1
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Sharma S, White AF, Beylkin G. Fast Exchange with Gaussian Basis Set Using Robust Pseudospectral Method. J Chem Theory Comput 2022; 18:7306-7320. [PMID: 36417710 DOI: 10.1021/acs.jctc.2c00720] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
Abstract
In this article, we present an algorithm to efficiently evaluate the exchange matrix in periodic systems when a Gaussian basis set with pseudopotentials is used. The usual algorithm for evaluating exchange matrix scales cubically with the system size because one has to perform O(N2) fast Fourier transform (FFT). Here, we introduce an algorithm that retains the cubic scaling but reduces the prefactor significantly by eliminating the need to do FFTs during each exchange build. This is accomplished by representing the products of Gaussian basis function using a linear combination of an auxiliary basis the number of which scales linearly with the size of the system. We store the potential due to these auxiliary functions in memory, which allows us to obtain the exchange matrix without the need to do FFT, albeit at the cost of additional memory requirement. Although the basic idea of using auxiliary functions is not new, our algorithm is cheaper due to a combination of three ingredients: (a) we use a robust pseudospectral method that allows us to use a relatively small number of auxiliary basis to obtain high accuracy; (b) we use occ-RI exchange, which eliminates the need to construct the full exchange matrix; and (c) we use the (interpolative separable density fitting) ISDF algorithm to construct these auxiliary basis sets that are used in the robust pseudospectral method. The resulting algorithm is accurate, and we note that the error in the final energy decreases exponentially rapidly with the number of auxiliary functions.
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Affiliation(s)
- Sandeep Sharma
- Department of Chemistry, University of Colorado Boulder, Boulder, Colorado80309, United States
| | - Alec F White
- Quantum Simulation Technologies, Inc., Boston, Massachusetts02135, United States
| | - Gregory Beylkin
- Department of Applied Mathematics, University of Colorado, Boulder, Colorado80309, United States
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2
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Sharma S, Beylkin G. Efficient Evaluation of Two-Center Gaussian Integrals in Periodic Systems. J Chem Theory Comput 2021; 17:3916-3922. [PMID: 34061523 DOI: 10.1021/acs.jctc.0c01195] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
By using Poisson's summation formula, we calculate periodic integrals over Gaussian basis functions by partitioning the lattice summations between the real and reciprocal space, where both sums converge exponentially fast with a large exponent. We demonstrate that the summation can be performed efficiently to calculate two-center Gaussian integrals over various kernels including overlap, kinetic, and Coulomb. The summation in real space is performed using an efficient flavor of the McMurchie-Davidson recurrence relation. The expressions for performing summation in the reciprocal space are also derived and implemented. The algorithm for reciprocal space summation allows us to reuse several terms and leads to a significant improvement in efficiency when highly contracted basis functions with large exponents are used. We find that the resulting algorithm is only between a factor of 5 and 15 slower than that for molecular integrals, indicating the very small number of terms needed in both the real and reciprocal space summations. An outline of the algorithm for calculating three-center Coulomb integrals is also provided.
