Does the quantum calculation confirm that small simulation boxes are biased?

EXPERIMENTS.md · lines 723–764

E17 — The finite-size claim does not survive DFT; a different pattern does

Date 2026-09-12 · Question Complete E4/E5: what is the finite-size shift in DFT, and does it match MACE? · Provenance scripts/dft_calibration.py, local

Method. As E4, with size-matched elemental references at each cell size, now with three occupancies at 16 atoms and four at 54. Each 54-atom SCF took 3,158-3,931 s.

Result.

Shift 16 -> 54 = +4.65 +/- 2.88 meV/atom, 1.6 sigma. Not significant, and consistent with the +1.21 that MACE predicted for the same two points (E3).

The finite-size claim of E3 is therefore not confirmed in DFT. It was measured in MACE, where 16-atom cells looked biased by up to 15 meV/atom. In DFT the 16-to-54 shift is within noise. The 128-atom point, which is where E3 saw the effect converge, remains unmeasured in DFT because it needs 23.45 GB (E5). "128 atoms is the minimum" stands only as a MACE result and must not be quoted as a DFT one.

A better-supported pattern, holding at two independent cell sizes:

MACE overstates configurational scatter by about 2.1x, and the two cell sizes agree to within 2%. Still only 3 and 4 occupancies, so the individual standard deviations are weakly determined; the consistency of the ratio across two independent cells is what gives this more weight than E16's single-size version of the same observation.

This corrects E2 in the favourable direction. The 23.3% flip probability reported there was computed from MACE's scatter. Using the DFT value of 4.03 meV/atom, the closest pair's 8.5 meV gap sits at 1.49 sigma, so the single-occupancy flip risk is about 7%, not 23%. The ranking problem is real and about a third the size first stated.