In most density functionals the energy is a functional of the electron density $n\left(\overrightarrow{r}\right)$ and a function of the nuclear positions $R_i.$ We consider, a functional of both$n\left(\overrightarrow{r}\right)$ and the nuclear density $\rho \left(\overrightarrow{r}\right)=\sum \delta \left(\overrightarrow{r}-R_i\right).\mathrm{}$ In reducing the two Kohn–Sham equations, a classical mapping valid for interacting electrons is invoked. The exchange-correlation is nonlocal and free of self-interaction errors. As a challenging application, we calculate the equation of state and the shock Hugoniot of deuterium relevant to topical shock experiments. The calculated Hugoniot is quite close to the SESAME and path-integral Monte Carlo Hugoniots. We also treat the nonequilibrium case, which is extremely difficult for standard methods. Here the ${\mathrm{D}}^{+}$ are assumed to be hotter than the electrons, and lead to the soft Hugoniots similar to those seen in the laser-shock data. The softening arises from hot ${\mathrm{D}}^{+}–e$ pairs occurring close to the zero of the electron chemical potential.

• Received 17 December 2001

DOI:https://doi.org/10.1103/PhysRevB.66.014110