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Affiliation(s)
- Sandeep Sharma
- Department of Chemistry, University of Colorado, Boulder, Boulder, Colorado 80302, United States
| | - Gregory Beylkin
- Department of Applied Mathematics, University of Colorado, Boulder, Boulder, Colorado 80309, United States
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3
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Wang X, Lewis CA, Valeev EF. Efficient evaluation of exact exchange for periodic systems via concentric atomic density fitting. J Chem Phys 2020; 153:124116. [DOI: 10.1063/5.0016856] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Xiao Wang
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, USA
- Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, USA
| | - Cannada A. Lewis
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, USA
| | - Edward F. Valeev
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, USA
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4
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Repisky M, Komorovsky S, Kadek M, Konecny L, Ekström U, Malkin E, Kaupp M, Ruud K, Malkina OL, Malkin VG. ReSpect: Relativistic spectroscopy DFT program package. J Chem Phys 2020; 152:184101. [DOI: 10.1063/5.0005094] [Citation(s) in RCA: 47] [Impact Index Per Article: 11.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023] Open
Affiliation(s)
- Michal Repisky
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, UiT The Arctic University of Norway, N-9037 Tromsø, Norway
| | - Stanislav Komorovsky
- Institute of Inorganic Chemistry, Slovak Academy of Sciences, Dubravska cesta 9, SK-84536 Bratislava, Slovakia
| | - Marius Kadek
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, UiT The Arctic University of Norway, N-9037 Tromsø, Norway
| | - Lukas Konecny
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, UiT The Arctic University of Norway, N-9037 Tromsø, Norway
| | - Ulf Ekström
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, N-0315 Oslo, Norway
| | - Elena Malkin
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, UiT The Arctic University of Norway, N-9037 Tromsø, Norway
| | - Martin Kaupp
- Technische Universität Berlin, Institute of Chemistry, Strasse des 17 Juni 135, D-10623 Berlin, Germany
| | - Kenneth Ruud
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, UiT The Arctic University of Norway, N-9037 Tromsø, Norway
| | - Olga L. Malkina
- Institute of Inorganic Chemistry, Slovak Academy of Sciences, Dubravska cesta 9, SK-84536 Bratislava, Slovakia
| | - Vladimir G. Malkin
- Institute of Inorganic Chemistry, Slovak Academy of Sciences, Dubravska cesta 9, SK-84536 Bratislava, Slovakia
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5
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Becker M, Sierka M. Density functional theory for molecular and periodic systems using density fitting and continuous fast multipole method: Stress tensor. J Comput Chem 2019; 40:2563-2570. [PMID: 31322769 DOI: 10.1002/jcc.26033] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/09/2019] [Revised: 06/24/2019] [Accepted: 06/27/2019] [Indexed: 11/06/2022]
Abstract
A full implementation of the analytical stress tensor for periodic systems is reported in the TURBOMOLE program package within the framework of Kohn-Sham density functional theory using Gaussian-type orbitals as basis functions. It is the extension of the implementation of analytical energy gradients (Lazarski et al., Journal of Computational Chemistry 2016, 37, 2518-2526) to the stress tensor for the purpose of optimization of lattice vectors. Its key component is the efficient calculation of the Coulomb contribution by combining density fitting approximation and continuous fast multipole method. For the exchange-correlation (XC) part the hierarchical numerical integration scheme (Burow and Sierka, Journal of Chemical Theory and Computation 2011, 7, 3097-3104) is extended to XC weight derivatives and stress tensor. The computational efficiency and favorable scaling behavior of the stress tensor implementation are demonstrated for various model systems. The overall computational effort for energy gradient and stress tensor for the largest systems investigated is shown to be at most two and a half times the computational effort for the Kohn-Sham matrix formation. © 2019 Wiley Periodicals, Inc.
