Prediction of Oxygen Evolution Activity for FeCoMn Oxide Catalysts via Machine Learning

Abstract

Electrolytic hydrogen production from water is a promising approach for obtaining clean energy. The development of efficient oxygen evolution reaction (OER) electrocatalysts is crucial for the generation of hydrogen through water electrolysis. Transition metal oxides, such as Fe, Co, and Mn, have shown potential as efficient OER electrocatalysts for water splitting. However, accurately predicting their electrocatalytic performance in complex compositional spaces remains a challenge, impeding the precise design of compositions and processes for optimal performance. Herein, a machine learning-based method is proposed for predicting the OER activity of (FeCoMn)O_x catalysts across a wide range of compositions. Physical features that are highly relevant to the OER overpotential (OP) are identified and analyzed. The random forest algorithm is successfully used to establish the relationship between composition and overpotential. The model demonstrates good accuracy in predicting the outcomes of new experiments, with a mean relative error (MRE) of 9.3%. The features based on covalent radius (RC) and the number of electrons in the outermost d orbitals (DEs) are the primary factors. Their variances (δ_RC and δ_DE) exhibit a linearly decreasing relationship with the overpotential (OP), providing direct guidance for designing OP-oriented components. This work presents an effective and innovative approach for predicting and analyzing the physical factors of transition metal oxide electrocatalysts, which can enhance the design of highly catalytic materials for electrocatalysis.

1. Introduction

As the global demand for renewable energy continues to increase, the utilization of water electrolysis technology, which converts electrical energy into hydrogen and oxygen, has gained significant attention [1,2,3]. In this process, the oxygen evolution reaction (OER) is a key step that involves a 4e-transfer and exhibits slow reaction kinetics [4,5,6,7]. Thus, the development of efficient OER electrocatalysts is crucial for the sustainable advancement of clean energy. However, the widespread application of traditional noble metal catalysts (such as RuO₂ and IrO₂) for the OER is limited due to their scarcity and high cost [8,9,10,11]. As a result, there is a growing focus on the search for efficient, cost-effective, and sustainable non-noble metal catalysts, making it a research hotspot.

Transition metal-based catalysts, including the oxides, hydroxides, phosphides, and borides of Mn, Fe, Co, and Ni, have shown significant promise for OER due to their high catalytic performance and potential as alternatives to noble metal catalysts [12]. However, these catalysts often face challenges, such as limited active sites and suboptimal electrocatalytic activity, which hinder their widespread application. Transition metal oxides (TMOs) possess intricate inherent characteristics that contribute to a diverse range of catalytically influential properties stemming from their unique electronic structures that can be tailored through compositional adjustments and structural modifications. The performance of TMOs in electrochemical applications is also greatly influenced by testing conditions, such as voltage ranges, current densities, and mass loading. In recent years, various techniques have been developed to optimize composition and structure, such as controlling the morphology of the catalyst to expose more active sites [13,14,15,16] or regulating mass loading to achieve the optimal balance of catalytic efficiency and stability [17,18,19]. Furthermore, heteroatoms are incorporated into monometallic metal oxides or cation substitution to create binary, ternary, and other multi-metal oxide catalysts [20]. This approach, particularly with first-row transition metals such as Fe, Ni, Co, Mn, and Cu, has demonstrated potential in modifying the electronic structure, enhancing conductivity, improving hydrogen adsorption energy, and increasing the number of active sites [21,22,23,24,25]. Pu et al. prepared 12% Ni-Co₃O₄ (the molar ratio of Ni to Co is 12%), which rendered the best activity [26]. This improvement is attributed to the unique synergistic effect between Co and Ni, as well as the modified electronic structure. Li et al. prepared a series of Fe-substituted cobalt spinel oxides, Fe_xNi_1−xCo₂O₄ (x = 0, 0.1, 0.25, 0.5, 0.75, 0.9, 1), where Fe_0.5Ni_0.5Co₂O₄ exhibited enhanced OER activity [27]. This improvement can be attributed to the synergistic effect of ternary mixed metals, particularly the incorporation of Fe and the uniform nanowire support on nickel foam (NF). Therefore, the optimization of the elemental composition in binary, ternary, and multi-metal oxide catalysts is an efficient way to enhance their catalytic performance [28,29,30]. The vast design space of binary, ternary, and multi-metal oxides makes it challenging to screen all potential catalysts and identify the optimal composition for catalytic performance. Traditional methods involve synthesizing and testing numerous compositions, which is both time-consuming and resource-intensive. This approach often leads to a bottleneck in the discovery process.

