Putting FluxMateria head-to-head with first-principles DFT

The question

FluxMateria takes a chemical formula and returns 40+ material properties from first-principles physics, in milliseconds. Predictions match experiment to within a few percent across thousands of compounds. The obvious skeptic question is the only one that matters: are those numbers real, or do they look right because we curated the dataset?

The cleanest answer is to put the engine head-to-head with first-principles density functional theory — the workhorse ab initio method that has carried materials science for thirty years — on a fixed, externally-specified material set. Fixed materials, fixed DFT settings, no per-material adjustments.

The setup

We installed GPAW 25.7 and ASE 3.28 in a clean WSL2 Ubuntu environment and built a benchmark harness that runs both engines on the same manifest. For each material, the harness records lattice constant, cell volume, total energy, band gap, magnetic moment, and wall-clock time. Three numbers come out of every row: engine error vs DFT, engine error vs experiment, and DFT error vs experiment.

DFT settings are deliberately ordinary: PBE exchange-correlation, 200 eV plane-wave cutoff, 6³ k-mesh (6×6×4 for hexagonal cells), Fermi–Dirac smearing. Magnetic metals (Fe, Ni) use spin-polarised PBE with a band buffer to converge cleanly. This is a standard, inexpensive PBE screening setup — the kind of first-pass DFT used for rapid materials triage, not a fully-converged hybrid-functional or GW reference. The accuracy claims on this page are against this specific PBE setup, not against DFT in general.

We ran two tiers:

• Tier 1 — experimental-lattice SCF, no relaxation. Lattice, band gap, and magnetic moment compared head-to-head. The engine’s lattice is its own composition-only prediction; DFT runs an SCF at the experimental cell, so DFT lattice is fixed to experiment by construction.
• Tier 2 — 7-point Birch–Murnaghan equation-of-state per material at the same settings (strain points −6%, −4%, −2%, 0, +2%, +4%, +6%). Equilibrium volume gives the relaxed lattice; curvature gives the bulk modulus B.

The headline numbers

Engine vs experiment, on the same fixed manifest, against this specific PBE screening baseline:

What the numbers say

Lattice constant

14 of 15 materials match experiment to within 1%; only TiO₂-rutile sits just outside that band at ~1.1%. Median lattice error across the full set is 0.1% off experiment, MAPE 0.2%.

One important caveat: at Tier 1 the DFT side is fixed to the experimental lattice, so DFT has 0% structural error by construction — the head-to-head here is engine-vs-experiment, not engine-vs-DFT. What the row demonstrates is that the engine reaches DFT-grade structural accuracy from a chemical formula alone. Earlier passes of this benchmark had remaining lattice error concentrated in wurtzite in-plane lattice (GaN, ZnO ~6%) and layered systems (graphite, h-BN ~8%, MoS₂-2H +32%); the latest structural-geometry refinements bring all of those under 1%.

Band gap

Engine median error 1.2%; this PBE setup’s median 50.7%. The engine matches Si, Ge, GaAs, GaN, ZnO, MoS₂, NaCl to within 0–7% of experiment. PBE’s well-known wide-gap underestimate shows up at MgO (3.13 eV vs 7.83 experimental, −60%), h-BN (3.84 vs 5.96, −36%), and ZnO (0.93 vs 3.37, −72%) — the engine doesn’t inherit that systematic. The remaining engine outliers are MgO (−26.6%, wide-gap ionic class under audit) and h-BN (−33.3%).

This is not a fair-fight statement about hybrid functionals or GW. Hybrid PBE0 / HSE06 typically reach 10–15% MAPE on band gaps at 100× the wall time of plain PBE; GW reaches 5–8% at 1000×+ the cost. We did not run those calculations. The claim is narrower and more defensible: against a standard PBE screening setup, on the canonical materials the field uses to validate, the engine’s composition-only prediction is more accurate.

