748 Garching, Germany
| | - Ria Broer
- Theoretical
Chemistry, Zernike Institute for Advanced Materials, University of Groningen, Nijenborgh 4, 9747AG Groningen, The Netherlands
| | - Roberto Cacciari
- Dipartimento
di Biotecnologie, Chimica e Farmacia, Università
di Siena, Via A. Moro 2, 53100 Siena, Italy
| | - Paul B. Calio
- Department
of Chemistry, Pritzker School of Molecular Engineering, James Franck
Institute, Chicago Center for Theoretical Chemistry, The University of Chicago, Chicago, Illinois 60637, United States
| | - Rebecca K. Carlson
- Department
of Chemistry, Chemical Theory Center, and Minnesota Supercomputing
Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, United
States
| | - Rafael Carvalho Couto
- Division
of Theoretical Chemistry and Biology, School of Engineering Sciences
in Chemistry, Biotechnology and Health, KTH Royal Institute of Technology, SE-106 91 Stockholm, Sweden
| | - Luis Cerdán
- Instituto
de Ciencia Molecular, Universitat de València, Catedrático José Beltrán
Martínez n. 2, 46980 Paterna, Spain
- Instituto
de Óptica (IO−CSIC), Consejo
Superior de Investigaciones Científicas, 28006, Madrid, Spain
| | - Liviu F. Chibotaru
- Department
of Chemistry, KU Leuven, Celestijnenlaan 200F, 3001 Leuven, Belgium
| | - Nicholas F. Chilton
- The Department
of Chemistry, The University of Manchester, M13 9PL, Manchester, U.K.
| | | | - Irene Conti
- Department
of Industrial Chemistry “Toso Montanari”, University of Bologna, 40136 Bologna, Italy
| | - Sonia Coriani
- Department
of Chemistry, Technical University of Denmark, Kemitorvet Bldg 207, 2800 Kongens Lyngby, Denmark
| | - Juliana Cuéllar-Zuquin
- Instituto
de Ciencia Molecular, Universitat de València, Catedrático José Beltrán
Martínez n. 2, 46980 Paterna, Spain
| | - Razan E. Daoud
- Dipartimento
di Biotecnologie, Chimica e Farmacia, Università
di Siena, Via A. Moro 2, 53100 Siena, Italy
| | - Nike Dattani
- HPQC Labs, Waterloo, N2T 2K9 Ontario Canada
- HPQC College, Waterloo, N2T 2K9 Ontario Canada
| | - Piero Decleva
- Istituto
Officina dei Materiali IOM-CNR and Dipartimento di Scienze Chimiche
e Farmaceutiche, Università degli
Studi di Trieste, I-34121 Trieste, Italy
| | - Coen de Graaf
- Department
of Physical and Inorganic Chemistry, Universitat
Rovira i Virgili, Tarragona 43007, Spain
- ICREA, Pg. Lluís
Companys 23, 08010 Barcelona, Spain
| | - Mickaël
G. Delcey
- Division
of Theoretical Chemistry and Biology, School of Engineering Sciences
in Chemistry, Biotechnology and Health, KTH Royal Institute of Technology, SE-106 91 Stockholm, Sweden
| | - Luca De Vico
- Dipartimento
di Biotecnologie, Chimica e Farmacia, Università
di Siena, Via A. Moro 2, 53100 Siena, Italy
| | - Werner Dobrautz
- Chalmers
University of Technology, Department of Chemistry
and Chemical Engineering, 41296 Gothenburg, Sweden
| | - Sijia S. Dong
- Department
of Chemistry, Chemical Theory Center, and Minnesota Supercomputing
Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, United
States
- Department
of Chemistry and Chemical Biology, Department of Physics, and Department
of Chemical Engineering, Northeastern University, Boston, Massachusetts 02115, United States
| | - Rulin Feng
- Department
of Chemistry, University at Buffalo, State
University of New York, Buffalo, New York 14260-3000, United States
- Department
of Chemistry, Fudan University, Shanghai 200433, China
| | - Nicolas Ferré
- Institut
de Chimie Radicalaire (UMR-7273), Aix-Marseille
Univ, CNRS, ICR 13013 Marseille, France
| | | | - Laura Gagliardi
- Department
of Chemistry, Chemical Theory Center, and Minnesota Supercomputing
Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, United
States
- Department
of Chemistry, Pritzker School of Molecular Engineering, James Franck
Institute, Chicago Center for Theoretical Chemistry, The University of Chicago, Chicago, Illinois 60637, United States
| | - Marco Garavelli
- Department
of Industrial Chemistry “Toso Montanari”, University of Bologna, 40136 Bologna, Italy
| | - Leticia González
- Institute
of Theoretical Chemistry, Faculty of Chemistry, University of Vienna, Währinger Straße 17, A-1090 Vienna, Austria
| | - Yafu Guan
- State Key
Laboratory of Molecular Reaction Dynamics and Center for Theoretical
Computational Chemistry, Dalian Institute
of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, People’s Republic of China
| | - Meiyuan Guo
- SSRL, SLAC National Accelerator Laboratory, Menlo Park, California 94025, United States
| | - Matthew R. Hennefarth
- Department
of Chemistry, Pritzker School of Molecular Engineering, James Franck
Institute, Chicago Center for Theoretical Chemistry, The University of Chicago, Chicago, Illinois 60637, United States
| | - Matthew R. Hermes
- Department
of Chemistry, Chemical Theory Center, and Minnesota Supercomputing
Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, United
States
- Department
of Chemistry, Pritzker School of Molecular Engineering, James Franck
Institute, Chicago Center for Theoretical Chemistry, The University of Chicago, Chicago, Illinois 60637, United States
| | - Chad E. Hoyer
- Department
of Chemistry, Chemical Theory Center, and Minnesota Supercomputing
Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, United
States
- Department
of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Miquel Huix-Rotllant
- Institut
de Chimie Radicalaire (UMR-7273), Aix-Marseille
Univ, CNRS, ICR 13013 Marseille, France
| | - Vishal Kumar Jaiswal
- Department
of Industrial Chemistry “Toso Montanari”, University of Bologna, 40136 Bologna, Italy
| | - Andy Kaiser
- Institut
für Physik, Universität Rostock, Albert-Einstein-Str. 23-24, 18059 Rostock, Germany
| | - Danil S. Kaliakin
- Chemistry
Department, Bowling Green State University, Overmann Hall, Bowling Green, Ohio 43403, United States
| | - Marjan Khamesian
- Department
of Chemistry − BMC, Uppsala University, P.O. Box 576, SE-75123 Uppsala, Sweden
| | - Daniel S. King
- Department
of Chemistry, Pritzker School of Molecular Engineering, James Franck
Institute, Chicago Center for Theoretical Chemistry, The University of Chicago, Chicago, Illinois 60637, United States
| | - Vladislav Kochetov
- Institut
für Physik, Universität Rostock, Albert-Einstein-Str. 23-24, 18059 Rostock, Germany
| | - Marek Krośnicki
- Institute
of Theoretical Physics and Astrophysics, Faculty of Mathematics, Physics
and Informatics, University of Gdańsk, ul Wita Stwosza 57, 80-952, Gdańsk, Poland
