1
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Mi W, Luo K, Trickey SB, Pavanello M. Orbital-Free Density Functional Theory: An Attractive Electronic Structure Method for Large-Scale First-Principles Simulations. Chem Rev 2023; 123:12039-12104. [PMID: 37870767 DOI: 10.1021/acs.chemrev.2c00758] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2023]
Abstract
Kohn-Sham Density Functional Theory (KSDFT) is the most widely used electronic structure method in chemistry, physics, and materials science, with thousands of calculations cited annually. This ubiquity is rooted in the favorable accuracy vs cost balance of KSDFT. Nonetheless, the ambitions and expectations of researchers for use of KSDFT in predictive simulations of large, complicated molecular systems are confronted with an intrinsic computational cost-scaling challenge. Particularly evident in the context of first-principles molecular dynamics, the challenge is the high cost-scaling associated with the computation of the Kohn-Sham orbitals. Orbital-free DFT (OFDFT), as the name suggests, circumvents entirely the explicit use of those orbitals. Without them, the structural and algorithmic complexity of KSDFT simplifies dramatically and near-linear scaling with system size irrespective of system state is achievable. Thus, much larger system sizes and longer simulation time scales (compared to conventional KSDFT) become accessible; hence, new chemical phenomena and new materials can be explored. In this review, we introduce the historical contexts of OFDFT, its theoretical basis, and the challenge of realizing its promise via approximate kinetic energy density functionals (KEDFs). We review recent progress on that challenge for an array of KEDFs, such as one-point, two-point, and machine-learnt, as well as some less explored forms. We emphasize use of exact constraints and the inevitability of design choices. Then, we survey the associated numerical techniques and implemented algorithms specific to OFDFT. We conclude with an illustrative sample of applications to showcase the power of OFDFT in materials science, chemistry, and physics.
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Affiliation(s)
- Wenhui Mi
- Key Laboratory of Material Simulation Methods & Software of Ministry of Education, College of Physics, Jilin University, Changchun 130012, PR China
- State Key Laboratory of Superhard Materials, Jilin University, Changchun 130012, PR China
- International Center of Future Science, Jilin University, Changchun 130012, PR China
| | - Kai Luo
- Department of Applied Physics, Nanjing University of Science and Technology, Nanjing 210094, PR China
| | - S B Trickey
- Quantum Theory Project, Department of Physics and Department of Chemistry, University of Florida, Gainesville, Florida 32611, United States
| | - Michele Pavanello
- Department of Physics and Department of Chemistry, Rutgers University, Newark, New Jersey 07102, United States
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2
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Svensson P, Campbell T, Graziani F, Moldabekov Z, Lyu N, Batista VS, Richardson S, Vinko SM, Gregori G. Development of a new quantum trajectory molecular dynamics framework. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2023; 381:20220325. [PMID: 37393934 PMCID: PMC10315217 DOI: 10.1098/rsta.2022.0325] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/14/2022] [Accepted: 01/19/2023] [Indexed: 07/04/2023]
Abstract
An extension to the wave packet description of quantum plasmas is presented, where the wave packet can be elongated in arbitrary directions. A generalized Ewald summation is constructed for the wave packet models accounting for long-range Coulomb interactions and fermionic effects are approximated by purpose-built Pauli potentials, self-consistent with the wave packets used. We demonstrate its numerical implementation with good parallel support and close to linear scaling in particle number, used for comparisons with the more common wave packet employing isotropic states. Ground state and thermal properties are compared between the models with differences occurring primarily in the electronic subsystem. Especially, the electrical conductivity of dense hydrogen is investigated where a 15% increase in DC conductivity can be seen in our wave packet model compared with other models. This article is part of the theme issue 'Dynamic and transient processes in warm dense matter'.
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Affiliation(s)
- Pontus Svensson
- Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, UK
| | - Thomas Campbell
- Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, UK
| | - Frank Graziani
- Lawrence Livermore National Laboratory, Livermore, CA 94550, USA
| | - Zhandos Moldabekov
- Center of Advanced Systems Understanding (CASUS), D-02826 Görlitz, Germany
- Helmholtz-Zentrum Dresden-Rossendorf (HZDR), D-01328 Dresden, Germany
| | - Ningyi Lyu
- Department of Chemistry, Yale University, New Haven, CT 06520, USA
| | - Victor S Batista
- Department of Chemistry, Yale University, New Haven, CT 06520, USA
- Yale Quantum Institute, Yale University, New Haven, CT 06511, USA
| | | | - Sam M Vinko
- Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, UK
- Central Laser Facility, STFC Rutherford Appleton Laboratory, Didcot OX11 0QX, UK
| | - Gianluca Gregori
- Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, UK
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3
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White TG, Dai J, Riley D. Dynamic and transient processes in warm dense matter. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2023; 381:20220223. [PMID: 37393937 PMCID: PMC10315215 DOI: 10.1098/rsta.2022.0223] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/05/2023] [Accepted: 05/22/2023] [Indexed: 07/04/2023]
Abstract
In this paper, we discuss some of the key challenges in the study of time-dependent processes and non-equilibrium behaviour in warm dense matter. We outline some of the basic physics concepts that have underpinned the definition of warm dense matter as a subject area in its own right and then cover, in a selective, non-comprehensive manner, some of the current challenges, pointing along the way to topics covered by the papers presented in this volume. This article is part of the theme issue 'Dynamic and transient processes in warm dense matter'.
