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Recent years have seen revived interest in computer-assisted organic synthesis 1,2 . The use of reaction- and neural-network algorithms that can plan multistep synthetic pathways have revolutionized this field 1,3-7 , including examples leading to advanced natural products 6,7 . Such methods typically operate on full, literature-derived 'substrate(s)-to-product' reaction rules and cannot be easily extended to the analysis of reaction mechanisms. Here we show that computers equipped with a comprehensive knowledge-base of mechanistic steps augmented by physical-organic chemistry rules, as well as quantum mechanical and kinetic calculations, can use a reaction-network approach to analyse the mechanisms of some of the most complex organic transformations: namely, cationic rearrangements. Such rearrangements are a cornerstone of organic chemistry textbooks and entail notable changes in the molecule's carbon skeleton 8-12 . The algorithm we describe and deploy at https://HopCat.allchemy.net/ generates, within minutes, networks of possible mechanistic steps, traces plausible step sequences and calculates expected product distributions. We validate this algorithm by three sets of experiments whose analysis would probably prove challenging even to highly trained chemists: (1) predicting the outcomes of tail-to-head terpene (THT) cyclizations in which substantially different outcomes are encoded in modular precursors differing in minute structural details; (2) comparing the outcome of THT cyclizations in solution or in a supramolecular capsule; and (3) analysing complex reaction mixtures. Our results support a vision in which computers no longer just manipulate known reaction types 1-7 but will help rationalize and discover new, mechanistically complex transformations., (© 2023. The Author(s), under exclusive licence to Springer Nature Limited.)

In everyday life, rolling motion is typically associated with cylindrical (for example, car wheels) or spherical (for example, billiard balls) bodies tracing linear paths. However, mathematicians have, for decades, been interested in more exotically shaped solids such as the famous oloids 1 , sphericons 2 , polycons 3 , platonicons 4 and two-circle rollers 5 that roll downhill in curvilinear paths (in contrast to cylinders or spheres) yet indefinitely (in contrast to cones, Supplementary Video 1). The trajectories traced by such bodies have been studied in detail 6-9 , and can be useful in the context of efficient mixing 10,11 and robotics, for example, in magnetically actuated, millimetre-sized sphericon-shaped robots 12,13 , or larger sphericon- and oloid-shaped robots translocating by shifting their centre of mass 14,15 . However, the rolling paths of these shapes are all sinusoid-like and their diversity ends there. Accordingly, we were intrigued whether a more general problem is solvable: given an infinite periodic trajectory, find the shape that would trace this trajectory when rolling down a slope. Here, we develop an algorithm to design such bodies-which we call 'trajectoids'-and then validate these designs experimentally by three-dimensionally printing the computed shapes and tracking their rolling paths, including those that close onto themselves such that the body's centre of mass moves intermittently uphill (Supplementary Video 2). Our study is motivated largely by fundamental curiosity, but the existence of trajectoids for most paths has unexpected implications for quantum and classical optics, as the dynamics of qubits, spins and light polarization can be exactly mapped to trajectoids and their paths 16 ., (© 2023. The Author(s), under exclusive licence to Springer Nature Limited.)

As the chemical industry continues to produce considerable quantities of waste chemicals 1,2 , it is essential to devise 'circular chemistry' 3-8 schemes to productively back-convert at least a portion of these unwanted materials into useful products. Despite substantial progress in the degradation of some classes of harmful chemicals 9 , work on 'closing the circle'-transforming waste substrates into valuable products-remains fragmented and focused on well known areas 10-15 . Comprehensive analyses of which valuable products are synthesizable from diverse chemical wastes are difficult because even small sets of waste substrates can, within few steps, generate millions of putative products, each synthesizable by multiple routes forming densely connected networks. Tracing all such syntheses and selecting those that also meet criteria of process and 'green' chemistries is, arguably, beyond the cognition of human chemists. Here we show how computers equipped with broad synthetic knowledge can help address this challenge. Using the forward-synthesis Allchemy platform 16 , we generate giant synthetic networks emanating from approximately 200 waste chemicals recycled on commercial scales, retrieve from these networks tens of thousands of routes leading to approximately 300 important drugs and agrochemicals, and algorithmically rank these syntheses according to the accepted metrics of sustainable chemistry 17-19 . Several of these routes we validate by experiment, including an industrially realistic demonstration on a 'pharmacy on demand' flow-chemistry platform 20 . Wide adoption of computerized waste-to-valuable algorithms can accelerate productive reuse of chemicals that would otherwise incur storage or disposal costs, or even pose environmental hazards., (© 2022. The Author(s), under exclusive licence to Springer Nature Limited.)

