Exchange and correlation potentials for electron-ion systems at finite temperatures

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 which are valid for lithium densities up to at least 80 g/cm 3 .

show abstract

“…Here we used the parametrization given by Perrot and Dharmawardana [54]. The LDA exchange free energy is then…”

Section: B Exchange Free Energymentioning

confidence: 99%

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

2012

View full text Add to dashboard Cite

show abstract

“…Compared to the ground-state situation, there is only a small literature on explicitly T-dependent functionals, that is, XC free energy functionals, and essentially all of those studies are at the level of the LDA [26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42] .…”

Section: Introductionmentioning

confidence: 99%

Temperature-dependent behavior of confined many-electron systems in the Hartree-Fock approximation

2012

View full text Add to dashboard Cite

Many-electron systems confined at substantial finite temperatures and densities present a major challenge to density functional theory. In particular, there is comparatively little systematic knowledge about the behavior of free-energy density functionals for temperatures and pressures of interest, for example, in the study of warm dense matter. As with ground-state functionals, development of approximate free-energy functionals is faced with significant needs for reliable assessment and calibration data. Here we address, in part, this need for detailed results on well-characterized systems. We present results on a comparatively simple, well-defined, computationally feasible but previously unexplored model, the thermal Hartree-Fock approximation. We discuss the main technical tasks (defining a suitable basis and evaluation of the required matrix elements) and give an illustrative initial application which probes both the content of the model and the solution techniques: a system of eight one-electron atoms with nuclei at fixed, arbitrary positions in a hard-walled box. Even this simple system produces physical behavior different from that produced by simple ground state density functionals used at finite temperature (a common approximation in the study of WDM).

show abstract

“…Because Θ ∼ 1, the use of ground-state density functional theory is inappropriate and extensions to finite T are indispensible; these require accurate exchange-correlation functionals for finite temperatures [13][14][15][16][17]. Because neither r s nor Θ is small, there are no small parameters, and weakcoupling expansions beyond Hartree-Fock such as the Montroll-Ward (MW) and e 4 (e4) approximations [18,19], as well as linear response theory within the random- phase approximation (RPA) break down [20,21]. Finite-T Singwi-Tosi-Land-Sjölander (STLS) [22,23] local-field corrections allow for an extension to moderate coupling [23], but exhibit non-physical behavior at short distances for moderate to low densities, so improved expressions are highly needed.…”

mentioning

confidence: 99%

“…phase approximation (RPA) break down [20,21]. Finite-T Singwi-Tosi-Land-Sjölander (STLS) [22,23] local-field corrections allow for an extension to moderate coupling [23], but exhibit non-physical behavior at short distances for moderate to low densities, so improved expressions are highly needed.…”

mentioning

confidence: 99%

Ab InitioQuantum Monte Carlo Simulation of the Warm Dense Electron Gas in the Thermodynamic Limit

et al. 2016

View full text Add to dashboard Cite

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 linear response theory we are able to remove finite-size errors from the potential energy over the entire warm dense regime, overcoming the deficiencies of the existing finite-size corrections by Brown et al. [PRL 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 Fxc of the macroscopic electron gas with an unprecedented accuracy of |∆V |/|V |, |∆Fxc|/|F |xc ∼ 10 −3 . A comparison of our new data to the recent parametrization of Fxc by Karasiev et al. [PRL 112, 076403 (2014)] reveals significant deviations to the latter.The uniform electron gas (UEG), consisting of electrons on a uniform neutralizing background, is one of the most important model systems in physics [1]. Besides being a simple model for metals, the UEG has been central to the development of linear response theory and more sophisticated perturbative treatments of solids, the formulation of the concepts of quasiparticles and elementary excitations, and the remarkable successes of density functional theory.The practical application of ground-state density functional theory in condensed matter physics, chemistry and materials science rests on a reliable parametrization of the exchange-correlation energy of the UEG [2], which in turn is based on accurate quantum Monte Carlo (QMC) simulation data [3]. However, the charged quantum matter in astrophysical systems such as planet cores and white dwarf atmospheres [4,5] is at temperatures way above the ground state, as are inertial confinement fusion targets [6][7][8], laser-excited solids [9], and pressure induced modifications of solids, such as insulator-metal transitions [10,11]. This unusual regime, in which strong ionic correlations coexist with electronic quantum effects and partial ionization, has been termed "warm dense matter" and is one of the most active frontiers in plasma physics and materials science.The warm dense regime is characterized by the existence of two comparable length scales and two comparable energy scales. The length scales are the mean interparticle distance,r, and the Bohr radius, a 0 ; the energy scales are the thermal energy, k B T , and the electronic Fermi energy, E F . The dimensionless parameters [12] r s =r/a 0 and Θ = k B T /E F are of order unity. Because Θ ∼ 1, the use of ground-state density functional theory is inappropriate and extensions to finite T are indispensible; these require accurate exchange-correlation functionals for finite temperatures [13][14][15][16][17]. Because neither r s nor Θ is small, there are no small parameters, and weakcoupling expansions beyond Hartree-Fock such as the Montroll-Ward (MW) and e 4 (e4) approximations [18,19], as well as linear response theory within the random- phase approximation (RPA) break down [20,21]. Finite-T Singwi-Tosi-Land-Sjölander (STLS) [22,23] local-fiel...

show abstract

Exchange and correlation potentials for electron-ion systems at finite temperatures

Cited by 197 publications

References 23 publications

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

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

Temperature-dependent behavior of confined many-electron systems in the Hartree-Fock approximation

Ab InitioQuantum Monte Carlo Simulation of the Warm Dense Electron Gas in the Thermodynamic Limit

Contact Info

Product

Resources

About