1
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Dornheim T, Schwalbe S, Moldabekov ZA, Vorberger J, Tolias P. Ab Initio Path Integral Monte Carlo Simulations of the Uniform Electron Gas on Large Length Scales. J Phys Chem Lett 2024; 15:1305-1313. [PMID: 38285536 PMCID: PMC10860150 DOI: 10.1021/acs.jpclett.3c03193] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/14/2023] [Revised: 01/17/2024] [Accepted: 01/22/2024] [Indexed: 01/31/2024]
Abstract
The accurate description of non-ideal quantum many-body systems is of prime importance for a host of applications within physics, quantum chemistry, materials science, and related disciplines. At finite temperatures, the gold standard is given by ab initio path integral Monte Carlo (PIMC) simulations, which do not require any empirical input but exhibit an exponential increase in the required computation time for Fermionic systems with an increase in system size N. Very recently, computing Fermionic properties without this bottleneck based on PIMC simulations of fictitious identical particles has been suggested. In our work, we use this technique to perform very large (N ≤ 1000) PIMC simulations of the warm dense electron gas and demonstrate that it is capable of providing a highly accurate description of the investigated properties, i.e., the static structure factor, the static density response function, and the local field correction, over the entire range of length scales.
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Affiliation(s)
- Tobias Dornheim
- Center
for Advanced Systems Understanding (CASUS), Helmholtz-Zentrum Dresden-Rossendorf (HZDR), D-02826 Görlitz, Germany
| | - Sebastian Schwalbe
- Center
for Advanced Systems Understanding (CASUS), Helmholtz-Zentrum Dresden-Rossendorf (HZDR), D-02826 Görlitz, Germany
| | - Zhandos A. Moldabekov
- Center
for Advanced Systems Understanding (CASUS), Helmholtz-Zentrum Dresden-Rossendorf (HZDR), D-02826 Görlitz, Germany
| | - Jan Vorberger
- Institute
of Radiation Physics, 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
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2
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Moldabekov Z, Schwalbe S, Böhme MP, Vorberger J, Shao X, Pavanello M, Graziani FR, Dornheim T. Bound-State Breaking and the Importance of Thermal Exchange-Correlation Effects in Warm Dense Hydrogen. J Chem Theory Comput 2024; 20:68-78. [PMID: 38133546 PMCID: PMC10782774 DOI: 10.1021/acs.jctc.3c00934] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/24/2023] [Revised: 12/01/2023] [Accepted: 12/01/2023] [Indexed: 12/23/2023]
Abstract
Hydrogen at extreme temperatures and pressures is of key relevance for cutting-edge technological applications, with inertial confinement fusion research being a prime example. In addition, it is ubiquitous throughout our universe and naturally occurs in a variety of astrophysical objects. In the present work, we present exact ab initio path integral Monte Carlo (PIMC) results for the electronic density of warm dense hydrogen along a line of constant degeneracy across a broad range of densities. Using the well-known concept of reduced density gradients, we develop a new framework to identify the breaking of bound states due to pressure ionization in bulk hydrogen. Moreover, we use our PIMC results as a reference to rigorously assess the accuracy of a variety of exchange-correlation (XC) functionals in density functional theory calculations for different density regions. Here, a key finding is the importance of thermal XC effects for the accurate description of density gradients in high-energy-density systems. Our exact PIMC test set is freely available online and can be used to guide the development of new methodologies for the simulation of warm dense matter and beyond.