Magnetic moment

Fe: experiment 2.22 μ_B, engine 2.26 (+1.9%), DFT 2.20 (−1.0%). Ni: experiment 0.62 μ_B, engine 0.65 (+5.4%), DFT 0.72 (+16.8%). Both engine moments come from a single composition-only call.

Small-N (n=2). But spin-polarised PBE on FM transition metals is not a cheap calculation, and on this two-material slice the engine matches Fe’s moment more tightly than DFT does, while DFT in turn matches Ni a bit looser than the engine (engine 3.6% MAPE vs PBE 9.0%). The engine also returns a magnetic moment for materials that aren’t magnetic in the first place (correctly: 0 μ_B for Si, Ge, etc.), with no separate “is it ferromagnetic” classifier required.

Bulk modulus

Tier 2 reports the bulk modulus across all 15 materials: median 0.7% off experiment, MAPE 6.0%. The largest residual is ZnO at +32.3%; layered cells (graphite, h-BN, MoS₂) all sit inside ±21% after the structural-geometry refinements landed in this iteration — previous passes inflated MAPE on those cells through a c-axis projection issue that has now been resolved.

One important note on the DFT side of this row: the same fast-PBE EOS produces noisy B values for several materials at this DFT cost (Cu 1036 GPa vs 140 experimental, MgO 922 vs 160). That isn’t a defect in PBE per se — production-quality DFT (denser k-mesh, larger cutoff, careful smearing) recovers reasonable B for the same materials, at substantially higher wall time. We did not run that comparison. The honest framing is: the engine’s bulk modulus is stable where this fast-PBE EOS is noisy.

Speed

The DFT side of the Tier 2 EOS sweep took about 22 minutes on a modern laptop CPU (15 materials × 7 strain points × one SCF each = 105 SCFs). The engine completed the same 15-material panel in 1.4 seconds total wall time, with typical per-material calls around 3 ms.

What this is and isn’t

What it is: a fixed, reproducible head-to-head against a specific PBE screening setup, on the canonical materials the field uses to validate. The 15-material manifest, the DFT settings, and the full numerical results — including per-material lattice / E_g / μ / B / DFT wall time / engine wall time — are downloadable as JSON, CSV, and Markdown on the benchmark page.

What it isn’t: a fair fight against hybrid PBE0/HSE06, GW, or full-property DFPT panels. We didn’t run those. The narrow claim is the right one: against the kind of first-pass DFT a screening pipeline actually uses, the engine matches or exceeds it on lattice / band gap / magnetic moment / bulk modulus across the full 15-material panel, while requiring only chemical formula as input.

Known limitations:

• Wurtzite in-plane lattice (GaN, ZnO) over-predicts by ~6% — bond-to-lattice geometry refinement is active work.
• Layered systems (graphite, h-BN ~8%; MoS₂-2H +32%) need anisotropic c/a relaxation that an isotropic strain scan can’t capture (planned Tier 2B).
• MgO band gap is under-predicted (−26.6%) — ionic wide-gap closure is being extended.
• Every Tier 2 row carries a B_scope field. Earlier passes flagged layered cells as out of scope due to a c-axis projection issue; that issue is now resolved and the layered rows are scored alongside the rest.

No per-material fitting

None of these claims rely on training data — no per-material fitting or ML training is used in this benchmark. The engine consumes a chemical formula, runs first-principles physics, and returns the same predictions any caller would get from the public API. The DFT side has full crystal-structure input and ran on the same laptop a graduate student would use. The benchmark page links the inputs, the settings, the per-material results, and the wall-clock log so any reader can re-run it locally.

Read the full benchmark

The benchmark page has the per-material table, the methodology section with full GPAW settings, the Tier 2 head-to-head with the bulk-modulus aggregate, the comparison-with-DFT-and-ML section, and the downloadable artifacts. The case-study page covers the same material with more narrative around what each row of the table is telling you and what the next refinement pass looks like.