1
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Gombás A, Surján PR, Szabados Á. Analysis and Assessment of Knowles' Partitioning in Many-Body Perturbation Theory. J Chem Theory Comput 2024; 20:5094-5104. [PMID: 38847107 DOI: 10.1021/acs.jctc.4c00166] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/26/2024]
Abstract
A detailed analysis of a new partitioning in many-body perturbation theory recently proposed by Knowles (J. Chem. Phys. 156, 011101, 2022), termed "perturbation adapted partitioning" (PAPT), is presented. Level shift and orbital rotation effects are identified as gears of the zero-order Hamiltonian. These two components are examined separately, revealing that, in themselves, neither of the two is competitive with the combined effect. The success of PAPT can be attributed to determining a set of molecular orbitals and corresponding orbital energies that can systematically outperform the canonical orbitals and Koopmans' energy-based Møller-Plesset partitioning. The self-consistent version of the method is also tested in terms of energy and convergence. Previous numerical studies are further complemented with an application to an inherent multireference example and an investigation of van der Waals interaction energies. In addition, a rigorous mathematical analysis of the consequence of the linear dependence of projection functions on the solution of the Knowles' equations is provided.
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Affiliation(s)
- András Gombás
- Laboratory of Theoretical Chemistry, Institute of Chemistry, Faculty of Science, ELTE Eötvös Loránd University, P.O.B. 32, H-1518 Budapest 112, Hungary
| | - Péter R Surján
- Laboratory of Theoretical Chemistry, Institute of Chemistry, Faculty of Science, ELTE Eötvös Loránd University, P.O.B. 32, H-1518 Budapest 112, Hungary
| | - Ágnes Szabados
- Laboratory of Theoretical Chemistry, Institute of Chemistry, Faculty of Science, ELTE Eötvös Loránd University, P.O.B. 32, H-1518 Budapest 112, Hungary
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2
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Ahirwar MB, Deshmukh MM. Fragments-in-fragments method for efficient and reliable estimates of individual hydrogen bond energies in large molecular clusters. J Comput Chem 2023. [PMID: 37191018 DOI: 10.1002/jcc.27133] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/04/2023] [Revised: 05/01/2023] [Accepted: 05/03/2023] [Indexed: 05/17/2023]
Abstract
The knowledge of individual hydrogen bond (HB) strength in molecular clusters is indispensable to get insights into the bulk properties of condensed systems. Recently, we have developed the molecular tailoring approach based (MTA-based) method for the estimation of individual HB energy in molecular clusters. However, the direct use of this MTA-based method to large molecular clusters becomes progressively difficult with the increase in the size of a cluster. To overcome this caveat, herein, we propose the use of linear scaling method (such as the original MTA method) for the estimation of single-point (SP) energies of large-sized parent molecular cluster and their respective fragments. Because the fragments of the MTA-based method, for the estimation of HB energy, are further fragmented, this proposed strategy is called as Fragments-in-Fragments (Frags-in-Frags) method. The SP energies of fragments and parent cluster calculated by the Frags-in-Frags approach were utilized to estimate the individual HB energy. The estimated individual HB energies, in various molecular clusters, by Frags-in-Frags method are found to be in excellent linear agreement with their MTA-based counterparts (R2 = 0.9975 of 348 data points). The difference being less than 0.5 kcal/mol in most of the cases. Furthermore, RMSD is 0.43 kcal/mol, MAE is 0.33 kcal/mol, and the standard deviation is 0.44 kcal/mol. Importantly, the Frags-in-Frags method not only enables the reliable estimation of HB energy in large molecular clusters but also requires less computational time and can be possible even with off-the-shelf hardware.
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Affiliation(s)
- Mini Bharati Ahirwar
- Department of Chemistry, Dr. Harisingh Gour Vishwavidyalaya (A Central University), Sagar, India
| | - Milind M Deshmukh
- Department of Chemistry, Dr. Harisingh Gour Vishwavidyalaya (A Central University), Sagar, India
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3
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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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4
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Shao X, Mi W, Pavanello M. Density Embedding Method for Nanoscale Molecule-Metal Interfaces. J Phys Chem Lett 2022; 13:7147-7154. [PMID: 35901490 DOI: 10.1021/acs.jpclett.2c01424] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
In this work, we extend the applicability of standard Kohn-Sham DFT (KS-DFT) to model realistically sized molecule-metal interfaces where the metal slabs venture into the tens of nanometers in size. Employing state-of-the-art noninteracting kinetic energy functionals, we describe metallic subsystems with orbital-free DFT and combine their electronic structure with molecular subsystems computed at the KS-DFT level resulting in a multiscale subsystem DFT method. The method reproduces within a few millielectronvolts the binding energy difference of water and carbon dioxide molecules adsorbed on the top and hollow sites of an Al(111) surface compared to KS-DFT of the combined supersystem. It is also robust for Born-Oppenheimer molecular dynamics simulations. Very large system sizes are approached with standard computing resources thanks to a parallelization scheme that avoids accumulation of memory at the gather-scatter stage. The results as presented are encouraging and open the door to ab initio simulations of realistically sized, mesoscopic molecule-metal interfaces.