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Affiliation(s)
- Zhandos Moldabekov
- Center
for Advanced Systems Understanding (CASUS), Görlitz D-02826, Germany
- Helmholtz-Zentrum
Dresden-Rossendorf (HZDR), Dresden D-01328, Germany
| | - Sebastian Schwalbe
- Center
for Advanced Systems Understanding (CASUS), Görlitz D-02826, Germany
- Helmholtz-Zentrum
Dresden-Rossendorf (HZDR), Dresden D-01328, Germany
| | | | - Jan Vorberger
- Helmholtz-Zentrum
Dresden-Rossendorf (HZDR), Dresden D-01328, Germany
| | - Xuecheng Shao
- Department
of Chemistry, Rutgers University, Newark, New Jersey 07102, United States
- Department
of Physics, Rutgers University, Newark, New Jersey 07102, United States
| | - Michele Pavanello
- Department
of Chemistry, Rutgers University, Newark, New Jersey 07102, United States
- Department
of Physics, Rutgers University, Newark, New Jersey 07102, United States
| | - Frank R. Graziani
- Lawrence
Livermore National Laboratory (LLNL), Livermore 94550, California, United States
| | - Tobias Dornheim
- Center
for Advanced Systems Understanding (CASUS), Görlitz D-02826, Germany
- Helmholtz-Zentrum
Dresden-Rossendorf (HZDR), Dresden D-01328, Germany
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3
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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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4
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Van Benschoten W, Petras HR, Shepherd JJ. Electronic Free Energy Surface of the Nitrogen Dimer Using First-Principles Finite Temperature Electronic Structure Methods. J Phys Chem A 2023; 127:6842-6856. [PMID: 37535315 PMCID: PMC10440793 DOI: 10.1021/acs.jpca.3c01741] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/14/2023] [Revised: 07/20/2023] [Indexed: 08/04/2023]
Abstract
We use full configuration interaction and density matrix quantum Monte Carlo methods to calculate the electronic free energy surface of the nitrogen dimer within the free-energy Born-Oppenheimer approximation. As the temperature is raised from T = 0, we find a temperature regime in which the internal energy causes bond strengthening. At these temperatures, adding in the entropy contributions is required to cause the bond to gradually weaken with increasing temperature. We predict a thermally driven dissociation for the nitrogen dimer between 22,000 to 63,200 K depending on symmetries and basis set. Inclusion of more spatial and spin symmetries reduces the temperature required. The origin of these observations is explored using the structure of the density matrix at various temperatures and bond lengths.
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Affiliation(s)
| | - Hayley R. Petras
- Department
of Chemistry, University of Iowa, Iowa City, Iowa 52242, United States
| | - James J. Shepherd
- Department
of Chemistry, University of Iowa, Iowa City, Iowa 52242, United States
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5
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Moldabekov Z, Böhme M, Vorberger J, Blaschke D, Dornheim T. Ab Initio Static Exchange-Correlation Kernel across Jacob's Ladder without Functional Derivatives. J Chem Theory Comput 2023; 19:1286-1299. [PMID: 36724889 PMCID: PMC9979610 DOI: 10.1021/acs.jctc.2c01180] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/03/2023]
Abstract
The electronic exchange─correlation (XC) kernel constitutes a fundamental input for the estimation of a gamut of properties such as the dielectric characteristics, the thermal and electrical conductivity, or the response to an external perturbation. In this work, we present a formally exact methodology for the computation of the system specific static XC kernel exclusively within the framework of density functional theory (DFT) and without employing functional derivatives─no external input apart from the usual XC-functional is required. We compare our new results with exact quantum Monte Carlo (QMC) data for the archetypical uniform electron gas model under both ambient and warm dense matter conditions. This gives us unprecedented insights into the performance of different XC functionals, and it has important implications for the development of new functionals that are designed for the application at extreme temperatures. In addition, we obtain new DFT results for the XC kernel of warm dense hydrogen as it occurs in fusion applications and astrophysical objects. The observed excellent agreement to the QMC reference data demonstrates that presented framework is capable to capture nontrivial effects such as XC-induced isotropy breaking in the density response of hydrogen at large wave numbers.
