Crystallization-induced deracemization converts a racemic suspension of a conglomerate-forming chiral compound into a single enantiomer with, in principle, 100% yield, either by continuous attrition (Viedma ripening) or by temperature cycling, in both cases driven by solution-phase racemization. When the process is run unseeded, however, the product enantiomer is selected stochastically: replicate runs under identical achiral conditions give either enantiomer with approximately 1:1 probability, and the operative pathway and its duration depend on the early nucleation stage. Deterministic selection has so far been achieved only by seeding with product-enantiomer crystals or via chiral influences (additives, circularly polarized light, isotopic substitution, process-step ordering) that were developed and validated for individual compound families, with bias-direction rules that can even invert between substrates. The open problem is to turn this stochastic symmetry breaking into a predictable, controllable outcome in a way that generalizes across compound classes without product-enantiomer seeding: a general design framework for a chiral influence whose direction and magnitude are predictable a priori for a new substrate. A related but separate open direction is a validated quantitative theory linking early-stage nucleation statistics to the final outcome, the deracemization pathway, and the time to enantiopurity. As of 2026 this remains unsolved; unbiased runs are still reported as unpredictable in the primary literature.

Background

A chiral molecule exists as two enantiomers, non-superimposable mirror images that a racemic mixture (racemate) contains in equal amounts. The degree of enantioenrichment is measured as the enantiomeric excess, ee=∣R−S∣/(R+S)\mathrm{ee}=|R-S|/(R+S) expressed as a percentage. Only a minority of chiral compounds (roughly 5-10%) crystallize as a conglomerate, a physical mixture of separate enantiopure crystals; the majority form racemic compounds in which each crystal contains both enantiomers. Solid-state deracemization by Viedma ripening (also called attrition-enhanced deracemization) applies to conglomerates: a racemic crystal slurry is ground continuously with beads in contact with a solution in which the enantiomers interconvert (racemization, usually base-catalyzed). Attrition produces small fragments whose higher solubility (the Gibbs-Thomson effect underlying Ostwald ripening, the growth of large crystals at the expense of small ones) drives dissolution-regrowth cycles; combined with racemization this makes the solid-phase enantiomeric excess grow autocatalytically, in the classic experiments exponentially, until the solid is enantiopure. The effect was discovered for sodium chlorate (an achiral molecule whose crystals are individually chiral) by Viedma in 2005. Temperature-cycling-induced deracemization (TCID) replaces grinding with programmed heating/cooling cycles: each heating step partially dissolves the solid (preferentially smaller crystals), each cooling step regrows material on the surviving crystals, and racemization in solution recycles the minority enantiomer, giving the same amplification under gentler, more scalable conditions. When deracemization is coupled to an asymmetric synthesis from achiral precursors and the chirality of the product arises without any chiral input, the overall transformation is called absolute asymmetric synthesis. Two facts define the control problem. First, in the absence of a deliberate chiral bias the amplified enantiomer is stochastic: unseeded replicate runs give either handedness with approximately 1:1 frequency (for N-succinopyridine obtained by absolute asymmetric synthesis, ten unseeded runs gave a 6:4 split; flavanone derivatives gave 5:5, 4:6 and 6:4 over ten runs each; anhydrous cytosine gave 5:5 over ten runs). This follows from symmetry: any protocol whose dynamics are invariant under mirror reflection must produce each enantiomer with equal probability, so deterministic selection of a specified enantiomer necessarily requires some chiral influence. Second, the early nucleation stage decides the pathway and its timescale: Steendam and co-workers (2015) showed that if supersaturation builds slowly enough that only one enantiomer nucleates, the system undergoes total spontaneous resolution directly to a single-chirality solid, whereas if both enantiomers precipitate, enantiopurity is restored only through the slower Viedma-ripening route, which they described as a safety catch. Deterministic selection has been demonstrated with product-enantiomer seeding, and, without seeding, with compound-specific chiral influences: circularly polarized light (chiral by virtue of photon spin) biasing one imine-form amino-acid derivative; tailor-made chiral additives on ethylenediammonium sulfate following a substrate-specific rule of reversal (the additive biases the product toward the opposite absolute configuration); catalytic amounts of chiral amino acids tilting p-anisoin toward the same configuration as the additive (with exceptions such as cysteine, serine and threonine); enantiopure family-member additives; isotopically substituted substrates; and the order in which process steps are executed. These rules do not transfer between systems and can invert, and the outcome is fragile: a solid-phase enantiomeric excess as small as about 0.2%, below the roughly 0.5% detection limit of routine chiral HPLC (high-performance liquid chromatography on a chiral stationary phase), can override an intentional additive bias; in temperature-cycled runs the outcome can be fixed by undetectable asymmetries in the seed-batch history, and an additive deliberately added to sodium chlorate TCID failed to select the final chirality at all when runs started from exactly zero enantiomeric excess. Mechanistically, the outcome of a single-vessel run is governed by the stochastic transient emergence of a crystal-size asymmetry between the two mirror-image crystal populations (the enantiomorphs, i.e., the crystals of one handedness), which the grinding or cycling then amplifies. Population-balance models (rate equations tracking the full crystal-size distribution of each enantiomorph population) and stochastic models reproduce the amplification kinetics, the effect of initial conditions, and the exact thermodynamic condition under which solid-state deracemization proceeds, but they do not predict the sign of the outcome from unbiased initial conditions, and the statistics of primary nucleation (the spontaneous formation of new crystals from solution, as opposed to growth on existing crystal surfaces), which fix pathway and duration, were still being measured and incorporated into models in 2025-2026.

Problem Statement

For a conglomerate-forming chiral compound undergoing unseeded solid-state deracemization, driven either by attrition (Viedma ripening) or by temperature cycling (TCID) with solution-phase racemization and with no seed crystals of the product enantiomer added, make the product enantiomer a predictable and controllable outcome in a way that generalizes across compound classes: establish a general design framework and transferable rules for a chiral influence (for example a chiral additive, an isotopic or optical bias, or a process-protocol asymmetry) that, for a new substrate, predict a priori, from the substrate's own properties and before its outcome is measured, the sign of the final enantiomeric excess and its magnitude, so that a specified product enantiomer is obtained deterministically without product-enantiomer seeding. The deliverable is the framework and its transferable rules themselves, stated generally enough to be applied without refitting to a new conglomerate-forming compound, and it must correctly predict the a priori sign and magnitude for at least two conglomerate-forming compounds belonging to different compound families and not used to construct the rules, with each prediction checked against the compound's measured outcome. Here “magnitude of effect” denotes both the final solid-phase enantiomeric excess reached and, for any protocol that does not yield the same enantiomer in every run, the probability that the specified enantiomer is obtained. Because any protocol whose dynamics are invariant under mirror reflection must produce each enantiomer with equal probability, answers must necessarily incorporate some chiral influence; what is required is that it be general and predictable rather than substrate-specific and empirical. Determination of the outcome by run-to-run chance, or control demonstrated only for a single substrate family, only by seeding with the product enantiomer, or only by rules that merely reproduce the outcome of the substrate used to construct them, does not answer the question.

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