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Affiliation(s)
- Thomas G. White
- Department of Physics, University of Nevada, Reno, NV 89557, USA
| | - Jiayu Dai
- College of Science, National University of Defense Technology, Changsha 410073, People’s Republic of China
| | - David Riley
- School of Mathematics and Physics, Queen’s University Belfast, Belfast BT7 1NN, UK
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4
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Dynamical Density of Two-Dimensional Dusty Plasmas. IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY, TRANSACTIONS A: SCIENCE 2022. [DOI: 10.1007/s40995-022-01386-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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5
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Xu Q, Jing X, Zhang B, Pask J, Suryanarayana P. Real-space density kernel method for Kohn-Sham density functional theory calculations at high temperature. J Chem Phys 2022; 156:094105. [DOI: 10.1063/5.0082523] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Qimen Xu
- Georgia Institute of Technology, United States of America
| | - Xin Jing
- School of Computational Science and Engineering, Georgia Institute of Technology, United States of America
| | - Boqin Zhang
- Georgia Institute of Technology, United States of America
| | - John Pask
- Physics, LLNL, United States of America
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6
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Shahzad A, Manzoor A, Wang W, Mahboob A, Kashif M, He MG. Dynamic Characteristics of Strongly Coupled Nonideal Plasmas. ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING 2021. [DOI: 10.1007/s13369-021-05954-4] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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7
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An Investigation into the Approximations Used in Wave Packet Molecular Dynamics for the Study of Warm Dense Matter. PLASMA 2021. [DOI: 10.3390/plasma4020020] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
Wave packet molecular dynamics (WPMD) has recently received a lot of attention as a computationally fast tool with which to study dynamical processes in warm dense matter beyond the Born–Oppenheimer approximation. These techniques, typically, employ many approximations to achieve computational efficiency while implementing semi-empirical scaling parameters to retain accuracy. We investigated three of the main approximations ubiquitous to WPMD: a restricted basis set, approximations to exchange, and the lack of correlation. We examined each of these approximations in regard to atomic and molecular hydrogen in addition to a dense hydrogen plasma. We found that the biggest improvement to WPMD comes from combining a two-Gaussian basis with a semi-empirical correction based on the valence-bond wave function. A single parameter scales this correction to match experimental pressures of dense hydrogen. Ultimately, we found that semi-empirical scaling parameters are necessary to correct for the main approximations in WPMD. However, reducing the scaling parameters for more ab-initio terms gives more accurate results and displays the underlying physics more readily.
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8
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Sharma A, Hamel S, Bethkenhagen M, Pask JE, Suryanarayana P. Real-space formulation of the stress tensor for O(N) density functional theory: Application to high temperature calculations. J Chem Phys 2020; 153:034112. [PMID: 32716199 DOI: 10.1063/5.0016783] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present an accurate and efficient real-space formulation of the Hellmann-Feynman stress tensor for O(N) Kohn-Sham density functional theory (DFT). While applicable at any temperature, the formulation is most efficient at high temperature where the Fermi-Dirac distribution becomes smoother and the density matrix becomes correspondingly more localized. We first rewrite the orbital-dependent stress tensor for real-space DFT in terms of the density matrix, thereby making it amenable to O(N) methods. We then describe its evaluation within the O(N) infinite-cell Clenshaw-Curtis Spectral Quadrature (SQ) method, a technique that is applicable to metallic and insulating systems, is highly parallelizable, becomes increasingly efficient with increasing temperature, and provides results corresponding to the infinite crystal without the need of Brillouin zone integration. We demonstrate systematic convergence of the resulting formulation with respect to SQ parameters to exact diagonalization results and show convergence with respect to mesh size to the established plane wave results. We employ the new formulation to compute the viscosity of hydrogen at 106 K from Kohn-Sham quantum molecular dynamics, where we find agreement with previous more approximate orbital-free density functional methods.
