Density Functional Methods for Plasmas and Liquid Metals

Abstract

Density functional theory (DFT)[1–3] has proved itself to be an effective first principles calculational method for the electronic and structural properties of a large variety of condensed matter systems. Most of these applications are to atomic, molecular, or solid systems where the ions merely provide a static “external potential” acting on the electronic system. DFT provides a means of reducing this many-electron problem to an effective “single-electron” problem couched in terms of a universal exchange correlation functional of the one-electron density. Given that the universe is mostly made up of ionized matter, i.e., plasmas, it is natural to turn to DFT to develop microscopic theories of matter in the plasma state. The main characteristics of the plasma state from our point of view are (i) the existence of electron populations in continuum as well as in bound states (ii) need to consider not just the electronic subsystem, but also the ionic subsystem, and (iii) finite temperature effects. Thus an Al-plasma at a temperature of 10⁵K and at a density of 1/10 of the normal solid density contains continuum electrons, and not just Al³⁺, but also Al²⁺, Al¹⁺, Al, and possibly even some Al-molecular species. Such a mixture is analogous to a molten alloy in many ways and could be much more complex because of partial electron-degeneracy effects and the complex nature of the continuum electron states. If the mass density of Al were maintained at the normal value and the temperature raised towards 10⁶K the dominant species evolve from Al^z+, z=3 to a Be-like “Aluminum” with a net charge of z=7, while the free electrons become classical. As another example consider a hydrogen plasma at sufficiently high temperatures and pressures; then it could well be a fully ionized system of electrons and protons. If the same hydrogen plasma were examined at a lower temperature of interest to planetary scientists, e.g., say, at T= 2eV, a pressure of 0.5 Mbar, and a mass density of around 0.2–0.5 g/cc, it would be found to contain e⁻, H⁻ H⁺, H⁺ ₂, H₂, and H⁻ ₂, interacting with each other, with most vibrational, rotational and electronic (bound- as well as continuum-) states occupied to form distributions consistent with the given temperature and chemical potentials. In other words, the electronic and ionic distributions are a function of each other and the pressure and temperature of the system.