Best practice for calculating E0s (Isolated Atoms) for MACE fine-tuning: Tetrahedron vs. Gaussian Smearing?

[dominicvarghese]

Hi everyone,

I am currently performing multi-head replay fine-tuning using the MACE-MATPES-R2SCAN foundation model. My fine-tuning dataset consists of PBEsol DFT calculations for $\text{KTaO}_3$ (wide band-gap insulator). For my bulk training data (NPT/NVT runs), I used the Tetrahedron method with Blöchl corrections (ISMEAR = -5) as it is generally preferred for insulators.

I am now generating the isolated atom energies (E0s) required for the fine-tuning process. When I attempt to calculate the isolated Oxygen energy using settings consistent with my bulk calculation (ISMEAR = -5), I obtain a positive total energy, which seems unphysical for a bound atom.

Simulation Details (Oxygen Atom):Box: $15 \times 15 \times 15$ Å
K-Points: 4x4x4 (as required by tetrahedron method)

INCAR
ENCUT   = 500       # Matches bulk exactly
PREC    = Accurate
EDIFF   = 1e-8
LREAL   = .FALSE.
ISYM    = 0         # Symmetry off
IBRION  = -1        # Static
NSW     = 0

Tetrahedron (ISMEAR = -5): TOTEN = 0.11612059 eV (Positive/Unphysical?)

With Gaussian smearing,
ISMEAR = 0, SIGMA = 0.20: TOTEN = -0.32510178 eV
ISMEAR = 0, SIGMA = 0.05: TOTEN = -0.09370829 eV

Given that ISMEAR = -5 is generally ill-defined for isolated atom, is it standard practice to switch to Gaussian smearing (ISMEAR = 0) just for the isolated atoms, even if the bulk data uses Tetrahedron? If switching to Gaussian is the correct approach, how should I select the SIGMA to ensure consistency with the MACE model's expectations?

Any advice on the correct protocol for generating these E0s would be greatly appreciated.

[dominicvarghese]

In my fine-tuning dataset, I trained the model using AIMD trajectories computed without spin polarization (PBEsol pseudopotential), since the target system (KTaO₃) is non-magnetic in the bulk. However, when computing isolated atomic reference energies, should these be calculated with or without spin polarization? For example, isolated oxygen atoms are spin-polarized in their ground state.

Since I am using multi-head attention fine-tuning of the MACE-MATPES-R2SCAN model, which choice of atomic reference energies is consistent with the training setup: spin-polarized or non-spin-polarized?

Additionally, if the spin treatment used for atomic reference energies differs from that used in the AIMD training data, what are the main sources of systematic error this mismatch could introduce in the trained model ? More like what would be the sign showing the model has some errors with the reference atomisation energy used?

[gabor1]

So the foundation models are trained with spin polarisation, both for the periodic data and the isolated atom data. For the MPtrj data we computed it ourselves, but for MATPES it's part of the dataset. The MACE is fitted to the atomisation energy, so with the isolated atom energies subtracted.

When you fine-tune, as you say there are options. If you follow the same recipe as was used for the foundation model that you are fine-tuning, take care of running the isolated atoms with spin polarised and getting the same magnetic moments, then the fine-tuning will have an easier time, less change is needed in the MACE parameters. It is not wrong to follow a different recipe, but then you might need more epochs in the fine-tuning, because you are asking the modified parameters to adapt to a slightly different set of E0s and so slightly different atomisation energy function.

[gabor1]

here are the links to the MATPES isolated atom calculations

https://s3.us-east-1.amazonaws.com/materialsproject-contribs/MatPES_2025_1/MatPES-PBE-atoms.json.gz
https://s3.us-east-1.amazonaws.com/materialsproject-contribs/MatPES_2025_1/MatPES-R2SCAN-atoms.json.gz