Thank all of you very much for your help. Concerning what prof. Sitangshu suggestion: the raising of the cutoff over plane waves works, now I can recover the right (semi)quadratic dispersion for the acoustic out-of-plane phonons. I used smeared occupation because if not effective charges are computed by ph.x, giving rise to the LO-TO splitting at long wavelength (it is just a workaround).
I will try, as a double check, to use the lattice parameter of the bulk system, as prof. Paulatto suggested. Regarding the residual strain, of course it vanishes when I increase the cut off performing vc-relax from scratch. I guess this is why my results was not as I expected. Finally my question about the possibility of obtain the correct LO behaviour at low q was related to the article that prof. Marzari reported. I'm glad to know that the corrections will be implemented in the new version of the code. Thank you very much again!
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