Experiments · E3
Withdrawn. The screening model showed small boxes off by up to 15 meV/atom, but a later quantum check found no clear size effect.
In the log: Finite-size behaviour in MACE: 16, 54, 128, 250 atoms
book/assets/diagrams/exp/E3.svg).No result paragraph for this entry was found in the log.
Date 2026-09-12 · Question How large must the cell be before one occupancy is
a usable number? · Provenance …/cellsize.py
Method. As E2, at four supercell sizes (n x n x n conventional bcc, 2n^3 sites), 16 occupancies each, two compositions. Deviation measured against the 250-atom cell.
| system | 16 | 54 | 128 | 250 (ref) |
|---|---|---|---|---|
| MoTaVW mean dH | -120.84 | -119.63 | -113.86 | -112.86 |
| deviation | 8.0 | 6.8 | 1.0 | - |
| MoNbTaVW mean dH | -115.82 | -99.88 | -100.12 | -100.75 |
| deviation | 15.1 | 0.9 | 0.6 | - |
| sd, MoTaVW | 8.35 | 7.13 | 4.53 | 2.82 |
| sd, MoNbTaVW | 11.17 | 6.55 | 4.21 | 3.60 |
Interpretation. The 16-atom cell is biased, not merely noisy — up to 15 meV/atom, larger than the gaps being ranked. 54 atoms is composition-dependent (0.9 meV for one system, 6.8 for the other), and a composition-dependent error reorders candidates rather than shifting them together. 128 atoms converges both to ~1 meV of the 250-atom reference.
Scatter falls more slowly than 1/sqrt(N) — 2.96x at 250 atoms where independent averaging predicts 3.95x — because random occupancies share correlated local environments. That is the argument for SQS over averaging.
Status of the claim. Measured in MACE only, and not confirmed - see E17, where the DFT shift from 16 to 54 atoms is +4.65 +/- 2.88 meV/atom, within noise. The 128-atom DFT point remains unmeasured.
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