Machine learning for design principles for single atom catalysts towards electrochemical reactions

Abstract

Machine learning (ML) integrated density functional theory (DFT) calculations have recently been used to accelerate the design and discovery of heterogeneous catalysts such as single atom catalysts (SACs) through the establishment of deep structure–activity relationships. This review provides recent progress in the ML-aided rational design of heterogeneous catalysts with the focus on SACs in terms of structure–activity relationships, feature importance analysis, high-throughput screening, stability, and metal–support interactions for electrochemistry. Support vector machine (SVM), random forest regression (RFR), and deep neural networks (DNN) along with atomic properties are mainly used for the design of SACs. The ML results have shown that the number of electrons in the d orbital, oxide formation enthalpy, ionization energy, Bader charge, d-band center, and enthalpy of vaporization are mainly the most important parameters for the defining of the structure–activity relationships for electrochemistry. However, the black-box nature of ML techniques occasionally makes a physical interpretation of descriptors, such as the Bader charge, d-band center, and enthalpy of vaporization, non-trivial. At the current stage, ML application is limited by the lack of a large and high-quality database. Future prospects for the development of a large database and a generalized ML algorithm for SAC design are discussed to give insights for further studies in this field.

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1. Introduction

Heterogeneous catalysts play important roles in the synthesis of high-value chemicals through thermal, electrochemical, and photochemical reactions. Designing improved catalysts requires deep understanding of how the composition and processing affect the properties at the interface, but their progress is hindered due to the complexity in experimental and theoretical investigations.¹ Thus the successes have often involved time- and resource-consuming trial-and-error experimental and theoretical investigations. On the other hand, recent advances in Quantum Mechanics (QM) calculations provides accurate information about how molecules react at the interface to form various products, but QM calculations are limited in the size of the system and the time scale of the simulations. In order to discover new catalysts for specific applications, a combination of time-consuming experimental and QM studies is used to develop atomic level understanding of the fundamental mechanisms and to develop preparation-structure or structure–activity relationships. Accordingly, there is a huge demand for the accelerated discovery of novel catalysts with desired activities. Machine Learning (ML)^2–4 as a data-intensive tool can accelerate time-consuming experimental and QM studies to predict the catalytic activity in a vast dimensional space of heterogeneous catalysis.

Fig. 1 illustrates the general workflow for the integration of QM calculations and ML for the accelerated discovery of heterogeneous and single atom catalysts (SACs). The predicted data from QM calculations and feature vectors are used to design and train ML algorithms. The trained ML algorithms will then be used for not only the prediction of the optimal activity of heterogeneous catalysts, but also for performing feature importance analysis. Subsequently, optimized catalysts will be used for the desired reaction to produce valuable chemicals and fuels.

Fig. 1 The general workflow for the integration of QM calculations and ML for the rational design of heterogeneous catalysts. The process contains several steps: data generation using QM calculations, training of ML, optimization, and feature importance analysis, and using designed catalysts to produce chemicals and fuels.

Although the ML-assisted prediction of a single physical property such as formation energies⁵ and band gaps⁶ is widely applied for the purpose of materials discovery,^7–10 its application for heterogeneous catalyst design and discovery^11,12 is still in its early stage.¹³ Here, ML as a supportive tool, aims to guide, not to replace experiments and QM calculations in the search for ideal catalysts.¹⁴ However, the main hurdles for employing ML in heterogeneous catalyst design are the lack of a consistent database, the lack of a universal ML algorithm, and the existence of only a few descriptors as input features for ML.¹⁵

Herein, we review recent studies reporting the incorporation of ML into QM calculations (typically density functional theory (DFT) calculations) and experiments to accelerate heterogeneous catalyst design and discovery for various reactions. Recent review papers have summarized the recent studies on the application of ML for catalytic reactions,^16–20 reaction prediction,²¹ discovery of catalysts,^13,22–27 inverse design of catalysts,²⁸ and catalysis informatics.^29,30 In this review paper, we focus mainly on the different aspects of ML in experimental and theoretical studies with an emphasis on the limitations and hurdles of ML in heterogeneous catalyst design. Inspired by the application of ML in heterogeneous catalyst design, we continue with a comprehensive review on the application of ML in SAC design and discovery with an emphasis on ML algorithms, different SACs, environmental effects, stability, support–metal interaction, structure–activity relationships, and high-throughput screening. Recent findings on the input features of ML and their importance for different electrochemical reactions will be reviewed, where the isolated electrons in d orbitals have been demonstrated to play a key role in the nitrogen reduction reaction (NRR).³¹ Subsequently, the application of different ML algorithms in several examples including the O₂ reduction reaction (ORR), O₂ evolution reaction (OER), CO₂ reduction reaction (CO₂RR), NRR, and H₂ evolution reaction (HER) will be provided to demonstrate the potential application of ML for the design and discovery of SACs for electroreduction reactions. Finally, a summary and future prospects in the area of ML-guided SAC and DAC discovery are provided and discussed.

2. Machine learning (ML) algorithms

The most important ML algorithms applied for the establishment of deep structure–activity relationships are normally support vector machine (SVM), random forest regression (RFR), deep neural networks (DNN), sure independence screening and sparsifying (SISSO), and Gaussian process regression (GPR). As shown in Fig. 2a, SVM as a binary classification and regression algorithm classifies data points into two distinct categories by using hyperplanes.³² The SVM assigns each point of training data to one of two classes and minimizes the error between the classes by dividing the categories using a hyperplane, which maximize the margin around the hyperplane. The hyperplane is completely defined by the data points that are closest to the plane and between the support vectors. SVM can also be used in mapping the non-separable data through the radial basis function (RBF) kernel by transforming a real space into a higher-dimensional space through several hyperplanes:^33,34

Fig. 2 Machine learning algorithms. (a) Schematic of the SVM algorithm. The hyperplane divides SACs into two distinct classes based on the largest distance between the data points placed between the support vectors. Class 1 and class 2 (red and blue circles) show the SACs with similar properties based on features x₁ and x₂. (b) Schematic of RFR algorithm. Orange and green circles represent decision nodes containing ‘if/then’ statements. The result that is predicted by the highest number of decision trees (majority voting) is given as the output of RFR algorithm. (c) Schematic of DNN. Circles represent neurons in the input, hidden, and output layers of the DNN. Neurons are interconnected using the black lines. (d) Schematic of the GPR algorithm. Predicted mean (red line) and confidence interval (light orange interval) for the GPR algorithm trained based on the input dataset (blue dots).

in which G is a radially symmetric function of its argument, G(r) = ϕ(|r|), x is the vector of joint angles or other parameters describing the current pose of the skeleton, x_k is the pose of the k^th example, and ω_k represents the different weights of each vertex coefficient. SVM is highly efficient in terms of memory usage; however, the boundary between categories may become obscured when there are a large number of training data points. SVM can also create both the linear and the non-linear model, and the latter one is based on a kernel-based regression technique.³⁵ When comparing SVMs and the kernel ridge regression (KRR) algorithm, no big performance differences are to be expected. Usually, SVMs arrive at a sparser representation, which can be of advantage; however, their performance relies on a good setting of the C and γ hyperparameters for the SVM method and the α and γ hyperparameters for the KRR method. Normally, the SVM method leads to faster predictions and consumes less memory, whereas the KRR method leads to less fitting time for large datasets. Nevertheless, because of the generally low computational cost of both algorithms, these differences are rarely significant for a relatively small number of data points. Unfortunately, neither method is feasible for large datasets as the size of the kernel matrix scales quadratically increases with the number of data points.³⁶

