Assembly theory explains and quantifies selection and evolution.

Scientists have grappled with reconciling biological evolution1,2 with the immutable laws of the Universe defined by physics. These laws underpin life's origin, evolution and the development of human culture and technology, yet they do not predict the emergence of these phenomena. Evolutionary theory explains why some things exist and others do not through the lens of selection. To comprehend how diverse, open-ended forms can emerge from physics without an inherent design blueprint, a new approach to understanding and quantifying selection is necessary3-5. We present assembly theory (AT) as a framework that does not alter the laws of physics, but redefines the concept of an 'object' on which these laws act. AT conceptualizes objects not as point particles, but as entities defined by their possible formation histories. This allows objects to show evidence of selection, within well-defined boundaries of individuals or selected units. We introduce a measure called assembly (A), capturing the degree of causation required to produce a given ensemble of objects. This approach enables us to incorporate novelty generation and selection into the physics of complex objects. It explains how these objects can be characterized through a forward dynamical process considering their assembly. By reimagining the concept of matter within assembly spaces, AT provides a powerful interface between physics and biology. It discloses a new aspect of physics emerging at the chemical scale, whereby history and causal contingency influence what exists.

Digitizing chemical discovery with a Bayesian explorer for interpreting reactivity data.

Interpreting the outcome of chemistry experiments consistently is slow and frequently introduces unwanted hidden bias. This difficulty limits the scale of collectable data and often leads to exclusion of negative results, which severely limits progress in the field. What is needed is a way to standardize the discovery process and accelerate the interpretation of high-dimensional data aided by the expert chemist's intuition. We demonstrate a digital Oracle that interprets chemical reactivity using probability. By carrying out >500 reactions covering a large space and retaining both the positive and negative results, the Oracle was able to rediscover eight historically important reactions including the aldol condensation, Buchwald-Hartwig amination, Heck, Mannich, Sonogashira, Suzuki, Wittig, and Wittig-Horner reactions. This paradigm for decoding reactivity validates and formalizes the expert chemist's experience and intuition, providing a quantitative criterion of discovery scalable to all available experimental data.

Author Correction: Controlling an organic synthesis robot with machine learning to search for new reactivity.

Change history: Owing to the misidentification of compound 22 in the original Letter, changes have been made to Fig. 5, Extended Data Fig. 2 and the main text; see accompanying Amendment.

Algorithm-Driven Robotic Discovery of Polyoxometalate-Scaffolding Metal-Organic Frameworks.

The experimental exploration of the chemical space of crystalline materials, especially metal-organic frameworks (MOFs), requires multiparameter control of a large set of reactions, which is unavoidably time-consuming and labor-intensive when performed manually. To accelerate the rate of material discovery while maintaining high reproducibility, we developed a machine learning algorithm integrated with a robotic synthesis platform for closed-loop exploration of the chemical space for polyoxometalate-scaffolding metal-organic frameworks (POMOFs). The eXtreme Gradient Boosting (XGBoost) model was optimized by using updating data obtained from the uncertainty feedback experiments and a multiclass classification extension based on the POMOF classification from their chemical constitution. The digital signatures for the robotic synthesis of POMOFs were represented by the universal chemical description language (χDL) to precisely record the synthetic steps and enhance the reproducibility. Nine novel POMOFs including one with mixed ligands derived from individual ligands through the imidization reaction of POM amine derivatives with various aldehydes have been discovered with a good repeatability. In addition, chemical space maps were plotted based on the XGBoost models whose F1 scores are above 0.8. Furthermore, the electrochemical properties of the synthesized POMOFs indicate superior electron transfer compared to the molecular POMs and the direct effect of the ratio of Zn, the type of ligands used, and the topology structures in POMOFs for modulating electron transfer abilities.

Publisher Correction: Controlling an organic synthesis robot with machine learning to search for new reactivity.

The chemical structure formatting in Fig. 5 has been corrected online.

Controlling an organic synthesis robot with machine learning to search for new reactivity.