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Affiliation(s)
- Martin Becker
- Otto-Schott-Institut für Materialforschung, Friedrich-Schiller-Universität Jena, Löbdergraben 32, Jena, D-07743, Germany
| | - Marek Sierka
- Otto-Schott-Institut für Materialforschung, Friedrich-Schiller-Universität Jena, Löbdergraben 32, Jena, D-07743, Germany
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6
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Jiang J, Wang ZG. Improved local lattice Monte Carlo simulation for charged systems. J Chem Phys 2018; 148:114105. [DOI: 10.1063/1.5023491] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Jian Jiang
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Zhen-Gang Wang
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
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7
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Varga Š. Communication: Renormalization method for infinite lattice sums revisited: Lattice sums with Bloch phase factors. J Chem Phys 2018; 148:051102. [DOI: 10.1063/1.5018359] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Štefan Varga
- Institute of Inorganic Chemistry, Slovak Academy of Sciences, Dúbravská Cesta 9, SK-84536 Bratislava, Slovakia
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8
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Le HA, Shiozaki T. Occupied-Orbital Fast Multipole Method for Efficient Exact Exchange Evaluation. J Chem Theory Comput 2018; 14:1228-1234. [DOI: 10.1021/acs.jctc.7b00880] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Hai-Anh Le
- Department of Chemistry, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208, United States
| | - Toru Shiozaki
- Department of Chemistry, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208, United States
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9
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Grundei MMJ, Burow AM. Random Phase Approximation for Periodic Systems Employing Direct Coulomb Lattice Summation. J Chem Theory Comput 2017; 13:1159-1175. [DOI: 10.1021/acs.jctc.6b01146] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Martin M. J. Grundei
- Department of Chemistry, Ludwig-Maximilians-Universität (LMU) Munich, Butenandtstrasse 7, D-81377 Munich, Germany
| | - Asbjörn M. Burow
- Department of Chemistry, Ludwig-Maximilians-Universität (LMU) Munich, Butenandtstrasse 7, D-81377 Munich, Germany
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10
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Łazarski R, Burow AM, Grajciar L, Sierka M. Density functional theory for molecular and periodic systems using density fitting and continuous fast multipole method: Analytical gradients. J Comput Chem 2016; 37:2518-26. [PMID: 27555218 DOI: 10.1002/jcc.24477] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/23/2016] [Revised: 08/02/2016] [Accepted: 08/04/2016] [Indexed: 11/10/2022]
Abstract
A full implementation of analytical energy gradients for molecular and periodic systems is reported in the TURBOMOLE program package within the framework of Kohn-Sham density functional theory using Gaussian-type orbitals as basis functions. Its key component is a combination of density fitting (DF) approximation and continuous fast multipole method (CFMM) that allows for an efficient calculation of the Coulomb energy gradient. For exchange-correlation part the hierarchical numerical integration scheme (Burow and Sierka, Journal of Chemical Theory and Computation 2011, 7, 3097) is extended to energy gradients. Computational efficiency and asymptotic O(N) scaling behavior of the implementation is demonstrated for various molecular and periodic model systems, with the largest unit cell of hematite containing 640 atoms and 19,072 basis functions. The overall computational effort of energy gradient is comparable to that of the Kohn-Sham matrix formation. © 2016 Wiley Periodicals, Inc.
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Affiliation(s)
- Roman Łazarski
- Otto-Schott-Institut für Materialforschung (OSIM), Friedrich-Schiller-Universität Jena, Löbdergraben 32, Jena, D-07743, Germany
| | - Asbjörn Manfred Burow
- Department of Chemistry, Chair of Theoretical Chemistry, University of Munich (LMU), Butenandtstrasse 7, Munich, D-81377, Germany
| | - Lukáš Grajciar
- Otto-Schott-Institut für Materialforschung (OSIM), Friedrich-Schiller-Universität Jena, Löbdergraben 32, Jena, D-07743, Germany
| | - Marek Sierka
- Otto-Schott-Institut für Materialforschung (OSIM), Friedrich-Schiller-Universität Jena, Löbdergraben 32, Jena, D-07743, Germany.
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11
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Łazarski R, Burow AM, Sierka M. Density Functional Theory for Molecular and Periodic Systems Using Density Fitting and Continuous Fast Multipole Methods. J Chem Theory Comput 2016; 11:3029-41. [PMID: 26575740 DOI: 10.1021/acs.jctc.5b00252] [Citation(s) in RCA: 35] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
An implementation of Kohn-Sham density functional theory within the TURBOMOLE program package with Gaussian-type orbitals (GTO) as basis functions is reported that treats molecular and periodic systems of any dimensionality on an equal footing. Its key component is a combination of density fitting/resolution of identity (DF) approximation and continuous fast multipole method (CFMM) applied for the electronic Coulomb term. This DF-CFMM scheme operates entirely in the direct space and partitions Coulomb interactions into far-field part evaluated using multipole expansions and near-field contribution calculated employing density fitting. Computational efficiency and favorable scaling behavior of our implementation approaching O(N) for the formation of Kohn-Sham matrix is demonstrated for various molecular and periodic systems including three-dimensional models with unit cells containing up to 640 atoms and 19072 GTO basis functions.
