1
|
Sadigh B, Åberg D, Pask J. Spectral-partitioned Kohn-Sham density functional theory. Phys Rev E 2023; 108:045204. [PMID: 37978681 DOI: 10.1103/physreve.108.045204] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/16/2023] [Accepted: 09/13/2023] [Indexed: 11/19/2023]
Abstract
We introduce a general, variational scheme for systematic approximation of a given Kohn-Sham free-energy functional by partitioning the density matrix into distinct spectral domains, each of which may be spanned by an independent diagonal representation without requirement of mutual orthogonality. It is shown that by generalizing the entropic contribution to the free energy to allow for independent representations in each spectral domain, the free energy becomes an upper bound to the exact (unpartitioned) Kohn-Sham free energy, attaining this limit as the representations approach Kohn-Sham eigenfunctions. A numerical procedure is devised for calculation of the generalized entropy associated with spectral partitioning of the density matrix. The result is a powerful framework for Kohn-Sham calculations of systems whose occupied subspaces span multiple energy regimes. As a case in point, we apply the proposed framework to warm- and hot-dense matter described by finite-temperature density functional theory, where at high energies the density matrix is represented by that of the free-electron gas, while at low energies it is variationally optimized. We derive expressions for the spectral-partitioned Kohn-Sham Hamiltonian, atomic forces, and macroscopic stresses within the projector-augmented wave (PAW) and the norm-conserving pseudopotential methods. It is demonstrated that at high temperatures, spectral partitioning facilitates accurate calculations at dramatically reduced computational cost. Moreover, as temperature is increased, fewer exact Kohn-Sham states are required for a given accuracy, leading to further reductions in computational cost. Finally, it is shown that standard multiprojector expansions of electronic orbitals within atomic spheres in the PAW method lack sufficient completeness at high temperatures. Spectral partitioning provides a systematic solution for this fundamental problem.
Collapse
Affiliation(s)
- Babak Sadigh
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - Daniel Åberg
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - John Pask
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| |
Collapse
|
2
|
Ovechkin AA, Loboda PA, Popova VV, Akulinina EY, Berezovskaya ME, Korolev AS, Kolchugin SV. Plasma ionization balance in chemical-picture and average-atom models. Phys Rev E 2023; 108:015207. [PMID: 37583194 DOI: 10.1103/physreve.108.015207] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/21/2022] [Accepted: 07/02/2023] [Indexed: 08/17/2023]
Abstract
We propose an approximate method to calculate ion partition functions in the context of the chemical-picture representation of plasmas as an interacting mixture of various ions and free electrons under the local-thermodynamic-equilibrium conditions. The method uses the superconfiguration approach and implies that the first-order corrections to the energies of excited electron configurations due to the electron-electron interaction may be replaced by a similar first-order correction to the energy of the basic configuration of an ion with the same number of bound electrons. The method enables one to significantly speed up the calculations and generally provides quite accurate results. Using the method proposed, plasma ionization balance and average ion charges calculated on the base of the chemical-picture representation show a good agreement with the relevant average-atom data. For the case of weak electron-ion nonideality, we provide approximate relations between the chemical-picture and average-atom values of the average ion charge, chemical potential, and plasma-density depression of ionization potential.