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Affiliation(s)
- Abhiraj Sharma
- College of Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
| | - Sebastien Hamel
- Physics Division, Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - Mandy Bethkenhagen
- College of Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, USAPhysics Division, Lawrence Livermore National Laboratory, Livermore, California 94550, USACNRS, École Normale Supérieure de Lyon, Laboratoire de Géologie de Lyon LGLTPE UMR5276, Centre Blaise Pascal, 46 Allée D'Italie, Lyon 69364, France
| | - John E Pask
- Physics Division, Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - Phanish Suryanarayana
- College of Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
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9
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Shao X, Jiang K, Mi W, Genova A, Pavanello M. DFTpy
: An efficient and object‐oriented platform for orbital‐free
DFT
simulations. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2020. [DOI: 10.1002/wcms.1482] [Citation(s) in RCA: 22] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Affiliation(s)
- Xuecheng Shao
- Department of Chemistry Rutgers University Newark New Jersey USA
| | - Kaili Jiang
- Department of Chemistry Rutgers University Newark New Jersey USA
| | - Wenhui Mi
- Department of Chemistry Rutgers University Newark New Jersey USA
| | - Alessandro Genova
- Department of Chemistry Rutgers University Newark New Jersey USA
- Kitware Inc., 1712 U.S. 9 Suite 300, Clifton Park New York New York USA
| | - Michele Pavanello
- Department of Chemistry Rutgers University Newark New Jersey USA
- Department of Physics Rutgers University Newark New Jersey USA
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10
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Liu Q, Lu D, Chen M. Structure and dynamics of warm dense aluminum: a molecular dynamics study with density functional theory and deep potential. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:144002. [PMID: 31739300 DOI: 10.1088/1361-648x/ab5890] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
We perform a systematic study on the structure and dynamics of warm dense aluminum (Al) at temperatures ranging from 0.5 to 5.0 eV with molecular dynamics utilizing both density functional theory (DFT) and the deep potential (DP) method. On one hand, unlike the Thomas-Fermi kinetic energy density functional (KEDF), we find that the orbital-free DFT method with the Wang-Teter non-local KEDF yields properties of warm dense Al that agree well with the Kohn-Sham DFT method, enabling accurate orbital-free DFT simulations of warm dense Al at relatively low temperatures. On the other hand, the DP method constructs a deep neural network that has a high accuracy in reproducing short- and long-ranged properties of warm dense Al when compared to the DFT methods. The DP method is orders of magnitudes faster than DFT and is well-suited for simulating large systems and long trajectories to yield accurate properties of warm dense Al. Our results suggest that the combination of DFT methods and the DP model is a powerful tool for accurately and efficiently simulating warm dense matter.
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Affiliation(s)
- Qianrui Liu
- Center for Applied Physics and Technology, HEDPS, College of Engineering and School of Physics, Peking University, Beijing 100871, People's Republic of China
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11
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Larder B, Gericke DO, Richardson S, Mabey P, White TG, Gregori G. Fast nonadiabatic dynamics of many-body quantum systems. SCIENCE ADVANCES 2019; 5:eaaw1634. [PMID: 31803829 PMCID: PMC6874487 DOI: 10.1126/sciadv.aaw1634] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/23/2018] [Accepted: 09/25/2019] [Indexed: 06/10/2023]
Abstract
Modeling many-body quantum systems with strong interactions is one of the core challenges of modern physics. A range of methods has been developed to approach this task, each with its own idiosyncrasies, approximations, and realm of applicability. However, there remain many problems that are intractable for existing methods. In particular, many approaches face a huge computational barrier when modeling large numbers of coupled electrons and ions at finite temperature. Here, we address this shortfall with a new approach to modeling many-body quantum systems. On the basis of the Bohmian trajectory formalism, our new method treats the full particle dynamics with a considerable increase in computational speed. As a result, we are able to perform large-scale simulations of coupled electron-ion systems without using the adiabatic Born-Oppenheimer approximation.
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Affiliation(s)
- B. Larder
- Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, UK
| | - D. O. Gericke
- Centre for Fusion, Space and Astrophysics, Department of Physics, University of Warwick, Coventry CV4 7AL, UK
| | - S. Richardson
- Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, UK
- AWE, Aldermaston, Reading, Berkshire RG7 4PR, UK
| | - P. Mabey
- LULI–CNRS, Ecole Polytechnique, CEA, Université Paris-Saclay, F-91128 Palaiseau Cedex, France
| | - T. G. White
- Department of Physics, University of Nevada, Reno, NV 89557, USA
| | - G. Gregori
- Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, UK
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12
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Choi Y, Dharuman G, Murillo MS. High-frequency response of classical strongly coupled plasmas. Phys Rev E 2019; 100:013206. [PMID: 31499843 DOI: 10.1103/physreve.100.013206] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/28/2019] [Indexed: 06/10/2023]
Abstract
The dynamic structure factor (DSF) of the Yukawa system is here obtained with highly converged molecular dynamics (MD) over the entire liquid phase. The data provide a rigorous test of theoretical models of ion-acoustic wave-dispersion relations, the intermediate scattering function, and the high-frequency response. We compare our MD results with seven diverse models, finding good agreement among those that enforce the three basic sum rules for dispersion properties, although one of the models has previously unreported spurious peaks. The MD simulations reveal that at intermediate frequencies ω, the high-frequency response of the DSF follows a power law, going approximately as ω^{-p}, where p>0, and p shows nontrivial dependencies on the wave vector q and the plasma parameters κ and Γ. In contrast, among the seven comparison models, the predicted high-frequency response is found to be independent of {q,κ,Γ}. This high-frequency power suggests a useful fitting form. In addition, these results expose limitations of several models and, moreover, suggest that some approaches are difficult or impossible to extend because of the lack of finite moments. We also find the double-plasmon resonance peak in our MD simulations that none of the theoretical models predicts.