In comparison with other algorithms, random forest regression (RFR) needs fewer hyperparameters with higher robustness.³⁷ In fact, as shown in Fig. 2b, the RFR algorithm acts as an aggregated decision tree algorithm to lower the bias by reaching a collective decision.³⁸ The issue with the RFR is that it is not accurate for out-of-sample predictions especially in the case of a small number of training data points.³⁹ Furthermore, feature importance analysis can be easily performed after the training of the RFR, SVM, and KRR algorithms.⁴⁰ Similar to SVM and KRR methods, the deep neural network (DNN) algorithm has the potential to learn system nonlinearity. As shown in Fig. 2c, DNN is a mimic of the combination of neurons inside the human brain, which is composed of several interconnected neurons in several layers. Similar to SVM and KRR methods, the number of neurons and layers as the hyperparameters for DNN should be optimized concerning the quality and accuracy of the output results for minimizing the loss functions such as root mean square error (RMSE), mean square error (MSE), and mean absolute error (MAE).^41–43

Compared with other ML techniques, the SISSO algorithm possesses high convenience and accuracy, while the fitting formulae generated by the SISSO model possess high efficiency and portability.⁴⁴ As shown in Fig. 2d, GPR is a Bayesian approach to bring waves to the ML area and works well with a small number of input data to provide uncertainty measurements on the predictions.⁴⁵

ML techniques can also be applied as the text mining tools to gather the large numbers of already available QM calculations and experimental data in the literature, construct readily available databases applicable in deep analysis, and study preparation-structure–activity relationships. ML techniques for text mining can be categorized into supervised, unsupervised, and semi-supervised techniques.^46,47 Supervised and semi-supervised algorithms such as neural networks and transfer learning can be used for text classification, information extraction, and analyzing the data, while unsupervised algorithms such as expectation-maximization (EM) mostly are used for text clustering, summarization, and dimensionality reduction.⁴⁷

3. Inspiration from heterogeneous catalyst design

Although ML techniques are widely used for the design of heterogeneous catalysts, their application to single atom catalysts (SACs) is in its infancy. Therefore, in accordance with the trends in ML-aided heterogeneous catalyst design which are discussed in this section, we will continue with the ML-aided design of SACs in section 4. The integration of ML with experimental- and QM-predicted data is widely used along with atomic and structural properties as the input features to predict the properties of heterogeneous catalysts.^48–52 For example, a ML algorithm was trained based on experimental data and structural properties as the input features to optimize the singlet oxygen (¹O₂) quantum yields of core–shell plasmonic photocatalysts applicable in organic synthesis and photodynamic therapy (PDT).⁵³ In addition, a ML model was trained based on DFT calculation data to predict and screen the surface reactivity of bimetallic alloys using atomic properties as the input features.⁵⁴ To shed light on the integration of ML with experiments and QM studies for heterogeneous catalyst design and discovery, more details are provided in the following subsections.

3.1 Integration of ML with experiments

Learning from experimental data is the earliest application of ML in heterogeneous catalyst design for electrocatalysis, photochemistry, and biocatalysis.^55–62 ML models can be trained based on experimental data to optimize the performance, decrease the number of experiments, and therefore to accelerate high-throughput experimentation.^63,64 The input features for ML models can be synthesis and reaction operation conditions to predict the catalytic performance.⁶⁵ For example, a ML algorithm was used to calculate the yields of dioctyl adipate synthesis by implementing the substrate molar ratio, enzyme amount, temperature, and reaction time as the input features.⁶⁶ Adaptive learning was applied to find high-activity AA′B₂O₆ cubic perovskite catalysts for the OER by establishing a relationship between the electronic structure properties as the input features and the OER activity of the perovskite catalysts. It was revealed that the orbital electronic structure characteristics of the B-site ion is an important factor for the OER.⁵¹ Also a multi-output support vector regression (SVR) as the ML algorithm was applied to predict the selectivity and conversion of methane oxidation.⁶⁷ Likewise, ML allows the optimization of experimental data to increase the efficiency of heterogeneous catalysts for the selective oxidation of methane.⁶⁸ In addition, ML was applied on experimental data to predict the activity and selectivity of bimetallic metal catalysts with TM–Pt–Pt(111) and Pt–TM–Pt(111) architectures for ethanol reforming.⁶⁹

One of the disadvantages of ML models is that they are only applicable for specific systems and are not transferable from one to another experiment due to the lack of consistent data and the presence of hidden variables for each specific experiment.^70,71

To overcome this issue, ML can be applied to analyze available data in the literature through data mining processes^72,73 to extract and analyze previously published experimental data for future heterogeneous catalyst discovery.^74–76 For example, ML was used to extract the data for the synthesis of oxide materials from 12 000 scientific articles.⁷⁷ In addition, several studies have recently reported data mining from the literature for the ML-assisted design and discovery of new heterogeneous catalysts for oxidative coupling of methane.^78–83Fig. 3 shows the workflow for the summary of a data mining sequence from the literature. It starts with a query search to find related papers from metadatabase, following by downloading and classifying the papers.^46,84 The classified papers can be used for text mining using several ML algorithms such as KRR, RFR, SVR, Extreme Gradient Boosting (XGB), extra trees regression (ETR), and artificial neural network (ANN) to extract the data. The extracted data can be used for regression, classification, and/or clustering purposes. For example, several ML algorithms such as XGB, RFR, and ETR were used to analyze the literature data for the oxidative coupling of methane on metal supported catalysts to discover new heterogeneous catalysts.^85,86 Similarly, the statistical analysis of available data in the literature for CO oxidation, water–gas shift reaction, and oxidative coupling of methane reactions was performed using several ML algorithms such as Kernel Ridge Regression (KRR), RFR, XGB, and SVR for heterogeneous catalyst discovery. Through feature importance analysis, reaction temperature was revealed as the key parameter for the three investigated reactions.⁸⁷ Very recently, suitable catalysts for environmental applications were discovered based on available data in the literature, from which binary and ternary element catalysts such as Mn_xCo_y and Zr_xMn_yCr_z were identified and optimized through ML for high NO_x conversion. An ANN algorithm was used to predict NO_x conversion efficiency as a function of temperature and the element molar ratio. The conversion reaches a maximum around 300 °C for the ternary element catalysts. Also, the loading amount of Zr was found to play an important role due to the fact that the Cr⁵⁺ species can reduce as the Zr loading amount increases, which can subsequently lower the NO_x conversion efficiency.⁸⁸ In addition, a ML algorithm along with 27 descriptors was applied to 2228 experimental data obtained from the literature⁸⁹ to predict the activity of heterogeneous catalysts, which reveals that temperature is the most important descriptor for the water–gas shift reaction.⁹⁰

Fig. 3 The workflow for data mining from the literature. Summary of the data mining sequence from the literature using several ML algorithms such as KRR, RFR, SVR, XGB, ETR, and ANN.

Moreover, learning from a large database in nanoscience can be used for rapid design and discovery of new heterogeneous catalysts using ML.⁹¹ However, the obtained dataset from the literature is mostly incomplete and inconsistent, which limits the application of ML. In order to generate a consistent database for the training of ML algorithms, high-throughput experimentation can be performed. As a result, high-throughput experimentation for oxidative coupling of methane was performed for 20 catalysts and 216 reaction conditions to produce a consistent dataset for ML to accurately predict C₂ yields.⁹² From feature importance analysis, temperature, in the range of 700 to 900 °C, is the most important parameter compared to other parameters such as the flow rate of argon, flow rate of O₂, flow rate of CH₄, contact time, and composition of the catalyst.

