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Sharma V, Collins LA, White AJ. Stochastic and mixed density functional theory within the projector augmented wave formalism for simulation of warm dense matter. Phys Rev E 2023; 108:L023201. [PMID: 37723794 DOI: 10.1103/physreve.108.l023201] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/02/2023] [Accepted: 05/08/2023] [Indexed: 09/20/2023]
Abstract
Stochastic density functional theory (DFT) and mixed stochastic-deterministic DFT are burgeoning approaches for the calculation of the equation of state and transport properties in materials under extreme conditions. In the intermediate warm dense matter regime, a state between correlated condensed matter and kinetic plasma, electrons can range from being highly localized around nuclei to delocalized over the whole simulation cell. The plane-wave basis pseudopotential approach is thus the typical tool of choice for modeling such systems at the DFT level. Unfortunately, stochastic DFT methods scale as the square of the maximum plane-wave energy in this basis. To reduce the effect of this scaling and improve the overall description of the electrons within the pseudopotential approximation, we present stochastic and mixed DFT approaches developed and implemented within the projector augmented wave formalism. We compare results between the different DFT approaches for both single-point and molecular dynamics trajectories and present calculations of self-diffusion coefficients of solid density carbon from 1 to 50 eV.
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Affiliation(s)
- Vidushi Sharma
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
- Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Lee A Collins
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Alexander J White
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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Abreu CRA, Tuckerman ME. Hamiltonian based resonance-free approach for enabling very large time steps in multiple time-scale molecular dynamics. Mol Phys 2021. [DOI: 10.1080/00268976.2021.1923848] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
Affiliation(s)
- Charlles R. A. Abreu
- Chemical Engineering Department, Escola de Química, Universidade Federal do Rio de Janeiro, Rio de Janeiro, RJ, Brazil
| | - Mark E. Tuckerman
- Department of Chemistry, New York University, New York, NY, USA
- Courant Institute of Mathematical Sciences, New York University, New York, NY, USA
- NYU-ECNU Center for Computational Chemistry at NYU Shanghai, Shanghai, People's Republic of China
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Wu CJ, Myint PC, Pask JE, Prisbrey CJ, Correa AA, Suryanarayana P, Varley JB. Development of a Multiphase Beryllium Equation of State and Physics-based Variations. J Phys Chem A 2021; 125:1610-1636. [PMID: 33587640 DOI: 10.1021/acs.jpca.0c09809] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We construct a family of beryllium (Be) multiphase equation of state (EOS) models that consists of a baseline ("optimal") EOS and variations on the baseline to account for physics-based uncertainties. The Be baseline EOS is constructed to reproduce a set of self-consistent data and theory including known phase boundaries, the principal Hugoniot, isobars, and isotherms from diamond-anvil cell experiments. Three phases are considered, including the known hexagonal closed-packed (hcp) phase, the liquid, and the theoretically predicted high-pressure body-centered cubic (bcc) phase. Since both the high-temperature liquid and high-pressure bcc phases lack any experimental data, we carry out ab initio density functional theory (DFT) calculations to obtain new information about the EOS properties for these two regions. At extremely high temperature conditions (>87 eV), DFT-based quantum molecular dynamics simulations are performed for multiple liquid densities using the state-of-the-art Spectral Quadrature methodology in order to validate our selected models for the ion- and electron-thermal free energies of the liquid. We have also performed DFT simulations of hcp and bcc with different exchange-correlation functionals to examine their impact on bcc compressibility, which bound the hcp-bcc transition pressure to within 4 ± 0.5 Mbar. Our baseline EOS predicts the first density maximum along the Hugoniot to be 4.4-fold in compression, while the hcp-bcc-liquid triple-point pressure is predicted to be at 2.25 Mbar. In addition to the baseline EOS, we have generated eight variations to accommodate multiple sources of potential uncertainties such as (1) the choice of free-energy models, (2) differences in theoretical treatments, (3) experimental uncertainties, and (4) lack of information. These variations are designed to provide a reasonable representation of nonstatistical uncertainties for the Be EOS and may be used to assess its sensitivity to different inertial-confinement fusion capsule designs.