Collapse
Affiliation(s)
- A A Ovechkin
- Russian Federal Nuclear Center-Zababakhin All-Russian Research Institute of Technical Physics (RFNC-VNIITF), 13, Vasilyeva st., Snezhinsk, Chelyabinsk region 456770, Russia
| | - P A Loboda
- Russian Federal Nuclear Center-Zababakhin All-Russian Research Institute of Technical Physics (RFNC-VNIITF), 13, Vasilyeva st., Snezhinsk, Chelyabinsk region 456770, Russia
- National Research Nuclear University-Moscow Engineering Physics Institute (MEPhI), 31, Kashirskoe sh., Moscow 115409, Russia
| | - V V Popova
- Russian Federal Nuclear Center-Zababakhin All-Russian Research Institute of Technical Physics (RFNC-VNIITF), 13, Vasilyeva st., Snezhinsk, Chelyabinsk region 456770, Russia
| | - E Yu Akulinina
- Russian Federal Nuclear Center-Zababakhin All-Russian Research Institute of Technical Physics (RFNC-VNIITF), 13, Vasilyeva st., Snezhinsk, Chelyabinsk region 456770, Russia
| | - M E Berezovskaya
- Russian Federal Nuclear Center-Zababakhin All-Russian Research Institute of Technical Physics (RFNC-VNIITF), 13, Vasilyeva st., Snezhinsk, Chelyabinsk region 456770, Russia
| | - A S Korolev
- Russian Federal Nuclear Center-Zababakhin All-Russian Research Institute of Technical Physics (RFNC-VNIITF), 13, Vasilyeva st., Snezhinsk, Chelyabinsk region 456770, Russia
| | - S V Kolchugin
- Russian Federal Nuclear Center-Zababakhin All-Russian Research Institute of Technical Physics (RFNC-VNIITF), 13, Vasilyeva st., Snezhinsk, Chelyabinsk region 456770, Russia
| |
Collapse
|
3
|
Bethkenhagen M, Sharma A, Suryanarayana P, Pask JE, Sadigh B, Hamel S. Properties of carbon up to 10 million kelvin from Kohn-Sham density functional theory molecular dynamics. Phys Rev E 2023; 107:015306. [PMID: 36797894 DOI: 10.1103/physreve.107.015306] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/03/2021] [Accepted: 12/22/2022] [Indexed: 06/18/2023]
Abstract
Accurately modeling dense plasmas over wide-ranging conditions of pressure and temperature is a grand challenge critically important to our understanding of stellar and planetary physics as well as inertial confinement fusion. In this work, we employ Kohn-Sham density functional theory (DFT) molecular dynamics (MD) to compute the properties of carbon at warm and hot dense matter conditions in the vicinity of the principal Hugoniot. In particular, we calculate the equation of state (EOS), Hugoniot, pair distribution functions, and diffusion coefficients for carbon at densities spanning 8 g/cm^{3} to 16 g/cm^{3} and temperatures ranging from 100 kK to 10 MK using the Spectral Quadrature method. We find that the computed EOS and Hugoniot are in good agreement with path integral Monte Carlo results and the sesame database. Additionally, we calculate the ion-ion structure factor and viscosity for selected points. All results presented are at the level of full Kohn-Sham DFT-MD, free of empirical parameters, average-atom, and orbital-free approximations employed previously at such conditions.
Collapse
Affiliation(s)
- Mandy Bethkenhagen
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
- École Normale Supérieure de Lyon, Université Lyon 1, Laboratoire de Géologie de Lyon, CNRS UMR 5276, 69364 Lyon, Cedex 07, France
| | - Abhiraj Sharma
- College of Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
| | - Phanish Suryanarayana
- College of Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
| | - John E Pask
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - Babak Sadigh
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - Sebastien Hamel
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| |
Collapse
|
4
|
Dharma-Wardana MWC, Stanek LJ, Murillo MS. Yukawa-Friedel-tail pair potentials for warm dense matter applications. Phys Rev E 2022; 106:065208. [PMID: 36671176 DOI: 10.1103/physreve.106.065208] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/22/2022] [Accepted: 12/01/2022] [Indexed: 06/17/2023]
Abstract
Accurate equations of state (EOS) and plasma transport properties are essential for numerical simulations of warm dense matter encountered in many high-energy-density situations. Molecular dynamics (MD) is a simulation method that generates EOS and transport data using an externally provided potential to dynamically evolve the particles without further reference to the electrons. To minimize computational cost, pair potentials needed in MD may be obtained from the neutral-pseudoatom (NPA) approach, a form of single-ion density functional theory (DFT), where many-ion effects are included via ion-ion correlation functionals. Standard N-ion DFT-MD provides pair potentials via the force matching technique but at much greater computational cost. Here we propose a simple analytic model for pair potentials with physically meaningful parameters based on a Yukawa form with a thermally damped Friedel tail (YFT) applicable to systems containing free electrons. The YFT model accurately fits NPA pair potentials or the nonparametric force-matched potentials from N-ion DFT-MD, showing excellent agreement for a wide range of conditions. The YFT form provides accurate extrapolations of the NPA or force-matched potentials for small and large particle separations within a physical model. Our method can be adopted to treat plasma mixtures, allowing for large-scale simulations of multispecies warm dense matter.