ML also has great potential to alter the current form of conventional experiments and increase the efficient heterogeneous catalyst discovery through automation.^93–95 In fact, ML-assisted robots can help to accelerate high-throughput experimentation without human interactions.^96–99 As a result, a ML-guided robot was used to carry out 688 experiments within an experimental space of ten variables, 1000 times faster than manual approaches. The ML-assisted high-throughput experimentation revealed a new photocatalyst mixture with six times more activity.¹⁰⁰

3.2 Integration of ML with Quantum Mechanics (QM)

Learning from Quantum Mechanics (QM) is highly desired due to the existence of enormous amounts of quantitative QM-predicted data as a training dataset for ML. The trained ML can be used for accelerated and accurate prediction of the catalytic properties and adsorption energies of reaction intermediates.¹⁰¹ Using the adsorption energies as the key parameter, the reaction barrier can be predicted, the reaction mechanism can be investigated, and the desired catalyst can be discovered. For example, the local similarity kernel and Bayesian linear regression as the ML algorithms were used for predicting the adsorption energies of NO, O, and N on a Rh₁–xAu_x alloy, based on the nanoparticle composition and size.^102,103 The findings were used to predict the rate of NO decomposition on RhAu nanoparticles, which indicates a maximum for catalytic activity at a particle diameter of 2.0 nm. In addition, structure–activity relationships were established for predicting CO and H adsorption energies based on structural properties using active learning across reaction intermediates.^104,105 In fact, an automated screening approach through the integration and optimization of ML was presented to guide DFT calculations for predicting catalytic activity.¹⁰⁵ The feasibility of this approach was demonstrated by screening various alloys combining 31 elements, which resulted in 131 candidate surfaces across 54 alloys being identified for the CO₂RR and identification of 258 surfaces across 102 alloys for the HER.^104,105 Likewise, active learning was then used to accelerate the screening of CO adsorption energy on Cu based components.¹⁰⁶

The ML-predicted adsorption energies of reaction intermediates were also used for the investigation and optimization of the reaction network of the syngas reaction (CO + H₂) over Rh(111) catalysts at 573 K and 1 atm. Gaussian process regression (GPR) as a ML algorithm was trained based on a few DFT calculations to predict the adsorption energies for all intermediates in the reaction network. A probable reaction network from syngas to acetaldehyde was revealed by using a simple classifier to select the potential rate-limiting steps, where only predicted potential rate-limiting steps were analyzed via further DFT calculations.¹⁰⁷

ML was also trained based on DFT-calculated data to accelerate the prediction of the adsorption energies of H and CH_x intermediates on Cu-based alloys using 12 properties as the input features. Amongst several ML algorithms, the ETR algorithm resulted in the highest accuracy. Based on feature importance analysis, the surface energy, element group, and melting point were identified to be the most important parameters for predicting adsorption energies.¹⁰⁸ In addition, ML was applied for predicting the adsorption energies of different intermediates on metal alloys.¹⁰⁹ ML was also used to predict the adsorption energies of H on Ni₂P(0001) surfaces. From the feature engineering perspective, the Ni–Ni bond length is the key parameter for HER activity, where a higher Ni–Ni bond length leads to lower HER activity.¹¹⁰ Similarly, ML was used to predict the adsorption energies of CO on bimetallic alloys, where feature engineering analysis resulted in the d-band shape and sp-band filling as key parameters.^111,112 Furthermore, to accurately predict the d-band as one of the most important parameters in CO adsorption, a GBR model was applied to several individual 3d, 4d, and 5d transition metal structures and their binary alloys for both the cases of metal impurities and overlayer-covered metal surfaces.^113,114 Recently, ML was integrated with DFT calculations to predict the adsorption energies of various molecules on metal oxide surfaces. Feature importance analysis indicates that the highest occupied molecular orbital (HOMO) of the adsorbates and the metal oxide surface energy are the most important parameters for molecular adsorption.¹¹⁵ ML in combination with DFT calculations was also used for the prediction of the adsorption energies of 12 elements on 38 metal surfaces by using SVR, RFR, and multi-layer perceptron regression (MLPR).¹¹⁶

The integration of ML and QM can also be performed to accelerate the discovery and high-throughput screening of heterogeneous catalysts. For example, ML integrated DFT calculations were used to accelerate the discovery and high-throughput screening of 2D MXenes for the HER.^117,118 SVR, GPR, RFR, and AdaBoost were used as ML algorithms to accelerate the prediction of ΔG_H*, based on the distance between the nearest neighbor O atoms as well as the surface oxygen–metal bond length as the most important parameters.¹¹⁷ Similarly, several ML models, such as DNN, KRR, SVM, and RFR, were used to accelerate the high-throughput screening of ΔG_H* by using several elemental properties as the input features. RFR led to the highest accuracy, with the lowest RMSE of 0.27 eV for the test data. Feature importance analysis shows that HER performance is highly dependent on charge and structural properties. S- and Os₂B-terminated Sc_n+1N_n (n = 1, 2, 3) were revealed as appropriate catalysts for the HER with ΔG_H* close to zero and satisfactory hydrogen coverages. It was also shown that S functional groups are of great importance in regulating the HER performance. This is because filling antibonding states with electrons weakens the adsorption of H*, which is a key step for the HER.¹¹⁸

For spinel structures, the ML model was used to accurately calculate the energy difference between the centers of the oxygen p and metal d bands to identify the better spinel oxide catalysts for the OER. It was shown that a [Mn]T[Al_0.5Mn_1.5]O–O₄ spinel catalyst has the optimal energy difference for high activity, as confirmed by experimental observations.¹¹⁹ ML was also applied to optimize TiO₂-supported Re and zeolite catalysts for methylation of aromatic hydrocarbons.¹²⁰ Similarly, ML was applied on the DFT-calculated data to predict how strain in platinum core–shell nanocatalysts can improve the ORR activity. It was revealed that the optimal strain depends on the nanoparticle size rather than the bimetallic material composition and shell thickness.¹²¹

As with experimental data, there is a large amount of QM-predicted data in the literature that can be mined for the purposes of ML analysis to commence a new direction using a large database in the rational design of heterogeneous catalysis and SACs.¹²² For example, ML was applied on literature data for CO₂ hydrogenation.¹²³ In addition, a dataset of 37 000 structures from the Catalysis-Hub database,¹²⁴ containing 11 adsorbates on 2000 metal alloy surfaces, was used for training a graph neural network (GNN) to predict adsorption energy based on relaxed structures.¹²⁵

ML can also be used for investigating reaction mechanisms and finding active sites for reactions. For instance, the LASSO ML algorithm was trained on DFT-calculated data for predicting the methane activation mechanism on rutile metal oxides.¹²⁶ It was revealed that the energy of methane activation decreased if the reacted atoms including O, C, H, and metal atoms could be placed in the same plane. In addition, ML was combined with multi-scale simulations and QM to identify the performance of surface sites on Au nanoparticles as well as dealloyed Au surfaces for the CO₂RR.¹²⁷ Based on ML results, surface defects are responsible for the high performance of Au surfaces. Similarly, ML was applied to DFT-calculated data to discover active bimetallic facets for the CO₂RR.¹²⁸ It was revealed that most facets of nickel gallium bimetallic materials lead to similar activity on Ni surfaces.

