How Accurate Are DFT Band Gaps? Computed vs Measured for 1,000+ Compounds
Key findings
- DFT gaps are systematically low. All three databases put the median gap at 0.70–0.72× the measured value, and the mean signed error is -0.92 to -0.85 eV.
- The error scales with the gap. Materials Project underestimates by 0.17 eV on average for compounds measured below 1 eV, and by 2.00 eV for those measured above 4 eV.
- The databases agree with each other more than with experiment. Mean absolute errors range over 0.96–1.02 eV. Their shared starting point (semi-local DFT) matters more than their differences.
- Some well-known insulators come out metallic. Hematite (Fe2O3, measured 2.2 eV) and Cr2O3 (measured 3.4 eV) are listed at 0.0 eV and 0.0 eV in the Materials Project summary data we ingested. Overall, 13–21% of measured semiconductors come out metallic. Rare-earth and actinide compounds are 30–56% of those false metals but only 17–21% of the matched set.
Computed vs measured, database by database
Each dot is a compound with a measured, non-zero band gap. The x-axis is the measured gap; the y-axis is the gap each database reports for its lowest-energy structure. Perfect agreement would sit on the dashed diagonal. Almost everything falls below it.
| Database | Compounds | MAE (eV) | Mean error (eV) | RMSE (eV) | R² | Underestimated | Median ratio | Called metallic |
|---|---|---|---|---|---|---|---|---|
| Materials Project | 1,004 | 0.96 | -0.85 | 1.30 | 0.35 | 86.1% | 0.72 | 18.1% |
| JARVIS-DFT | 701 | 1.02 | -0.92 | 1.39 | 0.37 | 87.4% | 0.70 | 21.4% |
| AFLOW | 567 | 1.01 | -0.90 | 1.38 | 0.40 | 86.4% | 0.72 | 12.7% |
The wider the gap, the bigger the miss
Mean signed error (DFT minus measured) grouped by the measured gap. Negative bars mean DFT is too low. The underestimate grows steadily from small-gap semiconductors to wide-gap insulators in every database. A constant correction can’t fix that.
| Measured gap (eV) | Materials Project error | n | JARVIS-DFT error | n | AFLOW error | n |
|---|---|---|---|---|---|---|
| 0–1 | -0.17 | 203 | -0.19 | 173 | -0.17 | 81 |
| 1–2 | -0.71 | 290 | -0.78 | 186 | -0.59 | 158 |
| 2–3 | -0.93 | 278 | -1.10 | 163 | -0.87 | 159 |
| 3–4 | -1.12 | 125 | -1.23 | 93 | -1.03 | 78 |
| 4–6 | -1.73 | 79 | -1.82 | 63 | -1.67 | 63 |
| 6+ | -2.75 | 29 | -2.57 | 23 | -2.70 | 28 |
Well-known semiconductors and insulators
Measured gaps against each database’s ground-state value, in eV. A dash means the database has no matching entry (or, for AFLOW, no gap on its lowest-energy structure).
| Compound | Measured | MP | MP error | JARVIS | JARVIS error | AFLOW | AFLOW error |
|---|---|---|---|---|---|---|---|
| GaP | 2.74 | 1.60 | -1.14 | 1.48 | -1.26 | — | — |
| TiO2 | 3.30 | 2.06 | -1.24 | 2.05 | -1.25 | — | — |
| Cu2O | 2.58 | 0.51 | -2.07 | 0.64 | -1.94 | — | — |
| CdO | 2.30 | 0.00 | -2.30 | 0.00 | -2.30 | — | — |
| SnO2 | 3.60 | 0.65 | -2.95 | 0.72 | -2.88 | — | — |
| In2O3 | 2.80 | 0.63 | -2.17 | 1.20 | -1.60 | 1.12 | -1.68 |
| InCuS2 | 1.50 | 0.00 | -1.50 | 0.02 | -1.48 | 0.42 | -1.08 |
| MoSe2 | 1.60 | 1.30 | -0.30 | 0.91 | -0.69 | — | — |
| HgS | 2.10 | 0.00 | -2.10 | 1.40 | -0.70 | 0.00 | -2.10 |
| AgBr | 2.52 | 0.73 | -1.79 | 0.64 | -1.88 | — | — |
| AgCl | 5.13 | 0.95 | -4.18 | 0.93 | -4.21 | — | — |
