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Dornheim T, Tolias P, Groth S, Moldabekov ZA, Vorberger J, Hirshberg B. Fermionic physics from ab initio path integral Monte Carlo simulations of fictitious identical particles. J Chem Phys 2023; 159:164113. [PMID: 37888764 DOI: 10.1063/5.0171930] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/11/2023] [Accepted: 10/06/2023] [Indexed: 10/28/2023] Open
Abstract
The ab initio path integral Monte Carlo (PIMC) method is one of the most successful methods in statistical physics, quantum chemistry and related fields, but its application to quantum degenerate Fermi systems is severely hampered by an exponential computational bottleneck: the notorious fermion sign problem. Very recently, Xiong and Xiong [J. Chem. Phys. 157, 094112 (2022)] have suggested to partially circumvent the sign problem by carrying out simulations of fictitious systems guided by an interpolating continuous variable ξ ∈ [-1, 1], with the physical Fermi- and Bose-statistics corresponding to ξ = -1 and ξ = 1. It has been proposed that information about the fermionic limit might be obtained by calculations within the bosonic sector ξ > 0 combined with an extrapolation throughout the fermionic sector ξ < 0, essentially bypassing the sign problem. Here, we show how the inclusion of the artificial parameter ξ can be interpreted as an effective penalty on the formation of permutation cycles in the PIMC simulation. We demonstrate that the proposed extrapolation method breaks down for moderate to high quantum degeneracy. Instead, the method constitutes a valuable tool for the description of large Fermi-systems of weak quantum degeneracy. This is demonstrated for electrons in a 2D harmonic trap and for the uniform electron gas (UEG), where we find excellent agreement (∼0.5%) with exact configuration PIMC results in the high-density regime while attaining a speed-up exceeding 11 orders of magnitude. Finally, we extend the idea beyond the energy and analyze the radial density distribution (2D trap), as well as the static structure factor and imaginary-time density-density correlation function (UEG).
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Affiliation(s)
- Tobias Dornheim
- Center for Advanced Systems Understanding (CASUS), D-02826 Görlitz, Germany
- Helmholtz-Zentrum Dresden-Rossendorf (HZDR), D-01328 Dresden, Germany
| | - Panagiotis Tolias
- Space and Plasma Physics, Royal Institute of Technology (KTH), Stockholm SE-100 44, Sweden
| | - Simon Groth
- Christian-Albrechts-Universität zu Kiel, D-24098 Kiel, Germany
| | - Zhandos A Moldabekov
- Center for Advanced Systems Understanding (CASUS), D-02826 Görlitz, Germany
- Helmholtz-Zentrum Dresden-Rossendorf (HZDR), D-01328 Dresden, Germany
| | - Jan Vorberger
- Helmholtz-Zentrum Dresden-Rossendorf (HZDR), D-01328 Dresden, Germany
| | - Barak Hirshberg
- School of Chemistry, Tel Aviv University, Tel Aviv 6997801, Israel
- The Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 6997801, Israel
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Dornheim T, Vorberger J, Moldabekov ZA, Böhme M. Analysing the dynamic structure of warm dense matter in the imaginary-time domain: theoretical models and simulations. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2023; 381:20220217. [PMID: 37393936 DOI: 10.1098/rsta.2022.0217] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/04/2022] [Accepted: 01/10/2023] [Indexed: 07/04/2023]
Abstract
Rigorous diagnostics of experiments with warm dense matter are notoriously difficult. A key method is X-ray Thomson scattering (XRTS), but the interpretation of XRTS measurements is usually based on theoretical models that entail various approximations. Recently, Dornheim et al. [Nat. Commun. 13, 7911 (2022)] introduced a new framework for temperature diagnostics of XRTS experiments that is based on imaginary-time correlation functions. On the one hand, switching from the frequency to the imaginary-time domain gives one direct access to a number of physical properties, which facilitates the extraction of the temperature of arbitrarily complex materials without relying on any models or approximations. On the other hand, the bulk of theoretical work in dynamic quantum many-body theory is devoted to the frequency domain, and, to the best of our knowledge, the manifestation of physics properties within the imaginary-time density-density correlation function (ITCF) remains poorly understood. In the present work, we aim to fill this gap by introducing a simple, semi-analytical model for the imaginary-time dependence of two-body correlations within the framework of imaginary-time path integrals. As a practical example, we compare our new model to extensive ab initio path integral Monte Carlo results for the ITCF of a uniform electron gas, and find excellent agreement over a broad range of wavenumbers, densities and temperatures. This article is part of the theme issue 'Dynamic and transient processes in warm dense matter'.
