Since the beginning of the 21st century, organocatalysts have established themselves as a third group of homogeneous catalysts, next to biocatalysts (enzymes) and transition metal-based catalysts . In particular, enantioselective organocatalysis has shown an impressive rise in the last decades, owing to the tunability of catalysts and different modes of activation, enabling a manifold of different transformations . The development of the field, driven by many researchers, led to the award of the Nobel Prize to List and MacMillan in 2021 ‘for the development of asymmetric organocatalysis’. Organocatalytic transformations have also seen the transition to industrial processes for the production of a variety of pesticides and medicinal compounds, as recently reviewed .

Despite the prominence of organocatalytic reactions, catalyst development has so far mostly been conducted guided by intuition of skilled organic chemists. Given that organocatalytic reactions are governed by different competing interactions, the influence of a change in molecular structure is often non-trivial, even for highly experienced experts. Thus, intuition-guided catalyst development is regarded as suboptimally efficient and furthermore highly subjective to the experience of the chemists carrying out the study . Considering the demand of organocatalysts, their accelerated and reliable development is highly desirable . In the spirit of accelerated discovery, the development of organocatalysts has been augmented with computational catalyst design . Multiple programs for automated catalyst simulation have been developed in the last decade. Notable examples include the development of ACE (Asymmetric Catalyst Evaluation) , AARON (Automated Reaction Optimiser for New Catalysts) or CatVS (Catalyst Virtual Screening) . Such tools have been extensively reviewed in the past years . Based on a known mechanism, the tools calculate the energies of relevant species either via force field or quantum chemical methods to assess the properties of a reaction such as activation energies or selectivity. Irrespective of the degree of automation, in silico calculations are often less time-sensitive than wet-lab experiments and can be used to reduce the number of required experiments. As such, these methods contribute to the acceleration of catalyst discovery, for example through high-throughput virtual screening.

Predating these computational techniques is the desire to understand and explain experimental outcomes in organic chemistry with physicochemical descriptors. A prominent early example are Hammett parameters, developed in 1937 , that relate substituent parameters to the equilibrium constant of the deprotonation of a substituted benzoic acid. The derived substituent parameters are used to gain insight into the mechanism of reactions by observing the influence of substituents on a reaction outcome. However, Hammett parameters have shown to not fully describe observed trends. Therefore, complementary representations capturing other properties of a molecule have been derived (vide infra) .

While traditional linear free energy relationships such as those using Hammett parameters used linear models, the emergence of ML has led to the development of more complex algorithms, better suited for extracting hidden patterns in data. The ability of ML to efficiently capture complex relationships allows to extract influences on catalyst properties and thus makes it suited towards the accelerated design of chemicals and materials, including organocatalysts . Due to this potential, an increasing number of research groups have used ML to predict and develop new organocatalytic reactions.

This review aims to provide a critical overview of developments in ML specifically for organocatalysis over the last decade, with a focus on its applications. We aim to provide a starting point to catalysis researchers who are interested in ML as well as an assessment of critical challenges to more experienced ML users. We will first give a primer on ML, equipping experimentalists with the knowledge necessary to follow the developments in the field. The rest of the review is divided into three parts: (1) ML for reactivity and selectivity prediction, (2) ML for the design of privileged organocatalysts and (3) ML for catalyst and reaction design. Ultimately, the review will give an outlook on the authors’ expectation of the future of the field.

Figure 1: Schematic depiction of available data sources for predictive modelling, each with its advantages and disadvantages. Icon ‘Manual experiments’ made by Eucalyp from flaticon.com. This content is not subject to CC BY 4.0. Icon ‘Computation’ made by Wichai.wi from flaticon.com. This content is not subject to CC BY 4.0. Icon ‘Literature’ made by Muhammad Atif from flaticon.com. This content is not subject to CC BY 4.0. Icon ‘HTE’ made by Nuricon from flaticon.com. This content is not subject to CC BY 4.0. Icon ‘Pros’ made by Aldo Cervantes from flaticon.com. This content is not subject to CC BY 4.0. Icon ‘Cons’ made by Yogi Aprelliyanto from flaticon.com. This content is not subject to CC BY 4.0.

Apart from experimental data, the creation of large amounts of in silico data is possible with sufficient computational resources . While this approach is useful in cases where the experimental determination is challenging, some experimental properties, like the reaction yield, remain elusive to be reliably computed due to the myriad of factors (side-reactions, impurities, solvation effects, interface effects,...) that influence this observable . Another pitfall regarding computational data is its accuracy with respect to the ground truth, in particular for multiple factors relevant throughout catalysis, such as non-covalent interactions (NCIs) for organocatalysis or spin properties for transition metal catalysis . While most quantities can in principle be computed with the highest accuracy using advanced tools, the associated computational cost needs to be considered .

