English

• Ammonia is an essential ingredient in the production of fertilizers [1,2]. However, the conventional method of producing ammonia, known as the Haber process, has certain drawbacks. It consumes a lot of energy and releases a significant amount of carbon dioxide into the environment, contributing to environmental degradation [3,4]. To tackle this problem, researchers are exploring new methods. One such alternative is to use nitrate for ammonia synthesis [5,6]. In this process, catalysts play a crucial role in speeding up chemical reactions [7,8]. One highly efficient catalyst for this process is the cobalt phosphide-based material structure. This structure can be used to electroreduce nitrates to produce ammonia, providing a promising way to synthesize ammonia [9]. By incorporating atomic substitution, the catalytic performance of these materials can be even further enhanced [10]. In current research, high-throughput cobalt phosphide catalyst screening experiments primarily use single-atom substitution to obtain new configurations [11]. However, there is a lack of experiments exploring cobalt phosphide catalyst configurations through diatomic substitution. The existing research focuses on a single target value for evaluating catalytic performance [12], and obtaining the target value is a time-consuming process [13]. The accuracy and efficiency of the catalyst performance obtained need to be improved. Hence, it is essential to develop a rapid multi-objective material design approach that ensures efficient catalyst material design.

  Machine learning models have proven to be effective in reducing the number of simulation calculations, thereby shortening the material design cycle [14–16]. However, the design of catalyst materials is associated with a limited number of data samples, resulting in low accuracy of predictive models. On the other hand, Symbolic regression derives feature equations from a set of predetermined independent variable data, which quickly identifies the relationship between independent variables and target values. It has shown outstanding performance in applications based on small sample data and has been successfully used in discovering material feature descriptors [17,18]. However, its application in predicting multi-objective attributes has been rarely reported in research.

  Symbolic regression techniques have recently been employed to forecast catalyst performance, which can be classified into four main types: Formular-based methods, such as linear regression (LR) [19], kernel ridge regression (KRR) [20], lasso-based least angle regression (LASSOLAR) [21], sure independent screening and sparsifying operator (SISSO) [22], support vector machine regression (SVR) [23], k-nearest neighbor regression (KNR) [24], and gaussian process regression (GPR) [25]. Regression methods utilizing expression trees include random forest regression (RFR) [26], extreme gradient boosting regression (XGBR) [27], and adaptive boosting regression (ABR) [28]. Neural network-based regression methods encompass feedforward neural network regression (FNNR) [29] and multilayer perceptron regression (MLPR) [30]. Regression techniques founded on optimization algorithms consist of stochastic gradient descent regression (SGDR) [31] and gradient boosting regression (GBR) [32].

  Based on the symbolic regression method mentioned above, it is possible to predict target values related to materials such as adsorption energy and formation energy, using attributes of atoms in the material structure, such as radius, electron count, and electronegativity. Therefore, this paper proposes a multi-target cobalt phosphide catalytic material design method based on the surrogate model. The surrogate model determines the relationship between the properties of substituting atoms and the formation energy, adsorption Gibbs free energy of nitrate ions, and hydrogenation Gibbs free energy. With the proposed method, fifteen effective diatomic substitution configurations for cobalt phosphide catalysts were identified. The method proposed in this article has the following characteristics: (1) It uses diatomic substitution to obtain cobalt phosphide substitution configuration. (2) By considering three target values, excellent catalysts can be obtained more accurately. (3) In terms of time consumption, this method is faster than traditional calculation methods.

  The accuracy of a model heavily relies on its features. In this paper, six physical or chemical properties were selected as features, namely: atomic radius (ra) of two replacing atoms, the sum of the outermost electron count in d and p orbitals (Edp), outermost electron count in d orbital (Nd), Pauli electronegativity (Nm), electron affinity (x), and first ionization energy (Im). The substitution method for the atoms is as follows: the first atom to be replaced is Co, with the set of substituting element being {'Sc', 'Y', 'Ti', 'Zr', 'Hf', 'V', 'Nb', 'Ta', 'Cr', 'Mo', 'W', 'Mn', 'Tc', 'Re', 'Fe', 'Ru', 'Os', 'Co', 'Rh', 'Ir', 'Ni', 'Pd', 'Pt', 'Cu', 'Ag', 'Au', 'Zn', 'Cd', 'Hg'}, and the second atom to be replaced is P, with the set of substituting element being {'B', 'C', 'Si', 'N', 'P', 'As', 'O', 'S', 'Se', 'Te', 'F', 'Cl', 'Br', 'I', 'Sc', 'Y', 'Ti', 'Zr', 'Hf', 'V', 'Nb', 'Ta', 'Cr', 'Mo', 'W', 'Mn', 'Tc', 'Re', 'Fe', 'Ru', 'Os', 'Co', 'Rh', 'Ir', 'Ni', 'Pd', 'Pt', 'Cu', 'Ag', 'Au', 'Zn', 'Cd', 'Hg'}. In previous studies on catalyst-catalyzed electrochemical reduction of nitrate to ammonia, formation energy, adsorption Gibbs free energy, and hydrogenation Gibbs free energy were considered as criteria for evaluating the stability of new catalyst configurations [33]. The specific steps are as follows: when metal or non-metal atoms replace Co and P atoms and adsorb on the surface of cobalt phosphide catalyst, nitrate ions adsorb on the substrate and transfer one proton and one electron at the negative electrode potential to form hydrogen nitrate ions. The chemical equation for this reaction step is