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Affiliation(s)
- Tobias Dornheim
- Center for Advanced Systems Understanding (CASUS), D-02826 Görlitz, Germany
- Helmholtz-Zentrum Dresden-Rossendorf (HZDR), D-01328 Dresden, Germany
| | - Jan Vorberger
- Helmholtz-Zentrum Dresden-Rossendorf (HZDR), D-01328 Dresden, Germany
| | - Zhandos A Moldabekov
- Center for Advanced Systems Understanding (CASUS), D-02826 Görlitz, Germany
- Helmholtz-Zentrum Dresden-Rossendorf (HZDR), D-01328 Dresden, Germany
| | - Maximilian Böhme
- Center for Advanced Systems Understanding (CASUS), D-02826 Görlitz, Germany
- Helmholtz-Zentrum Dresden-Rossendorf (HZDR), D-01328 Dresden, Germany
- Technische Universität Dresden, D-01062 Dresden, Germany
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3
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Dornheim T, Vorberger J, Militzer B, Moldabekov ZA. Momentum distribution of the uniform electron gas at finite temperature: Effects of spin polarization. Phys Rev E 2021; 104:055206. [PMID: 34942706 DOI: 10.1103/physreve.104.055206] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/03/2021] [Accepted: 10/25/2021] [Indexed: 11/07/2022]
Abstract
We carry out extensive direct path integral Monte Carlo (PIMC) simulations of the uniform electron gas (UEG) at finite temperature for different values of the spin-polarization ξ. This allows us to unambiguously quantify the impact of spin effects on the momentum distribution function n(k) and related properties. We find that interesting physical effects like the interaction-induced increase in the occupation of the zero-momentum state n(0) substantially depend on ξ. Our results further advance the current understanding of the UEG as a fundamental model system, and are of practical relevance for the description of transport properties of warm dense matter in an external magnetic field. All PIMC results are freely available online and can be used as a benchmark for the development of methods and applications.
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Affiliation(s)
- Tobias Dornheim
- Center for Advanced Systems Understanding (CASUS), D-02826 Görlitz, Germany.,Helmholtz-Zentrum Dresden-Rossendorf (HZDR), D-01328 Dresden, Germany
| | - Jan Vorberger
- Helmholtz-Zentrum Dresden-Rossendorf (HZDR), D-01328 Dresden, Germany
| | - Burkhard Militzer
- Department of Earth and Planetary Science, University of California, Berkeley, California 94720, USA.,Department of Astronomy, University of California, Berkeley, California 94720, USA
| | - Zhandos A Moldabekov
- Center for Advanced Systems Understanding (CASUS), D-02826 Görlitz, Germany.,Helmholtz-Zentrum Dresden-Rossendorf (HZDR), D-01328 Dresden, Germany
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Dornheim T, Cangi A, Ramakrishna K, Böhme M, Tanaka S, Vorberger J. Effective Static Approximation: A Fast and Reliable Tool for Warm-Dense Matter Theory. PHYSICAL REVIEW LETTERS 2020; 125:235001. [PMID: 33337174 DOI: 10.1103/physrevlett.125.235001] [Citation(s) in RCA: 19] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/06/2020] [Revised: 10/12/2020] [Accepted: 11/03/2020] [Indexed: 06/12/2023]
Abstract
We present an effective static approximation (ESA) to the local field correction (LFC) of the electron gas that enables highly accurate calculations of electronic properties like the dynamic structure factor S(q,ω), the static structure factor S(q), and the interaction energy v. The ESA combines the recent neural-net representation by T. Dornheim et al., [J. Chem. Phys. 151, 194104 (2019)JCPSA60021-960610.1063/1.5123013] of the temperature-dependent LFC in the exact static limit with a consistent large wave-number limit obtained from quantum Monte Carlo data of the on-top pair distribution function g(0). It is suited for a straightforward integration into existing codes. We demonstrate the importance of the LFC for practical applications by reevaluating the results of the recent x-ray Thomson scattering experiment on aluminum by Sperling et al. [Phys. Rev. Lett. 115, 115001 (2015)PRLTAO0031-900710.1103/PhysRevLett.115.115001]. We find that an accurate incorporation of electronic correlations in terms of the ESA leads to a different prediction of the inelastic scattering spectrum than obtained from state-of-the-art models like the Mermin approach or linear-response time-dependent density functional theory. Furthermore, the ESA scheme is particularly relevant for the development of advanced exchange-correlation functionals in density functional theory.