| | | | - Ernst D. Larsson
- Division
of Theoretical Chemistry, Chemical Centre, Lund University, P.O. Box 124, SE-22100, Lund, Sweden
| | - Susi Lehtola
- Molecular
Sciences Software Institute, Blacksburg, Virginia 24061, United States
- Department
of Chemistry, University of Helsinki, P.O. Box 55, FI-00014 University of Helsinki, Finland
| | - Marie-Bernadette Lepetit
- Condensed
Matter Theory Group, Institut Néel, CNRS UPR 2940, 38042 Grenoble, France
- Theory
Group, Institut Laue Langevin, 38042 Grenoble, France
| | - Hans Lischka
- Department
of Chemistry and Biochemistry, Texas Tech
University, Lubbock, Texas 79409-1061, United States
| | - Pablo López Ríos
- Electronic
Structure Theory Department, Max Planck
Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany
| | - Marcus Lundberg
- Department
of Chemistry − Ångström Laboratory, Uppsala University, SE-75120 Uppsala, Sweden
| | - Dongxia Ma
- Electronic
Structure Theory Department, Max Planck
Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany
- Department
of Chemistry, Chemical Theory Center, and Minnesota Supercomputing
Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, United
States
| | - Sebastian Mai
- Institute
of Theoretical Chemistry, Faculty of Chemistry, University of Vienna, Währinger Straße 17, A-1090 Vienna, Austria
| | - Philipp Marquetand
- Institute
of Theoretical Chemistry, Faculty of Chemistry, University of Vienna, Währinger Straße 17, A-1090 Vienna, Austria
| | | | - Francesco Montorsi
- Department
of Industrial Chemistry “Toso Montanari”, University of Bologna, 40136 Bologna, Italy
| | - Maximilian Mörchen
- ETH Zurich, Laboratory for Physical Chemistry, Vladimir-Prelog-Weg 2, 8093 Zurich, Switzerland
| | - Artur Nenov
- Department
of Industrial Chemistry “Toso Montanari”, University of Bologna, 40136 Bologna, Italy
| | - Vu Ha Anh Nguyen
- Department
of Chemistry, National University of Singapore, 3 Science Drive 3, 117543 Singapore
| | - Yoshio Nishimoto
- Graduate
School of Science, Kyoto University, Kyoto 606-8502, Japan
| | - Meagan S. Oakley
- Department
of Chemistry, Chemical Theory Center, and Minnesota Supercomputing
Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, United
States
| | - Massimo Olivucci
- Chemistry
Department, Bowling Green State University, Overmann Hall, Bowling Green, Ohio 43403, United States
- Dipartimento
di Biotecnologie, Chimica e Farmacia, Università
di Siena, Via A. Moro 2, 53100 Siena, Italy
| | - Markus Oppel
- Institute
of Theoretical Chemistry, Faculty of Chemistry, University of Vienna, Währinger Straße 17, A-1090 Vienna, Austria
| | - Daniele Padula
- Dipartimento
di Biotecnologie, Chimica e Farmacia, Università
di Siena, Via A. Moro 2, 53100 Siena, Italy
| | - Riddhish Pandharkar
- Department
of Chemistry, Chemical Theory Center, and Minnesota Supercomputing
Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, United
States
- Department
of Chemistry, Pritzker School of Molecular Engineering, James Franck
Institute, Chicago Center for Theoretical Chemistry, The University of Chicago, Chicago, Illinois 60637, United States
| | - Quan Manh Phung
- Department
of Chemistry, Graduate School of Science, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, Aichi 464-8602, Japan
- Institute
of Transformative Bio-Molecules (WPI-ITbM), Nagoya University, Furo-cho, Chikusa-ku, Nagoya, Aichi 464-8601, Japan
| | - Felix Plasser
- Department
of Chemistry, Loughborough University, Loughborough, LE11 3TU, U.K.
| | - Gerardo Raggi
- Department
of Chemistry − BMC, Uppsala University, P.O. Box 576, SE-75123 Uppsala, Sweden
- Quantum
Materials and Software LTD, 128 City Road, London, EC1V 2NX, United Kingdom
| | - Elisa Rebolini
- Scientific
Computing Group, Institut Laue Langevin, 38042 Grenoble, France
| | - Markus Reiher
- ETH Zurich, Laboratory for Physical Chemistry, Vladimir-Prelog-Weg 2, 8093 Zurich, Switzerland
| | - Ivan Rivalta
- Department
of Industrial Chemistry “Toso Montanari”, University of Bologna, 40136 Bologna, Italy
| | - Daniel Roca-Sanjuán
- Instituto
de Ciencia Molecular, Universitat de València, Catedrático José Beltrán
Martínez n. 2, 46980 Paterna, Spain
| | - Thies Romig
- Institut
für Physik, Universität Rostock, Albert-Einstein-Str. 23-24, 18059 Rostock, Germany
| | - Arta Anushirwan Safari
- Electronic
Structure Theory Department, Max Planck
Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany
| | - Aitor Sánchez-Mansilla
- Department
of Physical and Inorganic Chemistry, Universitat
Rovira i Virgili, Tarragona 43007, Spain
| | - Andrew M. Sand
- Department
of Chemistry, Chemical Theory Center, and Minnesota Supercomputing
Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, United
States
- Department
of Chemistry and Biochemistry, Butler University, Indianapolis, Indiana 46208, United States
| | - Igor Schapiro
- Institute
of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
| | - Thais R. Scott
- Department
of Chemistry, Chemical Theory Center, and Minnesota Supercomputing
Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, United
States
- Department
of Chemistry, Pritzker School of Molecular Engineering, James Franck
Institute, Chicago Center for Theoretical Chemistry, The University of Chicago, Chicago, Illinois 60637, United States
- Department
of Chemistry, University of California, Irvine, California 92697, United States
| | - Javier Segarra-Martí
- Instituto
de Ciencia Molecular, Universitat de València, Catedrático José Beltrán
Martínez n. 2, 46980 Paterna, Spain
| | - Francesco Segatta
- Department
of Industrial Chemistry “Toso Montanari”, University of Bologna, 40136 Bologna, Italy
| | - Dumitru-Claudiu Sergentu
- Department
of Chemistry, University at Buffalo, State
University of New York, Buffalo, New York 14260-3000, United States
- Laboratory
RA-03, RECENT AIR, A. I. Cuza University of Iaşi, RA-03 Laboratory (RECENT AIR), Iaşi 700506, Romania
| | - Prachi Sharma
- Department
of Chemistry, Chemical Theory Center, and Minnesota Supercomputing
Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, United
States
| | - Ron Shepard
- Chemical
Sciences and Engineering Division, Argonne
National Laboratory, Lemont, Illinois 60439, USA
| | - Yinan Shu
- Department
of Chemistry, Chemical Theory Center, and Minnesota Supercomputing
Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, United
States
| | - Jakob K. Staab
- The Department
of Chemistry, The University of Manchester, M13 9PL, Manchester, U.K.
