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Nakai H, Kobayashi M, Yoshikawa T, Seino J, Ikabata Y, Nishimura Y. Divide-and-Conquer Linear-Scaling Quantum Chemical Computations. J Phys Chem A 2023; 127:589-618. [PMID: 36630608 DOI: 10.1021/acs.jpca.2c06965] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/13/2023]
Abstract
Fragmentation and embedding schemes are of great importance when applying quantum-chemical calculations to more complex and attractive targets. The divide-and-conquer (DC)-based quantum-chemical model is a fragmentation scheme that can be connected to embedding schemes. This feature article explains several DC-based schemes developed by the authors over the last two decades, which was inspired by the pioneering study of DC self-consistent field (SCF) method by Yang and Lee (J. Chem. Phys. 1995, 103, 5674-5678). First, the theoretical aspects of the DC-based SCF, electron correlation, excited-state, and nuclear orbital methods are described, followed by the two-component relativistic theory, quantum-mechanical molecular dynamics simulation, and the introduction of three programs, including DC-based schemes. Illustrative applications confirmed the accuracy and feasibility of the DC-based schemes.
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Affiliation(s)
- Hiromi Nakai
- Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku, Tokyo169-8555, Japan.,Waseda Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku, Tokyo169-8555, Japan
| | - Masato Kobayashi
- Department of Chemistry, Faculty of Science, Hokkaido University, Kita 10 Nishi 8, Kita-ku, Sapporo, Hokkaido060-0810, Japan.,Institute for Chemical Reaction Design and Discovery (WPI-ICReDD), Hokkaido University, Kita 21 Nishi 10, Kita-ku, Sapporo, Hokkaido001-0021, Japan
| | - Takeshi Yoshikawa
- Faculty of Pharmaceutical Sciences, Toho University, 2-2-1 Miyama, Funabashi, Chiba274-8510, Japan
| | - Junji Seino
- Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku, Tokyo169-8555, Japan.,Waseda Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku, Tokyo169-8555, Japan
| | - Yasuhiro Ikabata
- Information and Media Center, Toyohashi University of Technology, 1-1 Hibarigaoka, Tempaku-cho, Toyohashi, Aichi441-8580, Japan.,Department of Computer Science and Engineering, Toyohashi University of Technology, 1-1 Hibarigaoka, Tempaku-cho, Toyohashi, Aichi441-8580, Japan
| | - Yoshifumi Nishimura
- Waseda Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku, Tokyo169-8555, Japan
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Nakai H. Development of Linear-Scaling Relativistic Quantum Chemistry Covering the Periodic Table. BULLETIN OF THE CHEMICAL SOCIETY OF JAPAN 2021. [DOI: 10.1246/bcsj.20210091] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Affiliation(s)
- Hiromi Nakai
- Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
- Waseda Research Institute for Science and Engineering (WISE), Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
- Elements Strategy Initiative for Catalysts and Batteries (ESICB), Kyoto University, Katsura, Kyoto 615-8520, Japan
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3
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Barca GMJ, McKenzie SC, Bloomfield NJ, Gilbert ATB, Gill PMW. Q-MP2-OS: Møller-Plesset Correlation Energy by Quadrature. J Chem Theory Comput 2020; 16:1568-1577. [PMID: 31972086 DOI: 10.1021/acs.jctc.9b01142] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We present a quadrature-based algorithm for computing the opposite-spin component of the MP2 correlation energy which scales quadratically with basis set size and is well-suited to large-scale parallelization. The key ideas, which are rooted in the earlier work of Hirata and co-workers, are to abandon all two-electron integrals, recast the energy as a seven-dimensional integral, approximate that integral by quadrature, and employ a cutoff strategy to minimize the number of intermediate quantities. We discuss our implementation in detail and show that it parallelizes almost perfectly on 840 cores for cyclosporine (a molecule with roughly 200 atoms), exhibits [Formula: see text] scaling for a sequence of polyglycines, and is principally limited by the accuracy of its quadrature.