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Affiliation(s)
- Roman Łazarski
- Otto-Schott-Institut für Materialforschung (OSIM), Friedrich-Schiller-Universität Jena , Löbdergraben 32, D-07743 Jena, Germany
| | - Asbjörn M Burow
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU) , Butenandtstrasse 7, D-81377 Munich, Germany
| | - Marek Sierka
- Otto-Schott-Institut für Materialforschung (OSIM), Friedrich-Schiller-Universität Jena , Löbdergraben 32, D-07743 Jena, Germany
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12
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Khoromskaia V, Khoromskij BN. Tensor numerical methods in quantum chemistry: from Hartree–Fock to excitation energies. Phys Chem Chem Phys 2015; 17:31491-509. [DOI: 10.1039/c5cp01215e] [Citation(s) in RCA: 41] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
Abstract
We resume the recent successes of the grid-based tensor numerical methods and discuss their prospects in real-space electronic structure calculations.
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Affiliation(s)
- Venera Khoromskaia
- Max-Planck-Institute for Dynamics of Complex Systems
- Magdeburg
- Germany
- Max-Planck Institute for Mathematics in the Sciences
- Leipzig
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13
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Arnold A, Fahrenberger F, Holm C, Lenz O, Bolten M, Dachsel H, Halver R, Kabadshow I, Gähler F, Heber F, Iseringhausen J, Hofmann M, Pippig M, Potts D, Sutmann G. Comparison of scalable fast methods for long-range interactions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:063308. [PMID: 24483585 DOI: 10.1103/physreve.88.063308] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/08/2013] [Indexed: 06/03/2023]
Abstract
Based on a parallel scalable library for Coulomb interactions in particle systems, a comparison between the fast multipole method (FMM), multigrid-based methods, fast Fourier transform (FFT)-based methods, and a Maxwell solver is provided for the case of three-dimensional periodic boundary conditions. These methods are directly compared with respect to complexity, scalability, performance, and accuracy. To ensure comparable conditions for all methods and to cover typical applications, we tested all methods on the same set of computers using identical benchmark systems. Our findings suggest that, depending on system size and desired accuracy, the FMM- and FFT-based methods are most efficient in performance and stability.
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Affiliation(s)
- Axel Arnold
- Institute for Computational Physics, University of Stuttgart, Stuttgart, Germany
| | - Florian Fahrenberger
- Institute for Computational Physics, University of Stuttgart, Stuttgart, Germany
| | - Christian Holm
- Institute for Computational Physics, University of Stuttgart, Stuttgart, Germany
| | - Olaf Lenz
- Institute for Computational Physics, University of Stuttgart, Stuttgart, Germany
| | - Matthias Bolten
- Department of Mathematics and Science, University of Wuppertal, Wuppertal, Germany
| | - Holger Dachsel
- Institute for Advanced Simulation, Jülich Supercomputing Centre, Forschungszentrum Jülich GmbH, Jülich, Germany
| | - Rene Halver
- Institute for Advanced Simulation, Jülich Supercomputing Centre, Forschungszentrum Jülich GmbH, Jülich, Germany
| | - Ivo Kabadshow
- Institute for Advanced Simulation, Jülich Supercomputing Centre, Forschungszentrum Jülich GmbH, Jülich, Germany
| | - Franz Gähler
- Faculty of Mathematics, Bielefeld University, Bielefeld, Germany
| | - Frederik Heber
- Institute for Numerical Simulation, University of Bonn, Bonn, Germany
| | | | - Michael Hofmann
- Department of Computer Science, Chemnitz University of Technology, Chemnitz, Germany
| | - Michael Pippig
- Department of Mathematics, Chemnitz University of Technology, Chemnitz, Germany
| | - Daniel Potts
- Department of Mathematics, Chemnitz University of Technology, Chemnitz, Germany
| | - Godehard Sutmann
- Institute for Advanced Simulation, Jülich Supercomputing Centre, Forschungszentrum Jülich GmbH, Jülich, Germany and ICAMS, Ruhr-University, Bochum, Germany
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14
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Yamada T, Brewster RP, Hirata S. Asymptotic expansion of two-electron integrals and its application to Coulomb and exchange lattice sums in metallic, semimetallic, and nonmetallic crystals. J Chem Phys 2013; 139:184107. [DOI: 10.1063/1.4828796] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Tomonori Yamada