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Affiliation(s)
- Christine J Wu
- Lawrence Livermore National Laboratory, Livermore, California 94588, United States
| | - Philip C Myint
- Lawrence Livermore National Laboratory, Livermore, California 94588, United States
| | - John E Pask
- Lawrence Livermore National Laboratory, Livermore, California 94588, United States
| | - Carrie J Prisbrey
- Lawrence Livermore National Laboratory, Livermore, California 94588, United States
| | - Alfredo A Correa
- Lawrence Livermore National Laboratory, Livermore, California 94588, United States
| | - Phanish Suryanarayana
- College of Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, United States
| | - Joel B Varley
- Lawrence Livermore National Laboratory, Livermore, California 94588, United States
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Abreu CRA, Tuckerman ME. Molecular Dynamics with Very Large Time Steps for the Calculation of Solvation Free Energies. J Chem Theory Comput 2020; 16:7314-7327. [PMID: 33197180 DOI: 10.1021/acs.jctc.0c00698] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
In multiple time scale molecular dynamics, the use of isokinetic constraints along with massive thermostatting has enabled the adoption of very large integration steps, well beyond the limits imposed by resonance artifacts in standard algorithms. In this work, we present two new contributions to this topic. First, we investigate the velocity distribution and the temperature-kinetic energy relationship associated with the isokinetic Nosé-Hoover family of methods, showing how they depend on the number of thermostats attached to each atomic degree of freedom. Second, we investigate the performance of these methods in the calculation of solvation free energies, the determination of which is often key for understanding the partition of a chemical species among distinct environments. We show how one can extract this property from canonical (constant-NVT) simulations and compare the result to experimental data obtained at a specific pressure. Finally, we demonstrate that large time steps can, in fact, be used to improve the efficiency of these calculations and that attaching multiple thermostats per degree of freedom is beneficial for effectively exploring the configurational space of a molecular system.
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Affiliation(s)
- Charlles R A Abreu
- Chemical Engineering Department, Escola de Química, Universidade Federal do Rio de Janeiro, Rio de Janeiro, RJ 21941-909, Brazil
| | - Mark E Tuckerman
- Department of Chemistry, New York University, New York, New York 10003, United States.,Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, United States.,NYU-ECNU Center for Computational Chemistry at NYU Shanghai, Shanghai 200062, China
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White AJ, Collins LA. Fast and Universal Kohn-Sham Density Functional Theory Algorithm for Warm Dense Matter to Hot Dense Plasma. PHYSICAL REVIEW LETTERS 2020; 125:055002. [PMID: 32794867 DOI: 10.1103/physrevlett.125.055002] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/06/2020] [Revised: 06/09/2020] [Accepted: 07/15/2020] [Indexed: 06/11/2023]
Abstract
Understanding many processes, e.g., fusion experiments, planetary interiors, and dwarf stars, depends strongly on microscopic physics modeling of warm dense matter and hot dense plasma. This complex state of matter consists of a transient mixture of degenerate and nearly free electrons, molecules, and ions. This regime challenges both experiment and analytical modeling, necessitating predictive ab initio atomistic computation, typically based on quantum mechanical Kohn-Sham density functional theory (KS-DFT). However, cubic computational scaling with temperature and system size prohibits the use of DFT through much of the warm dense matter regime. A recently developed stochastic approach to KS-DFT can be used at high temperatures, with the exact same accuracy as the deterministic approach, but the stochastic error can converge slowly and it remains expensive for intermediate temperatures (<50 eV). We have developed a universal mixed stochastic-deterministic algorithm for DFT at any temperature. This approach leverages the physics of KS-DFT to seamlessly integrate the best aspects of these different approaches. We demonstrate that this method significantly accelerated self-consistent field calculations for temperatures from 3 to 50 eV, while producing stable molecular dynamics and accurate diffusion coefficients.
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Affiliation(s)
- A J White
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - L A Collins
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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Lambert F, Recoules V. Plastic ablator and hydrodynamic instabilities: a first-principles set of microscopic coefficients. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:026405. [PMID: 23005867 DOI: 10.1103/physreve.86.026405] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/26/2012] [Indexed: 06/01/2023]
Abstract
We have performed orbital-free and quantum molecular dynamics simulations on plastic ablator along two isochores, namely 7 and 9 g cm(-3), from 5 to 40 eV. These thermodynamic conditions correspond to those encountered during inertial confinement fusion capsule implosion when hydrodynamic instabilities can take place. The coupling between orbital-free and quantum approaches allowed us to compute an exhaustive set of microscopic coefficients, i.e., equation-of-state, ionic diffusion coefficients, thermal and electrical conductivities, spanning phenomena that can mitigate the growth of classical Rayleigh-Taylor instability. Comparisons to widely used models in hydrodynamics codes are developed.