| Fe2O3 | 2.20 | 0.00 | -2.20 | 0.41 | -1.79 | — | — |
| Cr2O3 | 3.40 | 0.00 | -3.40 | 0.73 | -2.67 | — | — |
| MnO | 3.60 | 1.31 | -2.29 | 0.00 | -3.60 | — | — |
| NiO | 4.00 | 2.30 | -1.70 | 0.00 | -4.00 | — | — |
| CeO2 | 3.41 | 1.86 | -1.55 | 2.21 | -1.20 | — | — |
| ZrO2 | 4.99 | 3.53 | -1.46 | 3.76 | -1.23 | 3.48 | -1.51 |
| HfO2 | 5.55 | 4.02 | -1.53 | 4.12 | -1.43 | 4.02 | -1.53 |
| GeO2 | 5.54 | 1.22 | -4.32 | 1.29 | -4.25 | 1.23 | -4.31 |
| Si3N4 | 5.10 | 4.25 | -0.85 | 4.46 | -0.64 | 4.25 | -0.85 |
| BaO | 4.80 | 2.09 | -2.71 | 2.08 | -2.71 | 2.09 | -2.71 |
| SrO | 5.70 | 3.27 | -2.43 | 3.40 | -2.30 | 3.28 | -2.42 |
| KCl | 8.50 | 5.03 | -3.47 | 5.33 | -3.17 | 5.04 | -3.46 |
| LiF | 11.70 | 8.72 | -2.98 | 9.30 | -2.40 | 8.73 | -2.97 |
| CaF2 | 9.92 | 7.12 | -2.80 | 7.59 | -2.33 | 7.13 | -2.79 |
| MgF2 | 11.10 | 6.82 | -4.28 | 7.09 | -4.00 | 6.83 | -4.27 |
| BeO | 10.39 | 7.46 | -2.93 | 8.04 | -2.35 | 7.44 | -2.95 |
Where the comparison breaks down
The largest absolute misses, ranked by the Materials Project error. Two groups dominate: wide-gap ionic fluorides (such as RbF, KF and CsF), where semi-local DFT is known to be several eV low, and compounds with localised d or f electrons, which DFT often calls metallic.
Read this list critically. Literature compilations mix optical and fundamental gaps and different measurement temperatures. Some entries are disputed: rare-earth hexaborides such as NdB6 and PrB6 are metals in most references, so their listed “gap” is probably an optical feature. We publish the compilation values unedited so the comparison stays reproducible.
| Compound | Measured | MP | MP error | JARVIS | JARVIS error | AFLOW | AFLOW error |
|---|---|---|---|---|---|---|---|
| MnF2 | 9.90 | 2.37 | -7.54 | 1.92 | -7.98 | 2.59 | -7.31 |
| KTi2F7 | 6.40 | 0.00 | -6.40 | 0.00 | -6.40 | 2.29 | -4.11 |
| Yb2O3 | 5.22 | 0.00 | -5.22 | 0.00 | -5.22 | 0.41 | -4.81 |
| FeI2 | 5.15 | 0.00 | -5.15 | 0.00 | -5.15 | 0.00 | -5.15 |
| NdB6 | 4.90 | 0.00 | -4.90 | 0.00 | -4.90 | 0.00 | -4.90 |
| PrB6 | 4.90 | 0.00 | -4.90 | 0.00 | -4.90 | 0.00 | -4.90 |
| RbF | 10.40 | 5.52 | -4.88 | 5.96 | -4.44 | 5.54 | -4.86 |
| CeF3 | 4.85 | 0.00 | -4.85 | 0.00 | -4.85 | 5.73 | +0.88 |
| CsF | 10.00 | 5.26 | -4.74 | — | — | 5.28 | -4.72 |
| Eu2O3 | 4.50 | 0.00 | -4.50 | 3.91 | -0.59 | 0.18 | -4.32 |
| CaB6 | 4.50 | 0.00 | -4.50 | 0.04 | -4.46 | 0.00 | -4.50 |
| KF | 10.30 | 5.95 | -4.35 | 6.46 | -3.84 | 5.96 | -4.34 |
| GeO2 | 5.54 | 1.22 | -4.32 | 1.29 | -4.25 | 1.23 | -4.31 |
| NaF | 10.50 | 6.20 | -4.30 | 6.42 | -4.08 | 6.12 | -4.38 |
| MgF2 | 11.10 | 6.82 | -4.28 | 7.09 | -4.00 | 6.83 | -4.27 |
| AgCl | 5.13 | 0.95 | -4.18 | 0.93 | -4.21 | — | — |
| LaB6 | 4.10 | 0.00 | -4.10 | 0.00 | -4.10 | — | — |
| InAgO2 | 4.20 | 0.23 | -3.97 | 0.41 | -3.79 | 0.62 | -3.58 |
| Sr2Be2B2O7 | 8.00 | 4.08 | -3.92 | 4.17 | -3.83 | 4.09 | -3.91 |
| SrB6 | 3.68 | 0.00 | -3.68 | 0.02 | -3.66 | 0.00 | -3.68 |
Why DFT band gaps come out low
High-throughput databases run semi-local functionals (PBE, OptB88vdW) because they are affordable across hundreds of thousands of structures. These functionals suffer from self-interaction error and lack the derivative discontinuity of the exact functional. As a result, the Kohn-Sham gap they produce is systematically smaller than the fundamental gap you would measure.
