Hi Fabio,
A few clarifications:

i) I'm aware that setting KMP_DETERMINISTIC_REDUCTION=true can help, but in practice, it doesn't guarantee reproducibility on its own. Even building crystalOMP with stricter floating-point flags like -fp-model precise (or equivalent) doesn't always lead to fully consistent results, at least not in my experience with CRYSTAL.

ii) Yes, MPI reductions are typically deterministic, as most implementations use pairwise summation or other stable schemes. OpenMP, on the other hand, can still introduce variability due to threading and compiler optimizations.

iii) If you're seeing discrepancies around 1e-5, it's plausible that small numerical differences from OpenMP reductions are enough to drive the SCF, especially in extremely delicate cases like metallic systems treated at the HF level, toward slightly different solutions.

At this point, I’ve investigated what I could from our end. If maximum reproducibility is essential, I strongly recommend sticking with MPI-only parallelism.

Have a great day,
Giacomo