**Reproducibility of vibrational free energy by different methods**

P Korotaev and M Belov and A Yanilkin, COMPUTATIONAL MATERIALS SCIENCE, 150, 47-53 (2018).

DOI: 10.1016/j.commatsci.2018.03.057

The paper reviews several modern methods for calculation of Helmholtz free energy, associated with atomic vibrations: quasiharmonic approximation, self-consistent lattice dynamics method, calculation based on velocity autocorrelation function, temperature-dependent effective potential and thermodynamic integration. The results of free energy calculation by these methods are compared with each other in a wide temperature range, and their applicability is discussed. As a tool we use classical molecular dynamics modeling on the example of bcc molybdenum and fcc aluminum. The relation is observed between how the vibrational spectrum changes with temperature due to the anharmonicity of the potential and how free energy is reproduced. All methods are consistent with each other within 10 meV/at. at relatively low temperatures. At high temperatures, the discrepancy reaches tens of meV/at., although the relative error is less than 5%.

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