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Köppl C, Werner HJ. Parallel and Low-Order Scaling Implementation of Hartree–Fock Exchange Using Local Density Fitting. J Chem Theory Comput 2016; 12:3122-34. [DOI: 10.1021/acs.jctc.6b00251] [Citation(s) in RCA: 43] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Christoph Köppl
- Institut
für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring
55, 70569 Stuttgart, Germany
| | - Hans-Joachim Werner
- Institut
für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring
55, 70569 Stuttgart, Germany
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Kuźniarowicz P, Liu K, Aoki Y, Gu FL, Stachowicz A, Korchowiec J. Intermediate electrostatic field for the elongation method. J Mol Model 2014; 20:2277. [PMID: 24878802 PMCID: PMC4072069 DOI: 10.1007/s00894-014-2277-6] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/29/2013] [Accepted: 04/25/2014] [Indexed: 11/25/2022]
Abstract
A simple way to improve the accuracy of the fragmentation methods is proposed. The formalism was applied to the elongation (ELG) method at restricted open-shell Hartree-Fock (ROHF) level of theory. The α-helix conformer of polyglycine was taken as a model system. The modified ELG method includes a simplified electrostatic field resulting from point-charge distribution of the system's environment. In this way the long-distance polarization is approximately taken into account. The field attenuates during the ELG process to eventually disappear when the final structure is reached. The point-charge distributions for each ELG step are obtained from charge sensitivity analysis (CSA) in force-field atoms resolution. The presence of the intermediate field improves the accuracy of ELG calculations. The errors in total energy and its kinetic and potential contributions are reduced by at least one-order of magnitude. In addition the SCF convergence of ROHF scheme is improved.
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Affiliation(s)
- Piotr Kuźniarowicz
- Department of Molecular and Material Sciences, Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, 6-1 Kasuga-Park, Fukuoka, 816-8580 Japan
| | - Kai Liu
- Department of Material Sciences, Faculty of Engineering Sciences, Kyushu University, Kasuga, Fukuoka, 816-8580 Japan
| | - Yuriko Aoki
- Department of Material Sciences, Faculty of Engineering Sciences, Kyushu University, Kasuga, Fukuoka, 816-8580 Japan
| | - Feng Long Gu
- MOE Key Laboratory of Theoretical Chemistry of Environment; School of Chemistry and Environment, South China Normal University, Guangzhou, 510631 China
| | - Anna Stachowicz
- K. Gumiński Department of Theoretical Chemistry, Faculty of Chemistry, Jagiellonian University, Ingardena 3, 30-060 Krakow, Poland
| | - Jacek Korchowiec
- K. Gumiński Department of Theoretical Chemistry, Faculty of Chemistry, Jagiellonian University, Ingardena 3, 30-060 Krakow, Poland
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3
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A modified localization scheme for the three-dimensional elongation method applied to large systems. Chem Phys Lett 2013. [DOI: 10.1016/j.cplett.2013.02.039] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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4
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Liu K, Inerbaev T, Korchowiec J, Gu FL, Aoki Y. Geometry optimization for large systems by the elongation method. Theor Chem Acc 2012. [DOI: 10.1007/s00214-012-1277-9] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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5
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Bowler DR, Miyazaki T. O(N) methods in electronic structure calculations. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2012; 75:036503. [PMID: 22790422 DOI: 10.1088/0034-4885/75/3/036503] [Citation(s) in RCA: 210] [Impact Index Per Article: 17.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/21/2023]
Abstract
Linear-scaling methods, or O(N) methods, have computational and memory requirements which scale linearly with the number of atoms in the system, N, in contrast to standard approaches which scale with the cube of the number of atoms. These methods, which rely on the short-ranged nature of electronic structure, will allow accurate, ab initio simulations of systems of unprecedented size. The theory behind the locality of electronic structure is described and related to physical properties of systems to be modelled, along with a survey of recent developments in real-space methods which are important for efficient use of high-performance computers. The linear-scaling methods proposed to date can be divided into seven different areas, and the applicability, efficiency and advantages of the methods proposed in these areas are then discussed. The applications of linear-scaling methods, as well as the implementations available as computer programs, are considered. Finally, the prospects for and the challenges facing linear-scaling methods are discussed.