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Affiliation(s)
- Tobias Dornheim
- Center for Advanced Systems Understanding (CASUS), D-02826 Görlitz, Germany
| | - Attila Cangi
- Center for Advanced Systems Understanding (CASUS), D-02826 Görlitz, Germany
| | - Kushal Ramakrishna
- Center for Advanced Systems Understanding (CASUS), D-02826 Görlitz, Germany
- Helmholtz-Zentrum Dresden-Rossendorf (HZDR), D-01328 Dresden, Germany
- Technische Universität Dresden, D-01062 Dresden, Germany
| | - Maximilian Böhme
- Center for Advanced Systems Understanding (CASUS), D-02826 Görlitz, Germany
- Technische Universität Dresden, D-01062 Dresden, Germany
| | - Shigenori Tanaka
- Graduate School of System Informatics, Kobe University, Kobe 657-8501, Japan
| | - Jan Vorberger
- Helmholtz-Zentrum Dresden-Rossendorf (HZDR), D-01328 Dresden, Germany
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Dornheim T, Vorberger J, Bonitz M. Nonlinear Electronic Density Response in Warm Dense Matter. PHYSICAL REVIEW LETTERS 2020; 125:085001. [PMID: 32909774 DOI: 10.1103/physrevlett.125.085001] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/09/2020] [Accepted: 07/20/2020] [Indexed: 06/11/2023]
Abstract
Warm dense matter (WDM)-an extreme state with high temperatures and densities that occurs, e.g., in astrophysical objects-constitutes one of the most active fields in plasma physics and materials science. These conditions can be realized in the lab by shock compression or laser excitation, and the most accurate experimental diagnostics is achieved with lasers and free electron lasers which is theoretically modeled using linear response theory. Here, we present first ab initio path integral Monte Carlo results for the nonlinear density response of correlated electrons in WDM and show that for many situations of experimental relevance nonlinear effects cannot be neglected.
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Affiliation(s)
- Tobias Dornheim
- Center for Advanced Systems Understanding (CASUS), D-028262 Görlitz, Germany
| | - Jan Vorberger
- Helmholtz-Zentrum Dresden-Rossendorf, Bautzner Landstraße 400, D-01328 Dresden, Germany
| | - Michael Bonitz
- Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, Leibnizstraße 15, D-24098 Kiel, Germany
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Dornheim T, Vorberger J, Groth S, Hoffmann N, Moldabekov ZA, Bonitz M. The static local field correction of the warm dense electron gas: An ab initio path integral Monte Carlo study and machine learning representation. J Chem Phys 2019; 151:194104. [DOI: 10.1063/1.5123013] [Citation(s) in RCA: 42] [Impact Index Per Article: 8.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022] Open
Affiliation(s)
- T. Dornheim
- Center for Advanced Systems Understanding (CASUS), Görlitz, Germany
- Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, Leibnizstraße 15, D-24098 Kiel, Germany
| | - J. Vorberger
- Helmholtz-Zentrum Dresden-Rossendorf, Bautzner Landstraße 400, D-01328 Dresden, Germany
| | - S. Groth
- Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, Leibnizstraße 15, D-24098 Kiel, Germany
| | - N. Hoffmann
- Helmholtz-Zentrum Dresden-Rossendorf, Bautzner Landstraße 400, D-01328 Dresden, Germany
| | - Zh. A. Moldabekov
- Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, Leibnizstraße 15, D-24098 Kiel, Germany
- Institute for Experimental and Theoretical Physics, Al-Farabi Kazakh National University, Al-Farabi Str. 71, 050040 Almaty, Kazakhstan
| | - M. Bonitz
- Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, Leibnizstraße 15, D-24098 Kiel, Germany
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Woods ND, Payne MC, Hasnip PJ. Computing the self-consistent field in Kohn-Sham density functional theory. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2019; 31:453001. [PMID: 31300620 DOI: 10.1088/1361-648x/ab31c0] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
A new framework is presented for evaluating the performance of self-consistent field methods in Kohn-Sham density functional theory (DFT). The aims of this work are two-fold. First, we explore the properties of Kohn-Sham DFT as it pertains to the convergence of self-consistent field iterations. Sources of inefficiencies and instabilities are identified, and methods to mitigate these difficulties are discussed. Second, we introduce a framework to assess the relative utility of algorithms in the present context, comprising a representative benchmark suite of over fifty Kohn-Sham simulation inputs, the scf-x n suite. This provides a new tool to develop, evaluate and compare new algorithms in a fair, well-defined and transparent manner.
