Chemical accuracy for open-shell transition-metal complexes at polynomial cost without a hand-chosen active space
Difficulty 66: no black-box polynomial method reaches 1 kcal/mol for open-shell 3d clusters, and exponential scaling of the exact limit means a new idea is probably needed; comparable to the surface-code problem (56) but without a clear engineering path. Application value 68: catalyst, enzyme and magnet design depend on it. Leverage 66: it gates trustworthy ground truth for open-shell chemistry used to check DFT and ML models.
The problem
No cheap, black-box method yet gets energies of open-shell metal complexes right to 1 kcal/mol.
- 1Metals have near-tied electron states
- 2Cheap methods pick wrong winner
- 3Careful methods need expert input
- 4Cost explodes with size
- 5Goal: black-box 1 kcal/mol at polynomial cost
Task. Find a method with polynomial cost, size-extensivity and a built-in reliability indicator that gives errors of at most about 1 kcal/mol (never beyond 2) for spin-state splittings, bond energies and reaction energies of 3d transition-metal complexes and clusters with 50-200 atoms, without a user-chosen active space.
Built from
earlier problems → this oneThe problems this one is built from: progress or tools it needs (builds on), special cases that come first (generalizes), and weaker results on the way (implies). On the right, what builds on it.
- Start with
- Neural-network wavefunctions at chemical accuracy for 100+ electron molecules with transferable, amortised trainingComputational Chemistry · D54
- Step 2
- Step 3
- A transferable exchange–correlation functional free of delocalization and self-interaction errorComputational Chemistry · D72
- Step 4
- Chemical accuracy for open-shell transition-metal complexes at polynomial cost without a hand-chosen active spaceThis problem
- Then
- The electronic ground state and low-lying spectrum of the nitrogenase FeMo-cofactor in its protein environmentComputational Chemistry · D70
Path to understanding
foundations → problemThe research entries this problem rests on, in the order to read them. Each links to its explainer.
- Start with
- Step 2
- Step 3
- Strong correlation: multireference methods, DMRG and selected CIAlgorithm · host
- Then
- Chemical accuracy for open-shell transition-metal complexes at polynomial cost without a hand-chosen active spaceThe problem
State of the art
- Benchmarks. On experiment-derived spin-state energetics for first-row transition-metal complexes (the SSE17 set and its relatives, assembled by Radoń and co-workers), single-reference CCSD(T) is reported to be the most accurate of the widely tested methods, ahead of CASPT2, NEVPT2 and the best double-hybrid functionals; the published mean absolute errors are small but are not quoted here, since they were not re-checked against the primary tables for this entry. CCSD(T) requires a reasonable single-reference description, which fails for strongly correlated multi-metal clusters.
- Multireference. CASSCF/CASPT2 and NEVPT2 depend on active-space choices; DMRG and selected-CI methods handle CAS sizes of 30–100 orbitals but do not recover dynamic correlation cheaply (Chan and Sharma 2011). Automated active-space selection (AVAS, entropy-based DMRG selection) reduces but does not remove human choice.
- Alternatives. Auxiliary-field QMC with multideterminant trials, DMC with large trial expansions, and multireference coupled-cluster variants (Mk-MRCC, tailored CC) reach near-chemical accuracy on selected problems but are not black-box or low-scaling. Neural-network VMC has been applied to small transition-metal molecules.
- Gap. No method known to the authors of this entry combines polynomial cost, black-box use and 1 kcal/mol accuracy across open-shell 3d clusters; the Fe–S cluster and nitrogenase literature shows the failure case (many spin states within a few kcal/mol).
Realistic applications
Design of catalysts for nitrogen fixation, C–H activation and water oxidation, enzymes with metal centres, magnets and spin-crossover materials, and photoredox and battery chemistries all hinge on transition-metal energetics; reliable low-cost predictions would replace trial-and-error functional selection.
What counts as solved
A published method with code and documented scaling that achieves a mean absolute error at or below 1 kcal/mol and maximum error under 2 kcal/mol across a blind benchmark of at least 50 transition-metal species spanning spin states, ligand fields and nuclearities, without per-system active-space input, verified by an independent group.
How it gets verified
ReproductionA training run, experiment or computation rerun by someone else.
A published method with code and documented scaling must reach a mean absolute error of 1 kcal/mol or less (maximum under 2) on a blind benchmark of at least 50 transition-metal species spanning spin states, ligand fields and nuclearities, with no per-system active-space input, verified by an independent group. The benchmark and reference values are fixed before the method is run.
Claims under verification
+ add a claimNo claimed results on the Verification board for this problem yet.
Where the work is
The main missing piece is a method with controlled dynamic and static correlation; compute and benchmark data follow.
Bottlenecks
ranked by votes- #1TheoryStatic plus dynamic correlation at polynomial cost
Exact treatment of near-degenerate shells scales exponentially, and perturbative or local corrections lose accuracy when many states lie within kcal/mol.
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Connected problems
Progress
- Sep 27, 2018Electronic complexity of FeMocosource
Li et al. show the FeMoco model has many near-degenerate low-lying states and that the energy landscape is classically hard to converge (arXiv date).
- Aug 1, 2016Heat-bath CIsource
Selected CI approaches approximate FCI for CAS sizes beyond exact diagonalisation (date given as year/month).
- Jan 1, 2011DMRG in quantum chemistrysource
DMRG reviewed as a method for large active spaces (date given as the year of publication).
- Jan 1, 1980CASSCFsource
Complete-active-space SCF becomes the standard multireference method (date given as the year of publication).