Density-functional theory of hydrogen plasmas

The density-functional theory (DFT) for a system of ions and electrons having overall charge neutrality is presented. For a given temperature and free-electron density, the theory self-consistently determines the various pair-distribution functions, bound states, and the effective ion charge $\overline{Z}=Z-n_b$, where $n_b$ is the mean number of bound electrons per ion. With the use of a sufficiently large correlation sphere to represent the "physically relevant" part of the plasma, a Kohn-Sham-type Schrödinger equation is solved for the electrons. The density-functional equations for the ions reduce to a Gibbs-Boltzmann equation containing an effective ion-correlation potential. The latter is obtained from the hypernetted-chain equation. The electron exchange-correlation potential is obtained from quantum many-body theory. The method is applied to an electron-proton plasma (EPP) for a number of physical situations. The machine-simulation (MS) results in the classical one-component-plasma limit, as well as the standard "proton-in-jellium" results, are correctly recovered in suitable limits. The MS results for the EPP plasma are limited by classical approximations, but are found to be in reasonable agreement with our DFT results which are probably more well founded. A shallow $1s$-like bound state appears with increase of temperature or decrease of density. The proton-pair distribution function in the EPP shows the onset of short-range order only when $\Gamma \gtrsim 5$ or more. The electron-proton distribution function is found to be relatively insensitive to the details of the ion distribution for the static properties studied in this paper.