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Affiliation(s)
- Xuecheng Shao
- Department of Chemistry, Rutgers University, Newark, New Jersey 07102, United States
| | - Wenhui Mi
- International Center for Computational Method and Software, College of Physics, Jilin University, Changchun 130012, China
| | - Michele Pavanello
- Department of Chemistry, Rutgers University, Newark, New Jersey 07102, United States
- Department of Physics, Rutgers University, Newark, New Jersey 07102, United States
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5
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Peng L, Peng D, Gu FL, Yang W. Regularized Localized Molecular Orbitals in a Divide-and-Conquer Approach for Linear Scaling Calculations. J Chem Theory Comput 2022; 18:2975-2982. [PMID: 35416665 PMCID: PMC9972215 DOI: 10.1021/acs.jctc.2c00142] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Non-orthogonal localized molecular orbitals (NOLMOs) have been employed as building blocks for the divide-and-conquer (DC) linear scaling method. The NOLMOs are calculated from subsystems and used for constructing the density matrix (DM) of the entire system, instead of the subsystem DM in the original DC approach. Also, unlike the original DC method, the inverse electronic temperature parameter β is not needed anymore. Furthermore, a new regularized localization approach for NOLMOs has been developed, in which the localization cost function is a sum of the spatial spread function, as in the Boys method, and the kinetic energy, as a regularization measure to limit the oscillation of the NOLMOs. The optimal weight of the kinetic energy can be determined by optimization with analytical gradients. The resulting regularized NOLMOs have enhanced smoothness and better transferability because of reduced kinetic energies. Compared with the original DC, while NOLMO-DC has a similar computational linear scaling cost, the accuracy of NOLMO-DC is better by several orders of magnitude for large conjugated systems and by about 1 order of magnitude for other systems. The NOLMO-DC method is thus a promising development of the DC approach for linear scaling calculations.
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Affiliation(s)
- Liang Peng
- Key Laboratory of Theoretical Chemistry of Environment, Ministry of Education; School of Environment, South China Normal University, Guangzhou 510006, People’s Republic of China
| | - Daoling Peng
- Key Laboratory of Theoretical Chemistry of Environment, Ministry of Education; School of Environment, South China Normal University, Guangzhou 510006, People’s Republic of China
| | - Feng Long Gu
- Key Laboratory of Theoretical Chemistry of Environment, Ministry of Education; School of Environment, South China Normal University, Guangzhou 510006, People’s Republic of China
| | - Weitao Yang
- Department of Chemistry, Duke University, Durham, North Carolina 27708-0346, United States
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6
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Li W, Ma H, Li S, Ma J. Computational and data driven molecular material design assisted by low scaling quantum mechanics calculations and machine learning. Chem Sci 2021; 12:14987-15006. [PMID: 34909141 PMCID: PMC8612375 DOI: 10.1039/d1sc02574k] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/10/2021] [Accepted: 10/12/2021] [Indexed: 12/11/2022] Open
Abstract
Electronic structure methods based on quantum mechanics (QM) are widely employed in the computational predictions of the molecular properties and optoelectronic properties of molecular materials. The computational costs of these QM methods, ranging from density functional theory (DFT) or time-dependent DFT (TDDFT) to wave-function theory (WFT), usually increase sharply with the system size, causing the curse of dimensionality and hindering the QM calculations for large sized systems such as long polymer oligomers and complex molecular aggregates. In such cases, in recent years low scaling QM methods and machine learning (ML) techniques have been adopted to reduce the computational costs and thus assist computational and data driven molecular material design. In this review, we illustrated low scaling ground-state and excited-state QM approaches and their applications to long oligomers, self-assembled supramolecular complexes, stimuli-responsive materials, mechanically interlocked molecules, and excited state processes in molecular aggregates. Variable electrostatic parameters were also introduced in the modified force fields with the polarization model. On the basis of QM computational or experimental datasets, several ML algorithms, including explainable models, deep learning, and on-line learning methods, have been employed to predict the molecular energies, forces, electronic structure properties, and optical or electrical properties of materials. It can be conceived that low scaling algorithms with periodic boundary conditions are expected to be further applicable to functional materials, perhaps in combination with machine learning to fast predict the lattice energy, crystal structures, and spectroscopic properties of periodic functional materials.