| | - Tjerk P. Straatsma
- National
Center for Computational Sciences, Oak Ridge
National Laboratory, Oak Ridge, Tennessee 37831-6373, United States
- Department
of Chemistry and Biochemistry, University
of Alabama, Tuscaloosa, Alabama 35487-0336, United States
| | | | - Bruno Nunes Cabral Tenorio
- Department
of Chemistry, Technical University of Denmark, Kemitorvet Bldg 207, 2800 Kongens Lyngby, Denmark
| | - Donald G. Truhlar
- Department
of Chemistry, Chemical Theory Center, and Minnesota Supercomputing
Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, United
States
| | - Liviu Ungur
- Department
of Chemistry, National University of Singapore, 3 Science Drive 3, 117543 Singapore
| | - Morgane Vacher
- Nantes
Université, CNRS, CEISAM, UMR 6230, F-44000 Nantes, France
| | - Valera Veryazov
- Division
of Theoretical Chemistry, Chemical Centre, Lund University, P.O. Box 124, SE-22100, Lund, Sweden
| | - Torben Arne Voß
- Institut
für Physik, Universität Rostock, Albert-Einstein-Str. 23-24, 18059 Rostock, Germany
| | - Oskar Weser
- Electronic
Structure Theory Department, Max Planck
Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany
| | - Dihua Wu
- Department
of Chemistry, Chemical Theory Center, and Minnesota Supercomputing
Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, United
States
| | - Xuchun Yang
- Chemistry
Department, Bowling Green State University, Overmann Hall, Bowling Green, Ohio 43403, United States
| | - David Yarkony
- Department
of Chemistry, Johns Hopkins University, Baltimore, Maryland 21218, United States
| | - Chen Zhou
- Department
of Chemistry, Chemical Theory Center, and Minnesota Supercomputing
Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, United
States
| | - J. Patrick Zobel
- Institute
of Theoretical Chemistry, Faculty of Chemistry, University of Vienna, Währinger Straße 17, A-1090 Vienna, Austria
| | - Roland Lindh
- Department
of Chemistry − BMC, Uppsala University, P.O. Box 576, SE-75123 Uppsala, Sweden
- Uppsala
Center for Computational Chemistry (UC3), Uppsala University, PO Box 576, SE-751 23 Uppsala. Sweden
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5
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Izsák R, Ivanov AV, Blunt NS, Holzmann N, Neese F. Measuring Electron Correlation: The Impact of Symmetry and Orbital Transformations. J Chem Theory Comput 2023; 19:2703-2720. [PMID: 37022051 PMCID: PMC10210250 DOI: 10.1021/acs.jctc.3c00122] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/30/2023] [Indexed: 04/07/2023]
Abstract
In this perspective, the various measures of electron correlation used in wave function theory, density functional theory and quantum information theory are briefly reviewed. We then focus on a more traditional metric based on dominant weights in the full configuration solution and discuss its behavior with respect to the choice of the N-electron and the one-electron basis. The impact of symmetry is discussed, and we emphasize that the distinction among determinants, configuration state functions and configurations as reference functions is useful because the latter incorporate spin-coupling into the reference and should thus reduce the complexity of the wave function expansion. The corresponding notions of single determinant, single spin-coupling and single configuration wave functions are discussed and the effect of orbital rotations on the multireference character is reviewed by analyzing a simple model system. In molecular systems, the extent of correlation effects should be limited by finite system size and in most cases the appropriate choices of one-electron and N-electron bases should be able to incorporate these into a low-complexity reference function, often a single configurational one.