Machine learning (ML) is a powerful statistical technique that employs algorithms to map input data to desired information [31,32,33,34]. Data mining technology can be used to analyze the nonlinear relationship between the catalyst structure (geometric and electronic structure) and performance, thereby quickly predicting the performance of multiple catalysts and accelerating research progress [35,36,37,38]. These methods have proven to be valuable in accelerating the screening and discovery of new materials, particularly in fields such as biomaterials, electrocatalysis, and batteries [39]. However, the effectiveness of ML-based methods relies heavily on the availability and richness of data. Fortunately, there is a wealth of experimental and theoretical data in the literature and databases related to catalyst design and optimization, which can provide valuable insights for the development of new catalysts.

In this work, we introduced a data-driven approach to predict the overpotential (OP) of (Fe-Co-Mn)O_x catalysts using machine learning algorithms. By considering valence electrons, relative atomic mass, atomic number, the non-bonding atomic radius, covalent radius, first ionization energy, Pauling electronegativity, and the number of outermost d-orbital electrons, various physical features were successfully correlated with overpotential. According to the optimal value of the mean square error and mean absolute error, the random forest (RF) algorithm was chosen as the best model. This model was used to efficiently screen the Fe-Co-Mn ternary catalyst system and identify optimal composition ratios [40]. In order to verify the results of machine learning in the new experiments, we prepared five iron–cobalt–manganese oxide catalysts with different ratios using a hydrothermal method and tested their OER catalytic performance. The experimental results were basically consistent with machine learning prediction results, with a mean relative error (MRE) of 9.3%. This work provides an efficient new approach to predicting and designing transition metal oxide OER electrocatalysts.

2. Results and Discussion

2.1. Data Collection

All the data used in this work were collected and screened from Ahmed’s published research through high-throughput experiments [41]. We considered oxide catalysts belonging to the Fe_xCo_yMn_z system, where the molar fractions of each element (x, y, and z) were subject to the constraint x + y + z = 100%. The dataset comprises 66 entries. These entries cover the elemental compositions of various (Fe-Co-Mn)Ox materials. Therefore, the overall dataset consists of three elemental features (input variables) and one target OP (output variable). Figure 1 visualizes the original dataset by categorizing them based on the compositions of Fe, Co, Mn, and OP. As the compositions of Fe, Co, and Mn increase, the overall OP exhibits an initial decrease followed by an increase. This method clearly reveals the optimal composition for metal oxide catalysts in terms of overpotential. The comprehensive and complete dataset provides reliable evidence for predictive models and physical analysis.

2.2. Feature Construction

Feature selection plays a pivotal role in the performance of machine learning models. These features should not only be easily accessible but also accurately represent the geometrical and electronic characteristics of the metal atoms. This study considers eight independent features as follows: relative atomic mass (RAM), atomic number (AN), non-bonded atomic radius (RA), covalent radius (RC), valence electron number (VEN), first ionization energy (FIE), Pauling scale electronegativity (EP), and the number of electrons in the outermost d orbital (DE). The first four features primarily focus on the geometric structure of the catalysts, while the remaining four pertain to the electronic properties, indicating the active site’s ability to donate or accept electrons.

For Fe, Co, and Mn elements, the corresponding physical properties associated with these features were collected from the Royal Society of Chemistry’s interactive periodic table database [42]. Each catalyst sample was numerically represented using the composition (C_i) and relevant elemental properties. The feature transformation functions are given by Equations (1) and (2), with the aim of converting the original chemical element space into the primary physical feature space (

Table 1. Material physical features, abbreviations, units and transformation formulas.

