DFT Material Validation

This is the committed scientific ledger for the periodic PeriodicDFTSystem/run_periodic_scf path. It summarizes accepted generated reports without promoting their gitignored raw artifacts or rerunning any DFT calculation.

Results

Material and workload	Main result	Reference comparison	Status and boundary
Diamond Si, 8 atoms, PBE/GTH-q4, 25 Ha, 6×6×6	a₀ = 5.460859 Å, B₀ = 88.306 GPa, B₀′ = 4.3052, Δ = 1.942 meV/atom	All-electron PBE: lattice 0.166%, bulk modulus 0.232%, and B₀′ 0.153% relative error	Verified for this bulk-Si EOS workload. Broader chemistry and MLX-versus-QE PWscf parity remain proof-level or diagnostic.
Diamond Si fixed-cell relaxation, 8 atoms, PBE/GTH-q4, 25 Ha, 6×6×6	The atom displaced by (+0.04, -0.03, +0.02) Å converged in 7 accepted steps; final maximum force 8.832e-5 Ha/bohr, RMS force 2.437e-5 Ha/bohr, and final maximum step 1.480e-3 bohr	Translation-aligned maximum error from the source-defined ideal diamond positions: 0.000312 Å	Verified for this fixed-cell relaxation. Exact restart equivalence is CPU-tested; the Metal workload verifies accepted-step checkpoint publication. This row alone does not establish variable-cell relaxation.
2H-Si full-rank fixed-cell relaxation, 4 atoms, PBE/GTH-q4, 25 Ha, 6×6×4	The ideal P63/mmc lonsdaleite prototype converged in 3 accepted steps; final energy -15.76211219 Ha, maximum force 1.715e-5 Ha/bohr, and final maximum step 1.659e-4 bohr	Source prototype A_hP4_194_f-001, z = 1/16; maximum translation-aligned internal relaxation 0.003351 Å	Verified for this hexagonal fixed-cell workflow and complete-matrix identity. It does not establish stress, variable-cell relaxation, or broad Silicon polytype accuracy.
2H-Si variable-cell relaxation, 4 atoms, PBE/GTH-q4, 25 Ha, 6×6×4	Starting at 0.995 of the accepted scale, the cell accepted one step and converged at 0.9981142; final pressure was 2.66553e-6 Ha/bohr³, lattice error 0.1886%, and relaxation wall time 22.707 s.	A fresh 35 Ha SCF gave 2.88255e-6 Ha/bohr³; the 2.17019e-7 Ha/bohr³ drift passed the locked 5e-6 Pulay gate in 8.248 s. Complete validation wall was 30.956 s.	Current-verified on Apple M5 Max, AC power, normal power mode. Analytic electronic stress, float64 analytic Ewald stress, deterministic cell/coupled/restart gates, and the bounded material trajectory pass. This is not broad variable-cell transferability.
Diamond Si frozen-density bands, Γ-X-W-K-Γ-L	Indirect gap 0.578 eV, valence width 11.959 eV	Published PBE/GTH ordering and high-symmetry energies; PBE gap is not compared with the experimental 1.12 eV gap	Accepted band-path validation from a converged 6×6×6 density; not a general band-structure certification.
Diamond Si Gamma phonons, 2-atom primitive, PBE/GTH-q4, 25 Ha, full 4×4×4 electronic mesh	At 0.01 bohr, acoustic modes 3.739, 4.269, 7.517 cm⁻¹; optical triplet 509.325, 512.097, 512.103 cm⁻¹; no ASR correction	Quantum ESPRESSO tutorial optical context 516.175 cm⁻¹; local mean error 4.999 cm⁻¹. The 0.02→0.01 bohr maximum drift is 2.379 cm⁻¹	Current-verified on Apple M5 Max. Raw reciprocity, translational residual, acoustic overlap, stability, displacement convergence, reference, restart, wall, and memory gates pass. This is a bounded Gamma-point result, not phonon dispersion or LO-TO validation.
Diamond C, 8 atoms, PBE/GTH-q4, 40 Ha, 6×6×6, 7 volumes	a₀ = 3.574441 Å, B₀ = 438.100 GPa, Δ = 1.268 meV/atom	All-electron PBE: lattice 0.075% and bulk modulus 1.080% relative error	Verified for the accepted 40 Ha workload. A 40→50 Ha central three-volume screen changed the curve by 0.438 meV/atom; no full 50 Ha curve is required.