  $ \mathrm{NO}_3{ }^*+\mathrm{H}^{+}+\mathrm{e}^{-} \rightarrow \mathrm{NO}_3 \mathrm{H}^* $

  (1)

  For each substitution configuration, the formation energy (E_f), the adsorption Gibbs free energy of nitrate ions (ΔG(NO₃), and the hydrogenation Gibbs free energy (ΔG) must be taken into consideration [33,34]. The promising cobalt phosphide catalyst configurations should simultaneously fulfill three basic conditions: E_f < 0, ΔG(NO₃) < 0, and ΔG < 0.7. and the values of E_f, ΔG(NO₃) and ΔG were calculated by Eq. 2.

  {Ef=ETM&|x26;CoP+ECo−ECoP−ETMΔG(NO3)=G(NO3)−G(*)−G(HNO3)+1/2G(H2)+0.392ΔG=ΔE+ΔZPE−TΔS

  (2)

  where E_TM&CoP, E_Co, E_CoP, E_TM are the energies of TM-CoP, Co, CoP, and transition metal atoms from the bulk, respectively. G(NO₃), G(*), G(HNO₃), G(H₂) are the Gibbs free energy of NO₃^- adsorbed on substrates, as well as HNO₃ and H₂ molecules in the gas phase, respectively. ΔE represents the total energy difference between the reactants and the products. ΔZPE and ΔS denote the correction of zero-point energy and entropy, respectively. represents room temperature (298.15 K).

  Due to the time-consuming calculation process of VASP software, the number of training samples obtained is limited. By referring to previous research on the processing of the dataset and the impact of sample size on model training [35], this experiment uses a dataset consisting of 80 randomly sampled configuration samples, and three target values of these 80 samples will be calculated by VASP software, the detail of dataset is available in Note S1 (Supporting information). The dataset was divided into training and testing sets at an 8:2 ratio [36]. The prediction accuracy of the model was evaluated using Pearson's correlation coefficient (r), root mean square error (RMSE), and coefficient of determination (R²) [37–39]. More information on evaluation metrics is available in Note S2 (Supporting information). The model parameters for 14 symbolic regression algorithms were set according to [40,41], and the details can be found in Note S3 (Supporting information). Fifty random experiments were conducted to assess the predictive abilities of symbolic regression models for E_f, ΔG(NO₃) and ΔG. More information on train sets are available in Note S4 (Supporting information). Results obtained from the testing sets can be analyzed as follows.

  Results on E_f were illustrated in Fig. 1. It was clear that LASSOLAR, displayed the best accuracy with r = 0.82 and R² = 0.6. The results of XGBR, LR, KRR, SISSO, RFR, GBR and ABR were not notably different. Regarding the RMSE metric, the RMSE values for the XGBR is 0.31. Apart from the FNNR, MLPR, SGDR, SVR, KNR, and GPR models, whose RMSE values exceed 0.45, the rest of the models have RMSE values close to 0.4. The models FNNR, MLPR, SGDR, SVR, KNR, and GPR did not yield satisfactory results.

  Figure 1

  

  Figure 1.  In terms of E_f, the evaluation results of each algorithm on the testing set: (a) Result of r, (b) result of R², (c) result of RMSE.

  DownLoad: Full-Size Img PowerPoint

  Results on ΔG(NO₃) were illustrated in Fig. 2. It is observed that XGBR obtained results with r and R² values of 0.87 and 0.72, respectively. The r values obtained by using the RFR, GBR and ABR models were similar to those obtained by using XGBR, but the XGBR model outperformed the RFR, GBR and ABR models in terms of R² and RMSE values. The remaining models generally exhibited poorer performance, the RMSE of the other models were all greater than 1.

  Figure 2

  

  Figure 2.  In terms of ΔG(NO₃), the evaluation results of each algorithm on the testing set: (a) Result of r, (b) result of R², (c) result of RMSE.