ML integrated DFT calculations are able to predict the surface segregation energies of bimetallic catalysts through the establishment of structure–activity relationships.¹²⁹ ML was used for the prediction of reaction barriers on a variety of surfaces¹³⁰ and for the discovery of phase diagrams applicable in electrochemical reactions.¹³¹ In addition, symbolic regression as a ML technique in combination with QM calculations was used to accelerate the discovery of new perovskite catalysts with excellent OER activity. The ratio of octahedral factor to tolerance factor (μ/t) was revealed as a simple and important descriptor for the discovery of perovskite catalysts.¹³²

4. Single atom catalysts (SACs)

Along with the studies mentioned above on heterogeneous catalysis, single atom catalysts (SACs) have recently been applied to several photochemical and electroreduction reactions to produce a wide range of chemicals.^133–135 The unique properties and high atom-utilization efficiency of SACs make them interesting and promising.^136–138 With these increased applications, the rational design of SACs has come into the forefront to enable improvements in the efficiency and feasibility of optimizing the desired products.¹³⁹ DFT calculations are widely used for the rational design of SACs with efficient activity, selectivity, and stability. DFT calculations, however, are time-consuming and computationally expensive^140,141 because the complexity of structure–activity relationships requires performing a large number of non-trivial DFT calculations in a large parameter space, including the SAC type, environmental coordination, and reactants.¹⁴² On the other hand, ML is considered as a fast, accurate, inexpensive,¹⁴³ and supportive tool¹⁴⁴ to predict the properties of SACs towards their rational design.^145–147 As shown in Fig. 3, using ML, one can apply the available datasets from QM and DFT calculations to construct readily available databases applicable in the deep analysis and establishment of preparation-structure–activity relationships. The established relationships can be used to predict the adsorption energy (E_ads) or Gibbs free energy (ΔG) of various reaction intermediates adsorbed on SACs to discover more active and selective SACs. Once enough high quality databases are provided, a reliable ML model can be trained and constructed to address the electroreduction challenges.^148,149 ML in combination with DFT calculations commences a new direction for rapid and low cost rational design of SACs predicted to have optimal electroreduction catalytic activity.^150,151 For example, several studies have used ML to design single atom alloy catalysts (SAACs) with excellent stability and activity by predicting the E_ads, ΔG, or aggregation energies.^152–155 ML can also be used for the interpretation of characterization of SACs.^156,157 For example, as shown in Fig. 4, ML techniques have been used to interpret the EXAFS spectra based on which edge sites (zigzag or armchair) are responsible for the HER activity of a cobalt SAC embedded in graphene.¹⁴⁵ In the following subsection, the application of ML for the establishment of structure–activity relationship, feature engineering, high-throughput screening, and stability of SACs is broadly discussed. As the application of SACs in thermal and electrochemical reactions was presented in a recent review paper,¹⁵⁸ we only focus on the progress of ML for the design of SACs and DACs especially for electrochemical reactions.

Fig. 4 ML for the interpretation of the EXAFS of Co–N doped graphene. (a) Establishment of training data using MD-EXAFS calculations for Co–4N–P, Co–2N–A, and Co–2N–Z. (b) The architecture of the DNN composed of one input layer of the EXAFS spectrum, two hidden layers, and one output layer of the proportion vector. (c) The estimation of the local structural proportion from the experimental EXAFS measurement. Reproduced with permission from ref. 145, copyright 2021, Wiley-VCH. Results show that ML is an appropriate and powerful tool for the interpretation of EXAFS.

4.1 Structure–activity relationship and feature engineering

ML is a strong tool¹⁵⁹ to provide a fundamental understanding of structural sensitivity^160,161 through establishing deep relationships between catalytic activity and structural as well as atomic properties based on mechanisms and similarities in SACs.^13,32,162 ML is considered as a new direction for the rational design of SACs by exploring feature importance analysis for electroreduction reactions to introduce more perceptions on the origin of the activity and stability of SACs.^163–165 For example, ML integrated DFT was applied to establish a relationship between various descriptors and hydrogen adsorption free energy (ΔG_H*) for the HER by altering the size and dimensionality of a nitrogen-doped 2D-carbon substrate for 3d, 4d, and 5d transition metals (TMs) as SACs.¹⁶⁶ The sure independent screening and sparsifying operator (SISSO) as the supervised ML algorithm was applied with 10 input features including the d-state center (ε_d), covalent radius (r_cov), Bader charge (q), number of occupied d states (d_occ), Zunger radius (r_d), number of valence electrons (N_e), ionization energy (IE), electronegativity (EN), and formation energy of single atom sites (E_f). Our evaluation on this work using the SVM algorithm is shown in Fig. 6a, demonstrating that the number of occupied d states (d_occ) and Bader charge (q) are the most important parameters for the HER. Using the SISSO algorithm, the following general descriptor for HER activity containing four properties was obtained, in which EN is the electronegativity of the SACs:

Similarly, several atomic properties were implemented as input features to establish structure–activity relationships and predict the OER overpotential of SACs on carbon substrates. The full connection neural network (FCNN) ML algorithm trained using DFT-calculated data leads to an accurate prediction of overpotentials with a relative error of 6.49% and a 130 000 times reduction in the computational time. It was revealed that the d-electron count (d_e), the atomic radius of metal (At_R), and electron affinity (EA) are the most important parameters for OER overpotential. Moreover, an intrinsic descriptor (ϕ) that defines the overpotential of SACs based on their intrinsic atomic properties was proposed using ML and DFT:¹⁶⁷

where EN_C, At_RC, and N_C are the electronegativity of carbon, the atomic radius of carbon, and the nearest neighbor carbon atoms, respectively. EN_M, IE₁, and At_M are the electronegativity of metal, first ionization energy, and atomic mass, respectively.

In another study, atomic properties such as electronegativity, electron affinity, and radii of the metal atoms were considered as input features to reveal ORR activity for heterobimetallic SACs. Using RFR, the origin of the ORR activity of SACs was investigated experimentally or by establishing structure–activity relationships based on DFT-calculated data.¹⁶⁸ Similarly, atomic properties were used to predict the catalytic activity of SACs and bi-atom catalysts for the CO₂RR. Based on results from the GBR algorithm, Ag–MoPc was revealed as an excellent electrocatalyst with a limiting potential of −0.33 V.¹⁶⁹ Subsequently, the data from the abovementioned work were used as an example to evaluate the efficiency of a DFT–ML hybrid program for catalysis programming.¹⁷⁰

In order to observe the effect of substrates on the activity and stability of SACs, the combination of atomic and structural properties should be considered as input features for the training of ML algorithms. Therefore, several atomic as well as structural properties were used to establish structure–activity relationships for the discovery and design of bifunctional rhodium SACs on defective g-C₃N₄ for the OER and ORR using the GBR algorithm.¹⁷¹ The atomic and structural properties include the TM bond length and coordination atoms (dTM–N₁, dTM–C₁, and dTM–C₂), the d-band center (ε_d), the charge transfer of TM atoms (Q_e), the electronegativity (EN), the electron affinity (EA), the first ionization energy (IE₁), the radius of the TM atom (At_R), and the number of TM-d electrons (d_e). As shown in Fig. 5c, the GBR model predicts ΔG_*OH with an R² = 0.99 and a low RMSE = 0.03 eV. However, this work included only 16 points of input data, which is insufficient. Feature importance analysis revealed that the first ionization energy (IE₁) and the charge transfer of transition metal atoms (Q_e) are the key features (Fig. 6b). The most important descriptor IE₁, the energy needed to remove one or more electrons from a neutral atom to form a positively charged ion (which increases from left to right in each period), affects the OER and ORR activities.

