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Van den Bossche M. Three-Center Tight-Binding Together with Multipolar Auxiliary Functions. J Chem Theory Comput 2024; 20:2538-2550. [PMID: 38483273 DOI: 10.1021/acs.jctc.4c00018] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/27/2024]
Abstract
We present an ab initio tight-binding method that allows to improve on the effective potential and minimal basis approximations employed in semiempirical calculations. Three-center expansions are used to evaluate the zeroth-order Hamiltonian matrix elements and repulsive energy terms in the spirit of the Horsfield method. Self-consistency is handled by expanding atomic orbital products in an auxiliary basis following the work of Giese and York, combined with a two-center expansion of the exchange-correlation kernels. Together with nonminimal main basis sets (double-ζ plus polarization), we show that the resulting method trades a modest amount of accuracy for a significant gain in speed, compared to that of numerical atomic orbital density functional theory, in calculations on small molecules, bulk compounds, and metal nanoclusters.
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Giese TJ, York DM. Quantum mechanical force fields for condensed phase molecular simulations. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:383002. [PMID: 28817382 PMCID: PMC5821073 DOI: 10.1088/1361-648x/aa7c5c] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Molecular simulations are powerful tools for providing atomic-level details into complex chemical and physical processes that occur in the condensed phase. For strongly interacting systems where quantum many-body effects are known to play an important role, density-functional methods are often used to provide the model with the potential energy used to drive dynamics. These methods, however, suffer from two major drawbacks. First, they are often too computationally intensive to practically apply to large systems over long time scales, limiting their scope of application. Second, there remain challenges for these models to obtain the necessary level of accuracy for weak non-bonded interactions to obtain quantitative accuracy for a wide range of condensed phase properties. Quantum mechanical force fields (QMFFs) provide a potential solution to both of these limitations. In this review, we address recent advances in the development of QMFFs for condensed phase simulations. In particular, we examine the development of QMFF models using both approximate and ab initio density-functional models, the treatment of short-ranged non-bonded and long-ranged electrostatic interactions, and stability issues in molecular dynamics calculations. Example calculations are provided for crystalline systems, liquid water, and ionic liquids. We conclude with a perspective for emerging challenges and future research directions.
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Golze D, Iannuzzi M, Hutter J. Local Fitting of the Kohn–Sham Density in a Gaussian and Plane Waves Scheme for Large-Scale Density Functional Theory Simulations. J Chem Theory Comput 2017; 13:2202-2214. [DOI: 10.1021/acs.jctc.7b00148] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Dorothea Golze
- Department
of Chemistry, University of Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
- COMP/Department
of Applied Physics, Aalto University, P.O. Box 11100, Aalto FI-00076, Finland
| | - Marcella Iannuzzi
- Department
of Chemistry, University of Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
| | - Jürg Hutter
- Department
of Chemistry, University of Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
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4
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Giese T, Panteva MT, Chen H, York DM. Multipolar Ewald methods, 1: theory, accuracy, and performance. J Chem Theory Comput 2015; 11:436-50. [PMID: 25691829 PMCID: PMC4325605 DOI: 10.1021/ct5007983] [Citation(s) in RCA: 29] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/02/2014] [Indexed: 11/29/2022]
Abstract
The Ewald, Particle Mesh Ewald (PME), and Fast Fourier–Poisson (FFP) methods are developed for systems composed of spherical multipole moment expansions. A unified set of equations is derived that takes advantage of a spherical tensor gradient operator formalism in both real space and reciprocal space to allow extension to arbitrary multipole order. The implementation of these methods into a novel linear-scaling modified “divide-and-conquer” (mDC) quantum mechanical force field is discussed. The evaluation times and relative force errors are compared between the three methods, as a function of multipole expansion order. Timings and errors are also compared within the context of the quantum mechanical force field, which encounters primary errors related to the quality of reproducing electrostatic forces for a given density matrix and secondary errors resulting from the propagation of the approximate electrostatics into the self-consistent field procedure, which yields a converged, variational, but nonetheless approximate density matrix. Condensed-phase simulations of an mDC water model are performed with the multipolar PME method and compared to an electrostatic cutoff method, which is shown to artificially increase the density of water and heat of vaporization relative to full electrostatic treatment.