  DownLoad: Full-Size Img PowerPoint

  Results on ΔG were illustrated in Fig. 3. XGBR exhibited r = 0.75, while the RFR also performed well with r = 0.74. However, in terms of R², RFR lagged slightly behind XGBR, with XGBR yielded an R² value of 0.56, whereas the R² value of RFR was 0.53. The model performance of ABR was satisfactory, slightly lower than RFR. FNNR, MLPR, SGDR, SVR, KNR, and GPR models showed poor performance. In terms of the RMSE metric, the RMSE for XGBR was 0.60, while the RMSE for the other models all exceeded 0.65.

  Figure 3

  

  Figure 3.  In terms of ΔG, the evaluation results of each algorithm on the testing set: (a) Result of r, (b) result of R², (c) result of RMSE.

  DownLoad: Full-Size Img PowerPoint

  Based on comprehensive considerations, XGBR was the best surrogate model for predicting E_f, ΔG(NO₃) and ΔG. The XGBR not only showed high predictive accuracy but also remarkable stability, as evidenced by minimal variance in testing and training sets. Results on training sets are available in Supporting information. Meanwhile, this study conducted a 10-fold cross validation method on the XGBR model, using RMSE as the evaluation criterion. As shown in Fig. S4 (Supporting information), the results of the three target values in 10 verifications showed relatively stable performance, further proving the accuracy of the XGBR model. The GPR model tended to overfit, resulting in inaccurate predictions during testing. This overfitting issue stemmed from the limited data points in the original dataset, causing the model to lack sufficient information to identify underlying relationships in the data. The SISSO, GBR, RFR, and ABR models performed well in training experiments but experienced a noticeable decrease in performance during testing due to limited data availability. The LR, KRR and LASSOLAR models showed moderate performance. The remaining models in this experiment exhibited relatively poor performance, including FNNR, MLPR, SGDR, KNR and SVR.

  The results obtained from using the trained XGBR model were shown in Fig. S5 (Supporting information). In the training set, most of the XGBR-predicted values aligned with the actual values, with only a few values deviated by less than 0.5. This suggests that the trained XGBR model has a strong predictive capability. In the testing set, the predicted values showed a clear linear correlation with the actual values computed using VASP software. About half of the predicted points by XGBR matched the actual values, while the remaining points had errors of less than 0.5.

  The XGBR model was trained to identify material structures with better catalytic performance. The process of verifying the catalytic performance of the substituted configuration in this study is shown in Fig. S6 (Supporting information): Check if the formation energy of the substituted configuration is less than 0. If the condition is not met, the substituted configuration is considered unstable. If it is less than 0, check whether the Gibbs free energy of nitrate ions adsorption is less than 0. If it is greater than or equal to 0, it means that the adsorption process of the catalyst cannot occur spontaneously. When the adsorption Gibbs free energy is less than 0, and the hydrogenation Gibbs free energy is less than 0.7, the substituted configuration has good catalytic performance. Out of 259 configurations, 26 promising configurations were found. Among these, 15 configurations were confirmed to be promising through DFT calculation: Sc-F, Y-O, Sc-O, Sc-N, Hf-F, Y-Cl, Ti-O, Sc-Se, Sc-As, Sc-Te, Hf-Cl, Ti-S, Ti-Si, Sc-Sc and Hf-Sc. In these configurations, the former element replaced Co, while the latter element replaced P. According to Fig. 4, the Sc-O, Sc-N and Sc-Te substitution schemes had the most accurate predictions, with prediction errors for all three targets being less than 0.7. If only considering E_f and ΔG, the prediction errors of the three configurations (Sc-O, Sc-N, Hf-Sc) were less than 0.45. If only considering E_f and ΔG(NO₃), the prediction errors of the three configurations (Sc-Se, Ti-S, Ti-Si) were less than 0.3.

  Figure 4

  

  Figure 4.  The E_f, ΔG(NO₃) and ΔG of 15 configurations. Red data represents predicted values, green data represents true values.

  DownLoad: Full-Size Img PowerPoint

  For the remaining 11 substitution schemes deemed promising by XGBR but not in reality, the issue stems from considering E_f, ΔG(NO₃) and ΔG simultaneously. From the results shown in Fig. S7 (Supporting information), it is evident that focusing on a single target value leads to a notable increase in the likelihood of accurate predictions. The probabilities of successful identification were 96.2%, 84.61%, and 69.23% respectively, while one of E_f, ΔG(NO₃) and ΔG being considered. The probabilities of successful identification were 57.69%, 84.61%, and 65.38%, respectively, and while ΔG and ΔG(NO₃), E_f and ΔG(NO₃), and E_f and ΔG being considered. When considering three target simultaneously, the probability of successful identification was 57.69%. The ablation experiment revealed that when considering only E_f and ΔG(NO₃), as the two target values, the probability of prediction alignment with reality significantly increases. However, once the ΔG was introduced, it became challenging to find a combination that aligned with reality. The reason was that the XGBR model's poor performance in terms of the reduced the probability of successful identification.