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Affiliation(s)
- Yongjun Choi
- Institute for Cyber-Enabled Research, Michigan State University, East Lansing, Michigan 48824, USA
| | - Gautham Dharuman
- Computational Mathematics, Science and Engineering, Michigan State University, East Lansing, Michigan 48824, USA
| | - Michael S Murillo
- Computational Mathematics, Science and Engineering, Michigan State University, East Lansing, Michigan 48824, USA
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13
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Moldabekov ZA, Kählert H, Dornheim T, Groth S, Bonitz M, Ramazanov TS. Dynamical structure factor of strongly coupled ions in a dense quantum plasma. Phys Rev E 2019; 99:053203. [PMID: 31212426 DOI: 10.1103/physreve.99.053203] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/29/2019] [Indexed: 06/09/2023]
Abstract
The dynamical structure factor (DSF) of strongly coupled ions in dense plasmas with partially and strongly degenerate electrons is investigated. The main focus is on the impact of electronic correlations (nonideality) on the ionic DSF. The latter is computed by carrying out molecular dynamics (MD) simulations with a screened ion-ion interaction potential. The electronic screening is taken into account by invoking the Singwi-Tosi-Land-Sjölander approximation, and it is compared to the MD simulation data obtained considering the electronic screening in the random phase approximation and using the Yukawa potential. We find that electronic correlations lead to lower values of the ion-acoustic mode frequencies and to an extension of the applicability limit with respect to the wave-number of a hydrodynamic description. Moreover, we show that even in the limit of weak electronic coupling, electronic correlations have a nonnegligible impact on the ionic longitudinal sound speed. Additionally, the applicability of the Yukawa potential with an adjustable screening parameter is discussed, which will be of interest, e.g., for the interpretation of experimental results for the ionic DSF of dense plasmas.
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Affiliation(s)
- Zh A Moldabekov
- Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, Leibnizstraße 15, 24098 Kiel, Germany
- Institute for Experimental and Theoretical Physics, Al-Farabi Kazakh National University, 71 Al-Farabi Street, 050040 Almaty, Kazakhstan
| | - H Kählert
- Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, Leibnizstraße 15, 24098 Kiel, Germany
| | - T Dornheim
- Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, Leibnizstraße 15, 24098 Kiel, Germany
| | - S Groth
- Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, Leibnizstraße 15, 24098 Kiel, Germany
| | - M Bonitz
- Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, Leibnizstraße 15, 24098 Kiel, Germany
| | - T S Ramazanov
- Institute for Experimental and Theoretical Physics, Al-Farabi Kazakh National University, 71 Al-Farabi Street, 050040 Almaty, Kazakhstan
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14
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Constantin LA, Fabiano E, Della Sala F. Performance of Semilocal Kinetic Energy Functionals for Orbital-Free Density Functional Theory. J Chem Theory Comput 2019; 15:3044-3055. [DOI: 10.1021/acs.jctc.9b00183] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Lucian A. Constantin
- Center for Biomolecular Nanotechnologies @UNILE, Istituto Italiano di Tecnologia, Via Barsanti, I-73010 Arnesano, Italy
| | - Eduardo Fabiano
- Center for Biomolecular Nanotechnologies @UNILE, Istituto Italiano di Tecnologia, Via Barsanti, I-73010 Arnesano, Italy
- Institute for Microelectronics and Microsystems (CNR-IMM), Campus Unisalento, Via Monteroni, 73100 Lecce, Italy
| | - Fabio Della Sala
- Center for Biomolecular Nanotechnologies @UNILE, Istituto Italiano di Tecnologia, Via Barsanti, I-73010 Arnesano, Italy
- Institute for Microelectronics and Microsystems (CNR-IMM), Campus Unisalento, Via Monteroni, 73100 Lecce, Italy
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15
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Ma Q, Dai J, Kang D, Murillo MS, Hou Y, Zhao Z, Yuan J. Extremely Low Electron-ion Temperature Relaxation Rates in Warm Dense Hydrogen: Interplay between Quantum Electrons and Coupled Ions. PHYSICAL REVIEW LETTERS 2019; 122:015001. [PMID: 31012692 DOI: 10.1103/physrevlett.122.015001] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/02/2017] [Revised: 10/24/2018] [Indexed: 06/09/2023]
Abstract
Theoretical and computational modeling of nonequilibrium processes in warm dense matter represents a significant challenge. The electron-ion relaxation process in warm dense hydrogen is investigated here by nonequilibrium molecular dynamics using the constrained electron force field (CEFF) method. CEFF evolves wave packets that incorporate dynamic quantum diffraction that obviates the Coulomb catastrophe. Predictions from this model reveal temperature relaxation times as much as three times longer than prior molecular dynamics results based on quantum statistical potentials. Through analyses of energy distributions and mean free paths, this result can be traced to delocalization. Finally, an improved GMS [Gericke, Murillo, and Schlanges, Phys. Rev. E 78, 025401 (2008)PRESCM1539-375510.1103/PhysRevE.78.025401] model is proposed, in which the Coulomb logarithms are in good agreement with CEFF results.