Features	Abbreviation	Unit	Formula
valence electron number	VEN		$\begin{array}{}\mathrm{(1)}& \overline{X}=\sum _{i\in \left\{Fe,Co,M_n\right\}}{C}_i{P}_i\hfill \mathrm{(2)}& {\delta }_X=\sum _{i\in \left\{Fe,Co,Mn\right\}}{\left[P_i-\overline{X}\right]}^2{C}_i\hfill \end{array}$
relative atomic mass	RAM
atomic number	AN
non-boned atomic radius	RA	Å
covalent radius	RC	Å
first ionization energy	FIE	kJ mol−1
Pauling scale electronegativity	EP
the number of electrons in the outermost d orbital	DE

). Specifically, for each of the 66 catalyst samples, $\overline{X}$ computes the weighted average of the element content for each physical feature, while δ_X calculates the variance of each physical feature. This variance reflects the physical diversity among the chemical elements. In Equations (1) and (2), C_i is the mole fraction of each element, and P_i corresponds to the properties of each element, respectively. Thus, $\overline{X}$ and δ_X construct 16 descriptive features that may be physically relevant to the OP. The original dataset was converted into a new dataset of shape 66 × 16 (Table S1).

2.3. Prediction Model

Herein, we used 11 algorithms for model construction, including random forest (RF), Adaptive Boosting (boosting), K-Nearest Neighbors (KNNs), Bagged Classification and Regression Trees (CART_bagged), Gaussian Kernel Support Vector Machine (SVM_radial), Cubist, Full Quadratic K-Nearest Neighbors (full_quad_KNNs), neural network, Multivariate Adaptive Regression Splines (MARSs), Classification and Regression Trees (CARTs), and Polynomial Kernel Support Vector Machine (SVM_poly). Among them, SVM_radial, SVM_radial, and KNNs are linear models, and multicollinearity can lead to unstable coefficient estimates and unreliable hypothesis testing in regression models. Prior to implementing machine learning techniques, it was necessary to compute the Pearson correlation coefficient in order to remove any linear correlation between two variables. Figure 2 shows a heat map of Pearson correlation coefficients between feature parameters. Features with absolute correlation coefficients greater than 0.95 are considered highly correlated, as shown by the dark blue and dark red boxes in Figure 2. In a pair of highly correlated features, one of them can be expressed linearly and replaced by the other. Multiple variables, including δ_AN and δ_DE with a correlation of 1 and EA and RA with a correlation of −1, show a significant correlation. The linear model prediction, after eliminating collinearity, incorporates the five variables VEN, FIE, δ_VEN, δ_FIE, and δ_DE.

During the model training, 80% of the instances in the database were randomly selected as the training set, while the remaining 20% were designated as the testing set. The model’s quality was assessed by calculating the mean squared error (MSE) and mean absolute error (MAE) due to the continuous nature of overpotential. To determine the optimal parameters, a ten-fold cross-validation was conducted on each machine learning model, followed by a grid search on the training set. This method involved dividing the dataset into ten subsets, using one as the validation set and the remaining nine as the training set, which was repeated ten times to ensure the model’s stability and generalization ability. As shown in Figure 3a, the variation in parameters in the neural network algorithms had the most significant impact on the model’s predictive ability, while the CART_bagged model remained relatively unaffected. CART_bagged is a decision tree model that utilizes bagging to improve stability and predictive performance by averaging the results of multiple decision trees. After selecting the optimal parameters for each model, their predictive ability is evaluated on new datasets using the validation set. This analysis reveals that random forests have the best predictive performance (MSE = 30.45, Figure 3b). This ensemble learning method builds multiple decision trees and averages their results to improve prediction accuracy and stability.

The RF model was retrained using the optimized parameters on the training set. The diagonal scatter plot in Figure 4a displays the predicted OP and ground truth values of the RF model during both training and testing, utilizing the transformed and selected datasets. The results indicate a consistent trend between the RF-predicted OP and ground truth values, with a clear linear relationship observed in both the training and testing sets. This demonstrates the high accuracy of the well-trained RF model in predicting OP.

