The numerical code VAAQP (variational average atom in quantum plasmas), which is based on a fully variational model of equilibrium dense plasmas, is applied to equation-of-state calculations for aluminum, iron, copper, and lead in the warm-dense-matter regime. VAAQP does not impose the neutrality of the Wigner-Seitz ion sphere; it provides the average-atom structure and the mean ionization self-consistently from the solution of the variational equations. The formula used for the electronic pressure is simple and does not require any numerical differentiation. In this paper, the virial theorem is derived in both nonrelativistic and relativistic versions of the model. This theorem allows one to express the electron pressure as a combination of the electron kinetic and interaction energies. It is shown that the model fulfills automatically the virial theorem in the case of local-density approximations to the exchange-correlation free-energy. Applications of the model to the equation-of-state and Hugoniot shock adiabat of aluminum, iron, copper, and lead in the warm-dense-matter regime are presented. Comparisons with other approaches, including the inferno model, and with available experimental data are given. This work allows one to understand the thermodynamic consistency issues in the existing average-atom models. Starting from the case of aluminum, a comparative study of the thermodynamic consistency of the models is proposed. A preliminary study of the validity domain of the inferno model is also included.

A new code called VAAQP (Variational Average-Atom in Quantum Plasmas) is reported. The model as well as main results of previous studies are briefly recalled. The code is based on a new fully variational model of dense plasmas at equilibrium with quantum treatment of all electrons. The code can calculate the Average Atom structure and the mean ionization from the variational equations respecting the virial theorem and without imposing the neutrality of the Wigner-Seitz sphere. The formula obtained for the electronic pressure is simple and does not require any numerical differentiation. A description of the principal features of the code is given. The thermodynamic consistency of the results obtained with VAAQP is shown by a comparison with another approach on the example of the aluminium 10 eV isotherm EOS curve. A first comparison to an INFERNO-type model is also presented

The Debye-Hückel approximation to the free energy of a simple fluid is written as a functional of the pair correlation function. This functional can be seen as the Debye-Hückel equivalent to the functional derived in the hypernetted chain framework by Morita and Hiroike, as well as by Lado. It allows one to obtain the Debye-Hückel integral equation through a minimization with respect to the pair correlation function, leads to the correct form of the internal energy, and fulfills the virial theorem.