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Affiliation(s)
- Róbert Izsák
- Riverlane, St Andrews House, 59 St Andrews
Street, Cambridge CB2 3BZ, United Kingdom
| | - Aleksei V. Ivanov
- Riverlane, St Andrews House, 59 St Andrews
Street, Cambridge CB2 3BZ, United Kingdom
| | - Nick S. Blunt
- Riverlane, St Andrews House, 59 St Andrews
Street, Cambridge CB2 3BZ, United Kingdom
| | - Nicole Holzmann
- Riverlane, St Andrews House, 59 St Andrews
Street, Cambridge CB2 3BZ, United Kingdom
| | - Frank Neese
- Max-Planck
Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, D-45470 Mülheim an der Ruhr, Germany
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6
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Han R, Luber S, Li Manni G. Magnetic Interactions in a [Co(II) 3Er(III)(OR) 4] Model Cubane through Forefront Multiconfigurational Methods. J Chem Theory Comput 2023; 19:2811-2826. [PMID: 37126736 DOI: 10.1021/acs.jctc.2c01318] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/03/2023]
Abstract
Strong electron correlation effects are one of the major challenges in modern quantum chemistry. Polynuclear transition metal clusters are peculiar examples of systems featuring such forms of electron correlation. Multireference strategies, often based on but not limited to the concept of complete active space, are adopted to accurately account for strong electron correlation and to resolve their complex electronic structures. However, transition metal clusters already containing four magnetic centers with multiple unpaired electrons make conventional active space based strategies prohibitively expensive, due to their unfavorable scaling with the size of the active space. In this work, forefront techniques, such as density matrix renormalization group (DMRG), full configuration interaction quantum Monte Carlo (FCIQMC), and multiconfiguration pair-density functional theory (MCPDFT), are employed to overcome the computational limitation of conventional multireference approaches and to accurately investigate the magnetic interactions taking place in a [Co(II)3Er(III)(OR)4] (chemical formula [Co(II)3Er(III)(hmp)4(μ2-OAc)2(OH)3(H2O)], hmp = 2-(hydroxymethyl)-pyridine) model cubane water oxidation catalyst. Complete active spaces with up to 56 electrons in 56 orbitals have been constructed for the seven energetically lowest different spin states. Relative energies, local spin, and spin-spin correlation values are reported and provide crucial insights on the spin interactions for this model system, pivotal in the rationalization of the catalytic activity of this system in the water-splitting reaction. A ferromagnetic ground state is found with a very small, ∼50 cm-1, highest-to-lowest spin gap. Moreover, for the energetically lowest states, S = 3-6, the three Co(II) sites exhibit parallel aligned spins, and for the lower states, S = 0-2, two Co(II) sites retain strong parallel spin alignment.
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Affiliation(s)
- Ruocheng Han
- Department of Chemistry A, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland
| | - Sandra Luber
- Department of Chemistry A, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland
| | - Giovanni Li Manni
- Max Planck Institute for Solid State Research, Heisenbergstrasse 1, 70569 Stuttgart, Germany
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7
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Kulahlioglu AH, Dreuw A. The Multistate Quantum Monte Carlo Algebraic Diagrammatic Construction Method. J Phys Chem A 2023; 127:2161-2175. [PMID: 36847774 DOI: 10.1021/acs.jpca.2c08391] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/01/2023]
Abstract
A multistate formulation of the recently developed quantum Monte Carlo (QMC) algebraic diagrammatic construction (ADC) method, QMCADC, is presented. QMCADC solves the Hermitian eigenvalue problem of the second-order ADC scheme for the polarization propagator stochastically by combining ADC schemes with projector quantum Monte Carlo (PQMC). It allows for massively parallel distributed computing and exploits the sparsity of the effective ADC matrix, thereby relaxing memory and processing requirements of ADC methods significantly. Here, the theory and implementation of the multistate variant of QMCADC are described, and our first proof-of-principle calculations for various molecular systems are shown. Indeed, multistate QMCADC enables sampling of an arbitrary number of low-lying excited states and can reproduce their vertical excitation energies with a marginal controllable error. The performance of multistate QMCADC is examined in terms of state-wise and overall accuracy as well as with respect to the balance in the treatments of excited states relatively to each other. The results are very promising as they show bias and imbalances among excited states to diminish as the number of sampling points increases. Furthermore, the impact of the quality of trial wave functions on the vertical excitation energies is investigated. A black-box approach for the generation of high quality trial wave functions internally is given.
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Affiliation(s)
- Adem Halil Kulahlioglu
- Interdisciplinary Center for Scientific Computing, Ruprecht-Karls University, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
| | - Andreas Dreuw
- Interdisciplinary Center for Scientific Computing, Ruprecht-Karls University, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
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8
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Li Manni G, Kats D, Liebermann N. Resolution of Electronic States in Heisenberg Cluster Models within the Unitary Group Approach. J Chem Theory Comput 2023; 19:1218-1230. [PMID: 36735906 PMCID: PMC9979614 DOI: 10.1021/acs.jctc.2c01132] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023]
Abstract
In this work ground and excited electronic states of Heisenberg cluster models, in the form of configuration interaction many-body wave functions, are characterized within the spin-adapted Graphical Unitary Group Approach framework, and relying on a novel combined unitary and symmetric group approach. Finite-size cluster models of well-defined point-group symmetry and of general local-spin Slocal>12 are presented, including J1-J2 triangular and tetrahedral clusters, which are often used to describe magnetic interactions in biological and biomimetic polynuclear transition metal clusters with unique catalytic activity, such as nitrogen fixation and photosynthesis. We show that a unique block-diagonal structure of the underlying Hamiltonian matrix in the spin-adapted basis emerges when an optimal lattice site ordering is chosen that reflects the internal symmetries of the model investigated. The block-diagonal structure is bound to the commutation relations between cumulative spin operators and the Hamiltonian operator, that in turn depend on the geometry of the cluster investigated. The many-body basis transformation, in the form of the orbital/site reordering, exposes such commutation relations. These commutation relations represent a rigorous and formal demonstration of the block-diagonal structure in Hamiltonian matrices and the compression of the corresponding spin-adapted many-body wave functions. As a direct consequence of the block-diagonal structure of the Hamiltonian matrix, it is possible to selectively optimize electronic excited states without the overhead of calculating the lower-energy states by simply relying on the initial ansatz for the targeted wave function. Additionally, more compact many-body wave functions are obtained. In extreme cases, electronic states are precisely described by a single configuration state function, despite the curse of dimensionality of the corresponding Hilbert space. These findings are crucial in the electronic structure theory framework, for they offer a conceptual route toward wave functions of reduced multireference character, that can be optimized more easily by approximated eigensolvers and are of more facile physical interpretation. They open the way to study larger ab initio and model Hamiltonians of increasingly larger number of correlated electrons, while keeping the computational costs at their lowest. In particular, these elements will expand the potential of electronic structure methods in understanding magnetic interactions in exchange-coupled polynuclear transition metal clusters.