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Affiliation(s)
- Wei Li
- Key Laboratory of Mesoscopic Chemistry of Ministry of Education, Institute of Theoretical and Computational Chemistry, School of Chemistry and Chemical Engineering, Nanjing University Nanjing 210023 China
| | - Haibo Ma
- Key Laboratory of Mesoscopic Chemistry of Ministry of Education, Institute of Theoretical and Computational Chemistry, School of Chemistry and Chemical Engineering, Nanjing University Nanjing 210023 China
- Jiangsu Key Laboratory of Advanced Organic Materials, Jiangsu Key Laboratory of Vehicle Emissions Control, Nanjing University Nanjing 210023 China
| | - Shuhua Li
- Key Laboratory of Mesoscopic Chemistry of Ministry of Education, Institute of Theoretical and Computational Chemistry, School of Chemistry and Chemical Engineering, Nanjing University Nanjing 210023 China
| | - Jing Ma
- Key Laboratory of Mesoscopic Chemistry of Ministry of Education, Institute of Theoretical and Computational Chemistry, School of Chemistry and Chemical Engineering, Nanjing University Nanjing 210023 China
- Jiangsu Key Laboratory of Advanced Organic Materials, Jiangsu Key Laboratory of Vehicle Emissions Control, Nanjing University Nanjing 210023 China
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7
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Liang Q, Yang J. Third-Order Many-Body Expansion of OSV-MP2 Wave Function for Low-Order Scaling Analytical Gradient Computation. J Chem Theory Comput 2021; 17:6841-6860. [PMID: 34704757 DOI: 10.1021/acs.jctc.1c00581] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Abstract
We present a many-body expansion (MBE) formulation and implementation for efficient computation of analytical energy gradients from the orbital-specific-virtual second-order Møllet-Plesset perturbation theory (OSV-MP2) based on our earlier work (Zhou et al. J. Chem. Theory Comput. 2020, 16, 196-210). The third-order MBE(3) expansion of OSV-MP2 amplitudes and density matrices was developed to adopt the orbital-specific clustering and long-range termination schemes, which avoids term-by-term differentiations of the MBE energy bodies. We achieve better efficiency by exploiting the algorithmic sparsity that allows us to prune out insignificant fitting integrals and OSV relaxations. With these approximations, the present implementation is benchmarked on a range of molecules that show an economic scaling in the linear and quadratic regimes for computing MBE(3)-OSV-MP2 amplitude and gradient equations, respectively, and yields normal accuracy comparable to the original OSV-MP2 results. The MPI-3-based parallelism through shared memory one-sided communication is further developed for improving parallel scalability and memory accessibility by sorting the MBE(3) orbital clusters into independent tasks that are distributed on multiple processes across many nodes, supporting both global and local data locations in which selected MBE(3)-OSV-MP2 intermediates of different sizes are distinguished and accordingly placed. The accuracy and efficiency level of our MBE(3)-OSV-MP2 analytical gradient implementation is finally illustrated in two applications: we show that the subtle coordination structure differences of mechanically interlocked Cu-catenane complexes can be distinguished when tuning ligand lengths; and the porphycene molecular dynamics reveals the emergence of the vibrational signature arising from softened N-H stretching associated with hydrogen transfer, using an MP2 level of electron correlation and classical nuclei for the first time.
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Affiliation(s)
- Qiujiang Liang
- Department of Chemistry, The University of Hong Kong, Hong Kong SAR, P. R. China
| | - Jun Yang
- Department of Chemistry, The University of Hong Kong, Hong Kong SAR, P. R. China
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8
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Fujimori T, Kobayashi M, Taketsugu T. Energy-based automatic determination of buffer region in the divide-and-conquer second-order Møller-Plesset perturbation theory. J Comput Chem 2021; 42:620-629. [PMID: 33534916 PMCID: PMC7986104 DOI: 10.1002/jcc.26486] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/07/2020] [Revised: 12/19/2020] [Accepted: 01/15/2021] [Indexed: 11/21/2022]
Abstract
In the linear‐scaling divide‐and‐conquer (DC) electronic structure method, each subsystem is calculated together with the neighboring buffer region, the size of which affects the energy error introduced by the fragmentation in the DC method. The DC self‐consistent field calculation utilizes a scheme to automatically determine the appropriate buffer region that is as compact as possible for reducing the computational time while maintaining acceptable accuracy (J. Comput. Chem. 2018, 39, 909). To extend the automatic determination scheme of the buffer region to the DC second‐order Møller–Plesset perturbation (MP2) calculation, a scheme for estimating the subsystem MP2 correlation energy contribution from each atom in the buffer region is proposed. The estimation is based on the atomic orbital Laplace MP2 formalism. Based on this, an automatic buffer determination scheme for the DC‐MP2 calculation is constructed and its performance for several types of systems is assessed.
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Affiliation(s)
- Toshikazu Fujimori
- Graduate School of Chemical Sciences and EngineeringHokkaido UniversitySapporoJapan
| | - Masato Kobayashi
- Department of Chemistry, Faculty of ScienceHokkaido UniversitySapporoJapan
- WPI‐ICReDDHokkaido UniversitySapporoJapan
- ESICB, Kyoto UniversityKyotoJapan
| | - Tetsuya Taketsugu
- Department of Chemistry, Faculty of ScienceHokkaido UniversitySapporoJapan
- WPI‐ICReDDHokkaido UniversitySapporoJapan
- ESICB, Kyoto UniversityKyotoJapan
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9
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Li W, Dong H, Ma J, Li S. Structures and Spectroscopic Properties of Large Molecules and Condensed-Phase Systems Predicted by Generalized Energy-Based Fragmentation Approach. Acc Chem Res 2021; 54:169-181. [PMID: 33350806 DOI: 10.1021/acs.accounts.0c00580] [Citation(s) in RCA: 33] [Impact Index Per Article: 11.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2023]
Abstract
ConspectusThe structures and spectroscopic properties of molecules and condensed-phase systems are usually experimentally characterized by X-ray, infrared (IR), Raman, nuclear magnetic resonance (NMR), and electronic absorption/emission spectra. Quantum mechanics (QM) calculations are critical in quantitatively understanding the relationship between the structure and physicochemical properties of various chemical systems. However, it is very challenging to apply traditional QM methods to large molecules and condensed-phase systems with large unit cells due to their steep computational scaling with the system size. To overcome this difficulty, theoretical chemists have developed various linear (or low) scaling QM methods, among which energy-based fragmentation methods have achieved great success for large molecules or clusters. One of the most popular energy-based fragmentation methods is the generalized energy-based fragmentation (GEBF) approach developed by us.In this approach, the ground-state energy of a large molecule can be evaluated from the ground-state energies of a series of embedded subsystems. In this Account, we focus on the recent developments and applicability of the GEBF approach for the structures and spectroscopic properties of complicated large molecules and condensed-phase systems. With new fragmentation schemes, the GEBF approach can now describe ionic liquid clusters and metal-containing supramolecular systems accurately and can provide accurate binding energies for host-guest complexes. In addition, the GEBF approach is now available for describing the localized excited states of large systems including a chromophore. More importantly, the GEBF approach under periodic boundary conditions (PBC-GEBF) has been developed to deal with periodic molecular crystals and liquids. Then, the ground-state energy (or property) per unit cell of a periodic condensed phase system can be predicted with QM calculations on nonperiodic embedded subsystems. This feature enables accurate electron correlation calculations on molecular crystals and liquids to be feasible on ordinary workstations. The PBC-GEBF approach has been applied to predict the crystal structures, lattice energies, and spectroscopic properties of some typical molecular crystals and solutions. By combining the GEBF method and machine learning (ML) method, a GEBF-ML force field has been developed for long normal alkanes, and the IR spectra of long alkanes can be obtained from the GEBF-ML molecular dynamics (MD) simulations. The GEBF and its periodic variant are expected to play increasingly important roles in investigating real-life chemical systems of broad interests at the ab initio levels.