Collapse
Affiliation(s)
| | - Lucas J Stanek
- Department of Computational Mathematics, Science and Engineering, Michigan State University, East Lansing, Michigan 48824, USA
| | - Michael S Murillo
- Department of Computational Mathematics, Science and Engineering, Michigan State University, East Lansing, Michigan 48824, USA
| |
Collapse
|
5
|
Lv M, Li K, Wang C, Hu R, Zhao Y, Dai J. Bound electron screening effect on ion-ion potential of warm and hot dense matter. Phys Rev E 2021; 103:L051203. [PMID: 34134302 DOI: 10.1103/physreve.103.l051203] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/21/2020] [Accepted: 05/04/2021] [Indexed: 11/07/2022]
Abstract
The effects of bound electron screening in warm and hot dense matter are investigated analytically and a theoretical description of screened short-range repulsion is given meanwhile. An empirical ion-ion potential including the classic charge screening and chemical bond attraction at various temperatures and densities is proposed. By solving hypernetted chain equations and comparing the obtained radial distribution function (RDF) with ab initio simulations, the proposed ion-ion potential is found to be promising over a wide range of temperatures and densities for warm dense aluminum and iron. The elastic scattering amplitude and the x-ray absorption near the edge structure of warm dense aluminum calculated from the obtained RDF are in good agreement with experiment results.
Collapse
Affiliation(s)
- Meng Lv
- College of Physics, Sichuan University, Chengdu 610064, People's Republic of China
| | - Ke Li
- College of Physics, Sichuan University, Chengdu 610064, People's Republic of China
| | - Chuan Wang
- College of Physics, Sichuan University, Chengdu 610064, People's Republic of China
| | - Ronghao Hu
- College of Physics, Sichuan University, Chengdu 610064, People's Republic of China
| | - Yang Zhao
- Research Center of Laser Fusion, China Academy of Engineering Physics, P. O. Box 919-986, Mianyang 621900, People's Republic of China
| | - Jiayu Dai
- Department of Physics, College of Science, National University of Defense Technology, Changsha, Hunan 410073, People's Republic of China
| |
Collapse
|
6
|
Ovechkin AA, Loboda PA, Falkov AL, Sapozhnikov PA. Equation of state modeling with pseudoatom molecular dynamics. Phys Rev E 2021; 103:053206. [PMID: 34134221 DOI: 10.1103/physreve.103.053206] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2021] [Accepted: 04/28/2021] [Indexed: 11/07/2022]
Abstract
Using a modified version of the pseudoatom molecular-dynamics approach, the silicon and oxygen equations of state were generated and then employed to construct the equation of state of silicon dioxide. The results are supported by the close agreement with ab initio simulations of the silicon pressure and experimental shock Hugoniot of silicon dioxide. Ion thermal contributions to thermodynamic functions provided by the PAMD simulations are compared to their counterparts obtained with the one-component plasma and charged-hard-sphere approximations.
