Thermal Density Functional Theory in Context

This chapter introduces thermal density functional theory, starting from the ground-state theory and assuming a background in quantum mechanics and statistical mechanics. We review the foundations of density functional theory (DFT) by illustrating some of its key reformulations. The basics of DFT for thermal ensembles are explained in this context, as are tools useful for analysis and development of approximations. We close by discussing some key ideas relating thermal DFT and the ground state. This review emphasizes thermal DFT's strengths as a consistent and general framework.Comment: Submitted to Spring Verlag as chapter in "Computational Challenges in Warm Dense Matter", F. Graziani et al. ed

Nonresonant effects in one- and two-photon transitions

We investigate nonresonant contributions to resonant Rayleigh scattering cross sections of atoms. The problematic nonresonant contributions set a limit to the accuracy to which atomic spectra determine energy levels. We discuss the off-resonance effects in one-photon transitions. We also show that off-resonance contributions for the 1S-2S two-photon transition in atomic hydrogen are negligible at current and projected levels of experimental accuracy. The possibility of a differential measurement for the detection of off-resonance effects in one-photon transitions in atomic hydrogen is discussed.Comment: 13 pages, LaTeX, 3 figures; submitted to Can. J. Phys. (Oct 2001); discussion of one-photon transitions enhance

Accurate spline solutions of the Dirac equation with parity-nonconserving potential

The complete system of the B-spline solutions for the Dirac equation with the parity-nonconserving (PNC) weak interaction effective potential is obtained. This system can be used for the accurate evaluation of the radiative corrections to the PNC amplitudes in the multicharged ions and neutral atoms. The use of the scaling procedure allows for the evaluation of the PNC matrix elements with relative accuracy $10^{-7}$.Comment: 7 page

Issues and Challenges in Orbital-free Density Functional Calculations

Solving the Euler equation which corresponds to the energy minimum of a density functional expressed in orbital-free form involves related but distinct computational challenges. One is the choice between all-electron and pseudo-potential calculations and, if the latter, construction of the pseudo-potential. Another is the stability, speed, and accuracy of solution algorithms. Underlying both is the fundamental issue of satisfactory quality of the approximate functionals (kinetic energy and exchange-correlation). We address both computational issues and illustrate them by some comparative performance testing of our recently developed modified-conjoint generalized gradient approximation kinetic energy functionals. Comparisons are given for atoms, diatomic molecules, and some simple solids.Comment: submitted to Computer Physics Communication

Evaluation of the low-lying energy levels of two- and three-electron configurations for multi-charged ions

Accurate QED evaluations of the one- and two-photon interelectron interaction for low lying two- and three-electron configurations for ions with nuclear charge numbers $60\le Z \le 93$ are performed. The three-photon interaction is also partly taken into account. The Coulomb gauge is employed. The results are compared with available experimental data and with different calculations. A detailed investigation of the behaviour of the energy levels of the configurations $1s_{1/2}2s_{1/2} {}^1 S_0$, $1s_{1/2}2p_{1/2} {}^3 P_0$ near the crossing points Z=64 and Z=92 is carried out. The crossing points are important for the future experimental search for parity nonconserving (PNC) effects in highly charged ions

Kubo–Greenwood electrical conductivity formulation and implementation for projector augmented wave datasets

As the foundation for a new computational implementation, we survey the calculation of the complex electrical conductivity tensor based on the Kubo-Greenwood (KG) formalism (Kubo, 1957; Greenwood, 1958), with emphasis on derivations and technical aspects pertinent to use of projector augmented wave datasets with plane wave basis sets (BIlichl, 1994). New analytical results and a full implementation of the KG approach in an open-source Fortran 90 post-processing code for use with Quantum Espresso (Giannozzi et al., 2009) are presented. Named KGEC ([K]ubo [G]reenwood [E]lectronic [C]onductivity), the code calculates the full complex conductivity tensor (not just the average trace). It supports use of either the original KG formula or the popular one approximated in terms of a Dirac delta function. It provides both Gaussian and Lorentzian representations of the Dirac delta function (though the Lorentzian is preferable on basic grounds). KGEC provides decomposition of the conductivity into intra- and inter band contributions as well as degenerate state contributions. It calculates the dc conductivity tensor directly. It is MPI parallelized over k-points, bands, and plane waves, with an option to recover the plane wave processes for their use in band parallelization as well. It is designed to provide rapid convergence with respect to k-point density. Examples of its use are given.U.S. Dept. of Energy [DE-SC0002139]Pre-print submitted, no embargo.This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]

A Review of Equation-of-State Models for Inertial Confinement Fusion Materials

International audienceMaterial equation-of-state (EOS) models, generally providing the pressure and internal energy for a given density and temperature, are required to close the equations of hydrodynamics. As a result they are an essential piece of physics used to simulate inertial confinement fusion (ICF) implosions. Historically, EOS models based on different physical/chemical pictures of matter have been developed for ICF relevant materials such as the deuterium (D2) or deuterium-tritium (DT) fuel, as well as candidate ablator materials such as polystyrene (CH), glow-discharge polymer (GDP), beryllium (Be), carbon (C), and boron carbide (B4C). The accuracy of these EOS models can directly affect the reliability of ICF target design and understanding, as shock timing and material compressibility are essentially determined by what EOS models are used in ICF simulations. Systematic comparisons of current EOS models, benchmarking with experiments, not only help us to understand what the model differences are and why they occur, but also to identify the state-of-the-art EOS models for ICF target designers to use. For this purpose, the first Equation-of-State Workshop, supported by the US Department of Energy’s ICF program, was held at the Laboratory for Laser Energetics (LLE), University of Rochester on 31 May - 2nd June, 2017. This paper presents a detailed review on the findings from this workshop: (1) 5-10% model-model variations exist throughout the relevant parameter space, and can be much larger in regions where ionization and dissociation are occurring, (2) the D2 EOS is particularly uncertain, with no single model able to match the available experimental data, and this drives similar uncertainties in the CH EOS, and (3) new experimental capabilities such as Hugoniot measurements around 100 Mbar and high-quality temperature measurements are essential to reducing EOS uncertainty