Fig. 5 Density functional theory (DFT)-based machine learning (ML). Comparison of ML- and DFT-predicted (a) ΔG_O* using the RFR algorithm, reproduced with permission from ref. 173, copyright 2019, American Chemical Society. (b) Limiting potentials using the RFR algorithm, reproduced with permission from ref. 174, copyright 2020, Royal Society of Chemistry. (c) ΔG_OH* using the GBR algorithm. Reproduced with permission from ref. 171, copyright 2021, American Chemical Society. Results indicate that ML can be used for the out-of-sample (test set) predictions of activity for SACs using deep structure–activity relationships. However, the quantity of data points in the training dataset is not sufficient to give a generalized ML algorithm.

Fig. 6 Feature importance analysis. (a) The feature importance for SACs embedded in nitrogen-doped graphene indicating that the number of occupied d states (d_occ) and Bader charge (q) are the most important parameters for the HER. Please note that this is our evaluation on ref. 166. Reproduced with permission from ref. 166, copyright 2020, American Chemical Society. (b) The feature importance based on the GBR algorithm for rhodium SACs. Reproduced with permission from ref. 171, copyright 2021, American Chemical Society. First ionization energy (IE₁) and the charge transfer of TM atoms (Q_e) are the most important factors for ΔG_OH*. Inset shows the structure of rhodium SACs on defective g-C₃N₄ for the OER and ORR. (c) The feature importance based on the RFR algorithm for SACs embedded on nitrogen-doped carbon supports. Reproduced with permission from ref. 173, copyright 2019, American Chemical Society. The oxide formation enthalpy (H_f,ox) and the adjusted electron numbers of d/p orbitals (dp_e) are the most important factors for ΔG_O*. Inset shows the structure of SACs embedded on nitrogen-doped carbon supports for a two-electron ORR. (d) The feature importance for dual atom catalysts (DACs) based on a RFR algorithm indicating that the average distance between metal atoms and the coordinated N atoms (M₁₂–N), the distance between the two metal atoms (M₁–M₂), and the outer electron number of metal atoms (d_e) are the most important factors for the ORR limiting potentials. Reproduced with permission from ref. 174, copyright 2020, Royal Society of Chemistry. Inset shows the structure of DACs embedded in nitrogen-doped graphene for the ORR. Results indicate that feature engineering of SACs and DACs depends on the application and the type of substrate. Please see Table 2 for the abbreviations.

Similarly, atomic and structural properties including the number of electrons in d orbitals, the oxide formation enthalpy, the Pauling electronegativity of the metal atom, the sum of Pauling electronegativity of surrounding atoms, and the average pK_a values of the surrounding atoms were used to establish structure–activity relationships. To do this, the RFR algorithm was applied based on DFT-calculated data for 104 SACs embedded in graphene including M@C₃, M@C₄, M@pyridine-N₄, and M@pyrrole-N₄. The RFR algorithm revealed that the number of electrons in d orbitals is the most important parameter for the ORR, OER, and HER. The trained RFR algorithm was employed to predict the activity of 260 graphene-based SACs (M@N_xC_y), through which, it was revealed that Fe@pyrrole-N₁C₃ and Fe@pyrrole-N₂C₂ were more active than Fe@pyridine-N₁C₃ and Fe@pyridine-N₂C₂.¹⁷²

Comparably, 8 atomic and structural properties including the oxide formation enthalpy (H_f,ox), the number of electrons in d/p orbitals (dp_e), electron affinity (EA), electronegativity (EN), number of coordinated N atoms (N_N), first ionization energy (IE₁) of the central atoms, the sum of the electronegativity of neighboring C and N atoms (S_EN), and the distance ratio (D_R) were used to establish the structure–activity relationship for a two electron ORR using RFR. Fig. 5a shows the comparison of ML- and DFT-predicted ΔG_O* for this system. Through the feature importance analysis of 8 intrinsic features, it was revealed that the oxide formation enthalpy (H_f,ox) and the number of electrons in d/p orbitals (dp_e) are the most important parameters for determining the ΔG_O* of SACs (Fig. 6c).¹⁷³ The feature importance analysis implies that metals like Ag, Au, and Pd with a weaker affinity for oxygen can remarkably decrease band hybridization between the oxygen and metal, leading to enhanced H₂O₂ selectivity.

As the complexity of SAC structures increases, new and general descriptors will be needed for establishing the correct structure–activity relationships. For example, the number of isolated electrons in d-orbitals, obtained from a bidirectional activation mechanism, was suggested as a new input feature for the ML algorithm, which introduces new insights for the rational design of SACs. It was shown that this new descriptor is the most important parameter for the NRR, while the electron affinity of metal atoms was shown to be the most important parameter for the HER. ML using this new input features was therefore used to accelerate the computational screening, design, and discovery of SACs by establishing the structure–activity relationship for 126 SACs for the NRR, validated by experimental studies and DFT calculations.³¹

Unlike SACs, the geometry of dual atom catalysts (DACs) is more complex and the synergetic effect between the two metal atoms plays an important role in the performance. In other words, the linear relationships for DACs are significantly weakened, demonstrating that the DACs' activity requires new descriptors to consider the effects of both metals in the structure. Therefore, in order to consider the synergetic effect of the two metals, ML integrated DFT was used to identify the structure–activity relationship of DACs embedded on nitrogen-doped graphene for the ORR. Fig. 5b shows the ML- and DFT-predicted limiting potentials using the random forest regression (RFR) model.¹⁷⁴ Feature importance analysis indicates that the average distance between metal and N atoms (M₁₂–N), the distance between metal atoms (M₁–M₂), and the outer electron number of metal atoms (N_e,O) are the most important factors for the ORR limiting potentials (Fig. 6d).

In order to shed more light on the structure–activity relationships, the effect of different intermediates should also be considered on the activity of SACs. Therefore, in addition to atomic and structural properties, the properties of intermediates were also considered as input features for training the RFR algorithm to calculate the binding energies of H*, OH*, O*, and OOH* on SACs embedded in nitrogen-doped graphene using 1700 DFT-calculated data points. Based on feature importance analysis, the type of intermediate was found to be one of the most important features.¹⁷⁵

The input features with high feature importance can be used for descriptor-based SAC design to predict adsorption energies. For example, descriptor-based design was used to predict the adsorption energies of intermediates on SACs embedded in graphitic carbon nitride (g-C₃N₄), g-CN, and g-C₂N. It was shown that Ni@g-CN, Cu@g-CN, and Co@C₂N are excellent SACs for the CO₂RR.¹⁷⁶ It was also shown that catalytic activities are highly related to ΔG_OH*, ΔG_OCH*, the number of electrons in d orbitals, and the TM enthalpy of vaporization.

