Equation of state and the Hugoniot of laser shock-compressed deuterium: Demonstration of a basis-function-free method for quantum calculations

In most density functionals the energy is a functional of the electron density n(→r) and a function of the nuclear positions Rᵢ. We consider, a functional of bothn(→r) and the nuclear density ρ(→r)=∑δ(→r-Rᵢ). 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 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 D⁺--e pairs occurring close to the zero of the electron chemical potential.