Travis Sjostrom

Accurate Homogeneous Electron Gas Exchange-Correlation Free Energy for Local Spin-Density Calculations

An accurate analytical parametrization for the exchange-correlation free energy of the homogeneous electron gas, including interpolation for partial spin-polarization, is derived via thermodynamic analysis of recent restricted path integral Monte-Carlo (RPIMC) data. This parametrization constitutes the local spin density approximation (LSDA) for the exchange-correlation functional in density functional theory. The new finite-temperature LSDA reproduces the RPIMC data well, satisfies the correct high-density and lowand high-T asymptotic limits, and is well-behaved beyond the range of the RPIMC data, suggestive of broad utility.

Finite-temperature orbital-free DFT molecular dynamics: Coupling Profess and Quantum Espresso

Abstract Implementation of orbital-free free-energy functionals in the Profess code and the coupling of Profess with the Quantum Espresso code are described. The combination enables orbital-free DFT to drive ab initio molecular dynamics simulations on the same footing (algorithms, thermostats, convergence parameters, etc.) as for Kohn–Sham (KS) DFT. All the non-interacting free-energy functionals implemented are single-point: the local density approximation (LDA; also known as finite-T Thomas–Fermi, ftTF), the second-order gradient approximation (SGA or finite-T gradient-corrected TF), and our recently introduced finite-T generalized gradient approximations (ftGGA). Elimination of the KS orbital bottleneck via orbital-free methodology enables high-T simulations on ordinary computers, whereas those simulations would be costly or even prohibitively time-consuming for KS molecular dynamics (MD) on very high-performance computer systems. Example MD simulations on H over a temperature range 2000 K ≤ T ≤ 4,000,000 K are reported, with timings on small clusters (16–128 cores) and even laptops. With respect to KS-driven calculations, the orbital-free calculations are between a few times through a few hundreds of times faster.

Gradient corrections to the exchange-correlation free energy

We develop the first-order gradient correction to the exchange-correlation free energy of the homogeneous electron gas for use in finite-temperature density functional calculations. Based on this, we propose and implement a simple temperature-dependent extension for functionals beyond the local density approximation. These finite-temperature functionals show improvement over zero-temperature functionals, as compared to path-integral Monte Carlo calculations for deuterium equations of state, and perform without computational cost increase compared to zero-temperature functionals and so should be used for finite-temperature calculations. Furthermore, while the present functionals are valid at all temperatures including zero, non-negligible difference with zero-temperature functionals begins at temperatures above 10 000 K.

Fast and accurate quantum molecular dynamics of dense plasmas across temperature regimes

We develop and implement a new quantum molecular dynamics approximation that allows fast and accurate simulations of dense plasmas from cold to hot conditions. The method is based on a carefully designed orbital-free implementation of density functional theory. The results for hydrogen and aluminum are in very good agreement with Kohn-Sham (orbital-based) density functional theory and path integral Monte Carlo calculations for microscopic features such as the electron density as well as the equation of state. The present approach does not scale with temperature and hence extends to higher temperatures than is accessible in the Kohn-Sham method and lower temperatures than is accessible by path integral Monte Carlo calculations, while being significantly less computationally expensive than either of those two methods.

Uniform electron gas at finite temperatures

We calculate the free energy of the quantum uniform electron gas for temperatures from near zero to 100 times the Fermi energy, approaching the classical limit. An extension of the Vashista-Singwi theory to finite temperatures and self-consistent compressibility sum rule is presented. Comparisons are made to other local field correction methods, as well as recent quantum Monte Carlo simulation and classical map based results. Accurate fits to the exchange-correlation free energy from both theory and simulation are given for future practical applications.