Collapse
Affiliation(s)
- A A Ovechkin
- Russian Federal Nuclear Center, Zababakhin All-Russian Research Institute of Technical Physics (RFNC-VNIITF), Snezhinsk, Chelyabinsk region 456770, Russia
| | - P A Loboda
- Russian Federal Nuclear Center, Zababakhin All-Russian Research Institute of Technical Physics (RFNC-VNIITF), Snezhinsk, Chelyabinsk region 456770, Russia.,National Research Nuclear University, Moscow Engineering Physics Institute (MEPhI), Moscow 115409, Russia
| | - A L Falkov
- Russian Federal Nuclear Center, Zababakhin All-Russian Research Institute of Technical Physics (RFNC-VNIITF), Snezhinsk, Chelyabinsk region 456770, Russia
| | - P A Sapozhnikov
- Russian Federal Nuclear Center, Zababakhin All-Russian Research Institute of Technical Physics (RFNC-VNIITF), Snezhinsk, Chelyabinsk region 456770, Russia
| |
Collapse
|
7
|
Militzer B, González-Cataldo F, Zhang S, Driver KP, Soubiran F. First-principles equation of state database for warm dense matter computation. Phys Rev E 2021; 103:013203. [PMID: 33601631 DOI: 10.1103/physreve.103.013203] [Citation(s) in RCA: 16] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/29/2020] [Accepted: 12/11/2020] [Indexed: 06/12/2023]
Abstract
We put together a first-principles equation of state (FPEOS) database for matter at extreme conditions by combining results from path integral Monte Carlo and density functional molecular dynamics simulations of the elements H, He, B, C, N, O, Ne, Na, Mg, Al, and Si as well as the compounds LiF, B_{4}C, BN, CH_{4}, CH_{2}, C_{2}H_{3}, CH, C_{2}H, MgO, and MgSiO_{3}. For all these materials, we provide the pressure and internal energy over a density-temperature range from ∼0.5 to 50 g cm^{-3} and from ∼10^{4} to 10^{9} K, which are based on ∼5000 different first-principles simulations. We compute isobars, adiabats, and shock Hugoniot curves in the regime of L- and K-shell ionization. Invoking the linear mixing approximation, we study the properties of mixtures at high density and temperature. We derive the Hugoniot curves for water and alumina as well as for carbon-oxygen, helium-neon, and CH-silicon mixtures. We predict the maximal shock compression ratios of H_{2}O, H_{2}O_{2}, Al_{2}O_{3}, CO, and CO_{2} to be 4.61, 4.64, 4.64, 4.89, and 4.83, respectively. Finally we use the FPEOS database to determine the points of maximum shock compression for all available binary mixtures. We identify mixtures that reach higher shock compression ratios than their end members. We discuss trends common to all mixtures in pressure-temperature and particle-shock velocity spaces. In the Supplemental Material, we provide all FPEOS tables as well as computer codes for interpolation, Hugoniot calculations, and plots of various thermodynamic functions.
Collapse
Affiliation(s)
- 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
| | - Felipe González-Cataldo
- Department of Earth and Planetary Science, University of California, Berkeley, California 94720, USA
| | - Shuai Zhang
- Department of Earth and Planetary Science, University of California, Berkeley, California 94720, USA
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
- Laboratory for Laser Energetics, University of Rochester, Rochester, New York 14623, USA
| | - Kevin P Driver
- Department of Earth and Planetary Science, University of California, Berkeley, California 94720, USA
- Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - François Soubiran
- Department of Earth and Planetary Science, University of California, Berkeley, California 94720, USA
- CEA DAM-DIF, 91297 Arpajon, France
| |
Collapse
|
8
|
Starrett CE, Shaffer N. Multiple scattering theory for dense plasmas. Phys Rev E 2020; 102:043211. [PMID: 33212669 DOI: 10.1103/physreve.102.043211] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/26/2020] [Accepted: 10/04/2020] [Indexed: 06/11/2023]
Abstract
Dense plasmas occur in stars, giant planets, and in inertial fusion experiments. Accurate modeling of the electronic structure of these plasmas allows for prediction of material properties that can in turn be used to simulate these astrophysical objects and terrestrial experiments. But modeling them remains a challenge. Here we explore the Korringa-Kohn-Rostoker Green's function (KKR-GF) method for this purpose. We find that it is able to predict equation of state in good agreement with other state-of-the-art methods, where they are accurate and viable. In addition, it is shown that the computational cost does not significantly change with temperature, in contrast with other approaches. Moreover, the method does not use pseudopotentials-core states are calculated self consistently. We conclude that KKR-GF is a very promising method for dense plasma simulation.
Collapse
Affiliation(s)
- C E Starrett
- Los Alamos National Laboratory, P.O. Box 1663, Los Alamos, New Mexico 87545, USA
| | - N Shaffer
- Los Alamos National Laboratory, P.O. Box 1663, Los Alamos, New Mexico 87545, USA
| |
Collapse
|
9
|
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.
