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In the case of BaTiO3, we were able to compute the free energy of the cubic BaTiO3 even below the phase transition temperature because cubic BaTiO3 stayed cubic if we did not add initial perturbation (initial displacements and strains).

I am not sure if the same approach works for your system.
In SCPH or QHA calculations, the space group symmetry should not be lowered from the initial distorted structure (if the implementation is correct).

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@RicardoCecconello
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