Absolute homogeneous nucleation rates from simulation within an order of magnitude of experiment
Difficulty 62: needs accurate potentials, rare-event sampling free of collective-variable bias and error propagation through an exponential sensitivity at once; no consensus approach. Application value 52: crystallisation control, polymorph selection and cloud ice. Leverage 48: a validated method transfers to other first-order transitions.
The problem
Predicting how fast the first crystal seed appears in a liquid, from simulation alone, is still out of reach.
- 1Seed must form by chance
- 2Rare, so plain runs fail
- 3Biased sampling estimates barrier
- 4Rate depends exponentially on small energies
- 5Need accurate potentials with error bars
Setting. Classical nucleation theory gives a rate with a barrier , where is the crystal–liquid interface free energy, the crystal density and the chemical-potential driving force. Because enters cubed and squared in the denominator, small errors become huge errors in .
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
- Machine-learned interatomic potentials with calibrated, guaranteed error bounds outside the training distributionComputational Chemistry · D60
- 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
- Transferable ML potentials with non-local charge transfer, variable charge/spin states and long-range electrostaticsComputational Chemistry · D52
- Step 5
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
- Free-energy methods and enhanced samplingAlgorithm · host
- Then
- Absolute homogeneous nucleation rates from simulation within an order of magnitude of experimentThe problem
State of the art
- Review of the problem. Sosso et al. (Chem. Rev. 2016) catalogue open questions in simulating nucleation: dependence on force field, collective variables, finite size, and the gap between simulated and measured rates (often many orders of magnitude).
- Ab initio-quality ice nucleation. Piaggi, Weis, Panagiotopoulos, Debenedetti and Car (arXiv:2203.01376, published 2022) computed homogeneous ice nucleation in a DFT-trained machine-learned model of water using enhanced sampling, an important step but for one DFT functional whose water properties (melting point, density) differ from experiment, so absolute comparison with measured rates needs an offset of the supercooling scale.
- Heterogeneous nucleation. Zhou and Piaggi (arXiv:2511.13402) study the molecular mechanism of ice nucleation on feldspar with first-principles-trained models.
- Salts. Zimmermann, Vorselaars, Quigley and Peters (JACS 2015) computed NaCl nucleation rates, critical sizes and attachment kinetics from classical-force-field simulation; rates depend sensitively on the force field and on the solubility it predicts.
- ML for sampling. Zhu et al. (arXiv:2509.04291, 2025 review) survey ML-learned collective variables and sampling methods for rare events, including nucleation, and note lack of rigorous convergence tests.
- Not shown. To this entry's knowledge no study has computed absolute nucleation rates for a standard system with an ab initio-accurate potential and quantified uncertainty from the potential to agree with experiment within an order of magnitude.
Realistic applications
Controlling crystallisation of pharmaceuticals, polymorph selection, atmospheric ice formation in clouds (climate models), cement and mineral scaling, protein crystallisation and metallurgical grain refinement all rely on nucleation rates that current theory cannot predict.
What counts as solved
A peer-reviewed study (reproduced by an independent group) giving absolute or for ice and at least one salt in the stated range, with a documented uncertainty budget including potential error, agreeing with the bulk of experimental measurements to within a factor of 10 and sharing input files.
How it gets verified
ReproductionA training run, experiment or computation rerun by someone else.
A peer-reviewed study, reproduced by an independent group, must give absolute nucleation rates J(T) or J(S) for ice and at least one salt in the stated range, agree with the bulk of experimental measurements within a factor of 10, include an uncertainty budget with the potential error, and share its input files.
Claims under verification
+ add a claimNo claimed results on the Verification board for this problem yet.
Where the work is
Large-scale rare-event sampling with accurate potentials; theory for reaction coordinates and error propagation.
Bottlenecks
ranked by votes- #1TheorySensitivity of ln J to interfacial free energy
Small potential errors in gamma and delta-mu become many orders of magnitude in rate.
Community grades
Sign in to add your own grade.
Connected problems
Progress
- Sep 4, 2025ML and enhanced sampling reviewedsource
Zhu et al. review ML-based enhanced sampling.
- Mar 2, 2022Ab initio-ML ice nucleationsource
Piaggi et al. compute homogeneous ice nucleation in a DFT-trained model of water (arXiv date).
- Jun 14, 2016Nucleation simulation reviewedsource
Sosso et al. summarise the state of simulating nucleation (date approximate).