The discovery of chemical reactions is an inherently unpredictable and time-consuming process1. An attractive alternative is to predict reactivity, although relevant approaches, such as computer-aided reaction design, are still in their infancy2. Reaction prediction based on high-level quantum chemical methods is complex3, even for simple molecules. Although machine learning is powerful for data analysis4,5, its applications in chemistry are still being developed6. Inspired by strategies based on chemists' intuition7, we propose that a reaction system controlled by a machine learning algorithm may be able to explore the space of chemical reactions quickly, especially if trained by an expert8. Here we present an organic synthesis robot that can perform chemical reactions and analysis faster than they can be performed manually, as well as predict the reactivity of possible reagent combinations after conducting a small number of experiments, thus effectively navigating chemical reaction space. By using machine learning for decision making, enabled by binary encoding of the chemical inputs, the reactions can be assessed in real time using nuclear magnetic resonance and infrared spectroscopy. The machine learning system was able to predict the reactivity of about 1,000 reaction combinations with accuracy greater than 80 per cent after considering the outcomes of slightly over 10 per cent of the dataset. This approach was also used to calculate the reactivity of published datasets. Further, by using real-time data from our robot, these predictions were followed up manually by a chemist, leading to the discovery of four reactions.

Reaction Kinetics using a Chemputable Framework for Data Collection and Analysis.

Automated chemistry platforms have been widely explored, but many focus on fixed tasks for chemical synthesis or analysis. However, a typical synthetic chemistry workflow utilizes both, such as kinetic measurements for reaction development and optimization. Due to their repetitive and time-consuming nature, kinetic measurements are often omitted, which limits the mechanistic investigation of reactions. Herein, we present a "Chemputer" platform with on-line analytics (UV/Vis, NMR) which automates routine kinetic measurements. The system's capabilities are showcased by exploring an inverse electron-demand Diels-Alder using initial rate measurements, a metal complexation using variable time normalization analysis (VTNA), and formation of a series of tosylamide derivatives using Hammett analysis. Over 60 individual experiments are presented which required minimal intervention, highlighting the significant time savings of automation. Owing to the modular design of the platform, which facilitates rapid integration of commercial analytical tools, our approach is widely accessible and adjustable to the reaction under investigation. The platform is operated using the chemical programming language, XDL, hence experimental procedures and results are stored in a precise, computer-readable format. We propose that widespread adoption of this reporting protocol in the chemical community could build a database of validated kinetic data beneficial for Machine Learning.

Automated Library Generation and Serendipity Quantification Enables Diverse Discovery in Coordination Chemistry.

Library generation experiments are a key part of the discovery of new materials, methods, and models in chemistry, but the question of how to generate high quality libraries to enable discovery is nontrivial. Herein, we use coordination chemistry to demonstrate the automation of many of the workflows used for library generation in automated hardware including the Chemputer. First, we explore the target-oriented synthesis of three influential coordination complexes, to validate key synthetic operations in our system; second, the generation of focused libraries in chemical and process space; and third, the development of a new workflow for prospecting library formation. This involved Bayesian optimization using a Gaussian process as surrogate model combined with a metric for novelty (or serendipity) quantification based on mass spectrometry data. In this way, we show directed exploration of a process space toward those areas with rarer observations and build a picture of the diversity in product distributions present across the space. We show that this effectively "engineers" serendipity into our search through the unexpected appearance of acetic anhydride, formed in situ, and solvent degradation products as ligands in an isolable series of three Co(III) anhydride complexes.

Spontaneous formation of autocatalytic sets with self-replicating inorganic metal oxide clusters.

Here we show how a simple inorganic salt can spontaneously form autocatalytic sets of replicating inorganic molecules that work via molecular recognition based on the {PMo12} ≡ [PMo12O40]3- Keggin ion, and {Mo36} ≡ [H3Mo57M6(NO)6O183(H2O)18]22- cluster. These small clusters are able to catalyze their own formation via an autocatalytic network, which subsequently template the assembly of gigantic molybdenum-blue wheel {Mo154} ≡ [Mo154O462H14(H2O)70]14-, {Mo132} ≡ [MoVI72MoV60O372(CH3COO)30(H2O)72]42- ball-shaped species containing 154 and 132 molybdenum atoms, and a {PMo12}⊂{Mo124Ce4} ≡ [H16MoVI100MoV24Ce4O376(H2O)56 (PMoVI10MoV2O40)(C6H12N2O4S2)4]5- nanostructure. Kinetic investigations revealed key traits of autocatalytic systems including molecular recognition and kinetic saturation. A stochastic model confirms the presence of an autocatalytic network involving molecular recognition and assembly processes, where the larger clusters are the only products stabilized by the cycle, isolated due to a critical transition in the network.

Water-soluble Self-assembled {Pd84 }Ac Polyoxopalladate Nano-wheel as a Supramolecular Host.