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9
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Aikens CM, Jarrold CC. Virtual Issue on Experiment-Theory Synergies in the Study of Metal and Metal-Containing Clusters. J Phys Chem A 2023; 127:3-5. [PMID: 36632723 DOI: 10.1021/acs.jpca.2c08524] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/13/2023]
Affiliation(s)
- Christine M Aikens
- Department of Chemistry, Kansas State University, 213 CBC Building, 1212 Mid-Campus Dr. North, Manhattan, Kansas 66506, United States
| | - Caroline Chick Jarrold
- Department of Chemistry, Indiana University, 800 East Kirkwood Avenue, Bloomington, Indiana 47405, United States
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10
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Zhang X, Wang Z, Li Z, Shaik S, Wang B. [4Fe–4S]-Mediated Proton-Coupled Electron Transfer Enables the Efficient Degradation of Chloroalkenes by Reductive Dehalogenases. ACS Catal 2023. [DOI: 10.1021/acscatal.2c06306] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023]
Affiliation(s)
- Xuan Zhang
- State Key Laboratory Physical Chemistry of Solid Surfaces and Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, P. R. China
| | - Zikuan Wang
- Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, Mülheim an der Ruhr 45470, Germany
| | - Zhen Li
- State Key Laboratory Physical Chemistry of Solid Surfaces and Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, P. R. China
| | - Sason Shaik
- Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
| | - Binju Wang
- State Key Laboratory Physical Chemistry of Solid Surfaces and Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, P. R. China
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11
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Otten M, Hermes MR, Pandharkar R, Alexeev Y, Gray SK, Gagliardi L. Localized Quantum Chemistry on Quantum Computers. J Chem Theory Comput 2022; 18:7205-7217. [PMID: 36346785 DOI: 10.1021/acs.jctc.2c00388] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
Quantum chemistry calculations of large, strongly correlated systems are typically limited by the computation cost that scales exponentially with the size of the system. Quantum algorithms, designed specifically for quantum computers, can alleviate this, but the resources required are still too large for today's quantum devices. Here, we present a quantum algorithm that combines a localization of multireference wave functions of chemical systems with quantum phase estimation (QPE) and variational unitary coupled cluster singles and doubles (UCCSD) to compute their ground-state energy. Our algorithm, termed "local active space unitary coupled cluster" (LAS-UCC), scales linearly with the system size for certain geometries, providing a polynomial reduction in the total number of gates compared with QPE, while providing accuracy above that of the variational quantum eigensolver using the UCCSD ansatz and also above that of the classical local active space self-consistent field. The accuracy of LAS-UCC is demonstrated by dissociating (H2)2 into two H2 molecules and by breaking the two double bonds in trans-butadiene, and resource estimates are provided for linear chains of up to 20 H2 molecules.
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Affiliation(s)
- Matthew Otten
- HRL Laboratories, LLC, 3011 Malibu Canyon Road, Malibu, California90265, United States
| | - Matthew R Hermes
- Department of Chemistry, Pritzker School of Molecular Engineering, James Franck Institute, Chicago Center for Theoretical Chemistry, University of Chicago, Chicago, Illinois60637, United States
| | - Riddhish Pandharkar
- Department of Chemistry, Pritzker School of Molecular Engineering, James Franck Institute, Chicago Center for Theoretical Chemistry, University of Chicago, Chicago, Illinois60637, United States
| | - Yuri Alexeev
- Computational Science Division, Argonne National Laboratory, Lemont, Illinois60439, United States
| | - Stephen K Gray
- Center for Nanoscale Materials, Argonne National Laboratory, Lemont, Illinois60439, United States
| | - Laura Gagliardi
- Department of Chemistry, Pritzker School of Molecular Engineering, James Franck Institute, Chicago Center for Theoretical Chemistry, University of Chicago, Chicago, Illinois60637, United States.,Argonne National Laboratory, Lemont, Illinois60439, United States
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12
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Pandharkar R, Hermes MR, Cramer CJ, Gagliardi L. Localized Active Space-State Interaction: a Multireference Method for Chemical Insight. J Chem Theory Comput 2022; 18:6557-6566. [PMID: 36257065 DOI: 10.1021/acs.jctc.2c00536] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Multireference electronic structure methods, like the complete active space (CAS) self-consistent field model, have long been used to characterize chemically interesting processes. Important work has been done in recent years to develop modifications having a lower computational cost than CAS, but typically these methods offer no more chemical insight than that from the CAS solution being approximated. In this paper, we present the localized active space-state interaction (LASSI) method that can be used not only to lower the intrinsic cost of the multireference calculation but also to improve interpretability. The localized active space (LAS) approach utilizes the local nature of the electron-electron correlation to express a composite wave function as an antisymmetrized product of unentangled wave functions in local active subspaces. LASSI then uses these LAS states as a basis from which to express complete molecular wave functions. This not only makes the molecular wave function more compact but also permits flexibility in choosing those states to be included in the basis. Such selective inclusion of states translates to the selective inclusion of specific types of interactions, thereby allowing a quantitative analysis of these interactions. We demonstrate the use of LASSI to study charge migration and spin-flip excitations in multireference organic molecules. We also compute the J coupling parameter for a bimetallic compound using various LAS bases to construct the Hamiltonian to provide insights into the coupling mechanism.
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Affiliation(s)
- Riddhish Pandharkar
- Department of Chemistry, Pritzker School of Molecular Engineering, James Franck Institute, Chicago Center for Theoretical Chemistry, The University of Chicago, 5735 S Ellis Avenue, Chicago, Illinois60637, United States.,Argonne National Laboratory, Lemont, Illinois60439, USA
| | - Matthew R Hermes
- Department of Chemistry, Pritzker School of Molecular Engineering, James Franck Institute, Chicago Center for Theoretical Chemistry, The University of Chicago, 5735 S Ellis Avenue, Chicago, Illinois60637, United States
| | - Christopher J Cramer
- Underwriters Laboratories Inc., 333 Pfingsten Road., Northbrook, Illinois60062, United States
| | - Laura Gagliardi
- Department of Chemistry, Pritzker School of Molecular Engineering, James Franck Institute, Chicago Center for Theoretical Chemistry, The University of Chicago, 5735 S Ellis Avenue, Chicago, Illinois60637, United States.,Argonne National Laboratory, Lemont, Illinois60439, USA
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13
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Weser O, Liebermann N, Kats D, Alavi A, Li Manni G. Spin Purification in Full-CI Quantum Monte Carlo via a First-Order Penalty Approach. J Phys Chem A 2022; 126:2050-2060. [PMID: 35298155 PMCID: PMC8978180 DOI: 10.1021/acs.jpca.2c01338] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/05/2022]
Abstract
![]()
In this article,
we demonstrate that a first-order spin penalty
scheme can be efficiently applied to the Slater determinant based
Full-CI Quantum Monte Carlo (FCIQMC) algorithm, as a practical route
toward spin purification. Two crucial applications are presented to
demonstrate the validity and robustness of this scheme: the 1Δg ← 3Σg vertical excitation in O2 and
key spin gaps in a [Mn3(IV)O4] cluster.
