Murnaghan's equation of state for the electronic ground state energy

In this work, we study the formulae of Murnaghan's equation of state, reported in the literature and used to fit the theoretical electronic ground state energy and obtain thermodynamical quantities like the bulk modulus. We find that the expression of the energy-versus-volume dependence, obtained by a straightforward integration of the pressure-versus-volume equation of state, does not satisfy the requirement of independent parameters imposed by the least-square fitting process. Instead, a change in the definition of the integration constant leads to a well-behaved fitting function, which is recommended in order to obtain reliable thermodynamical quantities.