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Affiliation(s)
- Wei Li
- Institute of Theoretical and Computational Chemistry, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, People’s Republic of China
| | - Hao Dong
- Kuang Yaming Honors School and Institute for Brain Sciences, Nanjing University, Nanjing 210023, People’s Republic of China
| | - Jing Ma
- Institute of Theoretical and Computational Chemistry, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, People’s Republic of China
| | - Shuhua Li
- Institute of Theoretical and Computational Chemistry, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, People’s Republic of China
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10
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Ye HZ, Tran HK, Van Voorhis T. Bootstrap Embedding For Large Molecular Systems. J Chem Theory Comput 2020; 16:5035-5046. [PMID: 32589842 DOI: 10.1021/acs.jctc.0c00438] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
Abstract
Recent developments in quantum embedding theories have provided attractive approaches to correlated calculations for large systems. In this work, we extend our previous work [J. Chem. Theory Comput. 2019, 15, 4497-4506; J. Phys. Chem. Lett. 2019, 10, 6368-6374] on bootstrap embedding (BE) to enable correlated ab initio calculations at the coupled cluster with singles and doubles (CCSD) level for large molecules. We introduce several new algorithmic developments that significantly reduce the computational cost of BE, while maintaining its accuracy. The resulting implementation scales as O(N3) for the integral transform and O(N) for the CCSD calculation. Numerical results on a series of conjugated molecules suggest that BE with reasonably sized fragments can recover more than 99.5% of the total correlation energy of a full CCSD calculation, while the required computational resources (time and storage) compare favorably to one popular local correlation scheme: domain localized pair natural orbital (DLPNO). The largest BE calculation in this work involves ∼2900 basis functions and can be performed on a single node with 16 CPU cores and 64 GB of memory in a few days. We anticipate that these developments represent an important step toward the application of BE to solve practical problems.
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Affiliation(s)
- Hong-Zhou Ye
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Henry K Tran
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Troy Van Voorhis
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
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11
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Uratani H, Nakai H. Non-adiabatic molecular dynamics with divide-and-conquer type large-scale excited-state calculations. J Chem Phys 2020; 152:224109. [DOI: 10.1063/5.0006831] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022] Open
Affiliation(s)
- Hiroki Uratani
- Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, 3-4-1, Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
| | - 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), 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
- Elements Strategy Initiative for Catalysts and Batteries (ESICB), Kyoto University, Katsura, Kyoto 615-8245, Japan
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12
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Krstic PS, Han L, Irle S, Nakai H. Simulations of the synthesis of boron-nitride nanostructures in a hot, high pressure gas volume. Chem Sci 2018; 9:3803-3819. [PMID: 29780513 PMCID: PMC5939839 DOI: 10.1039/c8sc00667a] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/08/2018] [Accepted: 03/16/2018] [Indexed: 11/21/2022] Open
Abstract
We performed nanosecond timescale computer simulations of clusterization and agglomeration processes of boron nitride (BN) nanostructures in hot, high pressure gas, starting from eleven different atomic and molecular precursor systems containing boron, nitrogen and hydrogen at various temperatures from 1500 to 6000 K. The synthesized BN nanostructures self-assemble in the form of cages, flakes, and tubes as well as amorphous structures. The simulations facilitate the analysis of chemical dynamics and we are able to predict the optimal conditions concerning temperature and chemical precursor composition for controlling the synthesis process in a high temperature gas volume, at high pressure. We identify the optimal precursor/temperature choices that lead to the nanostructures of highest quality with the highest rate of synthesis, using a novel parameter of the quality of the synthesis (PQS). Two distinct mechanisms of BN nanotube growth were found, neither of them based on the root-growth process. The simulations were performed using quantum-classical molecular dynamics (QCMD) based on the density-functional tight-binding (DFTB) quantum mechanics in conjunction with a divide-and-conquer (DC) linear scaling algorithm, as implemented in the DC-DFTB-K code, enabling the study of systems as large as 1300 atoms in canonical NVT ensembles for 1 ns time.