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Affiliation(s)
- Giuseppe M J Barca
- Research School of Computer Science, Australian National University, Canberra, Australian Capital Territory 2601, Australia
| | - Simon C McKenzie
- School of Chemistry, University of Sydney, Sydney, New South Wales 2006, Australia.,Research School of Chemistry, Australian National University, Canberra, Australian Capital Territory 2601, Australia
| | - Nathaniel J Bloomfield
- Research School of Chemistry, Australian National University, Canberra, Australian Capital Territory 2601, Australia
| | - Andrew T B Gilbert
- Research School of Chemistry, Australian National University, Canberra, Australian Capital Territory 2601, Australia
| | - Peter M W Gill
- School of Chemistry, University of Sydney, Sydney, New South Wales 2006, Australia
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Nishizawa H, Nishimura Y, Kobayashi M, Irle S, Nakai H. Three pillars for achieving quantum mechanical molecular dynamics simulations of huge systems: Divide-and-conquer, density-functional tight-binding, and massively parallel computation. J Comput Chem 2016; 37:1983-92. [DOI: 10.1002/jcc.24419] [Citation(s) in RCA: 74] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/09/2016] [Revised: 05/12/2016] [Accepted: 05/17/2016] [Indexed: 11/10/2022]
Affiliation(s)
- Hiroaki Nishizawa
- Department of Theoretical and Computational Molecular Science; Institute for Molecular Science; Okazaki 444-8585 Japan
| | - Yoshifumi Nishimura
- Department of Theoretical and Computational Molecular Science; Institute for Molecular Science; Okazaki 444-8585 Japan
- Research Institute for Science and Engineering; Waseda University; Tokyo 169-8555 Japan
| | - Masato Kobayashi
- Department of Chemistry, Faculty of Science; Hokkaido University; Sapporo 060-0810 Japan
- ESICB, Kyoto University; Kyoto 615-8520 Japan
- PRESTO, Japan Science and Technology Agency; Kawaguchi 332-0012 Japan
| | - Stephan Irle
- Department of Chemistry; Graduate School of Science, and Institute of Transformative Bio-Molecules (WPI-ITbM), Nagoya University; Nagoya 464-8602 Japan
| | - Hiromi Nakai
- Research Institute for Science and Engineering; Waseda University; Tokyo 169-8555 Japan
- ESICB, Kyoto University; Kyoto 615-8520 Japan
- Department of Chemistry and Biochemistry, School of Advanced Science and Engineering; Waseda University; Tokyo 169-8555 Japan
- CREST, Japan Science and Technology Agency; Kawaguchi 332-0012 Japan
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5
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6
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Nagase S. Theory and Calculations of Molecules Containing Heavier Main Group Elements and Fullerenes Encaging Transition Metals: Interplay with Experiment. BULLETIN OF THE CHEMICAL SOCIETY OF JAPAN 2014. [DOI: 10.1246/bcsj.20130266] [Citation(s) in RCA: 46] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Affiliation(s)
- Shigeru Nagase
- Fukui Institute for Fundamental Chemistry, Kyoto University
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7
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Fedorov DG, Sugita Y, Choi CH. Efficient Parallel Implementations of QM/MM-REMD (Quantum Mechanical/Molecular Mechanics-Replica-Exchange MD) and Umbrella Sampling: Isomerization of H2O2 in Aqueous Solution. J Phys Chem B 2013; 117:7996-8002. [DOI: 10.1021/jp4029529] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Dmitri G. Fedorov
- NRI, National Institute of Advanced Industrial Science and Technology (AIST), Central 2, Umezono 1-1-1, Tsukuba 305-8568, Japan
| | - Yuji Sugita
- Theoretical Molecular Science Laboratory, RIKEN, 2-1 Hirosawa, Wako, Saitama
351-0198, Japan
| | - Cheol Ho Choi
- Department
of Chemistry and Green-Nano
Materials Research Center, College of Natural Sciences, Kyungpook National University, Taegu 702-701, South
Korea