Rock-salt MgO, 8 atoms, PBE, Mg-q2/O-q6, 70 Ha, 6×6×6, 7 volumes	a₀ = 4.259503 Å, B₀ = 146.914 GPa, Δ = 1.060 meV/atom	All-electron PBE: lattice 0.123% and bulk modulus 1.387% relative error	Core EOS properties validated. The strict whole-report gate remains failed because B₀′ = 3.39995 differs from 4.09093 by 16.89%, above the locked 15% threshold; this is retained as a likely Mg-q2 transferability limit.
MgO periodic forces at the accepted EOS cell	21 of 24 atom/axis comparisons pass 1e-4 Ha/bohr; maximum deviation 2.246e-4 Ha/bohr	Analytic force versus 48 reconverged ±0.01 bohr SCFs	Accepted with a known float32 total-energy precision limit. The three failures are O 6-x and O 7-y/z; the threshold was not weakened.
Rock-salt MgO primitive Mg-q10/O-q6 feasibility, 2 atoms, 40 Ha, density-reconstructed reduced 4×4×4	Cold wall 39.892 s; direct-Rayleigh seeded wall 42.780 s; peak temporary memory 63.8 MB; both reached 80 SCF iterations	Numerical diagnostic only; no EOS reference claim	Rejected: the cold direct orbital residual was 3.570e-6; refreshing the direct Rayleigh quotient improved the seeded residual to 3.013e-6, still above the locked 2e-6 gate. The matched full oracle and seven-point EOS were correctly skipped.
Rock-salt MgO CP2K-2026.1 UZH Mg-q2/O-q6 diagnostic, 8 atoms, 70 Ha, reduced 6×6×6, 7 volumes	a₀ = 4.252650 Å, B₀ = 146.708 GPa, B₀′ = 3.35102, Δ = 0.461 meV/atom; seven-point wall 64.575 s	All-electron PBE: lattice 0.0376%, bulk modulus 1.526%, and bulk derivative 18.09% relative error	Historical-frozen project diagnostic. The central reduced/full energies differed by 6.90e-10 Ha/cell, while wall fell from 105.081 to 8.840 s. The candidate is rejected because the locked bulk-derivative error remains above 15%; no force ladder was run.
fcc Al, 4 atoms, PBE/GTH-q3, Fermi-Dirac 0.00225 Ha, 15 Ha, reduced 15×15×15, 11 bands, 7 volumes	a₀ = 4.039885 Å, B₀ = 76.631 GPa, B₀′ = 4.58384, Δ = 0.230 meV/atom	All-electron PBE: lattice 0.024%, bulk modulus 1.137%, and B₀′ 0.851% relative error	Verified for this metallic EOS workload. The accepted mesh has 120 weighted representatives; the result does not establish broad Aluminum chemistry or metal transferability.
bcc Fe primitive cell, spin-PBE/GTH-q16, Fermi-Dirac 0.01 Ha, unfolded 4×4×4, 10 bands	The density-reconstructed reduced result gives 2.34075 μB/atom in 11.375 s; the matched full mesh gives 2.33818 μB/atom in 53.104 s.	Published PBE context 2.33 μB/atom; the full-mesh moment error is 0.00818 μB/atom.	Current-verified method oracle on Apple M5 Max, AC power, normal mode. Reduction changes free energy by 4.0505e-6 Ha/atom and moment by 0.002563 μB/atom, passing the locked 5e-5 and 0.02 gates. Older cutoff/k-point evidence still requires refreshed v2 identities.

Evidence Boundary

The compact reference bundles are committed under src/mlx_atomistic/benchmarks/data/; tests lock the fit and completion semantics. Raw SCF, EOS, band, and force reports remain under gitignored results/. Quantum ESPRESSO and CP2K are reference families only and are not installed, imported, or executed by the MLX runtime or routine CI.

These rows prove the listed fixed workloads. Aluminum closes one simple-metal case and Iron closes one collinear-magnetic q16 case, but the rows do not establish broad metallic, magnetic, or pseudopotential transferability. The retained Fe q8 failure makes that boundary explicit. The 2H-Si row closes one bounded variable-cell path; it does not establish universal periodic DFT accuracy or broad cell-relaxation transferability.

The periodic runtime has a numerically validated Fermi-Dirac occupation and free-energy path, including weighted k-points, odd electron counts, checkpoints, and analytic-force occupation propagation. The Aluminum row adds a source-bound material validation for that path. Capability and broader material accuracy remain separate claims.