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Affiliation(s)
- Qian Ma
- Department of Physics, National University of Defense Technology, Changsha, Hunan 410073, P. R. China
| | - Jiayu Dai
- Department of Physics, National University of Defense Technology, Changsha, Hunan 410073, P. R. China
| | - Dongdong Kang
- Department of Physics, National University of Defense Technology, Changsha, Hunan 410073, P. R. China
| | - M S Murillo
- Department of Computational Mathematics, Science and Engineering, Michigan State University, East Lansing, Michigan 48824, USA
| | - Yong Hou
- Department of Physics, National University of Defense Technology, Changsha, Hunan 410073, P. R. China
| | - Zengxiu Zhao
- Department of Physics, National University of Defense Technology, Changsha, Hunan 410073, P. R. China
| | - Jianmin Yuan
- Department of Physics, National University of Defense Technology, Changsha, Hunan 410073, P. R. China
- Graduate School of China Academy of Engineering Physics, Beijing 100193, P. R. China
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16
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Harbour L, Förster GD, Dharma-Wardana MWC, Lewis LJ. Ion-ion dynamic structure factor, acoustic modes, and equation of state of two-temperature warm dense aluminum. Phys Rev E 2018; 97:043210. [PMID: 29758670 DOI: 10.1103/physreve.97.043210] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2017] [Indexed: 11/07/2022]
Abstract
The ion-ion dynamical structure factor and the equation of state of warm dense aluminum in a two-temperature quasiequilibrium state, with the electron temperature higher than the ion temperature, are investigated using molecular-dynamics simulations based on ion-ion pair potentials constructed from a neutral pseudoatom model. Such pair potentials based on density functional theory are parameter-free and depend directly on the electron temperature and indirectly on the ion temperature, enabling efficient computation of two-temperature properties. Comparison with ab initio simulations and with other average-atom calculations for equilibrium aluminum shows good agreement, justifying a study of quasiequilibrium situations. Analyzing the van Hove function, we find that ion-ion correlations vanish in a time significantly smaller than the electron-ion relaxation time so that dynamical properties have a physical meaning for the quasiequilibrium state. A significant increase in the speed of sound is predicted from the modification of the dispersion relation of the ion acoustic mode as the electron temperature is increased. The two-temperature equation of state including the free energy, internal energy, and pressure is also presented.
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Affiliation(s)
- L Harbour
- Département de Physique and Regroupement Québécois sur les Matériaux de Pointe, Université de Montréal, C.P. 6128, Succursale Centre-Ville, Montréal, Québec, Canada H3C 3J7
| | - G D Förster
- Département de Physique and Regroupement Québécois sur les Matériaux de Pointe, Université de Montréal, C.P. 6128, Succursale Centre-Ville, Montréal, Québec, Canada H3C 3J7
| | | | - Laurent J Lewis
- Département de Physique and Regroupement Québécois sur les Matériaux de Pointe, Université de Montréal, C.P. 6128, Succursale Centre-Ville, Montréal, Québec, Canada H3C 3J7
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17
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Starrett CE. Thomas-Fermi simulations of dense plasmas without pseudopotentials. Phys Rev E 2017; 96:013206. [PMID: 29347227 DOI: 10.1103/physreve.96.013206] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/28/2017] [Indexed: 11/07/2022]
Abstract
The Thomas-Fermi model for warm and hot dense matter is widely used to predict material properties such as the equation of state. However, for practical reasons current implementations use pseudopotentials for the electron-nucleus interaction instead of the bare Coulomb potential. This complicates the calculation and quantities such as free energy cannot be converged with respect to the pseudopotential parameters. We present a method that retains the bare Coulomb potential for the electron-nucleus interaction and does not use pseudopotentials. We demonstrate that accurate free energies are obtained by checking variational consistency. Examples for aluminum and iron plasmas are presented.
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Affiliation(s)
- C E Starrett
- Los Alamos National Laboratory, P.O. Box 1663, Los Alamos, New Mexico 87545, USA
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18
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Suryanarayana P. On nearsightedness in metallic systems for O(N) Density Functional Theory calculations: A case study on aluminum. Chem Phys Lett 2017. [DOI: 10.1016/j.cplett.2017.04.095] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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19
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A strong diffusive ion mode in dense ionized matter predicted by Langevin dynamics. Nat Commun 2017; 8:14125. [PMID: 28134338 PMCID: PMC5290263 DOI: 10.1038/ncomms14125] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/27/2016] [Accepted: 11/07/2016] [Indexed: 11/09/2022] Open
Abstract
The state and evolution of planets, brown dwarfs and neutron star crusts is determined by the properties of dense and compressed matter. Due to the inherent difficulties in modelling strongly coupled plasmas, however, current predictions of transport coefficients differ by orders of magnitude. Collective modes are a prominent feature, whose spectra may serve as an important tool to validate theoretical predictions for dense matter. With recent advances in free electron laser technology, X-rays with small enough bandwidth have become available, allowing the investigation of the low-frequency ion modes in dense matter. Here, we present numerical predictions for these ion modes and demonstrate significant changes to their strength and dispersion if dissipative processes are included by Langevin dynamics. Notably, a strong diffusive mode around zero frequency arises, which is not present, or much weaker, in standard simulations. Our results have profound consequences in the interpretation of transport coefficients in dense plasmas.