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Kress JD, Cohen JS, Horner DA, Lambert F, Collins LA. Viscosity and mutual diffusion of deuterium-tritium mixtures in the warm-dense-matter regime. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:036404. [PMID: 21230193 DOI: 10.1103/physreve.82.036404] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/07/2010] [Indexed: 05/30/2023]
Abstract
We have calculated viscosity and mutual diffusion of deuterium-tritium (DT) in the warm, dense matter regime for densities from 5 to 20 g/cm{3} and temperatures from 2 to 10 eV, using both finite-temperature Kohn-Sham density-functional theory molecular dynamics (QMD) and orbital-free molecular dynamics (OFMD). The OFMD simulations are in generally good agreement with the benchmark QMD results, and we conclude that the simpler OFMD method can be used with confidence in this regime. For low temperatures (3 eV and below), one-component plasma (OCP) model simulations for diffusion agree with the QMD and OFMD calculations, but deviate by 30% at 10 eV. In comparison with the QMD and OFMD results, the OCP viscosities are not as good as for diffusion, especially for 5 g/cm{3} where the temperature dependence is significantly different. The QMD and OFMD reduced diffusion and viscosity coefficients are found to depend largely, though not completely, only on the Coulomb coupling parameter Γ , with a minimum in the reduced viscosity at Γ≈25 , approximately the same position found in the OCP simulations. The QMD and OFMD equations of state (pressure) are also compared with the hydrogen two-component plasma model.
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Affiliation(s)
- J D Kress
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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Collins P, Ezra GS, Wiggins S. Phase space structure and dynamics for the Hamiltonian isokinetic thermostat. J Chem Phys 2010; 133:014105. [DOI: 10.1063/1.3455712] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Sergi A. Phase space flows for non-Hamiltonian systems with constraints. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 72:031104. [PMID: 16241408 DOI: 10.1103/physreve.72.031104] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/24/2005] [Indexed: 05/04/2023]
Abstract
In this paper, non-Hamiltonian systems with holonomic constraints are treated by a generalization of Dirac's formalism. Non-Hamiltonian phase space flows can be described by generalized antisymmetric brackets or by general Liouville operators which cannot be derived from brackets. Both situations are treated. In the first case, a Nosé-Dirac bracket is introduced as an example. In the second one, Dirac's recipe for projecting out constrained variables from time translation operators is generalized and then applied to non-Hamiltonian linear response. Dirac's formalism avoids spurious terms in the response function of constrained systems. However, corrections coming from phase space measure must be considered for general perturbations.
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Affiliation(s)
- Alessandro Sergi
- Dipartimento di Fisica, Sezione Fisica Teorica, Universitá degli Studi di Messina, Contrada Papardo C.P., 50-98166 Messina, Italy.
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Iftimie R, Minary P, Tuckerman ME. Ab initio molecular dynamics: concepts, recent developments, and future trends. Proc Natl Acad Sci U S A 2005; 102:6654-9. [PMID: 15870204 PMCID: PMC1100773 DOI: 10.1073/pnas.0500193102] [Citation(s) in RCA: 144] [Impact Index Per Article: 7.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
The methodology of ab initio molecular dynamics, wherein finite-temperature dynamical trajectories are generated by using forces computed "on the fly" from electronic structure calculations, has had a profound influence in modern theoretical research. Ab initio molecular dynamics allows chemical processes in condensed phases to be studied in an accurate and unbiased manner, leading to new paradigms in the elucidation of microscopic mechanisms, rationalization of experimental data, and testable predictions of new phenomena. The purpose of this work is to give a brief introduction to the technique and to review several important recent developments in the field. Several illustrative examples showing the power of the technique have been chosen. Perspectives on future directions in the field also will be given.
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Affiliation(s)
- Radu Iftimie
- Département de Chimie, Université de Montréal, Montréal, QC, Canada H3C 3J7
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