Doubt regarding E0s

[Dheer-202]

I am training a fresh mace model on my refractory HEA. I have a doubt regarding E0s. From the documentation, I understand it is an isolated, atomic energy source placed in a vacuum. However, when I calculated my E0s for each atom using VASP, they were around -3 to -5 eV. With these values, the model is not fitting well, giving a large RMSE energy of 30meV. In the case of E0s "average", the model calculated energies around -10 to -11 eV, and the model fitted very well. The energies per atom in the bulk unit cell (BCC) are around -10 to -11 eV, which is quite close to the value calculated by Mace. So I wanted to ask, E0s is the energy of an atom in vacuum or energy per atom in a bulk unit cell. Why is there such a big disparity in the values of E0s.

[gabor1]

The choice of E0 is a crucial modeling choice. Using bulk energies/atom or isolated atom can both make sense, but you have to live with the with the consequences. Here is a summary.

What the E0 will do is set the MACE energy of the isolated atom once and for all. so if you are modeling bulk and bulk-like structures only, and you are never interested surfaces, adatoms, small clusters etc. then you don't might think you don't really care what the isolated atom energy is. if you pick it close to the bulk energy/atom, mace will have an easy time fitting your bulk-like structures, it only has to model the small deviation from the perfect bulk energy to your data. the consequence is that there will not be a big barrier to sublimation, since the isolated atoms are by definition the same energy as the bulk! if you run high temperature MD, this might give you nonsensical behaviour.

So generally we prefer to put real isolated atom DFT energies as E0. That means that for the isolated atom, we get the energy perfectly correct ! that's good, because there is no other way to get the isolated atom energy right, since there are no neighbours, all MACE features are zero there. But this does mean that MACE has to model a much wider range of energies, it has to learn that the energy decreases from the isolated atom energy (in your case 3-5 eV) to be near the bulk energy/atom (10-11 eV for you), and you may need more data to do this accurately. But what you gain is that sublimation barriers, even surface energies and cluster energies are probably going to be better.

30 meV/atom error is quite large. It is definitely not difficult to get a few meV/atom error even with isolated atom E0s. That should be your target. Things that can go wrong: using inaccurate DFT data (kpoints, basis set, cp2k...), sign errors in forces/gradients, stresses (unit errors especially with stresses). If you want us to help you debug your training, post the reference vs predicted energy,force,stress scatterplots here and we'll take a look.