The descriptors can also be used for establishing volcano-shaped relationships¹⁷⁷ from which SAC candidates for various electrocatalytic reactions can be found.¹⁷⁸ Therefore, a new intrinsic descriptor based on the bonding, topology, and electronic structure of SACs embedded in carbon supports, shown in Fig. 7a, was defined as follows:¹⁷⁹

Fig. 7 Volcano plots. (a) Structure of SACs embedded in nitrogen-doped graphene supports for the descriptor-based SAC design. Volcano plots for (b) overpotential (η), (c) onset potential (V_onset), and (d) Faraday efficiency (FE) based on the descriptor for SACs embedded in nitrogen-doped graphene supports. This indicates two definitive volcanoes in the plot for overpotential with Ti and Co located at the summits. Also, for the onset potential and Faraday efficiency, Co is in the summit of volcanoes with better CO₂RR performance. Reproduced with permission from ref. 179, copyright 2019, Wiley-VCH.

in which N_e, EN, and I_R are the valence electron number, electronegativity, and ionic radius of central metals, respectively. This descriptor was used for volcano plots of overpotential, onset potential, and Faraday efficiency, as shown in Fig. 7b–d, indicating two definitive volcanoes in the plot for overpotential with Ti and Co located at the summits. Another descriptor to consider the effect of supports was also introduced as follows:¹³⁹

in which EN_N, EN_C, N_N, N_C, and d_e represent the electronegativity of N atoms, the electronegativity of C atoms, the number of nearest-neighbor N atoms, the number of nearest-neighbor C atoms, and valence electrons in d orbitals, where α is the correction coefficient. These descriptors were used to predict the adsorption energies of different intermediates for the CO₂RR. Moreover, these descriptors were used for volcano plots of onset potential and overpotential with Ni and Pt located at the summits of volcano plots.

However universal and appropriate descriptors are still insufficient to establish structure–activity relationships for all types of SACs, supports, and electroreduction reactions.¹⁸⁰ Therefore, a large number of DFT calculations and ML analyses are still needed to screen different descriptors for each reaction system.¹⁸¹

4.2 High throughput computational screening for SACs

DFT calculations have been applied for high-throughput screening of SACs,^96,182–186 where, for example, S was found to be the best dopant in graphene-based Co SACs for the HER.¹⁸⁷ ML, however, can accelerate the screening of SACs and decrease the computational cost and time by screening for similarities in SACs and establishing deep structure–activity relationships.^{146,188–190} Therefore, the integration of ML algorithms and DFT calculations has been performed for the rapid and high-throughput screening of SACs.¹⁹¹ For example, ML combined DFT calculations were employed to screen and design MBene-based SACs for the HER. ΔG_H* values were calculated accurately via SVM algorithm by using atomic and structural features. The Bader charge transfer of the surface metal was revealed as the most important parameter for HER activity. Stable Co₂B₂ and Mn/Co₂B₂ were also identified as the efficient HER catalysts because |ΔG_H*| < 0.15 eV.¹⁹² In addition, the screening of SACs embedded on MXenes was performed using ML and DFT calculations to show the ability of ML to screen new candidates with excellent performance.¹⁹³ It shows that the HER catalytic activity is dependent on the synergistic effect between single metal atoms and substrates. In addition, the bag-tree algorithm as a supervised ML technique was applied for the separation of DFT-calculated data and converse prediction of HER performance.¹⁹⁴ ML integrated DFT calculations were applied to accelerate the discovery and screening of TMs and lanthanide (Ln) metals for SACs embedded in graphdiyne, based on the adsorption energies, adsorption trend, electronic structures, reaction pathway, and active sites.

In addition to the HER, ML algorithms were employed based on DFT-calculated data for the fast screening of efficient NRR and CO₂RR electrocatalysts.¹⁰⁵ For instance, graph-based convolutional neural network (GCNN) was applied for the accelerated screening of SACs for the NRR. The results show superior NRR selectivity over the HER with overpotentials of 0.44 V, 0.40 V, 0.24 V, 0.60 V, 0.17 V, 0.17 V, 0.64 V, 0.37 V and 0.58 V, respectively, for SACs embedded in MBenes, defect-engineered 2D-materials, and 2D p-conjugated polymers, TaB, NbTe₂, NbB, HfTe₂, MoB, MnB, HfSe₂, TaSe₂ and Nb.¹⁹⁵ A deep neural network (DNN) was used for rapid and high throughput screening of efficient SACs embedded on boron-doped graphene for the NRR. The adsorption and free energies were calculated using the light gradient boosting machine (LGBM) model based on the bonding characteristics and structural properties as input features. Feature importance analysis was also performed for nitrogen fixation, revealing that the TM coordination number and the number of hydrogen atoms are the key parameters.¹⁹⁶ Extreme gradient boosting regression (XGBR) was implemented as a supervised ML algorithm to screen ΔG_CO* and ΔG_H* for 1060 SACs embedded in metal–nonmetal co-doped graphene using simple features for the CO₂RR.¹⁹⁷ Based on feature importance analysis, the Pauling electronegativity (E_M), covalent radius (M_cov), and first ionization energy of metal atoms (1E_M) are the most important parameters on ΔG_CO*.

4.3 Stability of SACs

SAC's stability is the prerequisite for constructing high-activity SACs, which should be considered by studying metal–support interactions, aggregation energies, and adsorbate-induced structural changes.^198–201 In other words, constructing a strong coordination environment for achieving SACs with strong metal–support interactions is highly desirable and can be achieved by increasing either the anchoring capability of supports or the number of anchor sites.²⁰² The former can be performed by optimizing the coordination environment and the coordination atoms. The latter can be achieved by introducing intrinsic defects and structural engineering through controlling its size and morphology.

In this regard, ML can be applied as a new guideline to efficiently synthesize highly-loaded-yet-stable SACs with strong metal–support interactions.^36,203 For example, ML integrated DFT calculations were employed to correlate the stability of SACs embedded on oxide supports with the binding energy (E_bind) and cohesive energy of the bulk metal (E_c). Assisted by ML methods, it was found that the diffusion activation barrier (E_a) correlates with E_bind²/E_c in the physical descriptor space,²⁰⁴ while E_bind was previously explored to be correlated with E_c.²⁰⁵

Designed SACs should be thermodynamically stable with the lowest energy state. Therefore, thermodynamic stability and optimal combination of dual atomic catalysts embedded in graphdiyne were also investigated by using d-band center modifications and formation stability. Using Gaussian process regression (GPR) as the ML algorithm with seven input features, the potential f–d orbital coupling was found as the most important factor in tuning the d-band center with high stability.³³ Based on these results, the combination of lanthanide metals and transition metals leads to appropriate stability and activity. The thermodynamic stability of SAACs was also investigated in terms of aggregation energies and adsorbate (O*)-caused changes in the structure by using ML algorithms trained with DFT-calculated data for 38 different SAACs on a Cu support. A GPR model was applied on the aggregation energy and O* adsorption energies with a MAE of 0.092 and 0.091 eV, respectively. Moreover, the GPR model is extendable to other substrates, adsorbates, and larger cluster sizes to address the large number of degrees of freedom and decrease the calculation time.²⁰⁶

The zero-valence stability and electron transfer ability of SACs should also be investigated for the stability by considering the redox process between transition metals and a graphdiyne support using ML and DFT. It was indicated that amongst transition metals, Co, Pd, and Pt show high stability of zero-valence SACs based on the difference of energy barriers between gaining and losing electrons.²⁰⁷ Fuzzy C-Means (FCM) as an unsupervised ML algorithm was used for the separation of DFT-calculated data. The developed ML algorithm has been also applied to create a database capable of screening out SACs embedded in graphdiyne.²⁰⁷ The different number and directions of electron transfer between the transition metals and graphdiyne were also analyzed, finding that the initial one-electron transfer is the most difficult one.

Very recently, the stability of the SAAC configuration based on a ML based approach was examined to investigate the tendency of the promoter atom to diffuse into the bulk material, form surface clusters, or avoid alloying with the host.²⁰⁸ Decision trees, neural networks (NN), and SVM with atomic properties as the input feature were used to analyze DFT-calculated data. Then, a physical bond counting model was combined with a KRR algorithm to expand the domain where the model is useful.

