We developed a method to calculate the anharmonic free energy without requiring any adjustable parameter. The requisite computations are first-principles quasiharmonic calculations plus an additional Canonical (NVT) ensemble first-principles molecular-dynamics simulation and, therefore, are affordable. The thermodynamic properties of diamond and MgO at high temperature improve substantially after including the anharmonic free energy.
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Zhongqing Wu (2010) studied this question.
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