# DFT Cross-Check Benchmark — Tier 1 (Public Export)

Date: 2026-05-08T15:57:10Z
Originator: FluxMateria
Machine-readable artifacts: `dft_crosscheck_tier1_benchmark.json`, `dft_crosscheck_tier1_benchmark.csv`

## Methodology

Tier 1: experimental-lattice SCF (no relaxation), 200 eV plane-wave cutoff, 6^3 k-points (6x6x4 hexagonal). Comparison covers lattice, band gap, and magnetic moment (Fe / Ni).

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 0.0% (median 0.0%, n=15) |
| Band gap (eV) | MAPE 8.12% (median 1.21%, n=10) | MAPE 37.53% (median 36.52%, n=10) |
| Magnetic moment (μ_B) | MAPE 3.64% (median 3.64%, n=2) | MAPE 8.86% (median 8.86%, n=2) |
| Bulk modulus B (GPa) | — | — |

## Per-material Results — 15 materials

| Material | Family | a_exp | a_engine | a_DFT | a_engine_err | Eg_exp | Eg_engine | Eg_DFT | μ_exp | μ_engine | μ_DFT |
|---|---|---|---|---|---|---|---|---|---|---|---|
| `Si-diamond` | Group IV | 5.431 | 5.431 | 5.431 | -0.01% | 1.12 | 1.12 | 0.92 | 0.00 | 0.00 | 0.00 |
| `Ge-diamond` | Group IV | 5.658 | 5.655 | 5.658 | -0.06% | 0.66 | 0.66 | 0.43 | 0.00 | 0.00 | 0.00 |
| `GaAs-zb` | III-V | 5.653 | 5.647 | 5.653 | -0.11% | 1.43 | 1.43 | 1.22 | 0.00 | 0.00 | 0.00 |
| `GaN-wz` | III-V | 3.189 | 3.183 | 3.189 | -0.18% | 3.40 | 3.44 | 1.83 | 0.00 | 0.00 | 0.00 |
| `ZnO-wz` | II-VI | 3.249 | 3.230 | 3.249 | -0.58% | 3.37 | 3.40 | 0.93 | 0.00 | 0.00 | 0.00 |
| `MgO-rs` | oxide | 4.211 | 4.208 | 4.211 | -0.07% | 7.83 | 5.74 | 3.13 | 0.00 | 0.00 | 0.00 |
| `TiO2-rutile` | oxide | 4.594 | 4.545 | 4.594 | -1.07% | 3.05 | 3.39 | 1.78 | 0.00 | 0.00 | 0.00 |
| `NaCl-rs` | ionic | 5.640 | 5.630 | 5.640 | -0.18% | 8.60 | 9.17 | 5.38 | 0.00 | 0.00 | 0.00 |
| `Al-fcc` | metal | 4.046 | 4.049 | 4.046 | +0.07% | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| `Cu-fcc` | metal | 3.615 | 3.621 | 3.615 | +0.17% | 0.00 | 0.00 | 0.00 | 0.00 | 0.28 | 0.00 |
| `Fe-bcc` | magnetic-metal | 2.866 | 2.864 | 2.866 | -0.07% | 0.00 | 0.00 | 0.00 | 2.22 | 2.26 | 2.20 |
| `Ni-fcc` | magnetic-metal | 3.524 | 3.521 | 3.524 | -0.10% | 0.00 | 0.00 | 0.00 | 0.62 | 0.65 | 0.72 |
| `graphite` | layered | 2.461 | 2.461 | 2.461 | +0.02% | 0.00 | 5.73 | 1.28 | 0.00 | 0.00 | 0.00 |
| `hBN-hex` | layered | 2.504 | 2.507 | 2.504 | +0.12% | 5.96 | 3.97 | 3.84 | 0.00 | 0.00 | 0.00 |
| `MoS2-2H` | layered | 3.160 | 3.156 | 3.160 | -0.13% | 1.29 | 1.27 | 1.12 | 0.00 | 0.45 | 0.00 |

## 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 1 fixes the lattice at experimental input; the engine lattice is its own composition-only prediction while DFT runs an SCF at the experimental cell.