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Affiliation(s)
- N D Woods
- Theory of Condensed Matter, Cavendish Laboratory, University of Cambridge, Cambridge, CB3 0HE, United Kingdom
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8
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Islam MM, Gosh R, Bhuiyan G. Calculation of electrical resistivity of Na-based liquid binary alkali alloys. J Mol Liq 2019. [DOI: 10.1016/j.molliq.2019.111224] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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9
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Dornheim T, Groth S, Vorberger J, Bonitz M. Ab initio Path Integral Monte Carlo Results for the Dynamic Structure Factor of Correlated Electrons: From the Electron Liquid to Warm Dense Matter. PHYSICAL REVIEW LETTERS 2018; 121:255001. [PMID: 30608805 DOI: 10.1103/physrevlett.121.255001] [Citation(s) in RCA: 42] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/31/2018] [Indexed: 06/09/2023]
Abstract
The accurate description of electrons at extreme density and temperature is of paramount importance for, e.g., the understanding of astrophysical objects and inertial confinement fusion. In this context, the dynamic structure factor S(q,ω) constitutes a key quantity as it is directly measured in x-ray Thomson scattering experiments and governs transport properties like the dynamic conductivity. In this work, we present the first ab initio results for S(q,ω) by carrying out extensive path integral Monte Carlo simulations and developing a new method for the required analytic continuation, which is based on the stochastic sampling of the dynamic local field correction G(q,ω). In addition, we find that the so-called static approximation constitutes a promising opportunity to obtain high-quality data for S(q,ω) over substantial parts of the warm dense matter regime.
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Affiliation(s)
- T Dornheim
- Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, Leibnizstraße 15, D-24098 Kiel, Germany
| | - S Groth
- Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, Leibnizstraße 15, D-24098 Kiel, Germany
| | - J Vorberger
- Helmholtz-Zentrum Dresden-Rossendorf, D-01328 Dresden, Germany
| | - M Bonitz
- Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, Leibnizstraße 15, D-24098 Kiel, Germany
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10
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Diaw A, Murillo MS. A viscous quantum hydrodynamics model based on dynamic density functional theory. Sci Rep 2017; 7:15352. [PMID: 29127308 PMCID: PMC5681597 DOI: 10.1038/s41598-017-14414-9] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/09/2017] [Accepted: 10/11/2017] [Indexed: 11/21/2022] Open
Abstract
Dynamic density functional theory (DDFT) is emerging as a useful theoretical technique for modeling the dynamics of correlated systems. We extend DDFT to quantum systems for application to dense plasmas through a quantum hydrodynamics (QHD) approach. The DDFT-based QHD approach includes correlations in the the equation of state self-consistently, satisfies sum rules and includes irreversibility arising from collisions. While QHD can be used generally to model non-equilibrium, heterogeneous plasmas, we employ the DDFT-QHD framework to generate a model for the electronic dynamic structure factor, which offers an avenue for measuring hydrodynamic properties, such as transport coefficients via x-ray Thomson scattering.
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Affiliation(s)
- Abdourahmane Diaw
- Department of Computational Mathematics, Science and Engineering, Michigan State University East Lansing, Michigan, 48823, USA.
| | - Michael S Murillo
- Department of Computational Mathematics, Science and Engineering, Michigan State University East Lansing, Michigan, 48823, USA
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11
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Groth S, Dornheim T, Sjostrom T, Malone FD, Foulkes WMC, Bonitz M. Ab initio Exchange-Correlation Free Energy of the Uniform Electron Gas at Warm Dense Matter Conditions. PHYSICAL REVIEW LETTERS 2017; 119:135001. [PMID: 29341671 DOI: 10.1103/physrevlett.119.135001] [Citation(s) in RCA: 48] [Impact Index Per Article: 6.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/24/2017] [Indexed: 06/07/2023]
Abstract
In a recent Letter [T. Dornheim et al., Phys. Rev. Lett. 117, 156403 (2016)PRLTAO0031-900710.1103/PhysRevLett.117.156403], we presented the first quantum Monte Carlo (QMC) results for the warm dense electron gas in the thermodynamic limit. However, a complete parametrization of the exchange-correlation free energy with respect to density, temperature, and spin polarization remained out of reach due to the absence of (i) accurate QMC results below θ=k_{B}T/E_{F}=0.5 and (ii) QMC results for spin polarizations different from the paramagnetic case. Here we overcome both remaining limitations. By closing the gap to the ground state and by performing extensive QMC simulations for different spin polarizations, we are able to obtain the first completely ab initio exchange-correlation free energy functional; the accuracy achieved is an unprecedented ∼0.3%. This also allows us to quantify the accuracy and systematic errors of various previous approximate functionals.