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20
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Dharuman G, Verboncoeur J, Christlieb A, Murillo MS. Atomic bound state and scattering properties of effective momentum-dependent potentials. Phys Rev E 2016; 94:043205. [PMID: 27841554 DOI: 10.1103/physreve.94.043205] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2016] [Indexed: 06/06/2023]
Abstract
Effective classical dynamics provide a potentially powerful avenue for modeling large-scale dynamical quantum systems. We have examined the accuracy of a Hamiltonian-based approach that employs effective momentum-dependent potentials (MDPs) within a molecular-dynamics framework through studies of atomic ground states, excited states, ionization energies, and scattering properties of continuum states. Working exclusively with the Kirschbaum-Wilets (KW) formulation with empirical MDPs [C. L. Kirschbaum and L. Wilets, Phys. Rev. A 21, 834 (1980)0556-279110.1103/PhysRevA.21.834], optimization leads to very accurate ground-state energies for several elements (e.g., N, F, Ne, Al, S, Ar, and Ca) relative to Hartree-Fock values. The KW MDP parameters obtained are found to be correlated, thereby revealing some degree of transferability in the empirically determined parameters. We have studied excited-state orbits of electron-ion pair to analyze the consequences of the MDP on the classical Coulomb catastrophe. From the optimized ground-state energies, we find that the experimental first- and second-ionization energies are fairly well predicted. Finally, electron-ion scattering was examined by comparing the predicted momentum transfer cross section to a semiclassical phase-shift calculation; optimizing the MDP parameters for the scattering process yielded rather poor results, suggesting a limitation of the use of the KW MDPs for plasmas.
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Affiliation(s)
- Gautham Dharuman
- Department of Electrical and Computer Engineering, Michigan State University, East Lansing, Michigan 48824, USA
| | - John Verboncoeur
- Department of Electrical and Computer Engineering, Michigan State University, East Lansing, Michigan 48824, USA
- Department of Computational Mathematics, Science and Engineering, Michigan State University, East Lansing, Michigan 48824, USA
| | - Andrew Christlieb
- Department of Computational Mathematics, Science and Engineering, Michigan State University, East Lansing, Michigan 48824, USA
- Department of Mathematics, Michigan State University, East Lansing, Michigan 48824, USA
| | - Michael S Murillo
- New Mexico Consortium, Los Alamos, New Mexico 87544, USA
- Computational Physics and Methods Group, Los Alamos National Laboratory, Los Alamos, New Mexico 87544, USA
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21
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Cross JE, Mabey P, Gericke DO, Gregori G. Theory of density fluctuations in strongly radiative plasmas. Phys Rev E 2016; 93:033201. [PMID: 27078469 DOI: 10.1103/physreve.93.033201] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/17/2015] [Indexed: 11/07/2022]
Abstract
Derivation of the dynamic structure factor, an important parameter linking experimental and theoretical work in dense plasmas, is possible starting from hydrodynamic equations. Here we obtain, by modifying the governing hydrodynamic equations, a new form of the dynamic structure factor which includes radiative terms. The inclusion of such terms has an effect on the structure factor at high temperatures, which suggests that its effect must be taken into consideration in such regimes.
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Affiliation(s)
- J E Cross
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - P Mabey
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - D O Gericke
- Centre for Fusion, Space and Astrophysics, Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - G Gregori
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
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22
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Clérouin J, Arnault P, Ticknor C, Kress JD, Collins LA. Unified Concept of Effective One Component Plasma for Hot Dense Plasmas. PHYSICAL REVIEW LETTERS 2016; 116:115003. [PMID: 27035306 DOI: 10.1103/physrevlett.116.115003] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/06/2015] [Indexed: 06/05/2023]
Abstract
Orbital-free molecular dynamics simulations are used to benchmark two popular models for hot dense plasmas: the one component plasma (OCP) and the Yukawa model. A unified concept emerges where an effective OCP (EOCP) is constructed from the short-range structure of the plasma. An unambiguous ionization and the screening length can be defined and used for a Yukawa system, which reproduces the long-range structure with finite compressibility. Similarly, the dispersion relation of longitudinal waves is consistent with the screened model at vanishing wave number but merges with the OCP at high wave number. Additionally, the EOCP reproduces the overall relaxation time scales of the correlation functions associated with ionic motion. In the hot dense regime, this unified concept of EOCP can be fruitfully applied to deduce properties such as the equation of state, ionic transport coefficients, and the ion feature in x-ray Thomson scattering experiments.
