An efficient method to calculate the anharmonicity free energy

The anharmonicity resulted from the intrinsic phonon interaction is neglected by quasiharmonic approximation. Although the intensive researches about anharmonicity have been done, up to now the free energy contributed by the anharmonicity is still difficult to calculate. Here we put forward a new method that can well include the anharmonicity. We introduce the implicit temperature dependence of effective frequency by volume modification. The quasiharmonic approximation becomes a special case in our method corresponding to non volume modification. Although our method is simple and only a constant need to determine, the anharmonicity is well included. Thermodynamic properties of MgO predicted with our method are excellent consistent with the experiment results at very wide temperature range. We also believe that our method will be helpful to reveal the characteristic of anharmonicity and intrinsic phonon interaction.