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Affiliation(s)
- Zhandos Moldabekov
- Center
for Advanced Systems Understanding (CASUS), D-02826Görlitz, Germany,Helmholtz-Zentrum
Dresden-Rossendorf (HZDR), D-01328Dresden, Germany,E-mail:
| | - Maximilian Böhme
- Center
for Advanced Systems Understanding (CASUS), D-02826Görlitz, Germany
| | - Jan Vorberger
- Helmholtz-Zentrum
Dresden-Rossendorf (HZDR), D-01328Dresden, Germany
| | - David Blaschke
- Institute
of Theoretical Physics, University of Wroclaw, 50-204Wroclaw, Poland
| | - Tobias Dornheim
- Center
for Advanced Systems Understanding (CASUS), D-02826Görlitz, Germany,Helmholtz-Zentrum
Dresden-Rossendorf (HZDR), D-01328Dresden, Germany,E-mail:
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6
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Van Benschoten WZ, Shepherd JJ. Piecewise Interaction Picture Density Matrix Quantum Monte Carlo. J Chem Phys 2022; 156:184107. [DOI: 10.1063/5.0094290] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The density matrix quantum Monte Carlo (DMQMC) set of methods stochastically samples the exact $N$-body density matrix for interacting electrons at finite temperature. We introduce a simple modification to the interaction picture DMQMC method (IP-DMQMC) which overcomes the limitation of only sampling one inverse temperature point at a time, instead allowing for the sampling of a temperature range within a single calculation thereby reducing the computational cost. At the target inverse temperature, instead of ending the simulation, we incorporate a change of picture away from the interaction picture. The resulting equations of motion have piecewise functions and use the interaction picture in the first phase of a simulation, followed by the application of the Bloch equation once the target inverse temperature is reached. We find that the performance of this method is similar to or better than the DMQMC and IP-DMQMC algorithms in a variety of molecular test systems.
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7
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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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8
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Dornheim T, Vorberger J. Finite-size effects in the reconstruction of dynamic properties from ab initio path integral Monte Carlo simulations. Phys Rev E 2020; 102:063301. [PMID: 33466040 DOI: 10.1103/physreve.102.063301] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/20/2020] [Accepted: 11/15/2020] [Indexed: 06/12/2023]
Abstract
We systematically investigate finite-size effects in the dynamic structure factor S(q,ω) of the uniform electron gas obtained via the analytic continuation of ab initio path integral Monte Carlo data for the imaginary-time density-density correlation function F(q,τ). Using the recent scheme by Dornheim et al. [Phys. Rev. Lett. 121, 255001 (2018)PRLTAO0031-900710.1103/PhysRevLett.121.255001], we find that the reconstructed spectra are not afflicted with any finite-size effects for as few as N=14 electrons both at warm dense matter (WDM) conditions and at the margins of the strongly correlated electron liquid regime. Our results further corroborate the high quality of our current description of the dynamic density response of correlated electrons, which is of high importance for many applications in WDM theory and beyond.
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Affiliation(s)
- Tobias Dornheim
- Center for Advanced Systems Understanding (CASUS), D-02826 Görlitz, Germany
| | - Jan Vorberger
- Helmholtz-Zentrum Dresden-Rossendorf (HZDR), D-01328 Dresden, Germany
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9
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Peters LDM, Kussmann J, Ochsenfeld C. A Fermi smearing variant of the Tamm–Dancoff approximation for nonadiabatic dynamics involving S 1–S 0 transitions: Validation and application to azobenzene. J Chem Phys 2020; 153:094104. [DOI: 10.1063/5.0016487] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Laurens D. M. Peters
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, D-81377 München, Germany
| | - Jörg Kussmann
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, D-81377 München, Germany
| | - Christian Ochsenfeld
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, D-81377 München, Germany
- Max Planck Institute for Solid State Research, Heisenbergstr. 1, D-70569 Stuttgart, Germany
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10
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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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11
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Yoshikawa T, Doi T, Nakai H. Finite-temperature-based time-dependent density-functional theory method for static electron correlation systems. J Chem Phys 2020; 152:244111. [PMID: 32610978 DOI: 10.1063/1.5144527] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
In this study, we developed a time-dependent density-functional theory (TDDFT) with a finite-temperature (FT) scheme, denoted as FT-TDDFT. We introduced the concept of fractional occupation numbers for random phase approximation equation and evaluated the excited-state electronic entropy terms with excited-state occupation number. The orbital occupation numbers for the excited state were evaluated from the change in the ground-state electron configuration with excitation and deexcitation coefficients. Furthermore, we extended the FT formulation to the time-dependent density-functional tight-binding (TDDFTB) method for larger systems, denoted as FT-TDDFTB. Numerical assessment for the FT-(TD)DFT method showed smooth potential curves for double-bond rotation of ethylene in both ground and excited states. Excited-state calculations based on the FT-TDDFTB method were applied to the uniform π-stacking columns composed of trioxotriangulene, possessing neutral radicals in strong correlation systems.