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Affiliation(s)
- Predrag S Krstic
- Institute for Advanced Computational Science , Stony Brook University , Stony Brook , NY 11794-5250 , USA . .,Department of Materials Science and Chemical Engineering , Stony Brook University , Stony Brook , NY 11794-2275 , USA
| | - Longtao Han
- Institute for Advanced Computational Science , Stony Brook University , Stony Brook , NY 11794-5250 , USA . .,Department of Materials Science and Chemical Engineering , Stony Brook University , Stony Brook , NY 11794-2275 , USA
| | - Stephan Irle
- Computational Sciences & Engineering Division , Oak Ridge National Laboratory , Oak Ridge TN , 37831-6493 , USA
| | - Hiromi Nakai
- Department of Chemistry and Biochemistry , School of Advanced Science and Engineering , Waseda University , Tokyo 169-8555 , Japan.,Waseda Research Institute for Science and Engineering , Waseda University , Tokyo 169-8555 , Japan
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13
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Kobayashi M, Taketsugu T. Divide-and-Conquer Hartree–Fock–Bogoliubov Method and Its Application to Conjugated Diradical Systems. CHEM LETT 2016. [DOI: 10.1246/cl.160699] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023]
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14
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Second-order Møller–Plesset perturbation (MP2) theory at finite temperature: relation with Surján’s density matrix MP2 and its application to linear-scaling divide-and-conquer method. Theor Chem Acc 2015. [DOI: 10.1007/s00214-015-1710-y] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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15
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Tanaka S, Mochizuki Y, Komeiji Y, Okiyama Y, Fukuzawa K. Electron-correlated fragment-molecular-orbital calculations for biomolecular and nano systems. Phys Chem Chem Phys 2015; 16:10310-44. [PMID: 24740821 DOI: 10.1039/c4cp00316k] [Citation(s) in RCA: 189] [Impact Index Per Article: 21.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Abstract
Recent developments in the fragment molecular orbital (FMO) method for theoretical formulation, implementation, and application to nano and biomolecular systems are reviewed. The FMO method has enabled ab initio quantum-mechanical calculations for large molecular systems such as protein-ligand complexes at a reasonable computational cost in a parallelized way. There have been a wealth of application outcomes from the FMO method in the fields of biochemistry, medicinal chemistry and nanotechnology, in which the electron correlation effects play vital roles. With the aid of the advances in high-performance computing, the FMO method promises larger, faster, and more accurate simulations of biomolecular and related systems, including the descriptions of dynamical behaviors in solvent environments. The current status and future prospects of the FMO scheme are addressed in these contexts.
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Affiliation(s)
- Shigenori Tanaka
- Graduate School of System Informatics, Kobe University, 1-1 Rokkodai, Nada-ku, Kobe 657-8501, Japan.
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16
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Akimov AV, Prezhdo OV. Large-Scale Computations in Chemistry: A Bird’s Eye View of a Vibrant Field. Chem Rev 2015; 115:5797-890. [DOI: 10.1021/cr500524c] [Citation(s) in RCA: 159] [Impact Index Per Article: 17.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/08/2023]
Affiliation(s)
- Alexey V. Akimov
- Department
of Chemistry, University of South California, Los Angeles, California 90089, United States
| | - Oleg V. Prezhdo
- Department
of Chemistry, University of South California, Los Angeles, California 90089, United States
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17
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Affiliation(s)
- Michael A Collins
- †Research School of Chemistry, Australian National University, Canberra, ACT 0200, Australia
| | - Ryan P A Bettens
- ‡Department of Chemistry, National University of Singapore, 3 Science Drive 3, Singapore 117543, Singapore
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18
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Abstract
Conspectus Quantum mechanics (QM) has revolutionized our understanding of the structure and reactivity of small molecular systems. Given the tremendous impact of QM in this research area, it is attractive to believe that this could also be brought into the biological realm where systems of a few thousand atoms and beyond are routine. Applying QM methods to biological problems brings an improved representation to these systems by the direct inclusion of inherently QM effects such as polarization and charge transfer. Because of the improved representation, novel insights can be gleaned from the application of QM tools to biomacromolecules in aqueous solution. To achieve this goal, the computational bottlenecks of QM methods had to be addressed. In semiempirical theory, matrix diagonalization is rate limiting, while in density functional theory or Hartree-Fock theory electron repulsion integral computation is rate-limiting. In this Account, we primarily focus on semiempirical models where the divide and conquer (D&C) approach linearizes the matrix diagonalization step with respect to the system size. Through the D&C approach, a number of applications to biological problems became tractable. Herein, we provide examples of QM studies on biological systems that focus on protein solvation as viewed by QM, QM enabled structure-based drug design, and NMR and X-ray biological structure refinement using QM derived restraints. Through the examples chosen, we show the power of QM to provide novel insights into biological systems, while also impacting practical applications such as structure refinement. While these methods can be more expensive than classical approaches, they make up for this deficiency by the more realistic modeling of the electronic nature of biological systems and in their ability to be broadly applied. Of the tools and applications discussed in this Account, X-ray structure refinement using QM models is now generally available to the community in the refinement package Phenix. While the power of this approach is manifest, challenges still remain. In particular, QM models are generally applied to static structures, so ways in which to include sampling is an ongoing challenge. Car-Parrinello or Born-Oppenheimer molecular dynamics approaches address the short time scale sampling issue, but how to effectively use QM to study phenomenon covering longer time scales will be the focus of future research. Finally, how to accurately and efficiently include electron correlation effects to facilitate the modeling of, for example, dispersive interactions, is also a major hurdle that a broad range of groups are addressing The use of QM models in biology is in its infancy, leading to the expectation that the most significant use of these tools to address biological problems will be seen in the coming years. It is hoped that while this Account summarizes where we have been, it will also help set the stage for future research directions at the interface of quantum mechanics and biology.
