Classical mean-field approach for thermodynamics:Ab initiothermophysical properties of cerium

For evaluating the vibrational contribution of the lattice ion to the total free energy, an attempt is made to propose a classical mean-field model without involving any adjustable parameter, where the mean-field potential $g(r,V),$ seen by the lattice ion, is simply constructed in terms of the 0 K total energy. It is shown that as a second-order approximation of the mean-field potential, the well-known Dugdale and MacDonald expression of the Gr\"uneisen parameter γᵢₒₙ(V) is explicitly deduced. Furthermore, an ab initio scheme for calculating the various kinds of thermodynamic properties of a substance is developed. Our approach permits efficient computation. By taking Ce metal as a prototype, the ab initio calculated results show that at 590 K, the {γ}-Ce is more stable than {α}-Ce, and the experimental 300 K isotherm and the Hugoniot state are reproduced excellently.