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Results for “orbital-free density functional theory”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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30 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

First-principles equation of state of CHON resin for inertial confinement fusion applications

A wide-range (0 to 1044.0 g/ cm 3 and 0 to 10 9 K) equation-of-state (EOS) table for a CH 1.72 O 0.37 N 0.086 quaternary compound has been constructed based on density-functional theory (DFT) molecular-dynamics (MD) calculations using a combination of Kohn-Sham DFT MD, orbital-free DFT MD, and numerical extrapolation. The first-principles EOS data are compared with predictions of simple models, including the fully ionized ideal gas and the Fermi-degenerate electron gas models, to chart their temperature-density conditions of applicability. The shock Hugoniot, thermodynamic properties, and bulk sound velocities are predicted based on the EOS table and compared to those of C-H compounds. The Hugoniot results show the maximum compression ratio of the C-H-O-N resin is larger than that of CH polystyrene due to the existence of oxygen and nitrogen; while the other properties are similar between CHON and CH. Radiation hydrodynamic simulations have been performed using the table for inertial confinement fusion targets with a CHON ablator and compared with a similar design with CH. Here, the simulations show CHON outperforms CH as the ablator for laser-direct-drive target designs.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Assessing the source of error in the Thomas–Fermi–von Weizsäcker density functional

We investigate the source of error in the Thomas–Fermi–von Weizsäcker (TFW) density functional relative to Kohn–Sham density functional theory (DFT). In particular, through numerical studies on a range of materials, for a variety of crystal structures subject to strain and atomic displacements, we find that while the ground state electron density in TFW orbital-free DFT is close to the Kohn–Sham density, the corresponding energy deviates significantly from the Kohn–Sham value. Here, we show that these differences are a consequence of the poor representation of the linear response within the TFW approximation for the electronic kinetic energy, confirming conjectures in the literature. In so doing, we find that the energy computed from a non-self-consistent Kohn–Sham calculation using the TFW electronic ground state density is in very good agreement with that obtained from the fully self-consistent Kohn–Sham solution.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Orbital-Free Quantum Simulation Methods for Application to Warm Dense Matter (Final Technical Report)

Predictive simulations for prediction of condensed system behavior in state conditions far from ambient is increasingly crucial to DOE priorities. Warm dense matter (WDM) is the paradigm: temperature T > 1-15 eV, pressures P to 1 Mbar or greater. Experiments under such state conditions are difficult and costly. We summarize work driven by the need and opportunity to make free-energy density functional theory (DFT) as powerful a tool for ab initio simulation of matter under such extreme conditions as ground state DFT is for ordinary matter Advancing orbital-free DFT (OF-DFT) to eliminate the Kohn-Sham (KS) scaling bottleneck in such simulations is the other priority. The concurrent challenge for both goals is the intrinsic complexity of WDM. We summarize 15 years of successes and major progress on (1) free energy exchange-correlation functionals; (2) non-interacting free energy functionals (counterpart to T=0 Kohn-Sham kinetic energy density functionals); (3) rigorous results and constraints for free-energy DFT; (4) software for free energy DFT calculations in both conventional Kohn-Sham and OF-DFT form; (5) de-orbitalization of advanced orbital-dependent ground state functionals for use in OF-DFT; (6) demonstration calculations; (7) ancillary achievements (e.g. major review articles, secondary explorations motivated by primary goals).

36 MATERIALS SCIENCE↗
DOE OSTI2020

Towards accurate orbital-free simulations: A generalized gradient approximation for the noninteracting free energy density functional

For orbital-free ab initio molecular dynamics, especially on systems in extreme thermodynamic conditions, we provide the first pseudo-potential-adapted generalized gradient approximation (GGA) functional for the non-interacting free energy. This is achieved by systematic finite-temperature extension of our recent LKT ground state non-interacting kinetic energy GGA functional (Phys. Rev. B 98, 041111(R) (2018)). We test the performance of the new functional first via static lattice calculations on crystalline aluminum and silicon. Then we compare deuterium equation of state results against both path-integral Monte Carlo and conventional (orbital-dependent) Kohn-Sham results. The new functional, denoted LKTF, outperforms the previous best semi-local free energy functional, VT84F (Phys. Rev. B 88, 161108(R) (2013)), and provides modestly faster simulations. Finally, we discuss subtleties of identification of kinetic and entropic contributions to non-interacting free-energy functionals obtained by extension from ground state orbital-free kinetic energy functionals.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Real-space formulation of the stress tensor for O (N) density functional theory: Application to high temperature calculations

We present an accurate and efficient real-space formulation of the Hellmann–Feynman stress tensor for O (N) Kohn–Sham density functional theory (DFT). While applicable at any temperature, the formulation is most efficient at high temperature where the Fermi–Dirac distribution becomes smoother and the density matrix becomes correspondingly more localized. We first rewrite the orbital-dependent stress tensor for real-space DFT in terms of the density matrix, thereby making it amenable to O (N) methods. We then describe its evaluation within the O (N) infinite-cell Clenshaw–Curtis Spectral Quadrature (SQ) method, a technique that is applicable to metallic and insulating systems, is highly parallelizable, becomes increasingly efficient with increasing temperature, and provides results corresponding to the infinite crystal without the need of Brillouin zone integration. We demonstrate systematic convergence of the resulting formulation with respect to SQ parameters to exact diagonalization results and show convergence with respect to mesh size to the established plane wave results. Here, we employ the new formulation to compute the viscosity of hydrogen at 10 6 K from Kohn–Sham quantum molecular dynamics, where we find agreement with previous more approximate orbital-free density functional methods.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Properties of carbon up to 10 million kelvin from Kohn-Sham density functional theory molecular dynamics