The stability and activity of SACs embedded in N_xC_y (TM@N_xC_y) were screened and explored in terms of the structure, coordination, formation energy, structural and electrochemical stability, electronic properties, electrical conductivity, and reaction mechanism for the HER, OER, and ORR using DFT- and ML-based descriptors.²⁰⁹ Among various TM@N_xC_y SACs, TM@N₂C₂ shows higher electrochemical catalytic performance, tends to be more easily formed, and possesses longer durability without aggregation or dissolution. In the TM@N₂C₂ templates, Ni/Ru/Rh/Pt show low HER overpotentials. The ML-based descriptors indicate superior HER, OER, and ORR performances of TM@N₂C₂ compared to those of benchmark noble metal catalysts. It was shown for the first time that both TM and carbon atoms participates in H adsorption.

Table 1 shows the summary of applied ML algorithms and their applications in SAC designing through input feature engineering and feature importance analysis. The list of abbreviations for Table 1 is presented in Table 2. As shown in Table 1, SVM, KRR, RFR, and DNN are mostly used as the supervised ML algorithms for the design of SACs to describe the relationship between the input features and SAC activity. All the mentioned algorithms are normally applied in Scikit-learn.²¹⁰ Atomic properties are mainly used as the input features for the design of SACs from which the number of electrons in the d orbital and enthalpy of vaporization are usually the most important input features for ML algorithms. However, the application of ML is limited by the lack of not only a large and high-quality database but also a generalized ML algorithm for further studies in this field.

Table 1 Summary of ML algorithms and their applications in SACs' design. List of abbreviations is presented in Table 2

#	Support/substrate	ML algorithms	Reaction	Purpose	Input features	Most important features	Year	Ref.
1	CeO2, TiO2, MgO, ZnO, SeTiO3, MoS2, and graphene	LASSO, elastic net, ridge	—	Stability	E c, Ec^−1, Ec^0.5, Ec^−0.5, Ec^2, Ec^−2, ln(Ec), Eb, Eb^−1, Eb^0.5, Eb^−0.5, Eb^2, Eb^−2, ln(Eb), Eb^2/Ec	(Eb)^2/Ec	2020	204
2	Graphdiyne (bi-atom catalysts)	GPR	—	Optimal combination of metals for high stability	—	Potential f–d orbital coupling	2021	33
3	Graphdiyne	FCM	—	Clustering the data	EA, EN, Qe, εd, etc.	—	2019	207
4	Cu, Ru, Rh, Pd, Ag, Re, Os, Ir, Pt, and Au	GKR, SVM, GPR	—	Aggregation energy and ΔGO*	AtN, Atwt, AtPN, AtGN, AtR, EN, IE, EA, B01,O*, etc.	AtR, EN, and AtGN	2020	206
5	Transition metals	DT, SVM, NN, hybrid KRR	—	Stability	AtN, Atwt, AtGN, AtR, rcov, PEN, IE1, Ef, de, etc.	—	2020	208
6	NxCy	GNB, LR, KNN, radius neighbor classifier, support vector classifier, NN, DT, RFR, ETR, and GBR	HER, OER, and ORR	Stability and activity	AtN, IE1, etc.	—	2021	209
7	Graphene	KRR, RFR, NN, SISSO	HER	ΔGH*	ε d, rcov, q, dunocc, docc, N, rd, Ef, IE, EN	docc and q	2020	166
8	Graphene (dual atom catalysts)	RFR	ORR	U L	M1–M2, M12–N, AtR, Ne,O, PEN, IE1, EA of two metals	M12–N, M1–M2, and Ne,O	2020	174
9	Carbon	FCNN	OER	η	AtR, de, EN, EA, and IE1	de, AtR, and EA	2021	167
10	g-C3N4	GBR	OER and ORR	ΔGOH*	ε d, Qe, EN, EA, IE1, AtR, and de, etc.	IE1 and Qe	2021	171
11	Graphene	RFR	HER, ORR, OER	U L	de, Hf,ox, PEN, the sum of PEN, etc.	de	2020	172
12	2D materials	LSBoost	HER and N2RR	ΔG	EN, EA, IE, and diso,e, etc.	diso,e for NRR and EA for the HER	2021	31
13	Graphene	RFR and SVM	—	ΔGH*, ΔGOH*, ΔGO*, and ΔGOOH*	—	Adsorbate type	2020	175
14	2D materials	RFR	ORR	ΔGO*	H f,ox, dpe, EN, EA, IE1, NN, SEN, etc.	H f,ox and dpe	2019	173
15	Graphene	NN	HER	EXAFS spectra	Experimental EXAFS spectrum	—	2021	145
16	g-C3N4, CN, and C2N	ETR method	CO2RR	ΔGOH* and ΔGOCH*	AtN, de, AtR, EN, Hvap, IE, and EA	de and Hvap	2020	176
17	Transition metals	SVM, KRR, GBR, GPR, DTR, ETR, RFR, ABR, MLPR, KNR	CO2RR	ΔGCO*, ΔGCHO*, ΔGCOOH*, ΔGHCOO*, and ΔGCOH*	EN, Ne, and ratio of EN and Ne	Ratio of EN and Ne	2020	191
18	Au(111)	RFR	N2RR	ΔGN2*	AtR, EN, EA, AtGN, de	AtGN	2021	165
19	MBenes	SVM	HER	ΔGH*	Q, AtR of C, N, and B elements, molar ratio, AtR, and EA of metal	q	2020	192
20	MXenes	SVM, RFR, ANN, LASSO, KNN, Bayesian	HER	ΔGH* and E	—	Molar volume of the surface element	2021	193
21	MBenes and 2D-materials	LGBM	N2RR	ΔGN2*	—	N–N bond length	2021	195
22	Graphene	Extreme GBR	CO2RR and HER	ΔGCO*	—	—	2020	197
23	Graphdiyne	Bag-tree algorithm	HER	ΔGH*	—	—	2020	194
24	Graphdiyne	DNN and LGBM	N2RR and HER	ΔG	EN, AtN, AtR, NN, CN, etc.	CN	2020	196
25	C2N, C1N1, and C1S1	RFR	ORR and OER	ΔGO*	AtN, AtR, Ne,O, EN, IE1, EA, SEN, Hf,ox	H f,ox and Ne,O	2021	164
26	Cu	GBR, SVM, RFR	CO2RR	ΔGCO*	—	N e	2021	252

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Table 2 List of abbreviations for Table 1