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Affiliation(s)
- Takeshi Yoshikawa
- Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
| | - Toshiki Doi
- Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
| | - Hiromi Nakai
- Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
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12
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Gerolin A, Grossi J, Gori-Giorgi P. Kinetic Correlation Functionals from the Entropic Regularization of the Strictly Correlated Electrons Problem. J Chem Theory Comput 2020; 16:488-498. [PMID: 31855421 PMCID: PMC6964418 DOI: 10.1021/acs.jctc.9b01133] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/13/2019] [Indexed: 11/29/2022]
Abstract
In this work, we study the entropic regularization of the strictly correlated electrons formalism, discussing the implications for density functional theory and establishing a link with earlier works on quantum kinetic energy and classical entropy. We carry out a very preliminary investigation (using simplified models) on the use of the solution of the entropic regularized problem to build approximations for the kinetic correlation functional at large coupling strengths. We also analyze lower and upper bounds to the Hohenberg-Kohn functional using the entropic regularized strictly correlated electrons problem.
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Affiliation(s)
- Augusto Gerolin
- Department of Theoretical
Chemistry and Amsterdam Center for Multiscale Modeling, FEW, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands
| | - Juri Grossi
- Department of Theoretical
Chemistry and Amsterdam Center for Multiscale Modeling, FEW, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands
| | - Paola Gori-Giorgi
- Department of Theoretical
Chemistry and Amsterdam Center for Multiscale Modeling, FEW, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands
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13
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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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14
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Hollebon P, Ciricosta O, Desjarlais MP, Cacho C, Spindloe C, Springate E, Turcu ICE, Wark JS, Vinko SM. Ab initio simulations and measurements of the free-free opacity in aluminum. Phys Rev E 2019; 100:043207. [PMID: 31770899 DOI: 10.1103/physreve.100.043207] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/23/2018] [Indexed: 06/10/2023]
Abstract
The free-free opacity in dense systems is a property that both tests our fundamental understanding of correlated many-body systems, and is needed to understand the radiative properties of high energy-density plasmas. Despite its importance, predictive calculations of the free-free opacity remain challenging even in the condensed matter phase for simple metals. Here we show how the free-free opacity can be modelled at finite-temperatures via time-dependent density functional theory, and illustrate the importance of including local field corrections, core polarization, and self-energy corrections. Our calculations for ground-state Al are shown to agree well with experimental opacity measurements performed on the Artemis laser facility across a wide range of extreme ultraviolet wavelengths. We extend our calculations across the melt to the warm-dense matter regime, finding good agreement with advanced plasma models based on inverse bremsstrahlung at temperatures above 10 eV.
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Affiliation(s)
- P Hollebon
- Department of Physics, Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - O Ciricosta
- Department of Physics, Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - M P Desjarlais
- Pulsed Power Sciences Center, Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - C Cacho
- Central Laser Facility, STFC Rutherford Appleton Laboratory, Didcot OX11 0QX, United Kingdom
| | - C Spindloe
- Central Laser Facility, STFC Rutherford Appleton Laboratory, Didcot OX11 0QX, United Kingdom
| | - E Springate
- Central Laser Facility, STFC Rutherford Appleton Laboratory, Didcot OX11 0QX, United Kingdom
| | - I C E Turcu
- Central Laser Facility, STFC Rutherford Appleton Laboratory, Didcot OX11 0QX, United Kingdom
| | - J S Wark
- Department of Physics, Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - S M Vinko
- Department of Physics, Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
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15
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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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16
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Trushin E, Görling A. Topological Phase Transitions in Zinc-Blende Semimetals Driven Exclusively by Electronic Temperature. PHYSICAL REVIEW LETTERS 2018; 120:146401. [PMID: 29694127 DOI: 10.1103/physrevlett.120.146401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/27/2017] [Revised: 12/15/2017] [Indexed: 06/08/2023]
Abstract
We show that electronic phase transitions in zinc-blende semimetals with quadratic band touching (QBT) at the center of the Brillouin zone, like GaBi, InBi, or HgTe, can occur exclusively due to a change of the electronic temperature without the need to involve structural transformations or electron-phonon coupling. The commonly used Kohn-Sham density-functional methods based on local and semilocal density functionals employing the local density approximation (LDA) or generalized gradient approximations (GGAs), however, are not capable of describing such phenomena because they lack an intrinsic temperature dependence and account for temperature only via the occupation of bands, which essentially leads only to a shift of the Fermi level without changing the shape or topology of bands. Kohn-Sham methods using the exact temperature-dependent exchange potential, not to be confused with the Hartree-Fock exchange potential, on the other hand, describe such phase transitions. A simple modeling of correlation effects can be achieved by screening of the exchange. In the considered zinc-blende compounds the QBT is unstable at low temperatures and a transition to electronic states without QBT takes place. In the case of HgTe and GaBi Weyl points of type I and type II, respectively, emerge during the transitions. This demonstrates that Kohn-Sham methods can describe such topological phase transitions provided they are based on functionals more accurate than those within the LDA or GGA. Moreover, the electronic temperature is identified as a handle to tune topological materials.