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Affiliation(s)
- Kenneth M Merz
- Department of Chemistry and the Department of Biochemistry and Molecular Biology, Michigan State University , 578 S. Shaw Lane, East Lansing Michigan 48824-1322, United States
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19
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Hayami M, Seino J, Nakai H. Extension of accompanying coordinate expansion and recurrence relation method for general-contraction basis sets. J Comput Chem 2014; 35:1517-27. [PMID: 24889356 DOI: 10.1002/jcc.23646] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/24/2014] [Revised: 04/14/2014] [Accepted: 05/01/2014] [Indexed: 11/11/2022]
Abstract
An algorithm of the accompanying coordinate expansion and recurrence relation (ACE-RR), which is used for the rapid evaluation of the electron repulsion integral (ERI), has been extended to the general-contraction (GC) scheme. The present algorithm, denoted by GC-ACE-RR, is designed for molecular calculations including heavy elements, whose orbitals consist of many primitive functions with and without higher angular momentum such as d- and f-orbitals. The performance of GC-ACE-RR was assessed for (ss|ss)-, (pp|pp)-, (dd|dd)-, and (ff|ff)-type ERIs in terms of contraction length and the number of GC orbitals. The present algorithm was found to reduce the central processing unit time compared with the ACE-RR algorithm, especially for higher angular momentum and highly contracted orbitals. Compared with HONDOPLUS and GAMESS program packages, GC-ACE-RR computations for ERIs of three-dimensional gold clusters Aun (n = 1, 2, …, 10, 15, 20, and 25) are more than 10 times faster.
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Affiliation(s)
- Masao Hayami
- Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, Tokyo, 169-8555, Japan
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20
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Guo Y, Li W, Li S. Improved cluster-in-molecule local correlation approach for electron correlation calculation of large systems. J Phys Chem A 2014; 118:8996-9004. [PMID: 24963784 DOI: 10.1021/jp501976x] [Citation(s) in RCA: 36] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
An improved cluster-in-molecule (CIM) local correlation approach is developed to allow electron correlation calculations of large systems more accurate and faster. We have proposed a refined strategy of constructing virtual LMOs of various clusters, which is suitable for basis sets of various types. To recover medium-range electron correlation, which is important for quantitative descriptions of large systems, we find that a larger distance threshold (ξ) is necessary for highly accurate results. Our illustrative calculations show that the present CIM-MP2 (second-order Møller-Plesser perturbation theory, MP2) or CIM-CCSD (coupled cluster singles and doubles, CCSD) scheme with a suitable ξ value is capable of recovering more than 99.8% correlation energies for a wide range of systems at different basis sets. Furthermore, the present CIM-MP2 scheme can provide reliable relative energy differences as the conventional MP2 method for secondary structures of polypeptides.
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Affiliation(s)
- Yang Guo
- School of Chemistry and Chemical Engineering, Key Laboratory of Mesoscopic Chemistry of MOE, Institute of Theoretical and Computational Chemistry, Nanjing University , Nanjing 210093, P. R. China
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21
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Peng L, Gu FL, Yang W. Effective preconditioning for ab initio ground state energy minimization with non-orthogonal localized molecular orbitals. Phys Chem Chem Phys 2014; 15:15518-27. [PMID: 23943010 DOI: 10.1039/c3cp52989d] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The non-orthogonal localized molecular orbital (NOLMO) is the most localized representation of electronic degrees of freedom. As such, NOLMOs are thus potentially the most efficient for linear-scaling calculations of electronic structures for large systems. However, direct ab initio calculations with NOLMO have not been fully implemented and widely used, partly because of the slow convergence issue in the optimization of NOLMO. Towards realizing the potential of NOLMO for large systems, we applied an energy minimum variational principle for carrying out ab initio self-consistent-field (SCF) calculations with NOLMOs. We developed an effective preconditioning approach using the diagonal part of the second order derivatives and show that the convergence of the energy optimization is significantly improved. The speed of convergence of the energy and density are comparable with that of the conventional SCF approach, thus paving the way for the optimization of NOLMO in linear scaling calculations for large systems.
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Affiliation(s)
- Liang Peng
- Key Laboratory of Theoretical Chemistry of Environment, Ministry of Education, School of Chemistry and Environment, South China Normal University, Guangzhou 510006, China.
