Effective semiempirical ansatz for computing anharmonic free energies

A semiempirical ansatz to compute anharmonic contributions to the free energy neglected in quasiharmonic calculations is introduced. A parametrized temperature-dependent modification of the vibrational density of states designed to be used directly with the quasiharmonic free-energy expression is proposed. An approximate relationship between the modified frequencies and the renormalized frequencies is developed. This parametrization is shown to produce the correct low and high temperature behavior of the anharmonic free energy and other thermodynamics properties. It is shown that the thermodynamics properties of α- and β-Mg₂SiO₄ (forsterite and wadsleyite) and MgO (periclase) improve considerably after inclusion of anharmonic effects. Anharmonicity is shown to have a significant effect on the phase boundary of the forsterite to wadsleyite transformation. Inclusion of anharmonic effects can reconcile discrepancies between the measurements of the Clapeyron slope of this transition and the values predicted by quasiharmonic calculations.