Polyoxopalladates (POPs) are a class of self-assembling palladium-oxide clusters that span a variety of sizes, shapes and compositions. The largest of this family, {Pd84 }Ac , is constructed from 14 building units of {Pd6 } and lined on the inner and outer torus by 28 acetate ligands. Due to its high water solubility, large hydrophobic cavity and distinct 1 H NMR fingerprint {Pd84 }Ac is an ideal molecule for exploring supramolecular behaviour with small organic molecules in aqueous media. Molecular visualisation studies highlighted potential binding sites between {Pd84 }Ac and these species. Nuclear Magnetic Resonance (NMR) techniques, including 1 H NMR, 1 H Diffusion Ordered Spectroscopy (DOSY) and Nuclear Overhauser Spectroscopy (NOESY), were employed to study the supramolecular chemistry of this system. Here, we provide conclusive evidence that {Pd84 }Ac forms a 1 : 7 host-guest complex with benzyl viologen (BV2+ ) in aqueous solution.

Effective Storage of Electrons in Water by the Formation of Highly Reduced Polyoxometalate Clusters.

Aqueous solutions of polyoxometalates (POMs) have been shown to have potential as high-capacity energy storage materials due to their potential for multi-electron redox processes, yet the mechanism of reduction and practical limits are currently unknown. Herein, we explore the mechanism of multi-electron redox processes that allow the highly reduced POM clusters of the form {MO3}y to absorb y electrons in aqueous solution, focusing mechanistically on the Wells-Dawson structure X6[P2W18O62], which comprises 18 metal centers and can uptake up to 18 electrons reversibly (y = 18) per cluster in aqueous solution when the countercations are lithium. This unconventional redox activity is rationalized by density functional theory, molecular dynamics simulations, UV-vis, electron paramagnetic resonance spectroscopy, and small-angle X-ray scattering spectra. These data point to a new phenomenon showing that cluster protonation and aggregation allow the formation of highly electron-rich meta-stable systems in aqueous solution, which produce H2 when the solution is diluted. Finally, we show that this understanding is transferrable to other salts of [P5W30O110]15- and [P8W48O184]40- anions, which can be charged to 23 and 27 electrons per cluster, respectively.

Digitizing Chemistry Using the Chemical Processing Unit: From Synthesis to Discovery.

The digitization of chemistry is not simply about using machine learning or artificial intelligence systems to process chemical data, or about the development of ever more capable automation hardware; instead, it is the creation of a hard link between an abstracted process ontology of chemistry and bespoke hardware for performing reactions or exploring reactivity. Chemical digitization is therefore about the unambiguous development of an architecture, a chemical state machine, that uses this ontology to connect precise instruction sets to hardware that performs chemical transformations. This approach enables a universal standard for describing chemistry procedures via a chemical programming language and facilitates unambiguous dissemination of these procedures. We predict that this standard will revolutionize the ability of chemists to collaborate, increase reproducibility and safety, as we all as optimize for cost and efficiency. Most importantly, the digitization of chemistry will dramatically reduce the labor needed to make new compounds and broaden accessible chemical space. In recent years, the developments of automation in chemistry have gone beyond flow chemistry alone, with many bespoke workflows being developed not only for automating chemical synthesis but also for materials, nanomaterials, and formulation production. Indeed, the leap from fixed-configuration synthesis machines like peptide, nucleic acid, or dedicated cross-coupling engines is important for developing a truly universal approach to "dial-a-molecule". In this case, a key conceptual leap is the use of a batch system that can encode the chemical reagents, solvent, and products as packets which can be moved around the system, and a graph-based approach for the description of hardware modules that allows the compilation of chemical code that runs on, in principle, any hardware. Further, the integration of sensor systems for monitoring and controlling the state of the chemical synthesis machine, as well as high resolution spectroscopic tools, is vital if these systems are to facilitate closed-loop autonomous experiments. Systems that not only make molecules and materials, but also optimize their function, and use algorithms to assist with the development of new synthetic pathways and process optimization are also possible. Here, we discuss how the digitization of chemistry is happening, building on the plethora of technological developments in hardware and software. Importantly, digital-chemical robot systems need to integrate feedback from simple sensors, e.g., conductivity or temperature, as well as online analytics in order to navigate process space autonomously. This will open the door to accessing known molecules (synthesis), exploring whether known compounds/reactions are possible under new conditions (optimization), and searching chemical space for unknown and unexpected new molecules, reactions, and modes of reactivity (discovery). We will also discuss the role of chemical knowledge and how this can be used to challenge bias, as well as define and expand synthetically accessible chemical space using programmable robotic chemical state machines.

Environmental control programs the emergence of distinct functional ensembles from unconstrained chemical reactions.