Training algorithms to computationally plan multistep organic syntheses has been a challenge for more than 50 years 1-7 . However, the field has progressed greatly since the development of early programs such as LHASA 1,7 , for which reaction choices at each step were made by human operators. Multiple software platforms 6,8-14 are now capable of completely autonomous planning. But these programs 'think' only one step at a time and have so far been limited to relatively simple targets, the syntheses of which could arguably be designed by human chemists within minutes, without the help of a computer. Furthermore, no algorithm has yet been able to design plausible routes to complex natural products, for which much more far-sighted, multistep planning is necessary 15,16 and closely related literature precedents cannot be relied on. Here we demonstrate that such computational synthesis planning is possible, provided that the program's knowledge of organic chemistry and data-based artificial intelligence routines are augmented with causal relationships 17,18 , allowing it to 'strategize' over multiple synthetic steps. Using a Turing-like test administered to synthesis experts, we show that the routes designed by such a program are largely indistinguishable from those designed by humans. We also successfully validated three computer-designed syntheses of natural products in the laboratory. Taken together, these results indicate that expert-level automated synthetic planning is feasible, pending continued improvements to the reaction knowledge base and further code optimization.

Recent years have witnessed increased interest in systems that are capable of supporting multistep chemical processes without the need for manual handling of intermediates. These systems have been based either on collections of batch reactors 1 or on flow-chemistry designs 2-4 , both of which require considerable engineering effort to set up and control. Here we develop an out-of-equilibrium system in which different reaction zones self-organize into a geometry that can dictate the progress of an entire process sequence. Multiple (routinely around 10, and in some cases more than 20) immiscible or pairwise-immiscible liquids of different densities are placed into a rotating container, in which they experience a centrifugal force that dominates over surface tension. As a result, the liquids organize into concentric layers, with thicknesses as low as 150 micrometres and theoretically reaching tens of micrometres. The layers are robust, yet can be internally mixed by accelerating or decelerating the rotation, and each layer can be individually addressed, enabling the addition, sampling or even withdrawal of entire layers during rotation. These features are combined in proof-of-concept experiments that demonstrate, for example, multistep syntheses of small molecules of medicinal interest, simultaneous acid-base extractions, and selective separations from complex mixtures mediated by chemical shuttles. We propose that 'wall-less' concentric liquid reactors could become a useful addition to the toolbox of process chemistry at small to medium scales and, in a broader context, illustrate the advantages of transplanting material and/or chemical systems from traditional, static settings into a rotating frame of reference.

The ability to grow properly sized and good quality crystals is one of the cornerstones of single-crystal diffraction, is advantageous in many industrial-scale chemical processes 1-3 , and is important for obtaining institutional approvals of new drugs for which high-quality crystallographic data are required 4-7 . Typically, single crystals suitable for such processes and analyses are grown for hours to days during which any mechanical disturbances-believed to be detrimental to the process-are carefully avoided. In particular, stirring and shear flows are known to cause secondary nucleation, which decreases the final size of the crystals (though shear can also increase their quantity 8-14 ). Here we demonstrate that in the presence of polymers (preferably, polyionic liquids), crystals of various types grow in common solvents, at constant temperature, much bigger and much faster when stirred, rather than kept still. This conclusion is based on the study of approximately 20 diverse organic molecules, inorganic salts, metal-organic complexes, and even some proteins. On typical timescales of a few to tens of minutes, these molecules grow into regularly faceted crystals that are always larger (with longest linear dimension about 16 times larger) than those obtained in control experiments of the same duration but without stirring or without polymers. We attribute this enhancement to two synergistic effects. First, under shear, the polymers and their aggregates disentangle, compete for solvent molecules and thus effectively 'salt out' (that is, induce precipitation by decreasing solubility of) the crystallizing species. Second, the local shear rate is dependent on particle size, ultimately promoting the growth of larger crystals (but not via surface-energy effects as in classical Ostwald ripening). This closed-system, constant-temperature crystallization driven by shear could be a valuable addition to the repertoire of crystal growth techniques, enabling accelerated growth of crystals required by the materials and pharmaceutical industries.