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Affiliation(s)
- Timothy
J. Giese
- Center for Integrative Proteomics
Research, BioMaPS Institute for Quantitative Biology and Department
of Chemistry and Chemical Biology, Rutgers
University, Piscataway, New Jersey 08854-8087, United States
| | - Maria T. Panteva
- Center for Integrative Proteomics
Research, BioMaPS Institute for Quantitative Biology and Department
of Chemistry and Chemical Biology, Rutgers
University, Piscataway, New Jersey 08854-8087, United States
| | - Haoyuan Chen
- Center for Integrative Proteomics
Research, BioMaPS Institute for Quantitative Biology and Department
of Chemistry and Chemical Biology, Rutgers
University, Piscataway, New Jersey 08854-8087, United States
| | - Darrin M. York
- Center for Integrative Proteomics
Research, BioMaPS Institute for Quantitative Biology and Department
of Chemistry and Chemical Biology, Rutgers
University, Piscataway, New Jersey 08854-8087, United States
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Choi TH, Liang R, Maupin CM, Voth GA. Application of the SCC-DFTB Method to Hydroxide Water Clusters and Aqueous Hydroxide Solutions. J Phys Chem B 2013; 117:5165-79. [DOI: 10.1021/jp400953a] [Citation(s) in RCA: 51] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
Affiliation(s)
- Tae Hoon Choi
- Department of Chemical Engineering
Education, Chungnam National University, Daejeon 305-764, Republic of Korea
| | - Ruibin Liang
- Department of Chemistry, James
Franck Institute, and Computation Institute, University of Chicago, 5735 S. Ellis Ave., Chicago, Illinois 60637,
United States
| | - C. Mark Maupin
- Chemical and Biological Engineering
Department, Colorado School of Mines, Golden,
Colorado 80401, United States
| | - Gregory A. Voth
- Department of Chemistry, James
Franck Institute, and Computation Institute, University of Chicago, 5735 S. Ellis Ave., Chicago, Illinois 60637,
United States
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6
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Merlot P, Kjaergaard T, Helgaker T, Lindh R, Aquilante F, Reine S, Pedersen TB. Attractive electron-electron interactions within robust local fitting approximations. J Comput Chem 2013; 34:1486-96. [DOI: 10.1002/jcc.23284] [Citation(s) in RCA: 54] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/30/2012] [Revised: 03/01/2013] [Accepted: 03/05/2013] [Indexed: 11/07/2022]
Affiliation(s)
- Patrick Merlot
- Centre for Theoretical and Computational Chemistry; Department of Chemistry; University of Oslo; P.O. Box 1033; Blindern; N-0315; Oslo; Norway
| | - Thomas Kjaergaard
- Centre for Theoretical and Computational Chemistry; Department of Chemistry; University of Oslo; P.O. Box 1033; Blindern; N-0315; Oslo; Norway
| | - Trygve Helgaker
- Centre for Theoretical and Computational Chemistry; Department of Chemistry; University of Oslo; P.O. Box 1033; Blindern; N-0315; Oslo; Norway
| | - Roland Lindh
- Department of Chemistry-Ångström; Theoretical Chemistry Programme; Uppsala University; P.O. Box 518; S-75120; Uppsala; Sweden
| | | | - Simen Reine
- Centre for Theoretical and Computational Chemistry; Department of Chemistry; University of Oslo; P.O. Box 1033; Blindern; N-0315; Oslo; Norway
| | - Thomas Bondo Pedersen
- Centre for Theoretical and Computational Chemistry; Department of Chemistry; University of Oslo; P.O. Box 1033; Blindern; N-0315; Oslo; Norway
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7
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Barone V, Carnimeo I, Scalmani G. Computational Spectroscopy of Large Systems in Solution: The DFTB/PCM and TD-DFTB/PCM Approach. J Chem Theory Comput 2013; 9:2052-71. [DOI: 10.1021/ct301050x] [Citation(s) in RCA: 41] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023]
Affiliation(s)
- Vincenzo Barone
- Scuola Normale Superiore, Piazza
dei Cavalieri 7, 56126, Pisa, Italy
- INFN Sezione di Pisa, Edificio
C - Polo Fibonacci Largo B. Pontecorvo, 3-56127 Pisa, Italy
| | - Ivan Carnimeo
- Scuola Normale Superiore, Piazza
dei Cavalieri 7, 56126, Pisa, Italy
- INFN Sezione di Pisa, Edificio
