Anton-Schmidt equation of state

The Anton-Schmidt equation is an empirical equation of state for crystalline solids, e.g. for pure metals or intermetallic compounds.
Quantum mechanical investigations of intermetallic compounds show that the dependency of the pressure under isotropic deformation can be described empirically by
Integration of formula_2 leads to equation of the state for the total energy. The energy formula_3 required to compress a solid to volume formula_4 is
which gives 
The fitting parameters formula_7 and formula_8 are related to material properties, where
However, the fitting parameter formula_14 does not reproduce the total energy of the free atoms.
The total energy equation is used to determine elastic and thermal material constants in quantum chemical simulation packages.