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Affiliation(s)
| | | | - Christopher Ticknor
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Joel D Kress
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Lee A Collins
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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23
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Plagemann KU, Rüter HR, Bornath T, Shihab M, Desjarlais MP, Fortmann C, Glenzer SH, Redmer R. Ab initio calculation of the ion feature in x-ray Thomson scattering. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:013103. [PMID: 26274290 DOI: 10.1103/physreve.92.013103] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/10/2015] [Indexed: 06/04/2023]
Abstract
The spectrum of x-ray Thomson scattering is proportional to the dynamic structure factor. An important contribution is the ion feature which describes elastic scattering of x rays off electrons. We apply an ab initio method for the calculation of the form factor of bound electrons, the slope of the screening cloud of free electrons, and the ion-ion structure factor in warm dense beryllium. With the presented method we can calculate the ion feature from first principles. These results will facilitate a better understanding of x-ray scattering in warm dense matter and an accurate measurement of ion temperatures which would allow determining nonequilibrium conditions, e.g., along shock propagation.
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Affiliation(s)
| | - Hannes R Rüter
- Institut für Physik, Universität Rostock, D-18051 Rostock, Germany
| | - Thomas Bornath
- Institut für Physik, Universität Rostock, D-18051 Rostock, Germany
| | - Mohammed Shihab
- Institut für Physik, Universität Rostock, D-18051 Rostock, Germany
- Physics Department, Faculty of Science, Tanta University, 31527 Tanta, Egypt
| | | | - Carsten Fortmann
- Quantumwise A/S, Lersø Parkallé 107, DK-2100 Copenhagen, Denmark
| | - Siegfried H Glenzer
- High Energy Density Science, SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA
| | - Ronald Redmer
- Institut für Physik, Universität Rostock, D-18051 Rostock, Germany
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24
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Gill NM, Heinonen RA, Starrett CE, Saumon D. Ion-ion dynamic structure factor of warm dense mixtures. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:063109. [PMID: 26172810 DOI: 10.1103/physreve.91.063109] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/13/2015] [Indexed: 06/04/2023]
Abstract
The ion-ion dynamic structure factor of warm dense matter is determined using the recently developed pseudoatom molecular dynamics method [Starrett et al., Phys. Rev. E 91, 013104 (2015)]. The method uses density functional theory to determine ion-ion pair interaction potentials that have no free parameters. These potentials are used in classical molecular dynamics simulations. This constitutes a computationally efficient and realistic model of dense plasmas. Comparison with recently published simulations of the ion-ion dynamic structure factor and sound speed of warm dense aluminum finds good to reasonable agreement. Using this method, we make predictions of the ion-ion dynamical structure factor and sound speed of a warm dense mixture-equimolar carbon-hydrogen. This material is commonly used as an ablator in inertial confinement fusion capsules, and our results are amenable to direct experimental measurement.
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Affiliation(s)
- N M Gill
- 206 Allison Laboratory, Auburn University, Auburn, Alabama 36849, USA
- Los Alamos National Laboratory, P.O. Box 1663, Los Alamos, New Mexico 87545, USA
| | - R A Heinonen
- Los Alamos National Laboratory, P.O. Box 1663, Los Alamos, New Mexico 87545, USA
| | - C E Starrett
- Los Alamos National Laboratory, P.O. Box 1663, Los Alamos, New Mexico 87545, USA
| | - D Saumon
- Los Alamos National Laboratory, P.O. Box 1663, Los Alamos, New Mexico 87545, USA
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25
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Lehtomäki J, Makkonen I, Caro MA, Harju A, Lopez-Acevedo O. Orbital-free density functional theory implementation with the projector augmented-wave method. J Chem Phys 2015; 141:234102. [PMID: 25527914 DOI: 10.1063/1.4903450] [Citation(s) in RCA: 37] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present a computational scheme for orbital-free density functional theory (OFDFT) that simultaneously provides access to all-electron values and preserves the OFDFT linear scaling as a function of the system size. Using the projector augmented-wave method (PAW) in combination with real-space methods, we overcome some obstacles faced by other available implementation schemes. Specifically, the advantages of using the PAW method are twofold. First, PAW reproduces all-electron values offering freedom in adjusting the convergence parameters and the atomic setups allow tuning the numerical accuracy per element. Second, PAW can provide a solution to some of the convergence problems exhibited in other OFDFT implementations based on Kohn-Sham (KS) codes. Using PAW and real-space methods, our orbital-free results agree with the reference all-electron values with a mean absolute error of 10 meV and the number of iterations required by the self-consistent cycle is comparable to the KS method. The comparison of all-electron and pseudopotential bulk modulus and lattice constant reveal an enormous difference, demonstrating that in order to assess the performance of OFDFT functionals it is necessary to use implementations that obtain all-electron values. The proposed combination of methods is the most promising route currently available. We finally show that a parametrized kinetic energy functional can give lattice constants and bulk moduli comparable in accuracy to those obtained by the KS PBE method, exemplified with the case of diamond.
