Whether a racemic mixture of a chiral molecule will crystallize as a racemic compound, spontaneously resolve into enantiopure (conglomerate) crystals, or fail to crystallize at all cannot currently be predicted from molecular structure and crystallization conditions. Two-dimensional coarse-grained simulations showed that thermodynamic polymorph-landscape statistics — above all the number of low-energy competing polymorphs, which heterogeneous intermolecular interactions reduce — largely determine crystallization propensity and favor spontaneous resolution, and that the oligomeric clusters present in solution carry kinetic information about which crystal ultimately forms. What remains missing is the quantitative, predictive account of nucleation kinetics that this thermodynamic-landscape evidence does not supply: a theory that computes nucleation barriers and rates for the competing solid forms (racemic compound versus conglomerate versus amorphous) across supersaturation regimes, explains the kinetic advantage of enantiopure pre-nucleation aggregates, and demonstrably transfers from two-dimensional lattice models to three-dimensional, flexible, solvent-explicit molecular systems. The problem is open: follow-up work by the same group (2021, 2024) extended kinetic-outcome prediction within 2D coarse-grained models, but no rate theory or 3D solvent-explicit validation exists, and 2023–2025 reviews still list prediction of crystallization outcomes among the field's central open challenges.

Background

Chiral molecules exist as two mirror-image forms, or enantiomers, and a 50:50 mixture of them is called a racemate. When such a mixture crystallizes, most compounds pack both enantiomers into a single 'racemic compound' crystal, but a minority instead undergoes spontaneous resolution: the solution separates into a mechanical mixture of enantiomerically pure ('homochiral') crystals, called a conglomerate — the phenomenon with which Pasteur discovered molecular chirality. Because enantiomerically pure solids are central to pharmaceutical and fine-chemical manufacture, predicting whether a given chiral molecule will form a racemic compound or a conglomerate — or merely an amorphous solid — is a long-standing goal, made harder by polymorphism, the ability of a molecule to form multiple crystal structures (polymorphs) of similar energy.

Crystal structure prediction (CSP) methods enumerate possible crystal packings and rank them by lattice free energy, but they address thermodynamics only: they predict which structure is most stable, not which structure nucleates, how fast, or whether nucleation happens at all under given conditions of supersaturation, temperature, and composition. Classical nucleation theory (CNT) describes nucleation as a balance between a bulk free-energy gain and an interfacial penalty, but it does not discriminate among competing polymorphs on the basis of molecular structure. Which regime — thermodynamic or kinetic control — decides the outcome depends on the system and the conditions.

Carpenter and Grünwald (JACS 2020) attacked this question with molecular dynamics simulations of a family of two-dimensional, coarse-grained models of chiral molecules: rigid assemblies of circular 'functional-group' particles carrying short-ranged, direction-specific interactions, arranged on a hexagonal lattice, with no explicit solvent. Using an exact-cover enumeration algorithm (POLYNUM) they generated 10510^5–10710^7 candidate polymorphs per model (unit cells up to 14 molecules and 4 vacant sites) and found that crystallization propensity is largely governed by N0.95N_{0.95}, the number of competing polymorphs with low free energy (a 95%-threshold landscape statistic defined in the source study). Strongly heterogeneous interactions — interaction 'vectors' in which some functional-group contacts are much stronger than others, formalized in a geometric contact-vector model Ep=−ε⋅cpE_p=-\varepsilon\cdot c_p — reduce N0.95N_{0.95}, promote crystallization, and favor spontaneous resolution, rationalizing a range of experimental observations. Such a thermodynamic-landscape analysis leaves several questions unanswered: it supplies no kinetic theory of which polymorph nucleates under given conditions, no analysis in three dimensions with molecular flexibility and explicit solvent, no quantitative mechanism for the kinetic advantage of enantiopure (homochiral) oligomeric aggregates in solution, and its enumeration is truncated at finite unit-cell size, so it can miss low-energy polymorphs with very large unit cells or low packing fractions.

A direct follow-up (Carpenter and Grünwald, JACS 2021) showed in the same 2D model family that at high supersaturation the crystal that forms can be predicted from the similarity between oligomeric species in solution (pre-nucleation clusters — small, transient aggregates that precede crystal nucleation) and molecular motifs in the crystal; for racemic mixtures, kinetic information alone sufficed to predict whether spontaneous resolution occurs. A later study of cocrystallization (Pimonova, Carpenter and Grünwald, JACS 2024) found that even when a thermodynamically stable cocrystal exists, most simulated coformer systems do not cocrystallize — kinetic factors are decisive. These results sharpen, but do not close, the source question: the predictive descriptors remain two-dimensional, coarse-grained, solvent-free, and largely confined to the high-supersaturation regime, and they do not constitute a nucleation rate theory. Meanwhile the thermodynamic side has advanced independently — CSP-based assessments of conglomerate-forming potential and curated databases of known conglomerate formers — and recent reviews still list the prediction of which polymorph appears, and at what rate, among the central open problems of crystallization science.