Although 'active' surfactants, which are responsive to individual external stimuli such as temperature, electric or magnetic fields, light, redox processes or chemical agents, are well known, it would be interesting to combine several of these properties within one surfactant species. Such multi-responsive surfactants could provide ways of manipulating individual droplets and possibly assembling them into larger systems of dynamic reactors. Here we describe surfactants based on functionalized nanoparticle dimers that combine all of these and several other characteristics. These surfactants and therefore the droplets that they cover are simultaneously addressable by magnetic, optical and electric fields. As a result, the surfactant-covered droplets can be assembled into various hierarchical structures, including dynamic ones, in which light powers the rapid rotation of the droplets. Such rotating droplets can transfer mechanical torques to their non-nearest neighbours, thus acting like systems of mechanical gears. Furthermore, droplets of different types can be merged by applying electric fields and, owing to interfacial jamming, can form complex, non-spherical, 'patchy' structures with different surface regions covered with different surfactants. In systems of droplets that carry different chemicals, combinations of multiple stimuli can be used to control the orientations of the droplets, inter-droplet transport, mixing of contents and, ultimately, sequences of chemical reactions. Overall, the multi-responsive active surfactants that we describe provide an unprecedented level of flexibility with which liquid droplets can be manipulated, assembled and reacted.

Interest in assemblies of colloidal particles has long been motivated by their applications in photonics, electronics, sensors and microlenses. Existing assembly schemes can position colloids of one type relatively flexibly into a range of desired structures, but it remains challenging to produce multicomponent lattices, clusters with precisely controlled symmetries and three-dimensional assemblies. A few schemes can efficiently produce complex colloidal structures, but they require system-specific procedures. Here we show that magnetic field microgradients established in a paramagnetic fluid can serve as 'virtual moulds' to act as templates for the assembly of large numbers (∼10(8)) of both non-magnetic and magnetic colloidal particles with micrometre precision and typical yields of 80 to 90 per cent. We illustrate the versatility of this approach by producing single-component and multicomponent colloidal arrays, complex three-dimensional structures and a variety of colloidal molecules from polymeric particles, silica particles and live bacteria and by showing that all of these structures can be made permanent. In addition, although our magnetic moulds currently resemble optical traps in that they are limited to the manipulation of micrometre-sized objects, they are massively parallel and can manipulate non-magnetic and magnetic objects simultaneously in two and three dimensions.

In traditional photoconductors, the impinging light generates mobile charge carriers in the valence and/or conduction bands, causing the material's conductivity to increase. Such positive photoconductance is observed in both bulk and nanostructured photoconductors. Here we describe a class of nanoparticle-based materials whose conductivity can either increase or decrease on irradiation with visible light of wavelengths close to the particles' surface plasmon resonance. The remarkable feature of these plasmonic materials is that the sign of the conductivity change and the nature of the electron transport between the nanoparticles depend on the molecules comprising the self-assembled monolayers (SAMs) stabilizing the nanoparticles. For SAMs made of electrically neutral (polar and non-polar) molecules, conductivity increases on irradiation. If, however, the SAMs contain electrically charged (either negatively or positively) groups, conductivity decreases. The optical and electrical characteristics of these previously undescribed inverse photoconductors can be engineered flexibly by adjusting the material properties of the nanoparticles and of the coating SAMs. In particular, in films comprising mixtures of different nanoparticles or nanoparticles coated with mixed SAMs, the overall photoconductance is a weighted average of the changes induced by the individual components. These and other observations can be rationalized in terms of light-induced creation of mobile charge carriers whose transport through the charged SAMs is inhibited by carrier trapping in transient polaron-like states. The nanoparticle-based photoconductors we describe could have uses in chemical sensors and/or in conjunction with flexible substrates.

Spontaneous pattern formation by self-assembly is of long-standing and continuing interest not only for its aesthetic appeal, but also for its fundamental and technological relevance. So far, the study of self-organization processes has mainly focused on static structures, but dynamic systems--those that develop order only when dissipating energy--are of particular interest for studying complex behaviour. Here we describe the formation of dynamic patterns of millimetre-sized magnetic disks at a liquid-air interface, subject to a magnetic field produced by a rotating permanent magnet. The disks spin around their axes with angular frequency equal to that of the magnet, and are attracted towards its axis of rotation while repelling each other. This repulsive hydrodynamic interaction is due to fluid motion associated with spinning; the interplay between attractive and repulsive interactions leads to the formation of patterns exhibiting various types of ordering, some of which are entirely new. This versatile system should lead to a better understanding of dynamic self-assembly, while providing a test-bed for stability theories of interacting point vortices and vortex patches.