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Affiliation(s)
- D R Bowler
- London Centre for Nanotechnology, UCL, 17-19 Gordon St, London WC1H 0AH, UK.
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Rubensson EH, Rudberg E, Salek P. Methods for Hartree-Fock and Density Functional Theory Electronic Structure Calculations with Linearly Scaling Processor Time and Memory Usage. CHALLENGES AND ADVANCES IN COMPUTATIONAL CHEMISTRY AND PHYSICS 2011. [DOI: 10.1007/978-90-481-2853-2_12] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
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7
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Burger SK, Ayers PW. Quasi-Newton parallel geometry optimization methods. J Chem Phys 2010; 133:034116. [DOI: 10.1063/1.3455719] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022] Open
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Szwacki NG, Weber V, Tymczak C. Aromatic borozene. NANOSCALE RESEARCH LETTERS 2009; 4:1085-9. [PMID: 20596438 PMCID: PMC2893872 DOI: 10.1007/s11671-009-9362-2] [Citation(s) in RCA: 32] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/13/2009] [Accepted: 05/26/2009] [Indexed: 05/14/2023]
Abstract
Based on our comprehensive theoretical investigation and known experimental results for small boron clusters, we predict the existence of a novel aromatic inorganic molecule, B12H6. This molecule, which we refer to as borozene, has remarkably similar properties to the well-known benzene. Borozene is planar, possesses a large first excitation energy, D3hsymmetry, and more importantly is aromatic. Furthermore, the calculated anisotropy of the magnetic susceptibility of borozene is three times larger in absolute value than for benzene. Finally, we show that borozene molecules may be fused together to give larger aromatic compounds with even larger anisotropic susceptibilities.
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Affiliation(s)
- N Gonzalez Szwacki
- Department of Physics, Texas Southern University, Houston, TX, 77004, USA.
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9
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Brown P, Woods C, McIntosh-Smith S, Manby FR. Massively Multicore Parallelization of Kohn−Sham Theory. J Chem Theory Comput 2008; 4:1620-6. [DOI: 10.1021/ct800261j] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Philip Brown
- Centre for Computational Chemistry, School of Chemistry, University of Bristol, Bristol, BS8 1TS, United Kingdom, and ClearSpeed Technology plc, 3110 Great Western Court, Hunts Ground Road, Bristol, BS34 8HP, United Kingdom
| | - Christopher Woods
- Centre for Computational Chemistry, School of Chemistry, University of Bristol, Bristol, BS8 1TS, United Kingdom, and ClearSpeed Technology plc, 3110 Great Western Court, Hunts Ground Road, Bristol, BS34 8HP, United Kingdom
| | - Simon McIntosh-Smith
- Centre for Computational Chemistry, School of Chemistry, University of Bristol, Bristol, BS8 1TS, United Kingdom, and ClearSpeed Technology plc, 3110 Great Western Court, Hunts Ground Road, Bristol, BS34 8HP, United Kingdom
| | - Frederick R. Manby
- Centre for Computational Chemistry, School of Chemistry, University of Bristol, Bristol, BS8 1TS, United Kingdom, and ClearSpeed Technology plc, 3110 Great Western Court, Hunts Ground Road, Bristol, BS34 8HP, United Kingdom
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Rudberg E, Rubensson EH, Sałek P. Hartree–Fock calculations with linearly scaling memory usage. J Chem Phys 2008; 128:184106. [DOI: 10.1063/1.2918357] [Citation(s) in RCA: 35] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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11
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Elongation cutoff technique: low-order scaling SCF method. J Mol Model 2008; 14:651-8. [DOI: 10.1007/s00894-008-0295-y] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/15/2007] [Accepted: 02/21/2008] [Indexed: 10/22/2022]
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12
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Rubensson EH, Rudberg E, Sałek P. Density matrix purification with rigorous error control. J Chem Phys 2008; 128:074106. [DOI: 10.1063/1.2826343] [Citation(s) in RCA: 37] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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13
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Collins MA. Molecular potential energy surfaces constructed from interpolation of systematic fragment surfaces. J Chem Phys 2007; 127:024104. [PMID: 17640116 DOI: 10.1063/1.2746025] [Citation(s) in RCA: 53] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
A systematic method for approximating the ab initio electronic energy of molecules from the energies of molecular fragments has previously been presented. Here it is shown that this approach provides a feasible, systematic method for constructing a global molecular potential energy surface (PES) for reactions of a moderate-sized molecule from the corresponding surfaces for small molecular fragments. The method is demonstrated by construction of PESs for the reactions of a hydrogen atom with propane and n-pentane.