Problem Statement

Given a chiral molecule (or a family of chiral molecules) and crystallization conditions (supersaturation, composition, temperature), predict quantitatively the crystallization outcome of a racemic or enantiopure solution: which solid form appears — a racemic compound, an enantiopure (conglomerate) crystal, or an amorphous solid — and with what nucleation barriers and rates. This statement treats the open problem as one integrated objective with three components, all three of which are required: (i) a kinetic theory of polymorph selection that combines thermodynamic landscape statistics (such as N0.95N_{0.95}, the number of competing low-energy polymorphs) with nucleation kinetics, valid across supersaturation regimes including the crossover between thermodynamic and kinetic control, rather than a descriptive correlation or a descriptor validated only at high supersaturation; (ii) a mechanistic, quantitative account of the kinetic advantage of enantiopure solution oligomers (pre-nucleation clusters) — nucleation free-energy barriers, attachment/detachment rates, and the way solution oligomer distributions determine which polymorph nucleates; and (iii) validation of these predictions beyond two-dimensional coarse-grained lattice models, in three-dimensional, flexible, solvent-explicit molecular systems (comparison with experimental chiral compounds is a long-term target, not a completion requirement). A submission completes the objective when it supplies all three components: both supersaturation regimes and their crossover for (i); the named nucleation free-energy barriers, attachment/detachment rates, and oligomer-distribution link for (ii); and a demonstration in at least one three-dimensional, flexible, solvent-explicit molecular system for (iii).

References

  1. John E. Carpenter and Michael Grünwald, 'Heterogeneous Interactions Promote Crystallization and Spontaneous Resolution of Chiral Molecules', Journal of the American Chemical Society 142, 10755–10768 (2020). DOI: 10.1021/jacs.0c02097. https://doi.org/10.1021/jacs.0c02097 (source paper)
  2. John E. Carpenter and Michael Grünwald, 'Pre-Nucleation Clusters Predict Crystal Structures in Models of Chiral Molecules', Journal of the American Chemical Society 143, 21580–21593 (2021). DOI: 10.1021/jacs.1c09321. https://doi.org/10.1021/jacs.1c09321
  3. Yulia Pimonova, John E. Carpenter, and Michael Grünwald, 'Thermodynamic Stability Is a Poor Indicator of Cocrystallization in Models of Organic Molecules', Journal of the American Chemical Society 146, 2805–2815 (2024). DOI: 10.1021/jacs.3c13030. https://doi.org/10.1021/jacs.3c13030
  4. Aurora J. Cruz-Cabeza, Neil Feeder, and Roger J. Davey, 'Open questions in organic crystal polymorphism', Communications Chemistry 3, 142 (2020). DOI: 10.1038/s42004-020-00388-9. https://doi.org/10.1038/s42004-020-00388-9
  5. Caroline Desgranges and Jerome Delhommelle, 'Deciphering the complexities of crystalline state(s) with molecular simulations', Communications Chemistry 8, 281 (2025). DOI: 10.1038/s42004-025-01667-z. https://doi.org/10.1038/s42004-025-01667-z
  6. Yue Gui, Chengbin Huang, Chenyang Shi, Torsten Stelzer, Geoff G. Z. Zhang, and Lian Yu, 'Polymorphic selectivity in crystal nucleation', The Journal of Chemical Physics 156, 144504 (2022). DOI: 10.1063/5.0086308. https://doi.org/10.1063/5.0086308
  7. Mark P. Walsh, James A. Barclay, Callum S. Begg, Jinyi Xuan, Natalie T. Johnson, Jason C. Cole, and Matthew O. Kitching, 'Identifying a Hidden Conglomerate Chiral Pool in the CSD', JACS Au 2, 2235–2250 (2022). DOI: 10.1021/jacsau.2c00394. https://doi.org/10.1021/jacsau.2c00394
  8. Kennedy A. Borchardt-Setter and Lian Yu, 'Assessing the Potential for Chiral Separation by Crystallization Using Crystal Energies', Crystal Growth & Design 23, 3615–3622 (2023). DOI: 10.1021/acs.cgd.3c00077. https://doi.org/10.1021/acs.cgd.3c00077
  9. Gregory J. O. Beran, 'Frontiers of molecular crystal structure prediction for pharmaceuticals and functional organic materials', Chemical Science 14, 13290–13312 (2023). DOI: 10.1039/d3sc03903j. https://doi.org/10.1039/d3sc03903j
  10. Aaron R. Finney and Matteo Salvalaglio, 'Molecular simulation approaches to study crystal nucleation from solutions: Theoretical considerations and computational challenges', WIREs Computational Molecular Science 14, e1697 (2023). DOI: 10.1002/wcms.1697. https://doi.org/10.1002/wcms.1697
  11. Matthew D. Gourlay, John Kendrick, and Frank J. J. Leusen, 'Predicting the Spontaneous Chiral Resolution by Crystallization of a Pair of Flexible Nitroxide Radicals', Crystal Growth & Design 8, 2899–2905 (2008). DOI: 10.1021/cg701256e. https://doi.org/10.1021/cg701256e
  12. Rokas Elijošius, Emma King-Smith, Felix A. Faber, Louise Bernier, Simon Berritt, William P. Farrell, Xinjun Hou, Jacquelyn L. Klug-McLeod, Jason Mustakis, Neal W. Sach, Qingyi Yang, Roger M. Howard, and Alpha A. Lee, 'Predictive design of crystallographic chiral separation', Nature Communications 16, 7977 (2025). DOI: 10.1038/s41467-025-62825-4. https://doi.org/10.1038/s41467-025-62825-4