Many approaches to the origin of life focus on how the molecules found in biology might be made in the absence of biological processes, from the simplest plausible starting materials. Another approach could be to view the emergence of the chemistry of biology as process whereby the environment effectively directs "primordial soups" toward structure, function, and genetic systems over time. This does not require the molecules found in biology today to be made initially, and leads to the hypothesis that environment can direct chemical soups toward order, and eventually living systems. Herein, we show how unconstrained condensation reactions can be steered by changes in the reaction environment, such as order of reactant addition, and addition of salts or minerals. Using omics techniques to survey the resulting chemical ensembles we demonstrate there are distinct, significant, and reproducible differences between the product mixtures. Furthermore, we observe that these differences in composition have consequences, manifested in clearly different structural and functional properties. We demonstrate that simple variations in environmental parameters lead to differentiation of distinct chemical ensembles from both amino acid mixtures and a primordial soup model. We show that the synthetic complexity emerging from such unconstrained reactions is not as intractable as often suggested, when viewed through a chemically agnostic lens. An open approach to complexity can generate compositional, structural, and functional diversity from fixed sets of simple starting materials, suggesting that differentiation of chemical ensembles can occur in the wider environment without the need for biological machinery.

Formalising the Pathways to Life Using Assembly Spaces.

Assembly theory (referred to in prior works as pathway assembly) has been developed to explore the extrinsic information required to distinguish a given object from a random ensemble. In prior work, we explored the key concepts relating to deconstructing an object into its irreducible parts and then evaluating the minimum number of steps required to rebuild it, allowing for the reuse of constructed sub-objects. We have also explored the application of this approach to molecules, as molecular assembly, and how molecular assembly can be inferred experimentally and used for life detection. In this article, we formalise the core assembly concepts mathematically in terms of assembly spaces and related concepts and determine bounds on the assembly index. We explore examples of constructing assembly spaces for mathematical and physical objects and propose that objects with a high assembly index can be uniquely identified as those that must have been produced using directed biological or technological processes rather than purely random processes, thereby defining a new scale of aliveness. We think this approach is needed to help identify the new physical and chemical laws needed to understand what life is, by quantifying what life does.

Engineering Highly Reduced Molybdenum Polyoxometalates via the Incorporation of d and f Block Metal Ions.

The assembly of nanoscale polyoxometalate (POM) clusters has been dominated by the highly reduced icosahedral {Mo132 } "browns" and the toroidal {Mo154 } "blues" which are 45 % and 18 % reduced, respectively. We hypothesised that there is space for a greater diversity of structures in this immediate reduction zone. Here we show it is possible to make highly reduced mix-valence POMs by presenting new classes of polyoxomolybdates: [MoV 52 MoVI 12 H26 O200 ]42- {Mo64 } and [MoV 40 MoVI 30 H30 O215 ]20- {Mo70 }, 81 % and 57 % reduced, respectively. The {Mo64 } cluster archetype has a super-cube structure and is composed of five different types of building blocks, each arranged in overlayed Archimedean or Platonic polyhedra. The {Mo70 } cluster comprises five tripodal {MoV 6 } and five tetrahedral {MoV 2 MoVI 2 } building blocks alternatively linked to form a loop with a pentagonal star topology. We also show how the reaction yielding the {Mo64 } super-cube can be used in the enrichment of lanthanides which exploit the differences in selectivity in the self-assembly of the polyoxometalates.

Digitizing Chemical Synthesis in 3D Printed Reactionware.

Chemistry digitization requires an unambiguous link between experiments and the code used to generate the experimental conditions and outcomes, yet this process is not standardized, limiting the portability of any chemical code. What is needed is a universal approach to aid this process using a well-defined standard that is composed of syntheses that are employed in modular hardware. Herein we present a new approach to the digitization of organic synthesis that combines process chemistry principles with 3D printed reactionware. This approach outlines the process for transforming unit operations into digitized hardware and well-defined instructions that ensure effective synthesis. To demonstrate this, we outline the process for digitizing 3 MIDA boronate building blocks, an ester hydrolysis, a Wittig olefination, a Suzuki-Miyaura coupling reaction, and synthesis of the drug sulfanilamide.

Robotic Stepwise Synthesis of Hetero-Multinuclear Metal Oxo Clusters as Single-Molecule Magnets.