Based on these aforementioned findings, the RF model was utilized to predict and screen the Fe-Co-Mn ternary catalyst system in order to design the optimal components for a highly active FeCoMn catalyst. The search space was designed as Fe_xCo_yMn_z, where x, y, and z represent the mole fractions of Fe, Co, and Mn, respectively, ranging from 0 to 1 with a step of 0.01. To facilitate the description of the catalyst’s composition, a ternary phase diagram (Figure 4b) was created, with the mole fractions of Fe, Co, and Mn representing the three edges and the colors indicating the OER activity of the catalyst. It was observed that the FeCoMn ternary catalyst exhibited superior catalytic activity compared to binary compositions and single metal oxides. Among them, Fe₁₂Co₄₀Mn₄₈O_x showed the best catalytic activity with the overpotential measured at 10 mA cm⁻² of the current. Optimizing the components is an effective approach to enhance catalyst activity. Our work provides an efficient method for quickly determining the optimal component for catalyst optimization.

2.4. Experiment Validation

To validate the results predicted by machine learning, we prepared Fe₁₂Co₄₀Mn₄₈O_x, Fe₃₀Co₄₀Mn₃₀O_x, Fe₃₀Co₂₀Mn₅₀O_x, Fe₅₀Co₅₀O_x, and Co₅₀Mn₅₀O_x at five different ratios of FeCoMn oxide catalysts using a hydrothermal method. Their morphologies are shown in Figure S1, and they exhibit similar nanosheet-like structures. The elemental compositions were confirmed by inductively coupled plasma-optical emission spectrometer (ICP-OES) measurements (Table S2). We then tested the OER activity of the prepared samples in N₂ saturated in 1.0 M KOH (aq). Figure 5a shows the LSV curves of the samples, and the experimental overpotential and predicted overpotential 10 mA/cm⁻² are shown in

Table 2. Composition and overpotentials of different ratios of FeCoMn oxides.

Sample	Fe	Co	Mn	Experimental (mV)	Predicted (mV)
exp-1	0.12	0.4	0.48	344	369.3
exp-2	0.3	0.4	0.3	367	389.1
exp-3	0.3	0.2	0.5	372	415.6
exp-4	0.5	0.5	0	391	442.2
exp-5	0	0.5	0.5	356	385.6

. The ground truth values of the experimental OP and the OP predicted by the RF model are presented in Figure 5b. The results show a close match between the experimental and predicted values for the five catalysts, with an MRE of 9.3%. While deviations may occur due to factors such as data bias, model complexity, and overfitting, the trend of RF-predicted OP remains consistent with the experimental value. This demonstrates the successful application of the RF model in catalyst screening and design optimization. C_dl was calculated by measuring the cyclic voltammetry (CV) curve (Figure S2). As depicted in Figure S3, compared with the other four catalysts, Fe₁₂Co₄₀Mn₄₈O_x shows a higher C_dl value (3.23 mF cm⁻²), indicating that Fe₁₂Co₄₀Mn₄₈O_x has a larger electrochemically active surface area. The Tafel slopes of the five catalysts are shown in Figure S4. Compared with the other four catalysts, the Tafel slope of Fe₁₂Co₄₀Mn₄₈O_x is the smallest, which is 49.36 mV/dec, indicating that the OER kinetics of Fe₁₂Co₄₀Mn₄₈O_x are the fastest.