Comparison of density functional approximations and the finite-temperature Hartree-Fock approximation in warm dense lithium

We compare the behavior of the finite-temperature Hartree-Fock model with that of thermal density functional theory using both ground-state and temperature-dependent approximate exchange functionals. The test system is bcc Li in the temperature-density regime of warm dense matter (WDM). In this exchange-only case, there are significant qualitative differences in results from the three approaches. Those differences may be important for Born-Oppenheimer molecular dynamics studies of WDM with ground-state approximate density functionals and thermal occupancies. Such calculations require reliable regularized potentials over a demanding range of temperatures and densities. By comparison of pseudopotential and all-electron results at T=0 K for small Li clusters of local bcc symmetry and bond lengths equivalent to high density bulk Li, we determine the density ranges for which standard projector augmented wave (PAW) and norm-conserving pseudopotentials are reliable. Then, we construct and use all-electron PAW data sets with a small cutoff radius that are valid for lithium densities up to at least 80 g/cm{3}.

Temperature-Dependent Behavior of Confined Many-electron Systems in the Hartree-Fock Approximation

Many-electron systems at substantial finite temperatures and densities present a major challenge to density functional theory. Very little is known about the free-energy behavior over the temperature range of interest, for example, in the study of warm dense matter. As a result, it is difficult to assess the validity of proposed approximate free-energy density functionals. Here we address, at least in part, this need for detailed results on well-characterized systems for purposes of testing and calibration of proposed approximate functionals. We present results on a comparatively simple, well-defined, but computationally feasible model, namely thermally occupied Hartree-Fock states for eight one-electron atoms at arbitrary positions in a hard-walled box. We discuss the main technical tasks (defining a suitable basis and evaluation of the required matrix elements) and discuss the physics which emerges from the calculations.

Ionic Transport Coefficients of Dense Plasmas without Molecular Dynamics.

We present a theoretical model that allows a fast and accurate evaluation of ionic transport properties of realistic plasmas spanning from warm and dense to hot and dilute conditions, including mixtures. This is achieved by combining a recent kinetic theory based on effective interaction potentials with a model for the equilibrium radial density distribution based on an average atom model and the integral equations theory of fluids. The model should find broad use in applications where nonideal plasma conditions are traversed, including inertial confinement fusion, compact astrophysical objects, solar and extrasolar planets, and numerous present-day high energy density laboratory experiments.

Ab initio quantum Monte Carlo simulation of the warm dense electron gas

Warm dense matter is one of the most active frontiers in plasma physics due to its relevance for dense astrophysical objects and for novel laboratory experiments in which matter is being strongly compressed, e.g., by high-power lasers. Its description is theoretically very challenging as it contains correlated quantum electrons at finite temperature—a system that cannot be accurately modeled by standard analytical or ground state approaches. Recently, several breakthroughs have been achieved in the field of fermionic quantum Monte Carlo simulations. First, it was shown that exact simulations of a finite model system ( 30…100 electrons) are possible, which avoid any simplifying approximations such as fixed nodes [Schoof et al., Phys. Rev. Lett. 115, 130402 (2015)]. Second, a novel way to accurately extrapolate these results to the thermodynamic limit was reported by Dornheim et al. [Phys. Rev. Lett. 117, 156403 (2016)]. As a result, now thermodynamic results for the warm dense electron gas are available, w...

Innovations in Finite-Temperature Density Functionals

Reliable, tractable computational characterization of warm dense matter is a challenging task because of the wide range of important aggregation states and effective interactions involved. Contemporary best practice is to do ab initio molecular dynamics on the ion constituents with the forces from the electronic population provided by density functional calculations. Issues with that approach include the lack of reliable approximate density functionals and the computational bottleneck intrinsic to Kohn-Sham calculations. Our research is aimed at both problems, via the so-called orbital-free approach to density functional theory. After a sketch of the relevant properties of warm dense matter to motivate our research, we give a survey of our results for constraint-based non-interacting free energy functionals and exchange-correlation free-energy functionals. That survey includes comparisons with novel finite-temperature Hartree-Fock calculations and also presents progress on both pertinent exact results and matters of computational technique.