C - Polo Fibonacci Largo B. Pontecorvo, 3-56127 Pisa, Italy
| | - Giovanni Scalmani
- Gaussian, Inc., 340 Quinnipiac
Street Building 40, Wallingford, Connecticut 06492, United States
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Giese TJ, Chen H, Dissanayake T, Giambaşu GM, Heldenbrand H, Huang M, Kuechler ER, Lee TS, Panteva MT, Radak BK, York DM. A variational linear-scaling framework to build practical, efficient next-generation orbital-based quantum force fields. J Chem Theory Comput 2013; 9:1417-1427. [PMID: 23814506 DOI: 10.1021/ct3010134] [Citation(s) in RCA: 49] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We introduce a new hybrid molecular orbital/density-functional modified divide-and-conquer (mDC) approach that allows the linear-scaling calculation of very large quantum systems. The method provides a powerful framework from which linear-scaling force fields for molecular simulations can be developed. The method is variational in the energy, and has simple, analytic gradients and essentially no break-even point with respect to the corresponding full electronic structure calculation. Furthermore, the new approach allows intermolecular forces to be properly balanced such that non-bonded interactions can be treated, in some cases, to much higher accuracy than the full calculation. The approach is illustrated using the second-order self-consistent charge density-functional tight-binding model (DFTB2). Using this model as a base Hamiltonian, the new mDC approach is applied to a series of water systems, where results show that geometries and interaction energies between water molecules are greatly improved relative to full DFTB2. In order to achieve substantial improvement in the accuracy of intermolecular binding energies and hydrogen bonded cluster geometries, it was necessary to extend the DFTB2 model to higher-order atom-centered multipoles for the second-order self-consistent intermolecular electrostatic term. Using generalized, linear-scaling electrostatic methods, timings demonstrate that the method is able to calculate a water system of 3000 atoms in less than half of a second, and systems of up to one million atoms in only a few minutes using a conventional desktop workstation.
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Affiliation(s)
- Timothy J Giese
- BioMaPS Institute and Department of Chemistry and Chemical Biology, Rutgers University, Piscataway, NJ 08854-8087 USA
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Abstract
We discuss the source of errors in semiempirical density functional expansion (VE) methods. In particular, we show that VE methods are capable of well-reproducing their standard Kohn-Sham density functional method counterparts, but suffer from large errors upon using one or more of these approximations: the limited size of the atomic orbital basis, the Slater monopole auxiliary basis description of the response density, and the one- and two-body treatment of the core-Hamiltonian matrix elements. In the process of discussing these approximations and highlighting their symptoms, we introduce a new model that supplements the second-order density-functional tight-binding model with a self-consistent charge-dependent chemical potential equalization correction; we review our recently reported method for generalizing the auxiliary basis description of the atomic orbital response density; and we decompose the first-order potential into a summation of additive atomic components and many-body corrections, and from this examination, we provide new insights and preliminary results that motivate and inspire new approximate treatments of the core-Hamiltonian.
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Affiliation(s)
- Timothy J. Giese
- Department of Chemistry and Chemical Biology and BioMaPS Institute for Quantitative Biology, Rutgers University, Piscataway, NJ 08854-8087
| | - Darrin M. York
- Department of Chemistry and Chemical Biology and BioMaPS Institute for Quantitative Biology, Rutgers University, Piscataway, NJ 08854-8087
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