1
|
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.
Collapse
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
| |
Collapse
|
2
|
Yoshikawa T, Takanashi T, Nakai H. Quantum Algorithm of the Divide-and-Conquer Unitary Coupled Cluster Method with a Variational Quantum Eigensolver. J Chem Theory Comput 2022; 18:5360-5373. [PMID: 35926142 DOI: 10.1021/acs.jctc.2c00602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The variational quantum eigensolver (VQE) with shallow or constant-depth quantum circuits is one of the most pursued approaches in the noisy intermediate-scale quantum (NISQ) devices with incoherent errors. In this study, the divide-and-conquer (DC) linear scaling technique, which divides the entire system into several fragments, is applied to the VQE algorithm based on the unitary coupled cluster (UCC) method, denoted as DC-qUCC/VQE, to reduce the number of required qubits. The unitarity of the UCC ansatz that enables the evaluation of the total energy as well as various molecular properties as expectation values can be easily implemented on quantum devices because the quantum gates are unitary operators themselves. Based on this feature, the present DC-qUCC/VQE algorithm is designed to conserve the total number of electrons in the entire system using the density matrix evaluated on a quantum computer. Numerical assessments clarified that the energy errors of the DC-qUCC/VQE calculations decrease by using the constraint of the total number of electrons. Furthermore, the DC-qUCC/VQE algorithm could reduce the number of quantum gates and shows the possibility of decreasing incoherent errors.
Collapse
Affiliation(s)
- Takeshi Yoshikawa
- Faculty of Pharmaceutical Sciences, Toho University, 2-2-1 Miyama, Funabashi, Chiba 274-8510, Japan.,Waseda Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
| | - Tomoya Takanashi
- Waseda Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
| | - Hiromi Nakai
- Waseda Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan.,Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, 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
| |
Collapse
|
3
|
Pedroza-Montero JN, Calaminici P, Köster AM. First-principle polarizabilities of nanosystems from auxiliary density perturbation theory with MINRES. Theor Chem Acc 2022. [DOI: 10.1007/s00214-021-02864-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
|
4
|
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
| |
Collapse
|
5
|
KOBAYASHI M, FUJIMORI T, TAKETSUGU T. Automatic Determination of Buffer Region in Divide-anc-Conquer Quantum Chemical Calculations. JOURNAL OF COMPUTER CHEMISTRY-JAPAN 2021. [DOI: 10.2477/jccj.2021-0025] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022]
Affiliation(s)
- Masato KOBAYASHI
- Department of Chemistry, Faculty of Science, Hokkaido University, Kita 10 Nishi 8, Kita-ku, Sapporo 060-0810, Japan
| | - Toshikazu FUJIMORI
- Graduate School of Chemical Sciences and Engineering, Hokkaido University, Kita 10 Nishi 8,Kita-ku, Sapporo 060-0810, Japan
| | - Tetsuya TAKETSUGU
- Department of Chemistry, Faculty of Science, Hokkaido University, Kita 10 Nishi 8, Kita-ku, Sapporo 060-0810, Japan
| |
Collapse
|
6
|
Truflandier LA, Dianzinga RM, Bowler DR. Notes on density matrix perturbation theory. J Chem Phys 2020; 153:164105. [PMID: 33138442 DOI: 10.1063/5.0022244] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Density matrix perturbation theory (DMPT) is known as a promising alternative to the Rayleigh-Schrödinger perturbation theory, in which the sum-over-states (SOS) is replaced by algorithms with perturbed density matrices as the input variables. In this article, we formulate and discuss three types of DMPT, with two of them based only on density matrices: the approach of Kussmann and Ochsenfeld [J. Chem. Phys. 127, 054103 (2007)] is reformulated via the Sylvester equation and the recursive DMPT of Niklasson and Challacombe [Phys. Rev. Lett. 92, 193001 (2004)] is extended to the hole-particle canonical purification (HPCP) from Truflandier et al. [J. Chem. Phys. 144, 091102 (2016)]. A comparison of the computational performances shows that the aforementioned methods outperform the standard SOS. The HPCP-DMPT demonstrates stable convergence profiles but at a higher computational cost when compared to the original recursive polynomial method.
Collapse
Affiliation(s)
- Lionel A Truflandier
- Institut des Sciences Moléculaires (ISM), Université Bordeaux, CNRS UMR 5255, 351 cours de la Libération, 33405 Talence Cedex, France
| | - Rivo M Dianzinga
- Institut des Sciences Moléculaires (ISM), Université Bordeaux, CNRS UMR 5255, 351 cours de la Libération, 33405 Talence Cedex, France
| | - David R Bowler
- London Centre for Nanotechnology, UCL, 17-19 Gordon St., London WC1H 0AH, United Kingdom and Department of Physics and Astronomy, UCL, Gower St., London WC1E 6BT, United Kingdom
| |
Collapse
|
7
|
Yoshikawa T, Komoto N, Nishimura Y, Nakai H. GPU-Accelerated Large-Scale Excited-State Simulation Based on Divide-and-Conquer Time-Dependent Density-Functional Tight-Binding. J Comput Chem 2019; 40:2778-2786. [PMID: 31441083 DOI: 10.1002/jcc.26053] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/18/2019] [Revised: 08/04/2019] [Accepted: 08/07/2019] [Indexed: 01/09/2023]
Abstract
The present study implemented the divide-and-conquer time-dependent density-functional tight-binding (DC-TDDFTB) code on a graphical processing unit (GPU). The DC method, which is a linear-scaling scheme, divides a total system into several fragments. By separately solving local equations in individual fragments, the DC method could reduce slow central processing unit (CPU)-GPU memory access, as well as computational cost, and avoid shortfalls of GPU memory. Numerical applications confirmed that the present code on GPU significantly accelerated the TDDFTB calculations, while maintaining accuracy. Furthermore, the DC-TDDFTB simulation of 2-acetylindan-1,3-dione displays excited-state intramolecular proton transfer and provides reasonable absorption and fluorescence energies with the corresponding experimental values. © 2019 Wiley Periodicals, Inc.