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Affiliation(s)
- Simon Groth
- Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, D-24098 Kiel, Germany
| | - Tobias Dornheim
- Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, D-24098 Kiel, Germany
| | - Travis Sjostrom
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Fionn D Malone
- Department of Physics, Imperial College London, Exhibition Road, London SW7 2AZ, United Kingdom
- Physics Division, Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, California 94550, USA
| | - W M C Foulkes
- Department of Physics, Imperial College London, Exhibition Road, London SW7 2AZ, United Kingdom
| | - Michael Bonitz
- Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, D-24098 Kiel, Germany
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12
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Dornheim T, Groth S, Vorberger J, Bonitz M. Permutation-blocking path-integral Monte Carlo approach to the static density response of the warm dense electron gas. Phys Rev E 2017; 96:023203. [PMID: 28950530 DOI: 10.1103/physreve.96.023203] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/02/2017] [Indexed: 06/07/2023]
Abstract
The static density response of the uniform electron gas is of fundamental importance for numerous applications. Here we employ the recently developed ab initio permutation blocking path integral Monte Carlo (PB-PIMC) technique [T. Dornheim et al., New J. Phys. 17, 073017 (2015)10.1088/1367-2630/17/7/073017] to carry out extensive simulations of the harmonically perturbed electron gas at warm dense matter conditions. In particular, we investigate in detail the validity of linear response theory and demonstrate that PB-PIMC allows us to obtain highly accurate results for the static density response function and, thus, the static local field correction. A comparison with dielectric approximations to our new ab initio data reveals the need for an exact treatment of correlations. Finally, we consider a superposition of multiple perturbations and discuss the implications for the calculation of the static response function.
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Affiliation(s)
- Tobias Dornheim
- Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, D-24098 Kiel, Germany
| | - Simon Groth
- Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, D-24098 Kiel, Germany
| | - Jan Vorberger
- Helmholtz-Zentrum Dresden-Rossendorf, D-01328 Dresden, Germany
| | - Michael Bonitz
- Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, D-24098 Kiel, Germany
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13
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Patrick CE, Thygesen KS. Adiabatic-connection fluctuation-dissipation DFT for the structural properties of solids—The renormalized ALDA and electron gas kernels. J Chem Phys 2015; 143:102802. [DOI: 10.1063/1.4919236] [Citation(s) in RCA: 48] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022] Open
Affiliation(s)
- Christopher E. Patrick
- Center for Atomic-Scale Materials Design (CAMD), Department of Physics, Technical University of Denmark, DK—2800 Kongens Lyngby, Denmark
| | - Kristian S. Thygesen
- Center for Atomic-Scale Materials Design (CAMD), Department of Physics, Technical University of Denmark, DK—2800 Kongens Lyngby, Denmark
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14
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Wang W, Shang S, Wang Y, Darling K, Mathaudhu S, Hui X, Liu Z. Electron localization morphology of the stacking faults in Mg: A first-principles study. Chem Phys Lett 2012. [DOI: 10.1016/j.cplett.2012.09.028] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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15
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Bross H. LDA and GGA Investigations of Some Ground-State Properties and the Compton Profile of Copper with the All-Electron MAPW Method. ACTA ACUST UNITED AC 2012. [DOI: 10.5402/2012/975897] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
Abstract
The electronic structure is self-consistently evaluated both in the local-density and the generalized-gradient approximations. The convergence with respect to the intrinsic parameters of the modified augmented plane-wave scheme is thoroughly investigated. Besides the Ar-core, the less-extended Ne-core and the most appropriate exchange-correlations functionals are considered. It is studied how some characteristic ground-state properties and the Compton profiles depend on these choices. Apart from the long wave limit of the Compton profiles, most of the other properties are found in good agreement with the experimental facts.