- Department of Chemistry, University of Illinois at Urbana-Champaign, 600 South Mathews Avenue, Urbana, Illinois 61801, USA
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15
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Bodrenko IV, Della Sala F. A periodic charge-dipole electrostatic model. II. A kinetic-exchange-correlation correction. J Chem Phys 2013; 139:144109. [PMID: 24116605 DOI: 10.1063/1.4824189] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We extend the periodic charge-dipole electrostatic model, see I. V. Bodrenko, M. Sierka, E. Fabiano, and F. Della Sala, J. Chem. Phys. 137, 134702 (2012), to include a kinetic-exchange-correlation (KXC) correction. The KXC correction is approximated by means of an extended-Hückel-type formula, it is exact in the infinite jellium model and it is also computationally efficient as it requires only the computation of overlap integrals. Tests on the linear response of silver slabs to an external electrostatic perturbation show that the KXC correction yields a very accurate description of induced dipole and of the whole induced charge density profile. We also show that the KXC parameters are quite transferable and related to the atomic polarizability.
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Affiliation(s)
- I V Bodrenko
- National Nanotechnology Laboratory (NNL), Istituto Nanoscienze-CNR, Via per Arnesano 16, 73100 Lecce, Italy
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16
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Del Ben M, Hutter J, VandeVondele J. Electron Correlation in the Condensed Phase from a Resolution of Identity Approach Based on the Gaussian and Plane Waves Scheme. J Chem Theory Comput 2013; 9:2654-71. [DOI: 10.1021/ct4002202] [Citation(s) in RCA: 100] [Impact Index Per Article: 9.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Mauro Del Ben
- Institute of Physical Chemistry, University of Zürich, Winterthurerstrasse 190,
CH-8057 Zürich, Switzerland
| | - Jürg Hutter
- Institute of Physical Chemistry, University of Zürich, Winterthurerstrasse 190,
CH-8057 Zürich, Switzerland
| | - Joost VandeVondele
- Department
of Materials, ETH Zürich, Wolfgang-Pauli-Strasse 27, CH-8093 Zürich, Switzerland
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17
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Wen XD, Martin RL, Henderson TM, Scuseria GE. Density Functional Theory Studies of the Electronic Structure of Solid State Actinide Oxides. Chem Rev 2012; 113:1063-96. [DOI: 10.1021/cr300374y] [Citation(s) in RCA: 163] [Impact Index Per Article: 13.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Xiao-Dong Wen
- Theoretical
Division, Los Alamos National Laboratory, Los Alamos, New Mexico
87545, United States
| | - Richard L. Martin
- Theoretical
Division, Los Alamos National Laboratory, Los Alamos, New Mexico
87545, United States
| | - Thomas M. Henderson
- Department
of Chemistry and
Department of Physics and Astronomy, Rice University, Houston, Texas 77251, United States
| | - Gustavo E. Scuseria
- Department
of Chemistry and
Department of Physics and Astronomy, Rice University, Houston, Texas 77251, United States
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18
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Bodrenko IV, Sierka M, Fabiano E, Della Sala F. A periodic charge-dipole electrostatic model: parametrization for silver slabs. J Chem Phys 2012; 137:134702. [PMID: 23039605 DOI: 10.1063/1.4754719] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present an extension of the charge-dipole model for the description of periodic systems. This periodic charge-dipole electrostatic model (PCDEM) allows one to describe the linear response of periodic structures in terms of charge- and dipole-type gaussian basis functions. The long-range electrostatic interaction is efficiently described by means of the continuous fast multipole method. As a first application, the PCDEM method is applied to describe the polarizability of silver slabs. We find that for a correct description of the polarizability of the slabs both charges and dipoles are required. However a continuum set of parametrizations, i.e., different values of the width of charge- and dipole-type gaussians, leads to an equivalent and accurate description of the slabs polarizability but a completely unphysical description of induced charge-density inside the slab. We introduced the integral squared density measure which allows one to obtain a unique parametrization which accurately describes both the polarizability and the induced density profile inside the slab. Finally the limits of the electrostatic approximations are also pointed out.