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22
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Nakajima Y, Seino J, Nakai H. Analytical energy gradient based on spin-free infinite-order Douglas-Kroll-Hess method with local unitary transformation. J Chem Phys 2013; 139:244107. [DOI: 10.1063/1.4850638] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023] Open
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23
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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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24
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Wu A, Xu X. DCMB that combines divide-and-conquer and mixed-basis set methods for accurate geometry optimizations, total energies, and vibrational frequencies of large molecules. J Comput Chem 2012; 33:1421-32. [DOI: 10.1002/jcc.22973] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/24/2012] [Accepted: 03/02/2012] [Indexed: 11/06/2022]
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25
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Kobayashi M, Touma T, Nakai H. Dynamic hyperpolarizability calculations of large systems: The linear-scaling divide-and-conquer approach. J Chem Phys 2012; 136:084108. [DOI: 10.1063/1.3687341] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/30/2023] Open
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26
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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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27
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Matsui T, Baba T, Kamiya K, Shigeta Y. An accurate density functional theory based estimation of pKa values of polar residues combined with experimental data: from amino acids to minimal proteins. Phys Chem Chem Phys 2012; 14:4181-7. [DOI: 10.1039/c2cp23069k] [Citation(s) in RCA: 57] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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28
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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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29
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Mochizuki Y, Yamashita K, Nakano T, Okiyama Y, Fukuzawa K, Taguchi N, Tanaka S. Higher-order correlated calculations based on fragment molecular orbital scheme. Theor Chem Acc 2011. [DOI: 10.1007/s00214-011-1036-3] [Citation(s) in RCA: 72] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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Nakai H, Ohashi H, Imamura Y, Kikuchi Y. Bond energy analysis revisited and designed toward a rigorous methodology. J Chem Phys 2011; 135:124105. [PMID: 21974510 DOI: 10.1063/1.3636387] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The present study theoretically revisits and numerically assesses two-body energy decomposition schemes including a newly proposed one. The new decomposition scheme is designed to make the equilibrium bond distance equivalent with the minimum point of bond energies. Although the other decomposition schemes generally predict the wrong order of the C-C bond strengths of C(2)H(2), C(2)H(4), and C(2)H(6), the new decomposition scheme is capable of reproducing the C-C bond strengths. Numerical assessment on a training set of molecules demonstrates that the present scheme exhibits a stronger correlation with bond dissociation energies than the other decomposition schemes do, which suggests that the new decomposition scheme is a reliable and powerful analysis methodology.
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Affiliation(s)
- Hiromi Nakai
- Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, Tokyo 169-8555, Japan.
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31
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“Gold standard” coupled-cluster study of acetylene pentamers and hexamers via molecular tailoring approach. Theor Chem Acc 2011. [DOI: 10.1007/s00214-011-1029-2] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
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32
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Gordon MS, Fedorov DG, Pruitt SR, Slipchenko LV. Fragmentation Methods: A Route to Accurate Calculations on Large Systems. Chem Rev 2011; 112:632-72. [DOI: 10.1021/cr200093j] [Citation(s) in RCA: 836] [Impact Index Per Article: 64.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
Affiliation(s)
- Mark S. Gordon
- Department of Chemistry and Ames Laboratory, Iowa State University, Ames Iowa 50011, United States
| | - Dmitri G. Fedorov
- Nanosystem Research Institute, National Institute of Advanced Industrial Science and Technology (AIST), 1-1-1 Umezono, Tsukuba, Ibaraki 305-8568, Japan
| | - Spencer R. Pruitt
- Department of Chemistry and Ames Laboratory, Iowa State University, Ames Iowa 50011, United States
| | - Lyudmila V. Slipchenko
- Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, United States
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33
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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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34
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Katouda M, Kobayashi M, Nakai H, Nagase S. Two‐level hierarchical parallelization of second‐order Møller–plesset perturbation calculations in divide‐and‐conquer method. J Comput Chem 2011; 32:2756-64. [DOI: 10.1002/jcc.21855] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/08/2011] [Revised: 03/30/2011] [Accepted: 05/13/2011] [Indexed: 11/11/2022]
Affiliation(s)
- Michio Katouda
- Department of Theoretical and Computational Molecular Science, Institute for Molecular Science, Okazaki 444‐8585, Japan
| | - Masato Kobayashi
- Department of Theoretical and Computational Molecular Science, Institute for Molecular Science, Okazaki 444‐8585, Japan
- Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, Tokyo 169‐8555, Japan
| | - Hiromi Nakai
- Department of Theoretical and Computational Molecular Science, Institute for Molecular Science, Okazaki 444‐8585, Japan
- 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, Tokyo 102‐0075, Japan
| | - Shigeru Nagase
- Department of Theoretical and Computational Molecular Science, Institute for Molecular Science, Okazaki 444‐8585, Japan
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35
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Touma T, Kobayashi M, Nakai H. Finite-field evaluation of static (hyper)polarizabilities based on the linear-scaling divide-and-conquer method. Theor Chem Acc 2011. [DOI: 10.1007/s00214-011-0964-2] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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36
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37
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Kobayashi M, Kunisada T, Akama T, Sakura D, Nakai H. Reconsidering an analytical gradient expression within a divide-and-conquer self-consistent field approach: Exact formula and its approximate treatment. J Chem Phys 2011; 134:034105. [DOI: 10.1063/1.3524337] [Citation(s) in RCA: 43] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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38
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Divide-and-Conquer Approaches to Quantum Chemistry: Theory and Implementation. CHALLENGES AND ADVANCES IN COMPUTATIONAL CHEMISTRY AND PHYSICS 2011. [DOI: 10.1007/978-90-481-2853-2_5] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/13/2023]
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39
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Szabados Á, Nagy P. Spin component scaling in multiconfiguration perturbation theory. J Phys Chem A 2010; 115:523-34. [PMID: 21190320 DOI: 10.1021/jp108575a] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
We investigate a term-by-term scaling of the second-order energy correction obtained by perturbation theory (PT) starting from a multiconfiguration wave function. The total second-order correction is decomposed into several terms, based on the level and the spin pattern of the excitations. To define individual terms, we extend the same spin/different spin categorization of spin component scaling in various ways. When needed, identification of the excitation level is facilitated by the pivot determinant underlying the multiconfiguration PT framework. Scaling factors are determined from the stationary condition of the total energy calculated up to order 3. The decomposition schemes are tested numerically on the example of bond dissociation profiles and energy differences. We conclude that Grimme's parameters determined for single-reference Møller-Plesset theory may give a modest error reduction along the entire potential surface, if adopting a multireference based PT formulation. Scaling factors obtained from the stationary condition show relatively large variation with molecular geometry, at the same time they are more efficient in reducing the error when following a bond dissociation process.