Therefore, the use of experimental data is advantageous as less assumptions have to be made and the quantity of interest is directly represented. The results of a great number of experiments can be found in literature, as well as patents. Manual curation of this data is possible, but for larger amounts of data it is usually impractical. Therefore, automated extraction tools have been reported yielding the data in a structured format suitable for ML . While some important efforts have been made to establish uniform data reporting standards , they are getting picked up by the community rather slowly. With data from experiments conducted by different scientists under varying conditions and adhering to various standards, reproducibility remains a major challenge in organic chemistry and restricts the applicability of literature data for statistical modelling . Despite emerging high-throughput experimentation (HTE) pipelines , large datasets of high-quality are still scarce. While multiple large datasets are available for transition metal catalysis and biocatalysis , they are however not common for organocatalysis. Therefore, much research has been devoted to develop models that perform well on the available small data sets .

In order to be processed by any ML model, the data needs to be provided in a machine-readable way. Unlike chemists who typically use drawings of Lewis structures to represent molecules, computers require a numerical representation of the molecular structure. Since the information that describes the input directly influences what relationships a model can learn from the presented data, different representations might be suitable depending on the task.

Figure 2: Schematic depiction of different kinds of molecular representations for fluoronitroethane. Among the most common representations are string-based notations, such as SMILES, structural fingerprints, like the ECFP, or molecular graphs. Another way of encoding a molecule is through descriptors that often contain steric or electronic properties.

In graphs, the atoms and bonds are represented as nodes, and edges, respectively . While these kind of representations are well suited for the description of most organocatalysts with distinct bonds, they have limitations when describing coordination compounds as commonly found in transition metal catalysis for example .

Another kind of representation that has found considerable application for ML in organocatalysis, is the use of descriptors. These are sets of numerical or categorical values to encode a molecule. A plethora of descriptors with varying degree of computational effort for their calculation are available. Among the most commonly employed descriptors in organocatalysis are steric and electronic descriptors. Section 2.1 provides a detailed overview of examples where different kind of descriptors have been successfully applied for predictive modelling in organocatalysis. In contrast to the representations through graphs, or SMILES, which can be directly obtained from the molecular structure, the selection of appropriate descriptors is problem-specific and requires knowledge about the fundamental interactions governing the reaction outcome. Hence, making the selection of input features a key step for successful modelling .

The third important requirement for building a predictive model is the model architecture. Generally, ML algorithms can be divided into reinforced, unsupervised and supervised learning. In reinforcement learning, an agent is trained to make decisions by interacting with an environment, receiving feedback in the form of rewards or penalties, and adjusting its behaviour to maximise cumulative rewards over time .

While reinforcement learning has not yet found widespread application in organocatalysis, supervised and unsupervised learning are widely employed techniques. The latter uses unlabelled data (e.g., data without a label or numerical value), to identify patterns and relationships within the provided data. Popular tools are Principal Component Analysis (PCA), Uniform Manifold Approximation and Projection (UMAP) , or t-distributed Stochastic Neighbour Embedding (t-SNE) , which have found application in organocatalysis to reduce the dimension of the respective reaction space, e.g., for visualization purposes. Another widely applied unsupervised ML technique is clustering, which aims to group similar data points together and thus enables a diverse selection by uniformly sampling from the created space . Supervised learning requires labelled data and aims at identifying correlations between the target values and the corresponding input features. In the context of addressing chemical problems, this can be used to correlate reaction specific features with the reaction outcome, such as the yield or selectivity. A plethora of different supervised learning algorithms are available and a priori knowledge which architecture works best is challenging. Some of the most widely used algorithms include multivariate linear regression (MLR) in which the target is linearly modelled by multiple independent variables. Other notable architectures include decision trees , support vector machines and deep neural networks . While the accuracy of the model is paramount, interpretability is also highly desirable. In this regard, MLR bears the advantage that it yields a directly interpretable function which can be used for mechanistic inference. However, it is important to note that the caveat of correlation and causality must be considered. Also, for other kind of models, e.g., random forests, it is common practice to consider the importance of individual features for the model’s prediction to gain mechanistic insight. Careful attention must be paid to the collinearity of features , such that they are not too strongly related to each other, which complicates any quantitative interpretation of feature importance. Thus, thorough analysis and special strategies to address collinearity, such as hierarchical clustering or threshold-based pre-selection have to be considered to ensure reliable interpretability .

It is worth mentioning that all the above-mentioned techniques are not limited to applications in organocatalysis but are used for a wide variety of chemical problems.

Figure 3: Depiction of the energy diagram of a generic enantioselective reaction. In the centre, catalyst and substrate are separated. They associate with each other to either the pro-(R) or pro-(S) complex, with all these reactions taking place in a fast equilibrium (Curtin–Hammett conditions). From these complexes, the products are formed via separate transition states. The energy difference between these two transition states is termed ∆∆G‡ and determines the selectivity.