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Affiliation(s)
- Helmut Bross
- Arnold Sommerfeld Center, University of Munich, Theresienstraße. 37 IV, 80333 Munich, Germany
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16
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Neumayer P, Fortmann C, Döppner T, Davis P, Falcone RW, Kritcher AL, Landen OL, Lee HJ, Lee RW, Niemann C, Le Pape S, Glenzer SH. Plasmons in strongly coupled shock-compressed matter. PHYSICAL REVIEW LETTERS 2010; 105:075003. [PMID: 20868053 DOI: 10.1103/physrevlett.105.075003] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/19/2010] [Indexed: 05/29/2023]
Abstract
We present the first measurements of the plasmon dispersion and damping in laser shock-compressed solid matter. Petawatt laser produced K-α radiation scatters on boron targets compressed by a 10 ns-long 400 J laser pulse. In the vicinity of the Fermi momentum, the scattering spectra show dispersionless, collisionally damped plasmons, indicating a strongly coupled electron liquid. These observations agree with calculations that include the Born-Mermin approximation to account for electron-ion collisional damping and local field corrections reflecting electron-electron correlations.
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Affiliation(s)
- P Neumayer
- Lawrence Livermore National Laboratory, Livermore, California 94551, USA
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17
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Fortmann C, Wierling A, Röpke G. Influence of local-field corrections on Thomson scattering in collision-dominated two-component plasmas. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:026405. [PMID: 20365663 DOI: 10.1103/physreve.81.026405] [Citation(s) in RCA: 33] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/19/2009] [Revised: 01/26/2010] [Indexed: 05/29/2023]
Abstract
The dynamic structure factor, which determines the Thomson scattering spectrum, is calculated via an extended Mermin approach. It incorporates the dynamical collision frequency as well as the local-field correction factor. This allows to study systematically the impact of electron-ion collisions as well as electron-electron correlations due to degeneracy and short-range interaction on the characteristics of the Thomson scattering signal. As such, the plasmon dispersion and damping width is calculated for a two-component plasma, where the electron subsystem is completely degenerate. Strong deviations of the plasmon resonance position due to the electron-electron correlations are observed at increasing Brueckner parameters r(s). These results are of paramount importance for the interpretation of collective Thomson scattering spectra, as the determination of the free electron density from the plasmon resonance position requires a precise theory of the plasmon dispersion. Implications due to different approximations for the electron-electron correlation, i.e., different forms of the one-component local-field correction, are discussed.
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Affiliation(s)
- Carsten Fortmann
- Institut für Physik, Universität Rostock, 18051 Rostock, Germany.
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18
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Zhang YA, Wang YA. Perturbative total energy evaluation in self-consistent field Iterations: Tests on molecular systems. J Chem Phys 2009; 130:144116. [DOI: 10.1063/1.3104662] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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19
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Vibrational dynamics of Co67Zr33 semiconductor glassy alloy. J STRUCT CHEM+ 2009. [DOI: 10.1007/s10947-009-0032-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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Izmaylov AF, Scuseria GE. Why are time-dependent density functional theory excitations in solids equal to band structure energy gaps for semilocal functionals, and how does nonlocal Hartree–Fock-type exchange introduce excitonic effects? J Chem Phys 2008; 129:034101. [DOI: 10.1063/1.2953701] [Citation(s) in RCA: 69] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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21
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Vora AM. Study of superconducting state parameters of ternary metallic glasses through pseudopotential approach. SCIENCE AND TECHNOLOGY OF ADVANCED MATERIALS 2008; 9:025017. [PMID: 27877992 PMCID: PMC5099749 DOI: 10.1088/1468-6996/9/2/025017] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/17/2007] [Revised: 07/24/2008] [Accepted: 02/25/2008] [Indexed: 06/06/2023]
Abstract
A theoretical investigation on the screening dependence of the superconducting state parameters (SSPs) viz. the electron-phonon coupling strength λ, the Coulomb pseudopotential μ∗, the transition temperature TC, the isotope effect exponent α and the effective interaction strength N0V of some ternary metallic glasses such as Ti50Be34Zr10, (Mo0.6Ru0.4)78B22, (Mo0.6Ru0.4)80B20, (Mo0.4Ru0.6)80P20, (Mo0.6Ru0.4)70Si30, (Mo0.6Ru0.4)84B16, (Mo0.6Ru0.4)72Si28, (Mo0.6Ru0.4)86B14, (Mo0.6Ru0.4)76Si24, (Mo0.6Ru0.4)78Si22, (Mo0.6Ru0.4)80Si20, (Mo0.6Ru0.4)82Si18 and (Mo0.6Ru0.4)80P20 is reported for the first time using Ashcroft's empty core (EMC) model potential. Five local field correction functions proposed by Hartree (H), Taylor (T), Ichimaru-Utsumi (IU), Farid et al (F) and Sarkar et al (S) are used in the present investigation to study the effect of screening on the aforesaid properties. It is observed that λ and TC are reasonably sensitive to the selection of the local field correction functions, whereas μ∗, α and N0V show weak dependences on the local field correction functions. The transition temperature TC obtained from the H-local field correction function is found to be in excellent agreement with available experimental data. Also, the present results are found to be in qualitative agreement with other earlier reported data, which confirms the existence of the superconducting phase in the above ternary metallic glasses.