Collapse
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
| |
Collapse
|
10
|
Swift DC, Lockard T, Kraus RG, Benedict LX, Sterne PA, Bethkenhagen M, Hamel S, Bennett BI. Atom-in-jellium equations of state in the high-energy-density regime. Phys Rev E 2019; 99:063210. [PMID: 31330676 DOI: 10.1103/physreve.99.063210] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/28/2018] [Indexed: 06/10/2023]
Abstract
Recent path-integral Monte Carlo and quantum molecular dynamics simulations have shown that computationally efficient average-atom models can predict thermodynamic states in warm dense matter to within a few percent. One such atom-in-jellium model has typically been used to predict the electron-thermal behavior only, although it was previously developed to predict the entire equation of state (EOS). We report completely atom-in-jellium EOS calculations for Be, Al, Si, Fe, and Mo, as elements representative of a range of atomic number and low-pressure electronic structure. Comparing the more recent method of pseudoatom molecular dynamics, atom-in-jellium results were similar: sometimes less accurate, sometimes more. All these techniques exhibited pronounced effects of electronic shell structure in the shock Hugoniot which are not captured by Thomas-Fermi based EOS. These results demonstrate the value of a hierarchical approach to EOS construction, using average-atom techniques with shell structure to populate a wide-range EOS surface efficiently, complemented by more rigorous three-dimensional multiatom calculations to validate and adjust the EOS.
Collapse
Affiliation(s)
- Damian C Swift
- Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, California 94551, USA
| | - Thomas Lockard
- Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, California 94551, USA
| | - Richard G Kraus
- Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, California 94551, USA
| | - Lorin X Benedict
- Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, California 94551, USA
| | - Philip A Sterne
- Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, California 94551, USA
| | - Mandy Bethkenhagen
- Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, California 94551, USA
| | - Sebastien Hamel
- Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, California 94551, USA
| | - Bard I Bennett
- Los Alamos National Laboratory, PO Box 1663, Los Alamos, New Mexico 87545, USA
| |
Collapse
|
11
|
Driver KP, Soubiran F, Militzer B. Path integral Monte Carlo simulations of warm dense aluminum. Phys Rev E 2018; 97:063207. [PMID: 30011453 DOI: 10.1103/physreve.97.063207] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/17/2017] [Indexed: 06/08/2023]
Abstract
We perform first-principles path integral Monte Carlo (PIMC) and density functional theory molecular dynamics (DFT-MD) calculations to explore warm dense matter states of aluminum. Our equation of state (EOS) simulations cover a wide density-temperature range of 0.1-32.4gcm^{-3} and 10^{4}-10^{8} K. Since PIMC and DFT-MD accurately treat effects of the atomic shell structure, we find two compression maxima along the principal Hugoniot curve attributed to K-shell and L-shell ionization. The results provide a benchmark for widely used EOS tables, such as SESAME, QEOS, and models based on Thomas-Fermi and average-atom techniques. A subsequent multishock analysis provides a quantitative assessment for how much heating occurs relative to an isentrope in multishock experiments. Finally, we compute heat capacity, pair-correlation functions, the electronic density of states, and 〈Z〉 to reveal the evolution of the plasma structure and ionization behavior.
Collapse
Affiliation(s)
- K P Driver
- Department of Earth and Planetary Science, University of California, Berkeley, California 94720, USA
| | - F Soubiran
- Department of Earth and Planetary Science, University of California, Berkeley, California 94720, USA
| | - B Militzer
- Department of Earth and Planetary Science, University of California, Berkeley, California 94720, USA
- Department of Astronomy, University of California, Berkeley, California 94720, USA
| |
Collapse
|
12
|
Starrett CE. Thomas-Fermi simulations of dense plasmas without pseudopotentials. Phys Rev E 2017; 96:013206. [PMID: 29347227 DOI: 10.1103/physreve.96.013206] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/28/2017] [Indexed: 11/07/2022]
Abstract
The Thomas-Fermi model for warm and hot dense matter is widely used to predict material properties such as the equation of state. However, for practical reasons current implementations use pseudopotentials for the electron-nucleus interaction instead of the bare Coulomb potential. This complicates the calculation and quantities such as free energy cannot be converged with respect to the pseudopotential parameters. We present a method that retains the bare Coulomb potential for the electron-nucleus interaction and does not use pseudopotentials. We demonstrate that accurate free energies are obtained by checking variational consistency. Examples for aluminum and iron plasmas are presented.
Collapse
Affiliation(s)
- C E Starrett
- Los Alamos National Laboratory, P.O. Box 1663, Los Alamos, New Mexico 87545, USA
| |
Collapse
|