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Affiliation(s)
- Ágnes Szabados
- Laboratory of Theoretical Chemistry, Institute of Chemistry, Loránd Eötvös University, H-1518 Budapest, POB 32, Hungary.
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40
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41
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Kobayashi M, Yoshikawa T, Nakai H. Divide-and-conquer self-consistent field calculation for open-shell systems: Implementation and application. Chem Phys Lett 2010. [DOI: 10.1016/j.cplett.2010.10.005] [Citation(s) in RCA: 33] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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42
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Akama T, Fujii A, Kobayashi M, Nakai H. Is the divide-and-conquer Hartree–Fock method valid for calculations of delocalized systems? Mol Phys 2010. [DOI: 10.1080/00268970701642267] [Citation(s) in RCA: 33] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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43
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Abstract
The ability to perform ab initio electronic structure calculations that scales linearly with the system size is one of the central aims in theoretical chemistry. In this study, the implementation of the divide-and-conquer (DC) algorithm, an algorithm with the potential to aid the achievement of true linear scaling within Hartree-Fock (HF) theory is revisited. Standard HF calculations solve the Roothaan-Hall equations for the whole system; in the DC-HF approach, the diagonalization of the Fock matrix is carried out on smaller subsystems. The DC algorithm for HF calculations was validated on polyglycines, polyalanines and eleven real three-dimensional proteins of up to 608 atoms in this work. We also found that a fragment-based initial guess using molecular fractionation with conjugated caps (MFCC) method significantly reduces the number of SCF cycles and even is capable of achieving convergence for some globular proteins where the simple superposition of atomic densities (SAD) initial guess fails.
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Affiliation(s)
- Xiao He
- Department of Chemistry and the Quantum Theory Project, 2328 New Physics Building, P.O. Box 118435, University of Florida, Gainesville, Florida 32611-8435
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45
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Time-dependent Hartree–Fock frequency-dependent polarizability calculation applied to divide-and-conquer electronic structure method. Chem Phys Lett 2010. [DOI: 10.1016/j.cplett.2009.12.043] [Citation(s) in RCA: 33] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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46
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Rahalkar AP, Katouda M, Gadre SR, Nagase S. Molecular tailoring approach in conjunction with MP2 and Ri-MP2 codes: A comparison with fragment molecular orbital method. J Comput Chem 2010; 31:2405-18. [DOI: 10.1002/jcc.21533] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023]
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47
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Kobayashi M, Nakai H. Divide-and-conquer-based linear-scaling approach for traditional and renormalized coupled cluster methods with single, double, and noniterative triple excitations. J Chem Phys 2009; 131:114108. [DOI: 10.1063/1.3211119] [Citation(s) in RCA: 122] [Impact Index Per Article: 8.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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48
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Dong H, Hua S, Li S. Understanding the Role of Intra- and Intermolecular Interactions in the Formation of Single- and Double-Helical Structures of Aromatic Oligoamides: A Computational Study. J Phys Chem A 2009; 113:1335-42. [DOI: 10.1021/jp8071525] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Hao Dong
- Institute of Theoretical and Computational Chemistry, Key Laboratory of Mesoscopic Chemistry of Ministry of Education, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing, 210093, P. R. China
| | - Shugui Hua
- Institute of Theoretical and Computational Chemistry, Key Laboratory of Mesoscopic Chemistry of Ministry of Education, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing, 210093, P. R. China
| | - Shuhua Li
- Institute of Theoretical and Computational Chemistry, Key Laboratory of Mesoscopic Chemistry of Ministry of Education, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing, 210093, P. R. China
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49
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Makowski M, Korchowiec J, Gu FL, Aoki Y. Describing electron correlation effects in the framework of the elongation methodâElongation-MP2: Formalism, implementation and efficiency. J Comput Chem 2009; 31:1733-40. [DOI: 10.1002/jcc.21462] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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50
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KOBAYASHI M, AKAMA T, NAKAI H. Implementation of Divide-and-Conquer (DC) Electronic Structure Code to GAMESS Program Package. ACTA ACUST UNITED AC 2009. [DOI: 10.2477/jccj.h2027] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022]
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