Question about finite-size correction of SSCHA free energies

[zhaowb12138]

Dear developers,

I have a question about the finite-size convergence of SSCHA free energies in phase-stability calculations.

In my calculations, the Gibbs free-energy differences between competing phases are only a few meV/atom. Therefore, the difference between 2×2×2 and 3×3×3 SSCHA supercells can already affect the predicted phase stability.

In practice, 2×2×2 calculations are affordable, 3×3×3 calculations are already quite expensive, and systematic 4×4×4 or 5×5×5 calculations are often computationally prohibitive. However, I find that the Gibbs free energy printed by vc_relax can still change by several meV/atom when going from 2×2×2 to 3×3×3.

From reading the code, my understanding is that the Gibbs free energy printed by vc_relax uses the standard get_free_energy() on the current finite supercell, i.e. the SSCHA free energy per unit cell evaluated on the q-grid corresponding to the simulation supercell. It does not seem to automatically perform a dense-q interpolation.

I also noticed the function:

Ensemble.get_free_energy_interpolating(target_supercell)

My understanding is that this function interpolates the current SSCHA trial dynamical matrix to a larger target_supercell, recomputes the harmonic trial free energy on the denser q-grid, and keeps the anharmonic average from the current finite-supercell ensemble.

Is this the recommended way to post-process the Gibbs free energy printed by vc_relax when the 2×2×2 or 3×3×3 SSCHA free energies are not fully converged with respect to the supercell size?

In other words, when larger explicit SSCHA supercells are too expensive, is it appropriate to use get_free_energy_interpolating(target_supercell) to correct the q-grid error of the harmonic/trial free-energy part and use the result as an approximate thermodynamic-limit Gibbs free energy?

Also, is this correction expected to be reliable only when the anharmonic correction is weakly dependent on the supercell size? For strongly anharmonic systems, would explicit checks with larger supercells still be necessary?

Thank you very much for your advice.

[DjordjeDangic]

Hello,

The harmonic part part of the free energy (the part that you converge with get_free_energy_interpolating(target_supercell)) is usually much larger than the anharmonic part (it is certainly true in materials we check eg. https://scipost.org/SciPostPhys.20.6.170/pdf). You can check if that holds for your system. In case it does, I would say it is enough to converge the harmonic part and keep the anharmonic part from the small supercell. It is important though that your interpolated phonon band structure is converged with respect to the size of the SSCHA supercell.

Kind regards

[zhaowb12138]

Thank you very much for your helpful advice. I will try this approach and check the convergence of the interpolated phonon dispersion and the anharmonic contribution carefully.

Kind regards