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Affiliation(s)
- Jouko Lehtomäki
- COMP Centre of Excellence, Department of Applied Physics, Aalto University, P.O. Box 11100, 00076 Aalto, Finland
| | - Ilja Makkonen
- COMP Centre of Excellence, Department of Applied Physics, Aalto University, P.O. Box 11100, 00076 Aalto, Finland
| | - Miguel A Caro
- COMP Centre of Excellence, Department of Applied Physics, Aalto University, P.O. Box 11100, 00076 Aalto, Finland
| | - Ari Harju
- COMP Centre of Excellence, Department of Applied Physics, Aalto University, P.O. Box 11100, 00076 Aalto, Finland
| | - Olga Lopez-Acevedo
- COMP Centre of Excellence, Department of Applied Physics, Aalto University, P.O. Box 11100, 00076 Aalto, Finland
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26
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Reinholz H, Röpke G, Rosmej S, Redmer R. Conductivity of warm dense matter including electron-electron collisions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:043105. [PMID: 25974600 DOI: 10.1103/physreve.91.043105] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/16/2015] [Indexed: 06/04/2023]
Abstract
We present an approach that can resolve the controversy with respect to the role of electron-electron collisions in calculating the dynamic conductivity of dense plasmas. In particular, the dc conductivity is analyzed in the low-density, nondegenerate limit where the Spitzer theory is valid and electron-electron collisions lead to the well-known reduction in comparison to the result considering only electron-ion collisions (Lorentz model). With increasing degeneracy, the contribution of electron-electron collisions to the dc conductivity is decreasing and can be neglected for the liquid metal domain where the Ziman theory is applicable. We give expressions for the effect of electron-electron collisions in calculating the conductivity in the warm dense matter region, i.e., for strongly coupled Coulomb systems at arbitrary degeneracy.
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Affiliation(s)
- H Reinholz
- Universität Rostock, Institut für Physik, 18051 Rostock, Germany and University of Western Australia School of Physics, WA 6009 Crawley, Australia
| | - G Röpke
- Universität Rostock, Institut für Physik, 18051 Rostock, Germany
| | - S Rosmej
- Universität Rostock, Institut für Physik, 18051 Rostock, Germany
| | - R Redmer
- Universität Rostock, Institut für Physik, 18051 Rostock, Germany
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27
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Clérouin J, Robert G, Arnault P, Ticknor C, Kress JD, Collins LA. Evidence for out-of-equilibrium states in warm dense matter probed by x-ray Thomson scattering. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:011101. [PMID: 25679563 DOI: 10.1103/physreve.91.011101] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/19/2014] [Indexed: 06/04/2023]
Abstract
A recent and unexpected discrepancy between ab initio simulations and the interpretation of a laser shock experiment on aluminum, probed by x-ray Thomson scattering (XRTS), is addressed. The ion-ion structure factor deduced from the XRTS elastic peak (ion feature) is only compatible with a strongly coupled out-of-equilibrium state. Orbital free molecular dynamics simulations with ions colder than the electrons are employed to interpret the experiment. The relevance of decoupled temperatures for ions and electrons is discussed. The possibility that it mimics a transient, or metastable, out-of-equilibrium state after melting is also suggested.
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Affiliation(s)
| | | | | | - Christopher Ticknor
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Joel D Kress
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Lee A Collins
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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28
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Luo YS, Cang YP, Chen D. Insights into Elastic and Thermodynamics Properties of Binary Intermetallics in Ni-Al Alloys under Extreme Condition: Full-Electronic Quasi-Harmonic Study. CHINESE J CHEM PHYS 2014. [DOI: 10.1063/1674-0068/27/04/399-406] [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]
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29
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Rüter HR, Redmer R. Ab initio simulations for the ion-ion structure factor of warm dense aluminum. PHYSICAL REVIEW LETTERS 2014; 112:145007. [PMID: 24765982 DOI: 10.1103/physrevlett.112.145007] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/11/2013] [Indexed: 06/03/2023]
Abstract
We perform ab initio simulations based on finite-temperature density functional theory in order to determine the static and dynamic ion-ion structure factor in aluminum. We calculate the dynamic structure factor via the intermediate scattering function and extract the dispersion relation for the collective excitations. The results are compared with available experimental x-ray scattering data. Very good agreement is obtained for the liquid metal domain. In addition we perform simulations for warm dense aluminum in order to obtain the ion dynamics in this strongly correlated quantum regime. We determine the sound velocity for both liquid and warm dense aluminum which can be checked experimentally using narrow-bandwidth free electron laser radiation.
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Affiliation(s)
- Hannes R Rüter
- Universität Rostock, Institut für Physik, D-18051 Rostock, Germany
| | - Ronald Redmer
- Universität Rostock, Institut für Physik, D-18051 Rostock, Germany
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