In the absence of a robust spin adaptation/purification technique,
both applications would be unattainable by Slater determinant based
ground state methods, with any starting wave function collapsing into
the higher-spin ground state during the optimization. This strategy
can be coupled to other algorithms that use the Slater determinant
based FCIQMC algorithm as configuration interaction eigensolver, including
the Stochastic Generalized Active Space, the similarity-transformed
FCIQMC, the tailored-CC, and second-order perturbation theory approaches.
Moreover, in contrast to the GUGA-FCIQMC technique, this strategy
features both spin projection and total spin adaptation, making it
appealing when solving anisotropic Hamiltonians. It also provides
spin-resolved reduced density matrices, important for the investigation
of spin-dependent properties in polynuclear transition metal clusters,
such as the hyperfine-coupling constants.
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Affiliation(s)
- Oskar Weser
- Max-Planck-Institute for Solid State Research, 70569 Stuttgart, Germany
| | - Niklas Liebermann
- Max-Planck-Institute for Solid State Research, 70569 Stuttgart, Germany
| | - Daniel Kats
- Max-Planck-Institute for Solid State Research, 70569 Stuttgart, Germany
| | - Ali Alavi
- Max-Planck-Institute for Solid State Research, 70569 Stuttgart, Germany.,Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, U.K
| | - Giovanni Li Manni
- Max-Planck-Institute for Solid State Research, 70569 Stuttgart, Germany
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14
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Benediktsson B, Bjornsson R. Analysis of the Geometric and Electronic Structure of Spin-Coupled Iron-Sulfur Dimers with Broken-Symmetry DFT: Implications for FeMoco. J Chem Theory Comput 2022; 18:1437-1457. [PMID: 35167749 PMCID: PMC8908755 DOI: 10.1021/acs.jctc.1c00753] [Citation(s) in RCA: 11] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/02/2023]
Abstract
![]()
The open-shell electronic
structure of iron–sulfur clusters
presents considerable challenges to quantum chemistry, with the complex
iron–molybdenum cofactor (FeMoco) of nitrogenase representing
perhaps the ultimate challenge for either wavefunction or density
functional theory. While broken-symmetry density functional theory
has seen some success in describing the electronic structure of such
cofactors, there is a large exchange–correlation functional
dependence in calculations that is not fully understood. In this work,
we present a geometric benchmarking test set, FeMoD11, of synthetic
spin-coupled Fe–Fe and Mo–Fe dimers, with relevance
to the molecular and electronic structure of the Mo-nitrogenase FeMo
cofactor. The reference data consists of high-resolution crystal structures
of metal dimer compounds in different oxidation states. Multiple density
functionals are tested on their ability to reproduce the local geometry,
specifically the Fe–Fe/Mo–Fe distance, for both antiferromagnetically
coupled and ferromagnetically coupled dimers via the broken-symmetry
approach. The metal–metal distance is revealed not only to
be highly sensitive to the amount of exact exchange in the functional
but also to the specific exchange and correlation functionals. For
the antiferromagnetically coupled dimers, the calculated metal–metal
distance correlates well with the covalency of the bridging metal–ligand
bonds, as revealed via the corresponding orbital analysis, Hirshfeld
S/Fe charges, and Fe–S Mayer bond order. Superexchange via
bridging ligands is expected to be the dominant interaction in these
dimers, and our results suggest that functionals that predict accurate
Fe–Fe and Mo–Fe distances describe the overall metal–ligand
covalency more accurately and in turn the superexchange of these systems.
The best performing density functionals of the 16 tested for the FeMoD11
test set are revealed to be either the nonhybrid functionals r2SCAN and B97-D3 or hybrid functionals with 10–15% exact
exchange: TPSSh and B3LYP*. These same four functionals are furthermore
found to reproduce the high-resolution X-ray structure of FeMoco well
according to quantum mechanics/molecular mechanics (QM/MM) calculations.
Almost all nonhybrid functionals systematically underestimate Fe–Fe
and Mo–Fe distances (with r2SCAN and B97-D3 being
the sole exceptions), while hybrid functionals with >15% exact
exchange
(including range-separated hybrid functionals) overestimate them.
The results overall suggest r2SCAN, B97-D3, TPSSh, and
B3LYP* as accurate density functionals for describing the electronic
structure of iron–sulfur clusters in general, including the
complex FeMoco cluster of nitrogenase.
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Affiliation(s)
- Bardi Benediktsson
- Science Institute, University of Iceland, Dunhagi 3, 107 Reykjavik, Iceland
| | - Ragnar Bjornsson
- Science Institute, University of Iceland, Dunhagi 3, 107 Reykjavik, Iceland.,Max-Planck Institute for Chemical Energy Conversion, Stiftstrasse 34-36, 45470 Mülheim an der Ruhr, Germany
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15
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Affiliation(s)
- Milica Feldt
- Leibniz Institute for Catalysis: Leibniz-Institut fur Katalyse eV Theory & Catalysis Albert-Einstein-Str 29A 18059 Rostock GERMANY
| | - Quan Manh Phung
- Nagoya University: Nagoya Daigaku Department of Chemistry JAPAN
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16
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Kulahlioglu AH, Rehn D, Dreuw A. Quantum Monte Carlo formulation of the second order algebraic diagrammatic construction: Toward a massively parallel correlated excited state method. J Chem Phys 2022; 156:044105. [DOI: 10.1063/5.0071091] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Adem Halil Kulahlioglu
- Interdisciplinary Center for Scientific Computing, Ruprecht-Karls University, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
| | - Dirk Rehn
- Interdisciplinary Center for Scientific Computing, Ruprecht-Karls University, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
| | - Andreas Dreuw
- Interdisciplinary Center for Scientific Computing, Ruprecht-Karls University, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
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17
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Mejuto-Zaera C, Tzeli D, Williams-Young D, Tubman NM, Matoušek M, Brabec J, Veis L, Xantheas SS, de Jong WA. The Effect of Geometry, Spin, and Orbital Optimization in Achieving Accurate, Correlated Results for Iron-Sulfur Cubanes. J Chem Theory Comput 2022; 18:687-702. [PMID: 35034448 DOI: 10.1021/acs.jctc.1c00830] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
Abstract
Iron-sulfur clusters comprise an important functional motif in the catalytic centers of biological systems, capable of enabling important chemical transformations at ambient conditions. This remarkable capability derives from a notoriously complex electronic structure that is characterized by a high density of states that is sensitive to geometric changes. The spectral sensitivity to subtle geometric changes has received little attention from correlated, large active space calculations, owing partly to the exceptional computational complexity for treating these large and correlated systems accurately. To provide insight into this aspect, we report the first Complete Active Space Self Consistent Field (CASSCF) calculations for different geometries of the [Fe(II/III)4S4(SMe)4]-2 clusters using two complementary, correlated solvers: spin-pure Adaptive Sampling Configuration Interaction (ASCI) and Density Matrix Renormalization Group (DMRG). We find that the previously established picture of a double-exchange driven magnetic structure, with minute energy gaps (<1 mHa) between consecutive spin states, has a weak dependence on the underlying geometry. However, the spin gap between the singlet and the spin state 2S + 1 = 19, corresponding to a maximal number of Fe-d electrons being unpaired and of parallel spin, is strongly geometry dependent, changing by a factor of 3 upon slight deformations that are still within biologically relevant parameters. The CASSCF orbital optimization procedure, using active spaces as large as 86 electrons in 52 orbitals, was found to reduce this gap compared to typical mean-field orbital approaches. Our results show the need for performing large active space calculations to unveil the challenging electronic structure of these complex catalytic centers and should serve as accurate starting points for fully correlated treatments upon inclusion of dynamical correlation outside the active space.