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Affiliation(s)
- I V Bodrenko
- National Nanotechnology Laboratory (NNL), Istituto Nanoscienze-CNR, Via per Arnesano 16, 73100 Lecce, Italy
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19
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Götz K, Meier F, Gatti C, Burow AM, Sierka M, Sauer J, Kaupp M. Modeling environmental effects on charge density distributions in polar organometallics: validation of embedded cluster models for the methyl lithium crystal. J Comput Chem 2010; 31:2568-76. [PMID: 20740555 DOI: 10.1002/jcc.21548] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Abstract
The charge density and its Laplacian at the Li-C and C-H bond critical points and other features of the electron density distribution of the methyl lithium crystal have been compared by density functional methods for (i) the isolated (LiCH(3))(4) tetramer or larger clusters, (ii) for quantum mechanically treated clusters in polarizable continuum model (PCM) surroundings, (iii) for clusters augmented by the periodic electrostatic embedded cluster model (PEECM), and for (iv) the periodic crystal. Comparisons with identical functional and basis sets indicate that both PCM and PEECM embedding of only a tetramer did not fully account for the environmental effect. In contrast, embedding of a full unit cell gave results that were essentially converged to the periodic crystal data. Effects of basis set and exchange correlation functional on the QTAIM bond descriptors are of a comparable order of magnitude as the crystal environmental effects. In this context, embedded cluster computations provide distinct advantages over explicit solid-state calculations with respect to their freedom of the choice of computational and theoretical level. This is demonstrated by embedded MP2 calculations.
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Affiliation(s)
- Kathrin Götz
- Institut für Physikalische und Theoretische Chemie, Universität Würzburg, Am Hubland, 97074 Würzburg
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20
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Ammal SC, Heyden A. Modeling the noble metal/TiO2 (110) interface with hybrid DFT functionals: A periodic electrostatic embedded cluster model study. J Chem Phys 2010; 133:164703. [DOI: 10.1063/1.3497037] [Citation(s) in RCA: 54] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022] Open
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21
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Burow AM, Sierka M, Mohamed F. Resolution of identity approximation for the Coulomb term in molecular and periodic systems. J Chem Phys 2010; 131:214101. [PMID: 19968331 DOI: 10.1063/1.3267858] [Citation(s) in RCA: 58] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A new formulation of resolution of identity approximation for the Coulomb term is presented, which uses atom-centered basis and auxiliary basis functions and treats molecular and periodic systems of any dimensionality on an equal footing. It relies on the decomposition of an auxiliary charge density into charged and chargeless components. Applying the Coulomb metric under periodic boundary conditions constrains the explicit form of the charged part. The chargeless component is determined variationally and converged Coulomb lattice sums needed for its determination are obtained using chargeless linear combinations of auxiliary basis functions. The lattice sums are partitioned in near- and far-field portions which are treated through an analytical integration scheme employing two- and three-center electron repulsion integrals and multipole expansions, respectively, operating exclusively in real space. Our preliminary implementation within the TURBOMOLE program package demonstrates consistent accuracy of the method across molecular and periodic systems. Using common auxiliary basis sets the errors of the approximation are small, in average about 20 muhartree per atom, for both molecular and periodic systems.
