vibe-qcDocumentation

Construction A: independent bulk-reference limits

This assessment compares the registered MPA-0 potential, evaluated through construction A, with independent CRYSTAL23 PBE calculations. It addresses a small domain of bulk displacements and strains. It does not turn construction A into a different potential or extend the SECCM paper or its 0.18.x scope.

Matched inputs and observables

Each material has two atoms in a primitive cell. The baseline conventional lattice parameters are 3.567 angstrom for diamond and 4.212 angstrom for MgO. They define input geometries, not claimed zero-temperature equilibrium values. For s = a/sqrt(2), lattice rows in angstrom are (s,0,0), (s/2,s*sqrt(3)/2,0) and (s/2,s/(2*sqrt(3)),s*sqrt(2/3)). Diamond has fractional coordinates (0,0,0) and (1/4,1/4,1/4); MgO has Mg at (0,0,0) and O at (1/2,1/2,1/2). The same explicit Cartesian inputs and atom order feed both programs.

Four configurations per material are the baseline, atom-2 Cartesian x displacements of 0.02 and 0.08 angstrom, and a combined strain/displacement. For the latter, multiply lattice rows by the transpose of [[1.01,0.03,0],[0,0.99,0.015],[0,0,1.005]], hold fractional positions fixed, then add (0.03,-0.02,0.01) angstrom to atom 2. All calculations are neutral, restricted and fully 3D periodic; no geometry optimization is performed.

The energy observable is [E(configuration)-E(baseline)]/2, evaluated separately for each method and material, in eV/atom. This removes incompatible absolute energy origins without fitting an offset to the distorted cases. Force errors use all six Cartesian components, in eV/angstrom. Fractional changes are descriptive diagnostics, separate from the frozen absolute targets. In particular, a 10 meV/atom target can exceed a small distortion energy; passing it alone does not certify the local stiffness.

Reference and frozen criteria

The reference is CRYSTAL23 1.0.1 all-electron PBE/pob-TZVP-rev2, without Hubbard U or dispersion. The primary settings are SHRINK 8, XXLGRID, TOLINTEG 9 9 9 9 18 and TOLDEE 10. NODIRECT reuses integrals; BIPOSIZE is 50000000 words. P1 EXTERNAL geometries avoid assumptions about symmetry changes under distortion. GRADCAL supplies analytic forces.

Baseline, large displacement and shear controls increase SHRINK to 12, use XXXLGRID and TOLINTEG 10 10 10 10 20. Numerical acceptance requires relative energies to change by at most 0.001 eV/atom and force components by at most 0.005 eV/angstrom. Original pob-TZVP versus rev2 at the baseline and large displacement measures basis sensitivity; it is not a basis-limit extrapolation. A central reference force check uses 0.0003 angstrom and a 0.002 eV/angstrom bound.

The predictive targets, fixed before calculation, are 0.010 eV/atom for each relative-energy error, 0.10 eV/angstrom for each distorted case’s force component RMSE and 0.20 eV/angstrom for its maximum component error. Reference numerical convergence and predictive target satisfaction are separate verdicts. A model error beyond a target is retained as a limitation.

MPA-0 uses MPTrj plus sAlex PBE(+U) data, with no Hubbard U for these C/Mg/O comparisons. The independent reference uses Gaussian all-electron PBE, whereas the training labels use PAW calculations. Thus a discrepancy combines learned-model error with reference-representation/basis differences; it is not a clean measurement of regression error against the original training target. Construction A has the underlying checkpoint’s predictive error, up to the previously verified representation tolerance. Increasing cyclic replicas cannot correct a checkpoint error. These correlated configurations are not a statistically independent test set; training-set exclusion has not been established.

Measured results

Case

Energy error / meV per atom

Force RMSE / eV per angstrom

Maximum force error

Nominal energy / force targets

diamond-optical002

-0.692

0.0819

0.1419

pass / pass

diamond-optical008

-10.954

0.3132

0.5415

FAIL / FAIL

diamond-shear

-4.725

0.1455

0.2165

pass / FAIL

mgo-optical002

-0.144

0.0150

0.0261

pass / pass

mgo-optical008

-2.184

0.0555

0.0962

pass / pass

mgo-shear

-0.422

0.0315

0.0418

pass / pass

These are nominal comparisons against the primary reference, not an overall scientific PASS. All six tighter-setting controls pass: maximum relative-energy drift is 0.1142 meV/atom and maximum force drift is 0.002589 eV/angstrom. Changing original pob-TZVP to rev2 shifts the large-displacement relative energy by 0.234 meV/atom for diamond and 0.289 for MgO in magnitude; maximum force changes are 0.00952 and 0.01422 eV/angstrom. These are sensitivity measurements, not rigorous uncertainty bounds.

The reference force finite difference FAILS its frozen bound: -0.7445020 versus analytic -0.7502238 eV/angstrom, a discrepancy of 0.0057218. A bounded refinement at SHRINK 12, XXXLGRID, ITOL 10/20, TOLLDENS 10, TOLLGRID 18 and TOLDEE 12 completed only the negative endpoint. The center and positive endpoint exceeded the 5400-second case limit. No incomplete calculation is accepted. Reference force qualification therefore remains unresolved; the cause is not established.

Diamond’s large-displacement energy error exceeds its target even after the measured numerical/basis shifts. Its force errors are substantially larger than the measured reference sensitivities, but a fully qualified force benchmark still requires resolving the failed reference derivative check. Diamond relative distortion energies are underestimated by 17-19%; MgO optical distortion energies by 23-24%. Passing the coarse absolute MgO targets does not establish accurate stiffness or phonons. Construction A remains experimental.

Executed identity and portable data

Eight model calculations and twenty primary/control reference calculations completed through vq, followed by one completed and two timed-out refinement cases. All eight printed reference geometries agree with model inputs within 4.83e-12 angstrom. The model ran on CPU in float64 with MACE 0.3.16, PyTorch 2.8.0, ASE 3.29.0 and Python 3.13.15, using cyclic replicas (2,1,1). Python source was ab688071947746295642ad3f5e1e97ab03c24b5c, over the retained native core from 5dfc97f0ec269e681c84bfda9531a0336b2f19f6. The checkpoint SHA256 is 75428afe3a1d7d8062e19bcaabd5c433623cabf308242ec9fb493e38604fb638.

Portable numerical data contains all eight inputs, model/reference energies and forces, control results, frozen criteria, conversion constants and source/native/reference hashes. Full submitted inputs, QVF outputs, raw reference logs, runtime identities and queue receipts are retained with issue #732. Operational evidence remains outside the product source tree. No implementation or checkpoint changed in this assessment. No release, backport or training campaign was performed.

Interpretation

No independent vacancy, surface, charged/open-shell, stress, thermal or trajectory accuracy claim follows from this benchmark. The earlier force and cell finite differences verify conservative differentiation of the model, not agreement with an independent electronic Hamiltonian. Independent predictive validation of an intended application remains necessary.

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