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Abstract
We present an extension of Hohenberg-Kohn-Sham density functional theory to the domain of complex local potentials and complex electron densities. The approach is applicable to resonance (Siegert) [Phys. Rev. 56, 750 (1939)] states and other scattering and transport problems that can be described by a normalized state of a Hamiltonian containing a complex local potential. Such Hamiltonians are non-Hermitian and their eigenvalues are in general complex, the imaginary part being inversely proportional to the lifetime of the system. The one-to-one correspondence between complex local potentials nu and complex electron densities rho is established provided that the complex variables are sufficiently close to real local potentials and densities of nondegenerate ground states. We show that the exchange-correlation functionals, contributing to the complex energy, are determined through analytic continuation of their ground-state-theory counterparts. This implies that the exchange-correlation effects on the lifetime of a resonance are, under appropriate conditions, already determined by the functionals of the ground-state theory.
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Affiliation(s)
- Matthias Ernzerhof
- Département de Chimie, Université de Montréal, C.P. 6128 Succursale A, Montréal, Québec H3C 3J7, Canada.
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Farid B. Self-consistent density-functional approach to the correlated ground states and an unrestricted many-body perturbation theory. ACTA ACUST UNITED AC 2006. [DOI: 10.1080/01418639708241084] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- Behnam Farid
- a Cavendish Laboratory, Department of Physics , University of Cambridge , Madingley Road, Cambridge , CB3 OHE , England
- b Max-Planck-Institut für Festkörperforschung , Heisenbergstraße 1, 70569 , Stuttgart , Federal Republic of Germany
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Bretonnet JL. Excess entropy scaling for the diffusion coefficient in expanded liquid metals. J Chem Phys 2004; 120:11100-6. [PMID: 15268140 DOI: 10.1063/1.1740755] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Molecular-dynamics simulation is used to compute the pair correlation function and the velocity autocorrelation function of Cs and Rb along the liquid-vapor coexistence curve, from which the excess entropy S(ex) and the diffusion coefficient D are deduced. The numerical results of both physical properties are correlated and a scaling law between the excess entropy and the reduced diffusion coefficient D(*)(=D/D(0)) is investigated for different expressions of the reduction parameter D(0). The choice of thermodynamic states along the liquid--vapor coexistence curve gives us the possibility to extend the investigation of the relation between the reduced diffusion coefficient and the excess entropy over a wide area and to test the adequacy of the scaling law confidently.
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Affiliation(s)
- J L Bretonnet
- Laboratoire de Theorie de la Matiere Condensee, Universite de Metz, 1 bd. F. D. Arago, CP 87811, 57078 Metz, France.
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Stopping Power of an Electron Gas for Heavy Unit Charges: Models in the Kinetic Approximation. ADVANCES IN QUANTUM CHEMISTRY 2004. [DOI: 10.1016/s0065-3276(04)46010-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/16/2023]
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Benoit DM, Sebastiani D, Parrinello M. Accurate total energies without self-consistency. PHYSICAL REVIEW LETTERS 2001; 87:226401. [PMID: 11736413 DOI: 10.1103/physrevlett.87.226401] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/27/2001] [Indexed: 05/23/2023]
Abstract
We present a new way of calculating approximate but accurate total energies within the framework of density functional theory. Our technique is based on an expansion of the energy functional to second order and does not require self-consistent iterations of the total density. The functional can be minimized by using the same techniques as developed for variational density functional perturbation theory. The method is ideally suited to systems composed of weakly interacting fragments, but it can also be applied to semiconductors and insulators. We show the versatility of our approach in a variety of examples exhibiting different types of chemical bonding.