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Affiliation(s)
- Asbjörn M Burow
- Institut für Chemie, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099-D, Germany
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22
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Mullin JM, Roskop LB, Pruitt SR, Collins MA, Gordon MS. Systematic fragmentation method and the effective fragment potential: an efficient method for capturing molecular energies. J Phys Chem A 2010; 113:10040-9. [PMID: 19739681 DOI: 10.1021/jp9036183] [Citation(s) in RCA: 61] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
The systematic fragmentation method fragments a large molecular system into smaller pieces, in such a way as to greatly reduce the computational cost while retaining nearly the accuracy of the parent ab initio electronic structure method. In order to attain the desired (sub-kcal/mol) accuracy, one must properly account for the nonbonded interactions between the separated fragments. Since, for a large molecular species, there can be a great many fragments and therefore a great many nonbonded interactions, computations of the nonbonded interactions can be very time-consuming. The present work explores the efficacy of employing the effective fragment potential (EFP) method to obtain the nonbonded interactions since the EFP method has been shown previously to capture nonbonded interactions with an accuracy that is often comparable to that of second-order perturbation theory. It is demonstrated that for nonbonded interactions that are not high on the repulsive wall (generally >2.7 A), the EFP method appears to be a viable approach for evaluating the nonbonded interactions. The efficacy of the EFP method for this purpose is illustrated by comparing the method to ab initio methods for small water clusters, the ZOVGAS molecule, retinal, and the alpha-helix. Using SFM with EFP for nonbonded interactions yields an error of 0.2 kcal/mol for the retinal cis-trans isomerization and a mean error of 1.0 kcal/mol for the isomerization energies of five small (120-170 atoms) alpha-helices.
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Reif MM, Kräutler V, Kastenholz MA, Daura X, Hünenberger PH. Molecular dynamics simulations of a reversibly folding beta-heptapeptide in methanol: influence of the treatment of long-range electrostatic interactions. J Phys Chem B 2009; 113:3112-28. [PMID: 19228001 DOI: 10.1021/jp807421a] [Citation(s) in RCA: 65] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Eight 100-ns molecular dynamics simulations of a beta-heptapeptide in methanol at 340 K (within cubic periodic computational boxes of about 6-nm edge) are reported and compared. These simulations were performed with three different charge-state combinations at the peptide termini, one of them with or without a neutralizing chloride counterion, and using either the lattice-sum (LS) or reaction-field (RF) scheme to handle electrostatic interactions. The choice of the electrostatic scheme has essentially no influence on the folding-unfolding equilibrium when the peptide termini are uncharged and only a small influence when the peptide is positively charged at its N-terminus (with or without inclusion of a neutralizing chloride counterion). However, when the peptide is zwitterionic, the LS scheme leads to preferential sampling of the high-dipole folded helical state, whereas the RF scheme leads to preferential sampling of a low-dipole unfolded salt-bridged state. A continuum electrostatics analysis based on the sampled configurations (zwitterionic case) suggests that the LS scheme stabilizes the helical state through artificial periodicity, but that the magnitude of this perturbation is essentially negligible (compared to the thermal energy) for the large box size and relatively polar solvent considered. The results thus provide clear evidence (continuum electrostatics analysis) for the absence of LS artifacts and some indications (still not definitive because of the limited sampling of the folding-unfolding transition) for the presence of RF artifacts in this specific system.