Collapse
Affiliation(s)
- Takeshi Yoshikawa
- Waseda Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo, 169-8555, Japan
| | - Nana Komoto
- Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo, 169-8555, Japan
| | - Yoshifumi Nishimura
- Waseda Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo, 169-8555, Japan
| | - Hiromi Nakai
- Waseda Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo, 169-8555, Japan.,Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, 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
| |
Collapse
|
8
|
Nakai H, Yoshikawa T. Development of an excited-state calculation method for large systems using dynamical polarizability: A divide-and-conquer approach at the time-dependent density functional level. J Chem Phys 2017; 146:124123. [DOI: 10.1063/1.4978952] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022] Open
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
- Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
- CREST, Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan
- Elements Strategy Initiative for Catalysts and Batteries (ESICB), Kyoto University, Katsura, Kyoto 615-8520, Japan
| | - Takeshi Yoshikawa
- Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
| |
Collapse
|
9
|
Nakai H, Yoshikawa T, Nonaka Y. Efficient pole-search algorithm for dynamic polarizability: Toward alternative excited-state calculation for large systems. J Comput Chem 2017; 38:7-14. [PMID: 27706818 DOI: 10.1002/jcc.24507] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/05/2016] [Revised: 09/17/2016] [Accepted: 09/19/2016] [Indexed: 11/10/2022]
Abstract
This study presents an efficient algorithm to search for the poles of dynamic polarizability to obtain excited states of large systems with nonlocal excitation nature. The present algorithm adopts a homogeneous search with a constant frequency interval and a bisection search to achieve high accuracy. Furthermore, the subtraction process of the information about the detected poles from the total dynamic polarizability is used to extract the undetected pole contributions. Numerical assessments confirmed the accuracy and efficiency of the present algorithm in obtaining the excitation energies and oscillator strengths of all dipole-allowed excited states. A combination of the present pole-search algorithm and divide-and-conquer-based dynamic polarizability calculations was found to be promising to treat nonlocal excitations of large systems. © 2016 Wiley Periodicals, Inc.
Collapse
Affiliation(s)
- Hiromi Nakai
- Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, Tokyo, 169-8555, Japan.,Research Institute for Science and Engineering, Waseda University, Tokyo, 169-8555, Japan.,CREST, Japan Science and Technology Agency, Saitama, 332-0012, Japan.,ESICB, Kyoto University, Kyoto, 615-8520, Japan
| | - Takeshi Yoshikawa
- Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, Tokyo, 169-8555, Japan
| | - Yutaro Nonaka
- Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, Tokyo, 169-8555, Japan
| |
Collapse
|
10
|
Mejía-Rodríguez D, Venegas RID, Calaminici P, Köster AM. Robust and Efficient Auxiliary Density Perturbation Theory Calculations. J Chem Theory Comput 2015; 11:1493-500. [PMID: 26574360 DOI: 10.1021/ct501065g] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
A new iterative solver for the recently developed time-dependent auxiliary density perturbation theory is presented. It is based on the Eirola-Nevanlinna algorithm for large nonsymmetric linear equation systems. The new methodology is validated by static and dynamic polarizability calculations of small molecules. Comparison between the analytic and iterative solutions of the response equation system shows excellent agreement for the calculated static and dynamic polarizabilities. The new iterative solver reduces the formal scaling from [Symbol: see text](N(4)) to [Symbol: see text](N(3)). Furthermore, the observed computational scaling for linear alkane chains is N(1.6). This subquadratic behavior is possible in systems with a few hundred atoms because of the very small prefactors of the [Symbol: see text](N(3)) and [Symbol: see text](N(2)) steps remaining in the iterative solver. To demonstrate the potential of this new methodology, static polarizabilities of giant fullerenes up to C960, with more than 14,000 basis functions, are calculated.
Collapse
Affiliation(s)
- Daniel Mejía-Rodríguez
- Departamento de Quı́mica, Cinvestav , Avenida Instituto Politénico Nacional 2508, A.P. 14-740 México D.F. 07000, México
| | - Rogelio Isaac Delgado Venegas
- Departamento de Quı́mica, Cinvestav , Avenida Instituto Politénico Nacional 2508, A.P. 14-740 México D.F. 07000, México
| | - Patrizia Calaminici
- Departamento de Quı́mica, Cinvestav , Avenida Instituto Politénico Nacional 2508, A.P. 14-740 México D.F. 07000, México
| | - Andreas M Köster
- Departamento de Quı́mica, Cinvestav , Avenida Instituto Politénico Nacional 2508, A.P. 14-740 México D.F. 07000, México
| |
Collapse
|
11
|
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
| |
Collapse
|
12
|
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
|
13
|
Oliveira BGD. Structure, energy, vibrational spectrum, and Bader's analysis of π⋯H hydrogen bonds and H−δ⋯H+δdihydrogen bonds. Phys Chem Chem Phys 2013; 15:37-79. [DOI: 10.1039/c2cp41749a] [Citation(s) in RCA: 59] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/21/2023]
|
14
|
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]
|