An efficient stepwise synthesis method for discovering new heteromultinuclear metal clusters using a robotic workflow is developed where numerous reaction conditions for constructing heteromultinuclear metal oxo clusters in polyoxometalates (POMs) were explored using a custom-built automated platform. As a result, new nonanuclear tetrametallic oxo clusters {FeMn4}Lu2A2 in TBA5[(A-α-SiW9O34)2FeMn4O2{Lu(acac)2}2A2] (IIA; A = Ag, Na, K; TBA = tetra-n-butylammonium; acac = acetylacetonate) were discovered by the installation of diamagnetic metal cations A+ into a paramagnetic {FeMn4}Lu2 unit in TBA7[(A-α-SiW9O34)2FeMn4O2{Lu(acac)2}2] (I). POMs IIA exhibited single-molecule magnet properties with the higher energy barriers for magnetization reversal (IIAg, 40.0 K; IINa, 40.3 K; IIK, 26.7 K) compared with that of the parent I (19.7 K). Importantly, these clusters with unique properties were constructed as designed by a step of the predictable sequential multistep reactions with the time-efficient platform.

Facile and Reproducible Electrochemical Synthesis of the Giant Polyoxomolybdates.

Giant polyoxomolybdates are traditionally synthesized by chemical reduction of molybdate in aqueous solutions, generating complex nanostructures such as the highly symmetrical spherical {Mo102} and {Mo132}, ring-shaped {Mo154} and {Mo176}, and the gigantic protein sized {Mo368}, which combines both positive and negative curvature. These complex polyoxometalates are known to be highly sensitive to reaction conditions and are often difficult to reproduce, especially {Mo368}, which is often produced in yields far below 1%, meaning further investigation has always been limited. While the electrochemical properties of these materials have been studied, their electrochemical synthesis has not been explored. Herein, we demonstrate an alternative reliable synthetic method by means of electrochemistry. By using electrochemical synthesis, we have shown the synthesis of various reported polyoxomolybdates, along with some unreported structures with unique features that have yet to be reported by traditional synthetic methods. The six different giant polyoxomolybdates that were obtained via electrochemical synthesis range from the spherical {Mo102-xFex} and {Mo132} to the ring-shaped {Mo148} and {Mo154-x}, as well as the largest known polyoxometalate {Mo368}, with improved yield (up to 26.1% for {Mo368}), increased reproducibility, and shorter crystallization time compared to chemical reduction methods.

Enantioselective Recognition of Racemic Amino Alcohols in Aqueous Solution by Chiral Metal-Oxide Keplerate {Mo132 } Cluster Capsules.

Determining the relative configuration or enantiomeric excess of a substance may be achieved using NMR spectroscopy by employing chiral shift reagents (CSRs). Such reagents interact noncovalently with the chiral solute, resulting in each chiral form experiencing different magnetic anisotropy; this is then reflected in their NMR spectra. The Keplerate polyoxometalate (POM) is a molybdenum-based, water-soluble, discrete inorganic structure with a pore-accessible inner cavity, decorated by differentiable ligands. Through ligand exchange from the self-assembled nanostructure, a set of chiral Keplerate host molecules has been synthesised. By exploiting the interactions of analyte molecules at the surface pores, the relative configuration of chiral amino alcohol guests (phenylalaninol and 2-amino-1-phenylethanol) in aqueous solvent was establish and their enantiomeric excess was determined by 1 H NMR using shifts of ΔΔδ=0.06 ppm. The use of POMs as chiral shift reagents represents an application of a class that is yet to be well established and opens avenues into aqueous host-guest chemistry with self-assembled recognition agents.

Exploring the Geometric Space of Metal-Organic Polyhedrons (MOPs) of Metal-Oxo Clusters.

Metal organic polyhedra (MOPs) such as coordination cages and clusters are increasingly utilized across many fields, but their geometrically selective assembly during synthesis is nontrivial. When ligand coordination along these polyhedral edges is arranged in an unsymmetrical mode or the bridging ligand itself is nonsymmetric, a vast combinatorial space of potential isomers exists complicating formation and isolation. Here we describe two generalizable combinatorial methodologies to explore the geometrical space and enumerate the configurational isomers of MOPs with discrimination of the chiral and achiral structures. The methodology has been applied to the case of the octahedron {Bi6Fe13L12} which has unsymmetrical coordination of a carboxylate ligand (L) along its edges. For these polyhedra, the enumeration methodology revealed 186 distinct isomers, including 74 chiral pairs and 38 achiral. To explore the programming of these, we then used a range of ligands to synthesize several configurational isomers. Our analysis demonstrates that ligand halo-substituents influence isomer symmetry and suggests that more symmetric halo-substituted ligands counterintuitively yield lower symmetry isomers. We performed mass spectrometry studies of these {Bi6Fe13L12} clusters to evaluate their stability and aggregation behavior in solution and the gas phase showing that various isomers have different levels of aggregation in solution.