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Affiliation(s)
- Maria M Reif
- Laboratory of Physical Chemistry, ETH Zürich, CH-8093 Zürich, Switzerland
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Burow AM, Sierka M, Döbler J, Sauer J. Point defects in CaF2 and CeO2 investigated by the periodic electrostatic embedded cluster method. J Chem Phys 2009; 130:174710. [DOI: 10.1063/1.3123527] [Citation(s) in RCA: 79] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Peach MJG, Tellgren EI, Sałek P, Helgaker T, Tozer DJ. Structural and Electronic Properties of Polyacetylene and Polyyne from Hybrid and Coulomb-Attenuated Density Functionals. J Phys Chem A 2007; 111:11930-5. [DOI: 10.1021/jp0754839] [Citation(s) in RCA: 127] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Affiliation(s)
- Michael J. G. Peach
- Department of Chemistry, University of Durham, South Road, Durham DH1 3LE, U.K., Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Oslo, PO Box 1033, Blindern, N-0315 Oslo, Norway, and Laboratory of Theoretical Chemistry, AlbaNova University Center, Royal Institute of Technology, S-10691 Stockholm, Sweden
| | - Erik I. Tellgren
- Department of Chemistry, University of Durham, South Road, Durham DH1 3LE, U.K., Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Oslo, PO Box 1033, Blindern, N-0315 Oslo, Norway, and Laboratory of Theoretical Chemistry, AlbaNova University Center, Royal Institute of Technology, S-10691 Stockholm, Sweden
| | - Paweł Sałek
- Department of Chemistry, University of Durham, South Road, Durham DH1 3LE, U.K., Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Oslo, PO Box 1033, Blindern, N-0315 Oslo, Norway, and Laboratory of Theoretical Chemistry, AlbaNova University Center, Royal Institute of Technology, S-10691 Stockholm, Sweden
| | - Trygve Helgaker
- Department of Chemistry, University of Durham, South Road, Durham DH1 3LE, U.K., Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Oslo, PO Box 1033, Blindern, N-0315 Oslo, Norway, and Laboratory of Theoretical Chemistry, AlbaNova University Center, Royal Institute of Technology, S-10691 Stockholm, Sweden
| | - David J. Tozer
- Department of Chemistry, University of Durham, South Road, Durham DH1 3LE, U.K., Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Oslo, PO Box 1033, Blindern, N-0315 Oslo, Norway, and Laboratory of Theoretical Chemistry, AlbaNova University Center, Royal Institute of Technology, S-10691 Stockholm, Sweden
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Kräutler V, Hünenberger PH. A multiple time step algorithm compatible with a large number of distance classes and an arbitrary distance dependence of the time step size for the fast evaluation of nonbonded interactions in molecular simulations. J Comput Chem 2007; 27:1163-76. [PMID: 16739162 DOI: 10.1002/jcc.20436] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
A new algorithm is introduced to perform the multiple time step integration of the equations of motion for a molecular system, based on the splitting of the nonbonded interactions into a series of distance classes. The interactions between particle pairs in successive classes are updated at a progressively decreasing frequency. Unlike previous multiple time-stepping schemes relying on distance classes, the present algorithm sorts interacting particle pairs by their next update times rather than by their update frequencies. For this reason, the proposed scheme is extremely flexible with respect to the number of classes that can be employed (up to hundred or more) and the distance dependence of the relative time step size (arbitrary integer function of the distance). It can also easily be adapted to classes defined based on a criterion other than the interparticle distance (e.g., interaction magnitude). Different variants of the algorithm are tested in terms of accuracy and efficiency for simulations of a pure water system (6167 molecules) under truncated-octahedral periodic boundary conditions, and compared to the twin-range method standardly used with GROMOS96 (short- and long-range cutoff distances of 0.8 and 1.4 nm, pair list and intermediate-range interactions updated every five steps). In particular, multiple time-stepping schemes with an accuracy comparable to that of the twin-range method can be designed, that permit to increase the effective (long-range) cutoff distance from 1.4 to 3.0 nm with a performance loss of only about a factor 2. This result is quite encouraging, considering the benefits of doubling the cutoff radius in the context of (bio-)molecular simulations.
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Affiliation(s)
- Vincent Kräutler
- Laboratory of Physical Chemistry, Wolfgang-Pauli Strasse 10, HC1 G233, ETH-Hoenggerberg, CH-8093 Zürich, Switzerland
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