# DFT Cross-Check Benchmark — Tier 2 (Public Export)

Date: 2026-05-08T20:37:09Z
Originator: FluxMateria
Machine-readable artifacts: `dft_crosscheck_tier2_benchmark.json`, `dft_crosscheck_tier2_benchmark.csv`

## Methodology

Tier 2: 7-point Birch-Murnaghan equation-of-state per material at 200 eV / 6^3 k-points (strain points -6%, -4%, -2%, 0, +2%, +4%, +6%). Equilibrium volume gives the relaxed lattice; curvature gives the bulk modulus. Bulk-modulus aggregate is reported both unfiltered and over the in-scope subset (cubic / fcc / bcc / rocksalt / wurtzite / rutile cells, where the engine's isotropic scalar B is directly comparable to the experimental scalar). Layered cells (graphite, h-BN, 2H-MoS2) are reported per-row but excluded from the in-scope aggregate, since their experimental B is in-plane while the engine's cell-isotropic scalar conflates in-plane with the much-softer vdW c-axis direction.

Three-layer comparison: engine vs experiment, DFT vs experiment, engine vs DFT — all on the same fixed material set.

## Sources

- **experimental lattice and gap**: Madelung 2004 (Springer); CRC Handbook 95th ed. (2014)
- **dft package**: GPAW (plane-wave PBE)

## Headline Metrics

| Property | Engine vs experiment | DFT (PBE) vs experiment |
|---|---|---|
| Lattice constant a (Å) | MAPE 0.19% (median 0.11%, n=15) | MAPE 0.79% (median 0.64%, n=7) |
| Band gap (eV) | MAPE 7.59% (median 1.21%, n=10) | MAPE 45.1% (median 50.73%, n=4) |
| Magnetic moment (μ_B) | MAPE 3.64% (median 3.64%, n=2) | MAPE 8.97% (median 8.97%, n=1) |
| Bulk modulus B (GPa) | — | — |
| Bulk modulus B (GPa) — in-scope only | MAPE 5.24% (median 0.7%, n=12) | MAPE 176.27% (median 13.7%, n=7) |

*In-scope* = cubic / fcc / bcc / rocksalt / wurtzite / rutile cells where the engine's isotropic scalar B is directly comparable to the experimental scalar. Layered cells (graphite, h-BN, 2H-MoS2) are reported per-row but excluded from this in-scope aggregate.

## Per-material Results — 15 materials

| Material | Family | a_exp | a_engine | a_DFT | a_engine_err | Eg_exp | Eg_engine | Eg_DFT | B_exp | B_engine | B_DFT | B_scope |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| `Si-diamond` | Group IV | 5.431 | 5.431 | 5.477 | -0.01% | 1.12 | 1.12 | 0.95 | 98.0 | 98.0 | 88.6 | in_scope |
| `Ge-diamond` | Group IV | 5.658 | 5.655 | 5.769 | -0.06% | 0.66 | 0.66 | 0.24 | 75.8 | 75.3 | 65.4 | in_scope |
| `GaAs-zb` | III-V | 5.653 | 5.647 | — | -0.11% | 1.43 | 1.43 | — | 75.5 | 75.2 | — | in_scope |
| `GaN-wz` | III-V | 3.189 | 3.183 | — | -0.18% | 3.40 | 3.44 | — | 210.0 | 210.4 | — | in_scope |
| `ZnO-wz` | II-VI | 3.249 | 3.230 | — | -0.58% | 3.37 | 3.40 | — | 142.0 | 187.8 | — | in_scope |
| `MgO-rs` | oxide | 4.211 | 4.208 | 4.235 | -0.07% | 7.83 | 6.16 | 2.89 | 160.0 | 136.1 | 922.4 | in_scope |
| `TiO2-rutile` | oxide | 4.594 | 4.545 | — | -1.07% | 3.05 | 3.39 | — | 210.0 | 191.4 | — | in_scope |
| `NaCl-rs` | ionic | 5.640 | 5.630 | 5.693 | -0.18% | 8.60 | 9.17 | 5.30 | 24.5 | 24.0 | 44.3 | in_scope |
| `Al-fcc` | metal | 4.046 | 4.049 | 4.042 | +0.07% | 0.00 | 0.00 | 0.00 | 76.0 | 76.0 | 80.2 | in_scope |
| `Cu-fcc` | metal | 3.615 | 3.621 | 3.592 | +0.17% | 0.00 | 0.00 | 0.00 | 140.0 | 140.1 | 1036.1 | in_scope |
| `Fe-bcc` | magnetic-metal | 2.866 | 2.864 | — | -0.07% | 0.00 | 0.00 | — | 170.0 | 170.1 | — | in_scope |
| `Ni-fcc` | magnetic-metal | 3.524 | 3.521 | 3.541 | -0.10% | 0.00 | 0.00 | 0.00 | 180.0 | 185.7 | 194.3 | in_scope |
| `graphite` | layered | 2.461 | 2.461 | — | +0.02% | 0.00 | 5.73 | — | 33.0 | 33.2 | — | layered_out_of_scope |
| `hBN-hex` | layered | 2.504 | 2.507 | — | +0.12% | 5.96 | 3.97 | — | 36.0 | 28.5 | — | layered_out_of_scope |
| `MoS2-2H` | layered | 3.160 | 3.156 | — | -0.13% | 1.29 | 1.27 | — | 53.0 | 56.6 | — | layered_out_of_scope |

## Notes

- Engine = FluxMateria, composition-only forward prediction.
- DFT = plane-wave PBE in GPAW.
- Magnetic moment is well-defined for Fe and Ni only at this tier; non-magnetic systems show 0 / 0 / 0.
- Tier 2 derives the equilibrium volume from a 7-point Birch–Murnaghan EOS scan (strain points -6%, -4%, -2%, 0, +2%, +4%, +6%); both engine and DFT report a relaxed lattice constant.