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/$\mathrm{cm^3}$ to 16 g/$\mathrm{cm^3}$ and temperatures ranging from 100 kK to 10 MK using the Spectral Quadrature method. Here, 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.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Interpretable, extensible linear and symbolic regression models for charge density prediction using a hierarchy of many-body correlation descriptors

Here, density functional theory (DFT) is routinely used to make electronic structure predictions for high-throughput screening of materials and molecules for technologically relevant areas, like the identification of better catalysts, electronic materials, and drug discovery. However, the DFT formalism is limited by (a) its poor (quadratic-to-quartic) scaling, and (b) the need to perform repeated eigenvalue computations of the electronic Hamiltonian as part of its self-consistent field (SCF) iteration procedure to obtain the converged ground state electron density, ρ (r). Approaches that directly predict ρ (r) of a structure with high accuracy can accelerate conventional SCF calculations and can also be used in linearly scaling methods such as orbital-free DFT. To this end, we present a procedure to predict the ground state electron density of molecular and periodic three-dimensional systems directly from the atomic structure with a particular emphasis on physical interpretability. In our framework, ρ (r) is modeled using many-body correlation descriptors that accurately capture the effects of local atomic arrangements in the neighborhood of a grid point. Our use of a linear regression scheme to fit to charge density data enables transparent analysis of the relative contributions of various types of local atomic correlations. By systematically including increasingly complex correlations, our model is shown to accurately predict ρ (r) for a variety of chemically and electronically diverse systems — amorphous Ge, Al(001) slab, crystalline Ga 2 O 3 , molecular benzene, and polyethylene. We then demonstrate a symbolic regression-based protocol to construct easily computable, interpretable features from lower-order correlations that significantly improves our electron density predictions with effectively no increase in the computational cost.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Laplacian-level meta-generalized gradient approximation for solid and liquid metals

In this work, we derive and motivate a Laplacian-level, orbital-free meta-generalized-gradient approximation (LL-MGGA) for the exchange-correlation energy, targeting accurate ground-state properties of sp and sd metallic condensed matter, in which the density functional for the exchange-correlation energy is only weakly nonlocal due to perfect long-range screening. Our model for the orbital-free kinetic energy density restores the fourth-order gradient expansion for exchange to the r 2 SCAN meta-GGA [Furness et al., J. Phys. Chem. Lett. 11, 8208 (2020)], yielding a LL-MGGA we call OFR2. OFR2 matches the accuracy of SCAN for prediction of common lattice constants and improves the equilibrium properties of alkali metals, transition metals, and intermetallics that were degraded relative to the PBE GGA values by both SCAN and r 2 SCAN. We compare OFR2 to the r 2 SCAN -L LL-MGGA [Mejia-Rodriguez and Trickey, Phys. Rev. B 102, 121109(R) (2020)] and show that OFR2 tends to outperform r 2 SCAN -L for the equilibrium properties of solids, but r 2 SCAN -L much better describes the atomization energies of molecules than OFR2 does. For best accuracy in molecules and nonmetallic condensed matter, we continue to recommend SCAN and r 2 SCAN. Numerical performance is discussed in detail, and our paper provides an outlook to machine learning.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Real-space density kernel method for Kohn–Sham density functional theory calculations at high temperature

Kohn–Sham density functional theory calculations using conventional diagonalization based methods become increasingly expensive as temperature increases due to the need to compute increasing numbers of partially occupied states. In this work, we present a density matrix based method for Kohn–Sham calculations at high temperatures that eliminates the need for diagonalization entirely, thus reducing the cost of such calculations significantly. Specifically, we develop real-space expressions for the electron density, electronic free energy, Hellmann–Feynman forces, and Hellmann–Feynman stress tensor in terms of an orthonormal auxiliary orbital basis and its density kernel transform, the density kernel being the matrix representation of the density operator in the auxiliary basis. Using Chebyshev filtering to generate the auxiliary basis, we next develop an approach akin to Clenshaw–Curtis spectral quadrature to calculate the individual columns of the density kernel based on the Fermi operator expansion in Chebyshev polynomials and employ a similar approach to evaluate band structure and entropic energy components. We implement the proposed formulation in the SPARC electronic structure code, using which we show systematic convergence of the aforementioned quantities to exact diagonalization results, and obtain significant speedups relative to conventional diagonalization based methods. Finally, we employ the new method to compute the self-diffusion coefficient and viscosity of aluminum at 116 045 K from Kohn–Sham quantum molecular dynamics, where we find agreement with previous more approximate orbital-free density functional methods.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Improved first-principles equation-of-state table of deuterium for high-energy-density applications