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Affiliation(s)
- Michael A Collins
- Research School of Chemistry, Australian National University, Canberra ACT 0200, Australia.
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Weber V, Challacombe M. Parallel algorithm for the computation of the Hartree-Fock exchange matrix: Gas phase and periodic parallel ONX. J Chem Phys 2006; 125:104110. [PMID: 16999518 DOI: 10.1063/1.2222359] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In this paper we present an efficient parallelization of the ONX algorithm for linear computation of the Hartree-Fock exchange matrix [J. Chem. Phys. 106, 9708 (1997)]. The method used is based on the equal time (ET) partitioning recently introduced [J. Chem. Phys. 118, 9128 (2003)] and [J. Chem. Phys. 121, 6608 (2004)]. ET exploits the slow variation of the density matrix between self-consistent-field iterations to achieve load balance. The method is presented and some benchmark calculations are discussed for gas phase and periodic systems with up to 128 processors. The current parallel ONX code is able to deliver up to 77% overall efficiency for a cluster of 50 water molecules on 128 processors (2.56 processors per heavy atom) and up to 87% for a box of 64 water molecules (two processors per heavy atom) with periodic boundary conditions.
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Affiliation(s)
- Valéry Weber
- Department of Chemistry, University of Fribourg, 1700 Fribourg, Switzerland.
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Collins MA, Deev VA. Accuracy and efficiency of electronic energies from systematic molecular fragmentation. J Chem Phys 2006; 125:104104. [PMID: 16999512 DOI: 10.1063/1.2347710] [Citation(s) in RCA: 143] [Impact Index Per Article: 7.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
A systematic method for approximating the ab initio electronic energy of molecules from the energies of molecular fragments is tested on a large sample of typical organic molecular structures. The detailed methods, including some additional refinements for molecular rings and long range interactions, are described. The accuracy and computational efficiency of the systematic hierarchy of methods are reported.
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Affiliation(s)
- Michael A Collins
- Research School of Chemistry, Australian National University, Canberra ACT 0200, Australia.
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Abstract
A number of computational techniques are described that reduce the effort related to the continuous fast multipole method, used for the evaluation of Coulomb matrix elements as needed in Hartree-Fock and density functional theories. A new extent definition for Gaussian charge distributions is proposed, as well as a new way of dividing distributions into branches. Also, a new approach for estimating the error caused by truncation of multipole expansions is presented. It is found that the use of dynamically truncated multipole expansions gives a speedup of a factor of 10 in the work required for multipole interactions, compared to the case when all interactions are computed using a fixed multipole expansion order. Results of benchmark calculations on three-dimensional systems are reported, demonstrating the usefulness of our present implementation of the fast multipole method.
