Does the quantum calculation also give different energies for different random arrangements?

EXPERIMENTS.md · lines 110–149

E4 — Occupancy scatter in DFT at 16 atoms

Date 2026-09-12 · Question Is E2's scatter a MACE artefact? · Provenance scripts/dft_calibration.py, run locally in forager-qe:latest

Method. Three independent random occupancies of one 16-site MoTaVW cell. Quantum ESPRESSO 7.5, PBE, PSLibrary PAW, ecutwfc 50 Ry, ecutrho 400 Ry, 3x3x3 k-points, Marzari-Vanderbilt smearing 0.02 Ry, conv_thr 1e-7 Ry.

sd = 4.03 meV/atom, range = 7.96 meV/atom.

Completed with size-matched elemental references (Mo, Ta, V, W as bcc 2x2x2 at the same k-mesh), so the comparable quantity is a mixing enthalpy rather than a raw total:

The book's published QE value for MoTaVW is -58 meV/atom, which lies inside this independently recomputed distribution. The published number is right; the precision implied by ranking it against a -44 competitor is not — one occupancy draw carries about +/- 4 meV/atom, and that is now measured in DFT rather than inferred from MACE.

Interpretation. Not an artefact. DFT scatter is about half MACE's 8.35 meV for the same composition, consistent with MACE's inflated dynamic range partly carrying over. Two single-occupancy samples differ with sd ~5.7 meV, so the 8 meV gap in the published table sits at 1.4 sigma — roughly an 8% chance of inversion.

Note. Runtimes vary 319-1015 s for identical cells and k-meshes: SCF convergence is occupancy-dependent. An earlier reading of these as an MPI-rank effect was not supported and is withdrawn.