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Affiliation(s)
- Egor Trushin
- Lehrstuhl für Theoretische Chemie, Universität Erlangen-Nürnberg, Egerlandstr. 3, D-91058 Erlangen, Germany
| | - Andreas Görling
- Lehrstuhl für Theoretische Chemie, Universität Erlangen-Nürnberg, Egerlandstr. 3, D-91058 Erlangen, Germany
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17
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Groth S, Dornheim T, Bonitz M. Configuration path integral Monte Carlo approach to the static density response of the warm dense electron gas. J Chem Phys 2017; 147:164108. [DOI: 10.1063/1.4999907] [Citation(s) in RCA: 39] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022] Open
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
| | - Michael Bonitz
- Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, D-24098 Kiel, Germany
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18
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Kas JJ, Rehr JJ. Finite Temperature Green's Function Approach for Excited State and Thermodynamic Properties of Cool to Warm Dense Matter. PHYSICAL REVIEW LETTERS 2017; 119:176403. [PMID: 29219457 DOI: 10.1103/physrevlett.119.176403] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/24/2017] [Indexed: 06/07/2023]
Abstract
We present a finite-temperature extension of the retarded cumulant Green's function for calculations of exited-state, correlation, and thermodynamic properties of electronic systems. The method incorporates a cumulant to leading order in the screened Coulomb interaction W, and improves on the GW approximation of many-body perturbation theory. Results for the homogeneous electron gas are presented for a wide range of densities and temperatures, from cool to warm dense matter regimes, which reveal several hitherto unexpected properties. For example, correlation effects remain strong at high T while the exchange-correlation energy becomes small; also the spectral function broadens and damping increases with temperature, blurring the usual quasiparticle picture. These effects are evident, e.g., in Compton scattering which exhibits many-body corrections that persist at normal densities and intermediate T. The approach also yields exchange-correlation energies and potentials in good agreement with existing methods.
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Affiliation(s)
- J J Kas
- Department of Physics, University of Washington, Seattle, Washington 98195, USA
| | - J J Rehr
- Department of Physics, University of Washington, Seattle, Washington 98195, USA
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19
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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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20
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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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21
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Eich FG, Di Ventra M, Vignale G. Functional theories of thermoelectric phenomena. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:063001. [PMID: 27991434 DOI: 10.1088/1361-648x/29/6/063001] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We review the progress that has been recently made in the application of time-dependent density functional theory to thermoelectric phenomena. As the field is very young, we emphasize open problems and fundamental issues. We begin by introducing the formal structure of thermal density functional theory, a density functional theory with two basic variables-the density and the energy density-and two conjugate fields-the ordinary scalar potential and Luttinger's thermomechanical potential. The static version of this theory is contrasted with the familiar finite-temperature density functional theory, in which only the density is a variable. We then proceed to constructing the full time-dependent non equilibrium theory, including the practically important Kohn-Sham equations that go with it. The theory is shown to recover standard results of the Landauer theory for thermal transport in the steady state, while showing greater flexibility by allowing a description of fast thermal response, temperature oscillations and related phenomena. Several results are presented here for the first time, i.e. the proof of invertibility of the thermal response function in the linear regime, the full expression of the thermal currents in the presence of Luttinger's thermomechanical potential, an explicit prescription for the evaluation of the Kohn-Sham potentials in the adiabatic local density approximation, a detailed discussion of the leading dissipative corrections to the adiabatic local density approximation and the thermal corrections to the resistivity that follow from it.