Figure 4: Hammett parameters are derived from the equilibrium constant of substituted benzoic acids (example from Rogers et al. to correlate Hammett parameters of the arylpyrrolidine catalysts to the reaction kinetics of the aldol reaction).

As Hammett parameters account only for the electronic effect of substituents, much research has been devoted to develop physical-organic descriptors, which consider steric effects and separate the electronic effect into contributions from resonance and induction, among others .

In this chapter, we first discuss the evolution of physical-organic descriptors for the representation of organocatalysts . Later, we examine the effects of increasing data availability towards the application of ML in this field.

Drawing inspiration from linear free energy relationships, MLR models, pioneered by Norrby and co-workers and later further developed by Sigman and co-workers , are commonly used for the prediction of enantioselectivity. In such models, the substrates, catalysts, and other relevant reaction species are encoded via a suitable representation of expert-chosen descriptors. Subsequently, the target property of interest, commonly ∆∆G‡, is fitted to the representation via a linear fit of the form y = m1x1 + m2x2 +…+ mnxn + k, where y is the target property, m1, ... , mn are the regression coefficients, k is the offset and x1, …, xn are the molecular descriptors. The regression coefficients are also indicative of the importance of the respective molecular parameter. Thus, MLR models provide the capability to directly interpret the prediction results and form mechanistic hypotheses based on the importance of distinct descriptors.

Figure 5: Selected examples of popular descriptors applied to model organocatalytic reactions. Descriptors encompass steric features modelled via Sterimol parameters (example from Harper et al. correlating the Sterimol B1 and L parameters of the bisphenols to the enantioselectivity of the peptide catalysed desymmetrisation), electronic features modelled via vibrations or NPA charges (example from Crawford et al. ) and NCIs, modelled via interaction distances and energies with a defined probe (example from Orlandi et al. ).

Figure 6: Example bromocyclization reaction from Toste and co-workers using a DABCOnium catalyst system and CPA phase transfer catalyst .

Figure 7: Example from Neel et al. using a chiral ion pair catalyst for the selective fluorination of allylic alcohols .

After a systematic data set design involving eight phosphoric acids and eight boronic acids, the authors observed breaks in linearity of the model of enantioinduction for some catalyst combinations. Further experiments, such as non-linear effect studies and isotopic substitution experiments revealed multiple different mechanisms of enantioinduction for the respective combinations. To rationalise relevant interactions, MLR models were trained on subsets of the data set. For each different mechanism of enantioinduction previously elucidated, the authors developed a separate model to gain a sufficiently interpretable model, finding that some parameters remain important throughout the different subsets. This example demonstrates both the strength of careful data analysis and the intricacies of dealing with chemical reactivity data.

The above outlined examples demonstrate the relevance of efficient representations, to which the development of advanced descriptors contributed. However, the usage of descriptors also restricts the generalizability of models, as they have to be expert derived. Interestingly, descriptor-based MLR models have also been used to predict the Mayr–Patz nucleophilicity parameter N, which estimates the nucleophilicity of a nucleophile based on experimentally measured kinetic data. The MLR models are used to predict N for more than 1200 nucleophiles, enabling the prediction of N for further nucleophiles . While this complicates the usage of descriptors for a multitude of different reactions, it also enables an efficient representation by representing chemical hypotheses. Even though descriptors have been proposed for a number of different interactions, others are not easily represented via descriptors but remain highly important towards enantioselectivity, e.g., solvent-solute interactions.

When interpreting the importance of descriptors, effects such as overfitting and collinearity of features must be accounted for. Particularly in the low-data regime, the importance of selected features can vary based on the reactions that are contained in the training and test set. While descriptors can help in gaining mechanistic insight, it is important to not overinterpret the significance of single features to form a mechanistic hypothesis.

Ideally, to overcome issues such as a high dataset dependence, larger reaction datasets are available. In terms of data set sizes, the presented studies all worked in the low to medium data set size, with up to few hundred experiments , where careful considerations must be paid towards the applicability domain, overfitting and interpretability. With HTE platforms established and due to their importance to ML campaigns, the past few years have seen a trend in creating larger experimental chemical reactivity datasets, in particular for transition metal catalysis .

Figure 8: Data set created by Denmark and co-workers for the CPA-catalysed thiol addition to N-acylimines . The combinatorial data set encompasses the enantioselectivities from 5 thiols and 5 imines in combination with 43 CPA catalysts for a total of 1,075 data points.