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Affiliation(s)
- Carlos Mejuto-Zaera
- University of California, Berkeley, California 94720, United States.,Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Demeter Tzeli
- Laboratory of Physical Chemistry, Department of Chemistry, National and Kapodistrian University of Athens, Panepistimiopolis Zografou, Athens 15784, Greece.,Theoretical and Physical Chemistry Institute, National Hellenic Research Foundation, Vas. Constantinou 48, Athens 11635, Greece
| | - David Williams-Young
- Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Norm M Tubman
- Quantum Artificial Intelligence Lab. (QuAIL), Exploration Technology Directorate, NASA Ames Research Center, Moffett Field, California 94035, United States
| | - Mikuláš Matoušek
- J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.v.i., Dolejškova 3, 18223 Prague 8, Czech Republic
| | - Jiri Brabec
- J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.v.i., Dolejškova 3, 18223 Prague 8, Czech Republic
| | - Libor Veis
- J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.v.i., Dolejškova 3, 18223 Prague 8, Czech Republic
| | - Sotiris S Xantheas
- Advanced Computing, Mathematics and Data Division, Pacific Northwest National Laboratory, 902 Battelle Boulevard, P.O. Box 999, MS K1-83, Richland, Washington 99352, United States.,Department of Chemistry, University of Washington, Seattle, Washington 98185, United States
| | - Wibe A de Jong
- Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
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18
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Weser O, Guther K, Ghanem K, Li Manni G. Stochastic Generalized Active Space Self-Consistent Field: Theory and Application. J Chem Theory Comput 2021; 18:251-272. [PMID: 34898215 PMCID: PMC8757470 DOI: 10.1021/acs.jctc.1c00936] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
An algorithm to perform stochastic generalized active space calculations, Stochastic-GAS, is presented, that uses the Slater determinant based FCIQMC algorithm as configuration interaction eigensolver. Stochastic-GAS allows the construction and stochastic optimization of preselected truncated configuration interaction wave functions, either to reduce the computational costs of large active space wave function optimizations, or to probe the role of specific electron correlation pathways. As for the conventional GAS procedure, the preselection of the truncated wave function is based on the selection of multiple active subspaces while imposing restrictions on the interspace excitations. Both local and cumulative minimum and maximum occupation number constraints are supported by Stochastic-GAS. The occupation number constraints are efficiently encoded in precomputed probability distributions, using the precomputed heat bath algorithm, which removes nearly all runtime overhead of GAS. This strategy effectively allows the FCIQMC dynamics to a priori exclude electronic configurations that are not allowed by GAS restrictions. Stochastic-GAS reduced density matrices are stochastically sampled, allowing orbital relaxations via Stochastic-GASSCF, and direct evaluation of properties that can be extracted from density matrices, such as the spin expectation value. Three test case applications have been chosen to demonstrate the flexibility of Stochastic-GAS: (a) the Stochastic-GASSCF [5·(6, 6)] optimization of a stack of five benzene molecules, that shows the applicability of Stochastic-GAS toward fragment-based chemical systems; (b) an uncontracted stochastic MRCISD calculation that correlates 96 electrons and 159 molecular orbitals, and uses a large (32, 34) active space reference wave function for an Fe(II)-porphyrin model system, showing how GAS can be applied to systematically recover dynamic electron correlation, and how in the specific case of the Fe(II)-porphyrin dynamic correlation further differentially stabilizes the 3Eg over the 5A1g spin state; (c) the study of an Fe4S4 cluster's spin-ladder energetics via highly truncated stochastic-GAS [4·(5, 5)] wave functions, where we show how GAS can be applied to understand the competing spin-exchange and charge-transfer correlating mechanisms in stabilizing different spin-states.
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Affiliation(s)
- Oskar Weser
- Max-Planck-Institute for Solid State Research, Stuttgart, 70569, Germany
| | - Kai Guther
- Max-Planck-Institute for Solid State Research, Stuttgart, 70569, Germany.,RIKEN Center for Computational Science, 7-1-26 minatojima-minami, Chuo Kobe 650-0047, Japan
| | - Khaldoon Ghanem
- Max-Planck-Institute for Solid State Research, Stuttgart, 70569, Germany
| | - Giovanni Li Manni
- Max-Planck-Institute for Solid State Research, Stuttgart, 70569, Germany
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Beran P, Matoušek M, Hapka M, Pernal K, Veis L. Density Matrix Renormalization Group with Dynamical Correlation via Adiabatic Connection. J Chem Theory Comput 2021; 17:7575-7585. [PMID: 34762423 DOI: 10.1021/acs.jctc.1c00896] [Citation(s) in RCA: 21] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The quantum chemical version of the density matrix renormalization group (DMRG) method has established itself as one of the methods of choice for calculations of strongly correlated molecular systems. Despite its great ability to capture strong electronic correlation in large active spaces, it is not suitable for computations of dynamical electron correlation. In this work, we present a new approach to the electronic structure problem of strongly correlated molecules, in which DMRG is responsible for a proper description of the strong correlation, whereas dynamical correlation is computed via the recently developed adiabatic connection (AC) technique which requires only up to two-body active space reduced density matrices. We report the encouraging results of this approach on typical candidates for DMRG computations, namely, n-acenes (n = 2 → 7), Fe(II)-porphyrin, and the Fe3S4 cluster.