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Affiliation(s)
- F G Eich
- Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, D-22761 Hamburg, Germany. Department of Physics, University of Missouri-Columbia, Columbia, MO 65211, USA
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22
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Gould T, Lebègue S, Ángyán JG, Bučko T. A Fractionally Ionic Approach to Polarizability and van der Waals Many-Body Dispersion Calculations. J Chem Theory Comput 2016; 12:5920-5930. [PMID: 27951673 DOI: 10.1021/acs.jctc.6b00925] [Citation(s) in RCA: 57] [Impact Index Per Article: 7.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
By explicitly including fractionally ionic contributions to the polarizability of a many-component system, we are able to significantly improve on previous atom-wise many-body van der Waals approaches with essentially no extra numerical cost. For nonionic systems, our method is comparable in accuracy to existing approaches. However, it offers substantial improvements in ionic solids, e.g., producing better polarizabilities by over 65% in some cases. It has particular benefits for two-dimensional transition metal dichalcogenides and interactions of H2 with modified coronenes, ionic systems of nanotechnological interest. It thus offers an efficient improvement on existing approaches, valid for a wide range of systems.
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Affiliation(s)
- Tim Gould
- Qld Micro- and Nanotechnology Centre, Griffith University , Nathan, Qld 4111, Australia
| | - Sébastien Lebègue
- Université de Lorraine , Vandœuvre-lès-Nancy, F-54506, France.,CNRS, CRM2, UMR 7036 , Vandœuvre-lès-Nancy, F-54506, France
| | - János G Ángyán
- Université de Lorraine , Vandœuvre-lès-Nancy, F-54506, France.,CNRS, CRM2, UMR 7036 , Vandœuvre-lès-Nancy, F-54506, France.,Department of General and Inorganic Chemistry, Pannon University , Veszprém H-8201, Hungary
| | - Tomáš Bučko
- Department of Physical and Theoretical Chemistry, Faculty of Natural Sciences, Comenius University in Bratislava , Mlynská Dolina, Ilkovičova 6, SK-84215 Bratislava, Slovakia.,Institute of Inorganic Chemistry, Slovak Academy of Sciences , Dúbravská cesta 9, SK-84236 Bratislava, Slovakia
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23
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Dornheim T, Groth S, Sjostrom T, Malone FD, Foulkes WMC, Bonitz M. Ab Initio Quantum Monte Carlo Simulation of the Warm Dense Electron Gas in the Thermodynamic Limit. PHYSICAL REVIEW LETTERS 2016; 117:156403. [PMID: 27768371 DOI: 10.1103/physrevlett.117.156403] [Citation(s) in RCA: 56] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/28/2016] [Indexed: 06/06/2023]
Abstract
We perform ab initio quantum Monte Carlo (QMC) simulations of the warm dense uniform electron gas in the thermodynamic limit. By combining QMC data with the linear response theory, we are able to remove finite-size errors from the potential energy over the substantial parts of the warm dense regime, overcoming the deficiencies of the existing finite-size corrections by Brown et al. [Phys. Rev. Lett. 110, 146405 (2013)]. Extensive new QMC results for up to N=1000 electrons enable us to compute the potential energy V and the exchange-correlation free energy F_{xc} of the macroscopic electron gas with an unprecedented accuracy of |ΔV|/|V|,|ΔF_{xc}|/|F|_{xc}∼10^{-3}. A comparison of our new data to the recent parametrization of F_{xc} by Karasiev et al. [Phys. Rev. Lett. 112, 076403 (2014)] reveals significant deviations to the latter.
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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
| | - 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
| | - 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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24
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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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