Abbreviation	Explanation
GPR	Gaussian process regression
GKR	Gaussian kernel regression
GNB	Gaussian naive bayes
SVM	Support vector machine
LASSO	Least absolute shrinkage and selection operator
SISSO	Sure independence screening and sparsifying operator
FCM	Fuzzy C-means
GBR	Gradient boosting regression
LGBM	Light gradient boosting machine
LR	Logistic regression
KRR	Kernel ridge regression
RFR	Random forest regression
ERT	Extremely randomized trees
NN	Neural network
FCNN	Full connection neural network
DNN	Deep neural network
ANN	Artificial neural network
KNN	k-nearest neighbors
LSBoost	Least-squares boosting
DT	Decision tree
DTR	Decision tree regression
ETR	Extra tree regression
ABR	Adaptive boost regression
TPOT	Tree-based pipeline optimization tool
MLPR	Multilayer perceptron regression
KNR	k-neighbor regression
SAC	Single atom catalyst
SAAC	Single atom alloy catalyst
E c, Eb	Cohesive energy of bulk metals, binding energy
AtN, Atwt, AtR	Atomic number, atomic weight, atomic radius
AtPN, AtGN	Period number, group number
EN	Electronegativity
PEN	Pauling electronegativity
S EN	Sum of the electronegativity of coordinated atoms such as N and C
IE, IE1	Ionization energy, first ionization energy
EA	Electron affinity
ε d	d-states' center
r cov	Covalent radius
r d	Zunger radius
N e,O	Outer electron number
docc,e	Number of occupied d states
de	The electron numbers of d orbitals
diso,e	Isolated electrons in d orbitals
dpe	Adjusted electron numbers of d/p orbitals
N e	Number of valance electrons
E f	Formation energy of a single atom site
H f,ox	Oxide formation enthalpy
H Vap	Enthalpy of vaporization
Q, Qe	Bader charge, charge transfer of metal atoms
CN	Coordination number
N N	Number of coordinated N atoms
M1–M2	The distance between the two metal atoms
M12–N	The average distance between the two metal atoms and the coordinated N atoms
η	Overpotential
ΔG	Gibbs free energies
E	Adsorption energies
U L	Limiting potential
V onset	Onset potential

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Moreover, based on Table 1, the d-band center, enthalpy of vaporization, Bader charge, ionization energy, electron affinity, covalent radius, the electron numbers in the d orbital, formation energy, oxide formation enthalpy, etc. mainly are used as the key descriptors to describe the catalytic activity of SACs. Still, one of the main hurdles for employing ML in heterogeneous catalyst design is the lack of appropriate descriptors as input features for ML. An appropriate descriptor needs to simultaneously possess: (1) physical interpretation, (2) high simplicity, and (3) relatively high feature importance. To some extent, the black-box nature of ML techniques occasionally makes a physical interpretation of descriptors, such as the d-band center and enthalpy of vaporization, non-trivial. In particular, the d-band center is widely adopted as an efficient descriptor,²¹¹ typically with high feature importance to describe the reactivity of SACs. However, the d levels of atomically dispersed metal atoms on a graphene substrate may not form a band that makes evaluating the position of the d-band center impossible. Therefore, frontier molecular orbitals and the density of states (DOS) seem more appropriate descriptors than the d-band center.²¹² However, obtaining the frontier molecular orbital and DOS requires time-consuming DFT calculations, making this descriptor not worthwhile. In fact, the simplicity of descriptors requires using metal atom and substrate properties, being readily obtained without needing time-consuming DFT calculations. In contrast to Bader charge and DOS, descriptors such as the atomic number, number of electrons in d orbital, ionization energy, and coordination number of metal atoms possess simplicity requirements.

5. Summary and future prospects

Recently ML has gained much interest for rational deign of heterogeneous catalysts due to its potential for robust and fast prediction of catalyst properties by establishing structure–activity relationships. High throughput screening and feature importance analysis can be achieved through deep structure–activity establishment. However, ML is still at an early stage for the design of heterogeneous catalysts. In this review, high throughput screening and feature importance analysis using ML are provided as the guidelines for heterogeneous catalyst screening and discovery. Although much research has been carried out on the application of ML to improve the activity and stability of heterogeneous catalysts and SACs, there are still challenges to be resolved, requiring additional studies as follows:

(1) There remains room for ML to investigate the catalytic performances and stability,^213–216 and improve calculated parameters for stable SACs.^217,218 In addition, the ML technique can help to investigate the hybridization of SACs,²¹⁹ atomic interface effect,²²⁰ and aggregation energy.²⁰⁶ Moreover, SACs face challenges such as low metal loading, low selectivity and activity, and the lack of catalytic mechanisms.¹³⁶ Therefore ML can help the community to understand the reaction pathways and the catalytic mechanisms^221–225 to improve the selectivity and activity of highly loaded SACs on graphene supports.^226–229 In addition, there is a clear need for ML to consider environmental effects, interfacial engineering, SAC coverage, and the potential for agglomeration. ML can be used for the synthesis of highly loaded SACs, multi-metal SACs, and multi-atom catalysts.^230,231 In other words, since the structure–activity relationships for nanoclusters and DACs are much more complicated than those of SACs,²³² it will be useful to apply ML for predicting adsorption energies for them using new descriptors to consider the synergetic effect of several metals.²³³

(2) ML techniques continue to improve for studying adsorption energies, overpotentials, and metal–support interactions for various SACs, but the field of predictive SAC synthesis to guide experiments is much needed. Because SACs face tedious preparation processes,^8,234,235 ML can accelerate high-throughput experimentation for the synthesis and characterization of SACs.^{190,236–241} ML can also be applied to predict Faraday efficiency and onset potentials to help understand the volcano plots.

(3) A major hurdle for developing ML-aided heterogeneous catalyst design is the lack of sufficient and consistent datasets, data scarcity, bias, and noise from both experiments and QM calculations, which is a high priority to avoid overfitting.⁴⁸ In order to solve this issue, active learning and transfer learning can be applied, which are efficient in compensating for the lack of data. In other words, having a large database composed of DFT-calculated and experimental data is required to train the generalized ML algorithm for systematic and comprehensive discovery of SACs. We expect that in the near future, with a huge database and a universal ML algorithm, the applicability of theoretical calculations for electroreduction reactions using SACs will be improved greatly.²⁴² In addition, the vast parameter space for dynamic catalysts requires applying ML to screen candidate catalysts by predicting the regions with high selectivity and operability.²⁴³ The effect of the coordination number, coordination atoms, designed bond length, and bond angle on the current density, overpotentials, and reaction mechanism should be considered through ML.^244–246

(4) ML has the potential to predict the properties of SACs very quickly and accurately, but its application has been limited to specific systems using various ML algorithms. Therefore, a fair comparison to assess the strengths and best use of different ML algorithms is needed. Also, similar to ML-aided retrosynthesis and reaction planning,^72,247,248 a strong need is the development of a universal (generalized) ML algorithm that changes ML from a supportive tool to a surrogate tool for SAC design. This universal ML algorithm should be extended to widespread SACs and supports for all electroreduction reactions toward efficient and cost-effective potential SACs to balance between the activity and stability.²⁴⁹

(5) In Table 1, two-dimensional (2D) materials leading to reduced computational cost due to their simplicity in structure are shown. However, three-dimensional (3D) materials, such as oxides and nitrides,^250,251 play a major role in catalysis and should be extensively investigated by using existing or new ML algorithms.

Conflicts of interest

These authors respectfully declare that there are no conflicts of interest to acknowledge for this research.

Acknowledgements

Z. L. acknowledges support from the RGC (16304421), Innovation and Technology Commission (ITC-CNERC14SC01), Guangdong Science and Technology Department (Project#: 2020A0505090003), Research Fund of Guangdong-Hong Kong-Macao Joint Laboratory for Intelligent Micro-Nano Optoelectronic Technology (No. 2020B1212030010), IER foundation (HT-JD-CXY-201907), and Shenzhen Special Fund for Central Guiding the Local Science and Technology Development (2021Szvup136). Technical assistance from the Materials Characterization and Preparation Facilities of HKUST is greatly appreciated. W. A. G. acknowledges support from the DOE Liquid Sunlight Alliance (LiSA) (DE-SC0021266) and the US National Science Foundation (NSF CBET-2005250).

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