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Affiliation(s)
- Pavel Beran
- J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.v.i., Dolejškova 3, 18223 Prague 8, Czech Republic.,Faculty of Mathematics and Physics, Charles University, 121 16 Prague, Czech Republic
| | - Mikuláš Matoušek
- J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.v.i., Dolejškova 3, 18223 Prague 8, Czech Republic.,Faculty of Mathematics and Physics, Charles University, 121 16 Prague, Czech Republic
| | - Michał Hapka
- Institute of Physics, Lodz University of Technology, ul. Wolczanska 219, 90-924 Lodz, Poland.,Faculty of Chemistry, University of Warsaw, ul. L. Pasteura 1, 02-093 Warsaw, Poland
| | - Katarzyna Pernal
- Institute of Physics, Lodz University of Technology, ul. Wolczanska 219, 90-924 Lodz, Poland
| | - Libor Veis
- J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.v.i., Dolejškova 3, 18223 Prague 8, Czech Republic
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Li Manni G. Modeling magnetic interactions in high-valent trinuclear [Mn 3(IV)O 4] 4+ complexes through highly compressed multi-configurational wave functions. Phys Chem Chem Phys 2021; 23:19766-19780. [PMID: 34525156 DOI: 10.1039/d1cp03259c] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
In this work we apply a quantum chemical framework, recently designed in our laboratories, to rationalize the low-energy electronic spectrum and the magnetic properties of an homo-valent trinuclear [Mn3(IV)O4]4+ model of the oxygen-evolving center in photosystem II. The method is based on chemically motivated molecular orbital unitary transformations, and the optimization of spin-adapted many-body wave functions, both for ground- and excited-states, in the transformed MO basis. In this basis, the configuration interaction Hamiltonian matrix of exchange-coupled multi-center clusters is extremely sparse and characterized by a unique block diagonal structure. This property leads to highly compressed wave functions (oligo- or single-reference) and crucially enables state-specific optimizations. This work is the first showing that compression and selective targeting of ground- and excited-states wave functions is possible for systems with three magnetic centers that are not exactly half-filled, and that potentially exhibit frustrated spin interactions. The reduced multi-reference character of the wave function greatly simplifies the interpretation of the ground- and excited-state electronic structures, and provides a route for the direct rationalization of magnetic interactions in these compounds, often considered a challenge in polynuclear transition-metal chemistry. In this study, strong electron correlation effects have explicitly been described by conventional and stochastic multiconfigurational methodologies, while dynamic correlation effects have been accounted for by multiconfigurational second order perturbation theory, CASPT2. Ab initio results for the [Mn3(IV)O4]4+ system have been mapped to a three-site Heisenberg model with two magnetic coupling constants. The magnetic coupling constants and the temperature dependence of the effective magnetic moment predicted by the ab initio calculations are in good agreement with the available experimental data, and confirm the antiferromagnetic interaction among the three magnetic centers, while providing a simple and rigorous description of the noncollinearity of the local spins, that characterize most of the low-energy states for this system.
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Affiliation(s)
- Giovanni Li Manni
- Department of Electronic Structure Theory, Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany.
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Dobrautz W, Weser O, Bogdanov NA, Alavi A, Li Manni G. Spin-Pure Stochastic-CASSCF via GUGA-FCIQMC Applied to Iron-Sulfur Clusters. J Chem Theory Comput 2021; 17:5684-5703. [PMID: 34469685 PMCID: PMC8444347 DOI: 10.1021/acs.jctc.1c00589] [Citation(s) in RCA: 24] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2021] [Indexed: 11/28/2022]
Abstract
In this work, we demonstrate how to efficiently compute the one- and two-body reduced density matrices within the spin-adapted full configuration interaction quantum Monte Carlo (FCIQMC) method, which is based on the graphical unitary group approach (GUGA). This allows us to use GUGA-FCIQMC as a spin-pure configuration interaction (CI) eigensolver within the complete active space self-consistent field (CASSCF) procedure and hence to stochastically treat active spaces far larger than conventional CI solvers while variationally relaxing orbitals for specific spin-pure states. We apply the method to investigate the spin ladder in iron-sulfur dimer and tetramer model systems. We demonstrate the importance of the orbital relaxation by comparing the Heisenberg model magnetic coupling parameters from the CASSCF procedure to those from a CI-only (CASCI) procedure based on restricted open-shell Hartree-Fock orbitals. We show that the orbital relaxation differentially stabilizes the lower-spin states, thus enlarging the coupling parameters with respect to the values predicted by ignoring orbital relaxation effects. Moreover, we find that, while CASCI results are well fit by a simple bilinear Heisenberg Hamiltonian, the CASSCF eigenvalues exhibit deviations that necessitate the inclusion of biquadratic terms in the model Hamiltonian.
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Affiliation(s)
- Werner Dobrautz
- Max
Planck Institute for Solid State Research, Heisenbergstr. 1, 70569 Stuttgart, Germany
| | - Oskar Weser
- Max
Planck Institute for Solid State Research, Heisenbergstr. 1, 70569 Stuttgart, Germany
| | - Nikolay A. Bogdanov
- Max
Planck Institute for Solid State Research, Heisenbergstr. 1, 70569 Stuttgart, Germany
| | - Ali Alavi
- Max
Planck Institute for Solid State Research, Heisenbergstr. 1, 70569 Stuttgart, Germany
- Yusuf
Hamied Department of Chemistry, University
of Cambridge, Lensfield
Road, Cambridge CB2 1EW, United Kingdom
| | - Giovanni Li Manni
- Max
Planck Institute for Solid State Research, Heisenbergstr. 1, 70569 Stuttgart, Germany
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