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Affiliation(s)
- D M Benoit
- Max-Planck-Institute FKF, Heisenbergstrasse 1, D-70569 Stuttgart, Germany
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Ortner J, Tkachenko IM. Stopping power of strongly coupled electronic plasmas: sum rules and asymptotic forms. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 63:026403. [PMID: 11308581 DOI: 10.1103/physreve.63.026403] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/27/2000] [Indexed: 05/23/2023]
Abstract
The stopping power of coupled electronic plasmas is investigated. Within the dielectric formalism and employing the method of frequency moments for the dielectric function we obtain a general formula describing the linear stopping power of a coupled plasma. Analytical results for the low- and high-projectile-velocity asymptotic forms are obtained. A sum rule for the plasma heavy ions linear stopping power projectile velocity distribution is established to be related to the dielectric permeability "negative" frequency moment. This permits for a simple interpretation of stopping power data.
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Affiliation(s)
- J Ortner
- Institut für Physik, Humboldt Universität zu Berlin, D-10115 Berlin, Germany
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28
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Ultra-high Resolution Compton Scattering of Li Metal: Evaluation with Respect to the Correlation Corrected Occupation Number Density. ACTA ACUST UNITED AC 2001. [DOI: 10.1524/zpch.2001.215.11.1353] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
Abstract
Directional Compton profiles of Li metal measured with ultra-high momentum space resolution (0.02 a.u.) were analysed in terms of their reciprocal form factors
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Dharma-Wardana MW, Perrot F. Simple classical mapping of the spin-polarized quantum electron gas: distribution functions and local-field corrections. PHYSICAL REVIEW LETTERS 2000; 84:959-962. [PMID: 11017415 DOI: 10.1103/physrevlett.84.959] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/1999] [Indexed: 05/23/2023]
Abstract
We use the now well known spin unpolarized exchange-correlation energy E(xc) of the uniform electron gas as the basic "many-body" input to determine the temperature T(q) of a classical Coulomb fluid having the same correlation energy as the quantum system. It is shown that the spin-polarized pair distribution functions (SPDFs) of the classical fluid at T(q), obtained using the hypernetted chain equation, are in excellent agreement with those of the T = 0 quantum fluid obtained by quantum Monte Carlo (QMC) simulations. These methods are computationally simple and easily applied to problems which are currently beyond QMC simulations. Results are presented for the SPDFs and the local-field corrections to the response functions of the electron fluid at T = 0 and finite T.
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Affiliation(s)
- MW Dharma-Wardana
- National Research Council, Ottawa, Canada K1A 0R6 and and Centre d'Etudes de Bruyeres le Chatel, P.O. Box 12, 91689 Bruyeres le Chatel, France
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Schülke W, Höppner K, Kaprolat A. Semiempirical local-field correction function for electrons in Li metal. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:17464-17468. [PMID: 9985870 DOI: 10.1103/physrevb.54.17464] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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32
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Ortíz MA, Méndez-Moreno RM, Moreno M, Orozco S. Magnetic character of the deformable jellium. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:1423-1426. [PMID: 9985963 DOI: 10.1103/physrevb.54.1423] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Krakovsky A, Percus JK. Quasiparticle effective mass for the two- and three-dimensional electron gas. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 53:7352-7356. [PMID: 9982182 DOI: 10.1103/physrevb.53.7352] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Bretonnet JL, Boulahbak M. Semianalytical form for the local-field correction. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 53:6859-6861. [PMID: 9982106 DOI: 10.1103/physrevb.53.6859] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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35
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Krakovsky A, Percus JK. Hydrodynamic model of an inhomogeneous electron gas. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 52:7901-7906. [PMID: 9979784 DOI: 10.1103/physrevb.52.7901] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Moroni S, Ceperley DM, Senatore G. Static response and local field factor of the electron gas. PHYSICAL REVIEW LETTERS 1995; 75:689-692. [PMID: 10060089 DOI: 10.1103/physrevlett.75.689] [Citation(s) in RCA: 47] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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37
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Krakovsky A, Percus JK. Nonlinear calculation of the stopping power of a two-dimensional electron gas for heavy particles. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 52:R2305-R2308. [PMID: 9981397 DOI: 10.1103/physrevb.52.r2305] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Demkov AA, Ortega J, Sankey OF, Grumbach MP. Electronic structure approach for complex silicas. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 52:1618-1630. [PMID: 9981224 DOI: 10.1103/physrevb.52.1618] [Citation(s) in RCA: 71] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Delley B. DMol, a standard tool for density functional calculations: Review and advances. THEORETICAL AND COMPUTATIONAL CHEMISTRY 1995. [DOI: 10.1016/s1380-7323(05)80037-8] [Citation(s) in RCA: 83] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/03/2022]
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