The d-band center is the single most important descriptor in transition-metal catalysis. FluxMateria predicts it from atomic quantum numbers and surface geometry — across pure metals, facets, and binary alloys — with no DFT inputs.
Combined and per-category accuracy across the 100-case benchmark.
| Set | n | MAE (eV) | RMSE (eV) | ≤0.2 eV | ≤0.3 eV | ≤0.5 eV |
|---|---|---|---|---|---|---|
| Combined benchmark | 100 | 0.197 | 0.278 | 71% | 81% | 90% |
| Pure transition metals | 27 | 0.223 | 0.299 | 63% | 74% | 89% |
| Facet-specific surfaces | 41 | 0.154 | 0.206 | 83% | 90% | 93% |
| Binary alloys | 32 | 0.230 | 0.334 | 62% | 75% | 88% |
Per-period and per-facet residuals let users see where the predictor is strongest and where the known physics limits kick in.
| 3d (period 4) | n = 32 | 0.141 eV |
| 4d (period 5) | n = 34 | 0.181 eV |
| 5d (period 6) | n = 34 | 0.266 eV |
3d is cleanest. 5d carries larger residuals because spin–orbit and relativistic physics become material.
| (0001) | n = 2 | 0.076 eV |
| (211) | n = 6 | 0.115 eV |
| step | n = 1 | 0.113 eV |
| (110) | n = 12 | 0.135 eV |
| (100) | n = 12 | 0.186 eV |
| (111) | n = 8 | 0.187 eV |
Low-coordination and stepped surfaces are predicted tightly — exactly where real catalysis lives.
Three standard regressors were fitted on the same atomic descriptors with 5-fold cross-validation. The FluxMateria route is evaluated directly on the same held-out descriptor rows.
| Model | CV MAE (eV) | CV RMSE (eV) | Notes |
|---|---|---|---|
| Linear regression | 0.432 | 0.556 | OLS with bias term on the standardized feature set. |
| k-Nearest Neighbors (k = 3) | 0.388 | 0.657 | Inverse-distance weighted, standardized features. |
| Random Forest (20 × depth 4) | 0.295 | 0.470 | Bootstrap aggregation with square-root feature bagging. |
| FluxMateria physics engine | 0.223 | 0.299 | No ML training route; work-function metadata caveat disclosed. |
Feature set for all four models: atomic number, period, group, d-electron count, filling fraction, metallic radius, work function. Cross-validation on the 27-element pure-TM set with identical splits. The physics-derived predictor wins against every ML baseline trained on the same descriptors.
Where FluxMateria lands compared to established methods for the same quantity.
| Method | Type | MAE (eV) | Source |
|---|---|---|---|
| FluxMateria — pure TMs | First-principles, no fitting | 0.223 | this work |
| FluxMateria — facets | First-principles, no fitting | 0.154 | this work |
| FluxMateria — combined | First-principles, no fitting | 0.197 | this work |
| PBE-DFT (typical single method) | DFT | 0.15 – 0.30 | method-to-method spread |
| SISSO surrogate | ML on DFT features | 0.20 – 0.30 | Ghiringhelli et al., 2017 |
| Neural-network surrogate | ML on DFT features | 0.15 – 0.25 | Batchelor et al., 2019 |
| CGCNN (graph neural network) | GNN on DFT + structure | 0.15 – 0.20 | Xie & Grossman, 2018 |
FluxMateria matches DFT-trained ML surrogates on pure-TM and facet accuracy — without requiring a DFT training set and without any fitted coefficients.
The benchmark measures the operational FluxMateria predictor — the same path exposed to the universal material engine — against independent literature data.
The d-band center is computed directly from atomic quantum numbers and surface coordination, with closed-shell and relativistic corrections for heavier series.
Every reported number is measured on published literature values — nothing is fit or held out of the predictor.
Important scope note: this benchmark establishes FluxMateria as a physics-based predictor for the central descriptor in transition-metal catalysis. It does not claim to replace dedicated surface-science DFT for mechanism-level questions, reactor kinetics, or high-throughput screening at full scale — its role is to give a fast, physically grounded starting point that does not depend on trained ML surrogates.
Every predicted value was compared against one or more of these independent studies.
Hammer & Nørskov, Chem. Rev. 114, 4259 (2014)
Kitchin, Nørskov, Barteau, Chen, J. Chem. Phys. 120, 10240 (2004)
Greeley, Stephens, Bondarenko et al., Nat. Chem. 1, 552 (2009)
Hammer & Nørskov, Surf. Sci. 343, 211 (1995)
Chen & Mavrikakis, Chem. Rev. 121, 1007 (2021)
The five sources disagree by 0.05–0.35 eV per element across DFT methods, slab thicknesses, and facet choices. FluxMateria lands inside that window on the majority of cases.
Honest bounds on where the predictor is weaker — published up front.
Y, La, Ce show ~0.5 eV residuals because 4f/5d orbital mixing is not yet modelled. Not recommended for rare-earth catalysis.
Pt₃Ni, Pt₃Co, Pt₃Fe under-predict the ligand-induced deepening by 0.6–0.9 eV — a multi-body electronic coupling effect on the roadmap.
Larger residuals than 3d/4d. Spin–orbit splitting for open-shell 5d (W, Re) is the next physics upgrade.
Sc, Cr, Mn, Hf, Ta, Nb, Zr, Tc, La, Ce have only one literature entry for cross-check. More sources will sharpen the validation.
This benchmark establishes the d-band center as a production-grade physics descriptor. It feeds the catalyst scoring layer and downstream discovery workflows inside the FluxMateria platform.
d-band centers are computed from Flux surface and electronic descriptors. Benchmark references are used to measure descriptor accuracy.