{ "snapshot_id": "dband_center_benchmark_2026-04-14", "generated_at_utc": "2026-04-14T00:00:00+00:00", "study_name": "d-Band Center Descriptor Benchmark", "benchmark_mode": "public_production_stack", "description": "Benchmark for the d-band center (Hammer-Norskov descriptor) across pure transition metals, facet-specific surfaces, and binary alloys. Predictions use the Flux Physics d-band route from composition and crystal facet.", "engine_notes": "FluxMateria physics engine. The d-band center is predicted from Flux atomic descriptors (Z, period, group) and surface coordination, with closed-shell and relativistic corrections for heavier series.", "summary": { "total_cases": 100, "combined_mae_eV": 0.197, "combined_rmse_eV": 0.278, "within_0p2_eV_pct": 71.0, "within_0p3_eV_pct": 81.0, "within_0p5_eV_pct": 90.0, "fitted_parameters": 0, "training_data_required": false }, "category_metrics": [ { "category": "pure_transition_metals", "label": "Pure transition metals", "n": 27, "mae_eV": 0.223, "rmse_eV": 0.299, "within_0p2_eV_pct": 63, "within_0p3_eV_pct": 74, "within_0p5_eV_pct": 89, "notes": "3d, 4d, 5d series plus group 3 f-block boundary elements (Y, La, Ce).", "families_covered": [ "3d transition metals (Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu)", "4d transition metals (Y, Zr, Nb, Mo, Tc, Ru, Rh, Pd, Ag)", "5d transition metals (La, Ce, Hf, Ta, W, Re, Os, Ir, Pt, Au)" ] }, { "category": "facet_surfaces", "label": "Facet-specific surfaces", "n": 41, "mae_eV": 0.154, "rmse_eV": 0.206, "within_0p2_eV_pct": 83, "within_0p3_eV_pct": 90, "within_0p5_eV_pct": 93, "notes": "Close-packed, open, stepped, and (0001) facets across 3d/4d/5d metals.", "families_covered": [ "(111) close-packed surfaces", "(100) open surfaces", "(110) stepped surfaces", "(211) stepped/kinked surfaces", "(0001) HCP basal surfaces", "Step-edge geometries" ] }, { "category": "binary_alloys", "label": "Binary transition-metal alloys", "n": 32, "mae_eV": 0.230, "rmse_eV": 0.334, "within_0p2_eV_pct": 62, "within_0p3_eV_pct": 75, "within_0p5_eV_pct": 88, "notes": "Composition-weighted prediction with strain contribution from size mismatch.", "families_covered": [ "Pt-based alloys (Pt-Ni, Pt-Co, Pt-Fe, Pt-Cu, Pt-Ti, Pt-V, Pt-Au)", "Pd-based alloys (Pd-Au, Pd-Ag, Pd-Cu, Pd-Ni)", "Au/Ag-based alloys", "Ni-Co, Ni-Fe skin alloys", "Rh, Mo, Fe, Co intermetallics" ] } ], "breakdown_by_period": [ { "period": "3d (period 4)", "n": 32, "mae_eV": 0.141, "within_0p3_eV_pct": 91 }, { "period": "4d (period 5)", "n": 34, "mae_eV": 0.181, "within_0p3_eV_pct": 82 }, { "period": "5d (period 6)", "n": 34, "mae_eV": 0.266, "within_0p3_eV_pct": 71 } ], "breakdown_by_facet": [ { "facet": "(0001)", "n": 2, "mae_eV": 0.076 }, { "facet": "(211)", "n": 6, "mae_eV": 0.115 }, { "facet": "step", "n": 1, "mae_eV": 0.113 }, { "facet": "(110)", "n": 12, "mae_eV": 0.135 }, { "facet": "(100)", "n": 12, "mae_eV": 0.186 }, { "facet": "(111)", "n": 8, "mae_eV": 0.187 } ], "ml_baseline_comparison": { "description": "Same atomic feature set fed to standard ML regressors with 5-fold cross-validation. The FluxMateria route is evaluated directly on the same held-out descriptor rows.", "feature_set": ["Z", "period", "group", "d_electron_count", "filling_fraction", "metallic_radius_pm", "work_function_eV"], "cv_folds": 5, "sample_size": 27, "models": [ { "model": "Linear regression (OLS)", "cv_mae_eV": 0.432, "cv_rmse_eV": 0.556 }, { "model": "k-Nearest Neighbors (k=3)", "cv_mae_eV": 0.388, "cv_rmse_eV": 0.657 }, { "model": "Random Forest (20 trees, depth 4)","cv_mae_eV": 0.295, "cv_rmse_eV": 0.470 }, { "model": "FluxMateria physics engine (no fitting)", "cv_mae_eV": 0.223, "cv_rmse_eV": 0.299 } ] }, "state_of_the_art_comparison": [ { "method": "FluxMateria physics engine (pure TMs)", "type": "First-principles, no fitting", "mae_eV": 0.223, "source": "this work" }, { "method": "FluxMateria physics engine (facets)", "type": "First-principles, no fitting", "mae_eV": 0.154, "source": "this work" }, { "method": "FluxMateria physics engine (combined)", "type": "First-principles, no fitting", "mae_eV": 0.197, "source": "this work" }, { "method": "PBE-DFT (typical, single method)", "type": "DFT", "mae_eV_range": [0.15, 0.30], "source": "method-to-method spread across literature" }, { "method": "SISSO surrogate", "type": "ML on DFT features", "mae_eV_range": [0.20, 0.30], "source": "Ghiringhelli et al., 2017" }, { "method": "Neural network fits", "type": "ML on DFT features", "mae_eV_range": [0.15, 0.25], "source": "Batchelor et al., 2019" }, { "method": "CGCNN (graph neural network)", "type": "GNN on DFT + structure", "mae_eV_range": [0.15, 0.20], "source": "Xie & Grossman, 2018" } ], "literature_sources_used_for_validation": [ { "id": "HN14", "citation": "Hammer & Nørskov, Chem. Rev. 114, 4259 (2014)" }, { "id": "K04", "citation": "Kitchin, Nørskov, Barteau, Chen, J. Chem. Phys. 120, 10240 (2004)" }, { "id": "GN09", "citation": "Greeley, Stephens, Bondarenko et al., Nat. Chem. 1, 552 (2009)" }, { "id": "N95", "citation": "Hammer & Nørskov, Surf. Sci. 343, 211 (1995)" }, { "id": "CM20", "citation": "Chen & Mavrikakis, Chem. Rev. 121, 1007 (2021)" } ], "known_limitations": [ "Group 3 f-block boundary elements (Y, La, Ce) exhibit higher residual (~0.5 eV) due to 4f/5d orbital mixing.", "Pt-3d skin alloys (Pt3Ni, Pt3Co, Pt3Fe) under-predict the ligand-induced deepening by ~0.6-0.9 eV.", "Period 6 (5d) surfaces carry larger residuals than 3d/4d due to spin-orbit and relativistic effects.", "Single-source elements (Sc, Cr, Mn, Hf, Ta, Nb, Zr, Tc, La, Ce) are cross-validated against only one literature entry." ] }