In order to further understand the relationship between characteristic values and overpotentials, the Shapley Additive Explanation (SHAP) values of the characteristics in 66 sets of data instances were calculated. We evaluated the contribution of feature values to prediction results using the scatter plot of the feature impact from SHAP (Figure 6). In the figure, all features were sorted vertically from large to small by the sum of SHAP values, while the SHAP value distribution of each feature is displayed on the horizontal axis. Each dot represents a catalyst; the color of the dot represents the numerical value of the corresponding feature of the catalyst, and the position of the dot represents the SHAP value of the corresponding feature of the catalyst. Based on the results from SHAP plots, we can observe whether each feature has a positive or negative impact on the prediction outcome. Figure 6 displays the distribution of SHAP values for all feature values, arranged in descending order of feature importance. In the graph, δ_RC is at the top of the SHAP plot, indicating that it is the most important feature. δ_RC, δ_DE, δ_AN, δ_RAM, δ_RA, and δ_EP are widely dispersed in the SHAP plot. This indicates that they significantly influence the prediction of overpotential. When the values of these features are larger, their SHAP values become more negative. This implies that these features are negatively correlated with the predicted overpotential. The variance of the covalent radius and the variance of Pauling electronegativity reveal the stability of covalent radii data for different proportions of Fe, Co, and Mn metals. Smaller feature values indicate greater dataset stability and reduced fluctuations, implying minimal differences among the data points. Therefore, metal dopants with similar radii and small electronegativity differences can effectively modulate the geometric and electronic structures, thereby optimizing OER performance.

Moreover, the literature has shown that the number of electrons in the outermost d orbital has a direct impact on the d-band center energy of the metal active center, while the covalent radius is closely linked to the formation of covalent bonds between the metal atom and its coordination with oxygen atoms. This results in a lower d-band center energy for metals with more outermost d electrons, leading to a more stable energy-level structure. This, in turn, affects the interaction between metal sites and adsorbates, ultimately influencing the catalytic performance. Additionally, smaller covalent radii correspond to shorter bond distances and stronger covalent bonds. Metals with a higher number of d electrons form shorter metal–oxygen bonds, resulting in the release of additional active sites and stabilization of intermediate adsorption states, thereby enhancing catalyst activity. It is evident that these factors are closely interconnected, and understanding their interrelationships and effects is crucial to comprehend catalyst activity mechanisms and design efficient OER catalysts.

3. Materials and Methods

The data flow of this article is based on analysis using the R language package of mr13. Firstly, the collected data were split 7:3 into training and validation sets. Secondly, 11 algorithms were used for model construction, including random forest (RF), Adaptive Boosting (boosting), K-Nearest Neighbors (KNNs), Bagged Classification and Regression Trees (CART_bagged), Gaussian Kernel Support Vector Machine (SVM_radial), Cubist, Full Quadratic K-Nearest Neighbors (full_quad_KNNs), neural network, Multivariate Adaptive Regression Splines (MARSs), Classification and Regression Trees (CARTs), and Polynomial Kernel Support Vector Machine (SVM_poly). For each machine learning model, parameter tuning of the model was performed using ten-fold cross-validation. Since the overpotential is a continuous variable, the goodness of the model is evaluated by calculating the mean squared error (MSE) and the mean absolute error (MAE), and the model parameter with the smallest MSE and MAE is selected as the best model. The experimental procedures for catalyst synthesis and electrochemical characterization are detailed in the Supplementary Information section.

4. Conclusions

A machine learning-based method was proposed to predict the activity of (Fe-Co-Mn)O_x catalysts in high-dimensional composition space. Physical features related to OER catalyst overpotential were constructed, including valence electron count, relative atomic mass, atomic number, non-bonding atomic radius, covalent radius, first ionization energy, Pauling electronegativity, and outermost d-orbital electron count. The random forest algorithm demonstrated the best-fitting performance and was used to predict overpotential. Experimental validation with five proportions of (Fe-Co-Mn)O_x catalysts resulted in a mean relative error (MRE) of 9.3% and a mean squared error (MSE) of 30.45. The most influential features were found to be the variance in covalent radius (RC) and outermost d orbital electron number (DE), which showed a linear decrease with overpotential (OP). This model was used to efficiently screen the Fe-Co-Mn ternary catalyst system and identify optimal composition ratios, reducing the number and time of experiments and overall development cost. This approach provides a valuable tool for predicting the activity of FeCoMn oxide OER electrocatalysts and has the potential to be extended to other electrocatalyst design applications.