A Hubbard U correction (applied by Materials Project and AFLOW to selected transition-metal compounds) opens gaps in correlated oxides, but only for the elements it is applied to. Hybrid functionals such as HSE06, meta-GGAs such as TB-mBJ, and GW calculations get much closer to experiment at higher cost. For screening, treat a database gap as a lower bound, and expect the shortfall to grow with the gap. Different databases can also disagree with each other substantially; see how much materials databases disagree.
How this comparison was built
- Measured gaps come from the Zhuo et al. compilation as distributed by Matbench (4,589 compositions after merging duplicates). Compositions are matched to database entries by reduced formula. Doped or non-stoichiometric compositions have no database counterpart and drop out.
- Each database contributes the gap of its lowest-energy entry for that composition, or of a sibling within 10 meV/atom of it, so a gap from a high-energy polymorph is never used.
- Error statistics cover compounds with a non-zero measured gap. The median ratio excludes compounds a database calls metallic (gap ≤ 0.05 eV), which are counted separately.
- Charts plot a random sample of up to 900 compounds per database. Statistics and the CSV use every match. Warehouse build 20260925T154847Z; page built 2026-09-30.
Download and cite
Every row behind this page (3,424 rows) as CSV, with source identifiers so each value can be traced back.
Download CSVLatticeGraph (2026). "How Accurate Are DFT Band Gaps? Computed vs Measured for 1,000+ Compounds." LatticeGraph Data Atlas, snapshot 2026-09-30 (warehouse 20260925T154847Z). https://latticegraph.com/atlas/dft-band-gap-accuracy
Please also cite the original datasets listed under Sources.
Datasets and licences
- 4,589 compositions with measured band gaps compiled from the literature, 2,140 of them non-zero. Distributed through Matbench.Y. Zhuo, A. Mansouri Tehrani, J. Brgoch, J. Phys. Chem. Lett. 9, 1668–1673 (2018); A. Dunn et al., npj Computational Materials 6, 138 (2020).License: CC BY 4.0
- Summary endpoint, release 2025.09.25.A. Jain et al., APL Materials 1, 011002 (2013).License: CC BY 4.0
- 3D dataset, release 2026.03 (OptB88vdW gaps).K. Choudhary et al., npj Computational Materials 6, 173 (2020).License: US Government public domain (NIST)
- Entries carrying a band gap, release 2026.03.S. Curtarolo et al., Computational Materials Science 58, 218–226 (2012).License: CC BY 4.0
Frequently asked questions
How much does DFT underestimate band gaps?
Against 1,120 compounds with measured band gaps, standard DFT gaps from Materials Project, JARVIS-DFT and AFLOW come out 28–30% below experiment at the median (DFT/measured ratio 0.70–0.72). They underestimate in 86–87% of cases, with a mean absolute error of 0.96–1.02 eV.
Why does DFT underestimate band gaps?
Semi-local functionals such as PBE (GGA) suffer from self-interaction error and lack the derivative discontinuity of the exact functional. The Kohn-Sham gap they report is therefore not the true fundamental gap and is systematically too small. Hybrid functionals (HSE06), meta-GGAs such as TB-mBJ, and many-body GW calculations reduce the error at higher computational cost.
Is the DFT band gap error constant?
No. It grows with the size of the gap. For compounds measured below 1 eV, Materials Project's mean error is -0.17 eV; for compounds measured above 4 eV it is -2.00 eV. A single scissor shift will over-correct small-gap materials and under-correct insulators.
Can DFT predict whether a material is a metal?
Not reliably at this level of theory. Of the measured semiconductors and insulators we matched, 13–21% are predicted to be metallic (gap ≤ 0.05 eV), depending on the database. Rare-earth and actinide compounds are over-represented: 30–56% of these false metals contain an f-block element, against 17–21% of all matched compounds.
Related studies
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