The size of the data set allowed the authors to perform various ML experiments: a random (600:475) split on the data set, a substrate test set where ∆∆G‡ of known catalysts with new substrate combinations were predicted, a catalyst test set where the substrates were known but the catalysts not and a test set were both components were not known beforehand. Even in the most challenging case, predictions were highly accurate with a mean absolute deviation of 0.24 kcal/mol. Further, the authors performed a split where the models were only trained on reactions with an ee < 80% (718:357 split), still showing good extrapolation performance with an error of only 0.33 kcal/mol on the test set with higher enantioselectivity.

Throughout the development of organocatalysis, privileged catalysts, i.e., catalysts which catalyse a wide variety of different reactions through the same mechanism of enantioinduction, have emerged in multiple organocatalytic transformations . The examples discussed in Section 2 all have seen the application of ML techniques to predict the selectivity of a reaction of interest. However, since the mechanism of enantioinduction is similar for multiple reactions catalysed by a privileged catalyst class, these ’related’ reactions can in principle be modelled together. The reactions are assumed to be mechanistically transferable.

The similarity of multiple reactions led to two different applications of ML to organocatalysis: (1) prediction of reaction properties (e.g., selectivity) for multiple mechanistically transferable reactions, and (2) employing ML in the search to predict the generality of a catalyst. This chapter will discuss prominent examples in both applications.

The key to modelling transferable reactions together is to find a representation that can describe all relevant reacting species. While such representations commonly exist in chemistry, e.g., SMILES and graphs, the most common representation for transferable reactions is via expert-chosen descriptors. As such, the space of relevant reactions has to be carefully studied, e.g., with respect to the different reactant or catalyst classes. Once this space is defined, the descriptors have to be chosen such that they are specific enough to provide information to the ML model while also general enough to cover the space of interest.

One pioneering study in the field of mechanistic transferability for enantioselectivity prediction was published by Reid and Sigman in 2019. The authors manually combined 367 different published reactions of BINOL-phosphoric acid catalysed nucleophilic additions to imines, comprising alcohols, thiols, phosphonates, diazoacetamides, peroxides, benzothiazolines and more as nucleophiles. Apart from reactant classes, the reactions also vary in additives, and solvent among others. Since these reactions all adhere to the same mechanism of enantioinduction, the authors chose to consider them in the same ML campaign, even though the nucleophiles vary significantly. As descriptors, the authors used the overlapping features of nucleophiles, imines and catalysts to derive steric and electronic parameters as well as topological descriptors for solvents, where less structural overlap is present .

Figure 10: Study from Reid and Sigman developing statistical models for CPA-catalysed nucleophilic addition reactions to imines for different classes of nucleophiles .

Figure 11: Selected examples of studies where mechanistic transferability was exploited to model multiple reactions together. (A): Liles et al. used univariate classification and MLR to develop a new CPA catalyst achieving high enantioselectivity for transfer hydrogenations. A comprehensive model for multiple reactions was developed under the assumption of mechanistic transferability . (B): List and co-workers employed Support Vector Machines trained on data of different cyclisations to find an optimal catalyst for tetrahydropyran synthesis . R = general residue, Ar = aromatic residue.

Mechanistic model transferability for CPA-catalysed Minisci reactions was utilised for the derivatization of quinolines and pyridines. Models trained on these compound classes show good generalisation towards other nitrogen-containing heteroaromatics including pyrimidines and pyrazines.

The importance of mechanistic understanding for model building was underlined by Kuang et al. , where the authors considered multi-catalyst enantioselective reactions, where one catalyst was an organocatalyst, either CPA or an amine. The co-catalyst was included in the ML model by being considered as a nucleophile or electrophile, depending on the reaction mechanism. Descriptors allowed for the inclusion of a variety of co-catalysts, ranging from Fe-piano stool complexes to copper complexes. The consideration of co-catalysis into model development further expands the considerable reaction space in organocatalysis.

While it is important to consider catalysts achieving high enantiomeric excess (ee) on relevant reactions, the deployment of general catalysts that provide a reasonable ee for a variety of reactions has gained more attention over the last years . Catalysts that fulfil such demands are coined ‘general catalysts’.

While the concept of generality was recently explored in a closed-loop fashion for Suzuki–Miyaura cross couplings to find the most general catalyst and reaction conditions , the application of this concept in the context of ML has found comparatively less attention in organocatalysis, despite the prominence of privileged catalysts.

Despite the intuitive explanation of generality to chemists, a clear mathematical definition of chemical generality remains elusive, exacerbating the integration of the generality concept towards machine learning algorithms. As such, different implementations were chosen to tackle this problem.

Figure 12: Generality approach by Denmark and co-workers for the iodination of arylpyridines. From the relevant chemical space, a representative subset of 18 catalysts is selected. For each of the 13 model substrates, a catalyst-substrate model is trained. Catalysts that are top performers for multiple substrates are considered general catalysts.