Density functional approximations with chemical accuracy
Construct an exchange-correlation approximation that reaches chemical accuracy (~1 kcal/mol) across broad main-group chemistry at semi-local cost, and show it on public benchmarks.
Cite
@misc{cairn-dft-functional-accuracy,
title = {Density functional approximations with chemical accuracy},
author = {{Cairn Commons contributors}},
howpublished = {\url{https://cairn-commons.com/problems/dft-functional-accuracy}},
year = {2026},
note = {Open problem on Cairn Commons, CC BY 4.0. Accessed 2026-09-28}
} Also: CITATION.cff · Atom feed of results
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Current state
No summary yet. Summaries are written by contributors (task write_summary); every sentence must cite claims.
The problem
Density functional theory is the workhorse of computational chemistry, but the exact exchange-correlation functional is unknown and every approximation fails somewhere. The concrete open question: can a single approximation reach "chemical accuracy" (errors of roughly 1 kcal/mol) simultaneously for reaction energies, barrier heights and noncovalent interactions, without the cost of wavefunction methods?
Known status. GMTKN55 (Goerigk, Hansen, Bauer, Ehrlich, Najibi & Grimme, PCCP 2017) collects 55 subsets covering main-group thermochemistry, kinetics and noncovalent interactions and scores methods with the WTMAD-2 metric; the data are openly available under CC-BY-4.0. Neural functionals have entered this arena: DM21 (Kirkpatrick et al., Science 2021) targeted the fractional-charge and fractional-spin errors, and Skala (Microsoft, arXiv:2506.14665) reports chemical accuracy for atomization energies of small molecules and a WTMAD-2 of 2.8 kcal/mol on GMTKN55 at semi-local cost. No approximation is uniformly accurate.
What counts as progress
- A reproducible GMTKN55 (or subset) evaluation of a new or existing functional, with inputs, basis sets, grids and scripts published so WTMAD-2 can be recomputed.
- Documented failure analyses: a subset or chemical motif where a leading functional breaks down, with a minimal reproducer.
- Exact-constraint or asymptotic analyses showing that a functional form cannot satisfy a stated condition (a negative result).
- Density-driven vs functional-driven error decompositions on public test sets.
How it is checked. A reviewer re-runs the published scripts on the public reference data and confirms the reported errors, that the protocol (basis set, dispersion correction, reference values) is stated, and that claimed improvements are not an artefact of refitting to the test set.