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Affiliation(s)
- Elias Rudberg
- Department of Chemistry, University of Warwick, Coventry CV4 7AL, United Kingdom
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17
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Chen XH, Zhang JZH. Molecular fractionation with conjugated caps density matrix with pairwise interaction correction for protein energy calculation. J Chem Phys 2006; 125:44903. [PMID: 16942188 DOI: 10.1063/1.2218341] [Citation(s) in RCA: 39] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Pairwise interaction correction (PIC) is introduced to account for electron density polarization due to short-range interactions such as hydrogen bonding and close contact between molecular fragments in the molecular fractionation with conjugated caps density matrix (MFCC-DM) approach for energy calculation of protein and other polymers [Chen et al., J. Chem. Phys. 122, 184105 (2005)]. With this PIC, the accuracy of the calculated protein energy and other electronic properties are improved, and the MFCC approach can be applied to study real proteins with short-range structural complexity. In the present MFCC-DM-PIC approach, the short-range interresidual interactions are represented by a pair of small molecules (interacting units) which are made from the two residues that fall within a certain distance criterion. The density matrices of fragments, concaps, interacting units and pairs are calculated by conventional Hartree-Fock or density functional theory methods and are combined to construct the full density matrix which is finally employed to calculate the total energy, electron density, electrostatic potential, dipole moment, etc., of the protein. Numerical tests on seven conformationally varied peptides are presented to demonstrate the accuracy of the MFCC-DM-PIC method.
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Affiliation(s)
- X H Chen
- Department of Chemistry, New York University, New York, New York 10003, USA
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Geudtner G, Janetzko F, Köster AM, Vela A, Calaminici P. Parallelization of the deMon2k code. J Comput Chem 2006; 27:483-90. [PMID: 16435308 DOI: 10.1002/jcc.20361] [Citation(s) in RCA: 45] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Abstract
The parallelization of the LCGTO-KS-DFT code deMon2k is presented. The parallelization of the three-center electron repulsion integrals, the numerical integration using a direct grid algorithm and the matrix multiplication and diagonalization are described. The efficiency of the parallelization is analyzed by selected benchmark calculations. It is shown that geometry optimizations of systems with more than 8,000 basis functions are feasible on cluster architectures.
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Affiliation(s)
- Gerald Geudtner
- Departamento de Química, CINVESTAV, Avenida Instituto Politécnico Nacional 2508, A.P. 14-740 México D.F. 07000, México.
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Chen X, Zhang Y, Zhang JZH. An efficient approach for ab initio energy calculation of biopolymers. J Chem Phys 2005; 122:184105. [PMID: 15918692 DOI: 10.1063/1.1897382] [Citation(s) in RCA: 84] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present a new method for efficient total-energy calculation of biopolymers using the density-matrix (DM) scheme based on the molecular fractionation with conjugate caps (MFCC) approach. In this MFCC-DM method, a biopolymer such as a protein is partitioned into properly capped fragments whose density matrices are calculated by conventional ab initio methods which are then assembled to construct the full system density matrix. The assembled full density matrix is then employed to calculate the total energy and dipole moment of the protein using Hartree-Fock or density-functional theory methods. Using this MFCC-DM method, the self-consistent-field procedure for solving the full Hamiltonian problem is avoided and an efficient approach for ab initio energy calculation of biopolymers is achieved. Two implementations of the approach are presented in this paper. Systematic numerical studies are carried out on a series of extended polyglycines CH3CO-(GLY)n-NHCH3(n = 3-25) and excellent results are obtained.
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Affiliation(s)
- Xihua Chen
- Department of Chemistry, New York University, New York, New York 10003, USA
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Deev V, Collins MA. Approximateab initioenergies by systematic molecular fragmentation. J Chem Phys 2005; 122:154102. [PMID: 15945620 DOI: 10.1063/1.1879792] [Citation(s) in RCA: 225] [Impact Index Per Article: 11.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A scheme is introduced for generating a hierarchy of molecular fragmentations by which the total electronic energy can be approximated from the energies of the fragments. Higher levels in the hierarchy produce molecular fragments of larger size and approximate the total electronic energy more reliably. A correction to account for nonbonded interactions is also presented. The accuracy of the approach is tested for a number of examples, and shown to be essentially independent of the level of ab initio theory employed. The computational cost increases linearly with the size of the molecule.
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Affiliation(s)
- Vitali Deev
- Research School of Chemistry, Australian National University, Canberra ACT 0200, Australia
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