Here, we present a first-principles equation-of-state (EOS) table of deuterium aimed at improving the previously established first-principles equation-of-state table (FPEOS). The EOS table presented here, referred to as iFPEOS, introduces (1) a universal density functional theory (DFT) treatment of all density and temperature conditions, (2) a fully consistent treatment of exchange-correlation (XC) thermal effects across the entire range of temperatures covered, and (3) quantum treatment of ions. Based on ab initio molecular dynamics driven by thermal density functional theory, iFPEOS includes density points in the range 1×10 –3 $\leqslant$ ρ $\leqslant$ 1.6×10 3 g/cm 3 and temperature points in the range 800 K $\leqslant$ T $\leqslant$ 256 MK, thus covering the challenging warm dense matter (WDM) regime. For an improved description of the electronic structure, iFPEOS employs an advanced free-energy XC density functional with explicit temperature dependence, which is at the metageneralized gradient approximation level of DFT. We use the latest orbital-free free-energy density functional for the high-temperature regime where it shows excellent agreement with standard Mermin-Kohn-Sham DFT. For quantum treatment of ions we use path-integral molecular dynamics in order to take into account nuclear quantum effects. Results are compared to other EOS models and most recent experimental measurements of deuterium properties such as the molecular-toatomic fluid transition, the principal and reshock Hugoniot, and sound speed. We find that iFPEOS provides an improved agreement with experimental data compared to other first-principles EOS models in the WDM regime for pressures up to 200 GPa and temperatures up to 60 000 K. For higher pressures and temperatures, however, iFPEOS is in agreement with other models in predicting lower compressibility and higher sound speed along the Hugoniot, compared to experiment.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Path Integral Monte Carlo Simulations of Iron Plasmas (Final Technical Report)

This documents is the final technical report for our grant entitled "Path Integral Monte Carlo Simulations of Iron Plasmas" that focused on developing path integral Monte Carlo (PIMC) computer simulations. This techniques will be developed to study plasmas composed of heavier elements including iron and other third row elements. Equations of state (EOS) and transport properties will be derived in the regime of warm dense matter (WDM) and dense plasmas where existing first-principles methods cannot be applied. While standard density functional theory (DFT) has been used to accurately predict the structure of many solids and liquids up to temperatures on the order of 100,000 K, this method is not applicable at much higher temperature because the number of partially occupied electronic orbitals reaches intractably large numbers or the use of finite-temperature free energy functionals in orbital-free DFT introduces an uncontrolled approximation. Here we focus on PIMC methods that become more and more efficient with increasing temperatures and still include all electronic correlation effects. In this approach, electronic excitations increase the efficiency rather than reduce it. While it had commonly been assumed this method could only be applied to elements without core electrons, we showed that PIMC with free-particle nodes works well for first-row elements (PRL 108 (2012) 115502). Most recently, we extended the applicability range of all-electron PIMC to second-row elements by adopting localized nodal surfaces (PRL 115 (2015) 176403). To simulate third-row elements efficiently under WDM conditions, we propose a new method to remove core electrons by introducing pseudo-nodes. We explain our approach step by step and present preliminary results. We focus our method development on getting PIMC simulations of iron to work because of its fundamental importance for WDM and astrophysics. Then we move on to krypton and copper-doped beryllium, a ICF ablator material. We plan to continue working on key second-row material such as Na, Mg, MgO, Al, silica, and silicon-doped plastic ablators. Our collaborators at LLNL, will use our PIMC EOS data both as comparisons to existing semi-empirical, EOS-generating schemes, and as input for continuum radiation hydrodynamics simulations. We will establish an efficient pipeline from PIMC to macroscopic continuum studies of materials response. An emphasis will be placed on benchmarking such methods for plasmas of heavy elements at the very high temperatures (~100 eV) and low densities that are generated when Hohlraum radiation heats the ablator material in indirect drive laser experiments. Results from changes to the EOS will be of immeasurable importance to the designers at the National Ignition Facility (NIF) and at other facilities. Starting with our EOS of Cu-doped Be, our second collaborator at LLE, will perform real-time simulations of laser fusion experiments at the Omega laser and at the NIF to determine how sensitive the compression path depends on the ablator EOS. Since our collaborator also has experience in performing orbital-free DFT calculations, we propose to compare predictions from this method with PIMC results. In joint publications, we plan to analyze the accuracy of different free-energy functionals in order to understand why existing orbital-free DFT calculations do not predict compression peaks along the shock Hugoniot curve that we see with PIMC. The peaks are caused by the ionization of various electron shells. Their accurate characterization is important to compare with experimental results. We will break new ground by developing PIMC techniques that can simulate iron and all other third row elements in the plasma and WDM regimes. We introduce the concept of pseudo-nodes for the efficient treatment of the core-electrons. The EOS and transport properties will be derived and published online in the form of a new WDM database. Our PIMC EOS calculations will benchmark and possibly replace semi-analytical EOS tables like QEOS or SESAME, which will impact the hydrocode simulation community and will affect the design of NIF targets. Our PIMC results will help to improve the accuracy of orbital-free DFT simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