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Yoshikawa T, Kobayashi M, Fujii A, Nakai H. Novel Approach to Excited-State Calculations of Large Molecules Based on Divide-and-Conquer Method: Application to Photoactive Yellow Protein. J Phys Chem B 2013; 117:5565-73. [DOI: 10.1021/jp401819d] [Citation(s) in RCA: 33] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
| | - Masato Kobayashi
- Waseda Institute for Advanced Study, Waseda University, Tokyo 169-8050, Japan
| | | | - Hiromi Nakai
- CREST, Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi, Saitama
332-0012, Japan
- ESICB, Kyoto University, Kyotodaigaku-Katsura, Nishigyoku,
Kyoto 615-8520, Japan
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Kristensen K, Kjærgaard T, Høyvik IM, Ettenhuber P, Jørgensen P, Jansik B, Reine S, Jakowski J. The divide–expand–consolidate MP2 scheme goes massively parallel. Mol Phys 2013. [DOI: 10.1080/00268976.2013.783941] [Citation(s) in RCA: 30] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Affiliation(s)
- Kasper Kristensen
- a qLEAP – Center for Theoretical Chemistry, Department of Chemistry , Aarhus University , Langelandsgade 140, Aarhus C , 8000 , Denmark
| | - Thomas Kjærgaard
- a qLEAP – Center for Theoretical Chemistry, Department of Chemistry , Aarhus University , Langelandsgade 140, Aarhus C , 8000 , Denmark
| | - Ida-Marie Høyvik
- a qLEAP – Center for Theoretical Chemistry, Department of Chemistry , Aarhus University , Langelandsgade 140, Aarhus C , 8000 , Denmark
| | - Patrick Ettenhuber
- a qLEAP – Center for Theoretical Chemistry, Department of Chemistry , Aarhus University , Langelandsgade 140, Aarhus C , 8000 , Denmark
| | - Poul Jørgensen
- a qLEAP – Center for Theoretical Chemistry, Department of Chemistry , Aarhus University , Langelandsgade 140, Aarhus C , 8000 , Denmark
| | - Branislav Jansik
- b IT4Innovations , VSB – Technical University of Ostrava , 17. listopadu 15/2172, Ostrava , Czech Republic
| | - Simen Reine
- c Centre for Theoretical and Computational Chemistry, Department of Chemistry , Oslo University , Postbox 1033, Blindern, 0315, Oslo , Norway
| | - Jacek Jakowski
- d National Institute for Computational Sciences , JICS-ORNL , One Bethel Valley Road, Bldg. 5100 ms 6173, Oak Ridge , Tennessee , 37831 , USA
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Kobayashi M, Nakai H. An effective energy gradient expression for divide-and-conquer second-order Møller–Plesset perturbation theory. J Chem Phys 2013; 138:044102. [DOI: 10.1063/1.4776228] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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NAKAI H. Discovery of Chemical Principles:Symmetry Rules for Degenerate Excitations. JOURNAL OF COMPUTER CHEMISTRY-JAPAN 2012. [DOI: 10.2477/jccj.2012-0004] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022]
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Kobayashi M, Nakai H. How does it become possible to treat delocalized and/or open-shell systems in fragmentation-based linear-scaling electronic structure calculations? The case of the divide-and-conquer method. Phys Chem Chem Phys 2012; 14:7629-39. [DOI: 10.1039/c2cp40153c] [Citation(s) in RCA: 66] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
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Kristensen K, Høyvik IM, Jansik B, Jørgensen P, Kjærgaard T, Reine S, Jakowski J. MP2 energy and density for large molecular systems with internal error control using the Divide-Expand-Consolidate scheme. Phys Chem Chem Phys 2012; 14:15706-14. [DOI: 10.1039/c2cp41958k] [Citation(s) in RCA: 49] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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Yoshikawa T, Kobayashi M, Nakai H. Linear-scaling divide-and-conquer second-order Møller–Plesset perturbation calculation for open-shell systems: implementation and application. Theor Chem Acc 2011. [DOI: 10.1007/s00214-011-1008-7] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
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