  VASP software and model-based methods were used to calculate the three target values of 80 experimental samples and 26 validation samples. The obtained computational cost is shown in Fig. S8 (Supporting information), which reduces the time cost by 7 times, 42 times, and 53 times respectively. The model-based approach greatly improves the efficiency of computation, which is of great significance for the low-efficiency problem of traditional DFT calculations.

  The XGBR model is a black box algorithm. To analyze its role in the catalytic performance of cobalt phosphide catalysts, this experiment conducted feature importance analysis on all input features of the XGBR model in the original dataset, as shown in Fig. S9 (Supporting information). Edp1 & ra2 and Edp1 & ra1 are the most important descriptors for predicting E_f and ΔG in the XGBR model, while Edp2 and x2 are the most relevant descriptors for ΔG(NO₃). That is to say, in the new configuration of cobalt phosphide catalysts, the three properties of substituted atoms: The sum of the outermost electron counts in d and p orbitals, electron affinity, and atomic radius are the most important descriptors of catalytic activity.

  In conclusion, a model-based method was proposed to accelerate the design of multi-objective catalytic materials. Its efficiency was demonstrated in the application of multi-objective cobalt phosphide catalytic materials design. In the application, one cobalt atom and one phosphide atom in cobalt phosphide materials were substituted to generate new configures, and E_f, ΔG(NO₃) and ΔG were considered as multi-objective attributes. The results based on 50 randomly experiments and 10-fold cross validation confirmed that the XGBR model emerged as the best-performing symbolic regression model. A surrogate model was trained by using XGBR. In predicting E_f, ΔG(NO₃) and ΔG, the r values were 0.91, 0.94 and 0.9 respectively, the R² values were 0.80, 0.85 and 0.81 respectively, and the RMSE values were 0.29, 0.44 and 0.46 respectively. The surrogate model was used to assess 259 configures, which had not been assessed by DFT calculation. The surrogate model identified 26 promising configurations, with 15 configurations confirmed to match the results obtained by DFT calculation. Furthermore, by comparing the computation time of model-based methods with VASP software, the proposed method is about 7 times more efficient than traditional calculation methods. The advantage of XGBR in predicting E_f, ΔG(NO₃) and ΔG of cobalt phosphide catalytic materials was demonstrated, thereby offering a new pathway for the rational design of excellent catalytic material substitution strategies and accelerating the discovery of DFT-based new materials. The proposed method had low accuracy when predicting ΔG value. The next step will focus on how to improve the prediction accuracy of ΔG value and apply the proposed method to other catalytic material systems to study the versatility of the method. Meanwhile, Improve the efficiency of first-principles calculations based on localized orbital density functional theory, further accelerate the speed of multi-objective material design, and develop a cloud computing-based multi-objective material design and prediction platform to expedite material discovery.

  Declaration of competing interest

  The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

  CRediT authorship contribution statement

  Baolei Li: Conceptualization, Writing – original draft, Writing – review & editing, Funding acquisition, Software. Da Wang: Methodology, Writing – original draft, Writing – review & editing. Miao Yu: Investigation, Data curation, Validation. Chaozheng He: Investigation, Funding acquisition, Supervision, Validation. Xue Li: Supervision, Funding acquisition, Resources. Jing Zhai: Resources. Mdmahadi Hasan: Resources. Chenxu Zhao: Resources. Min Wang: Funding acquisition, Visualization. Dingcai Shen: Funding acquisition, Visualization.

  Acknowledgments

  This work was supported by the Jiangxi Provincial Natural Science Foundation (No. 20224BAB212022), Science and Technology Project of Education Department of Jiangxi Province (No. GJJ211435), the National Key Research and Development Program of China (No. 2021YFA1400204) and the Project of China Postdoctoral Science Foundation (No. 2022M712909), the Natural Science Foundation of China (No. 21603109), the Henan Joint Fund of the National Natural Science Foundation of China (No. U1404216).

  Supplementary materials

  Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.cclet.2024.110454.

  
  
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  Figure 1  In terms of E_f, the evaluation results of each algorithm on the testing set: (a) Result of r, (b) result of R², (c) result of RMSE.

  下载: 全尺寸图片 幻灯片
  

  Figure 2  In terms of ΔG(NO₃), the evaluation results of each algorithm on the testing set: (a) Result of r, (b) result of R², (c) result of RMSE.

  下载: 全尺寸图片 幻灯片
  

  Figure 3  In terms of ΔG, the evaluation results of each algorithm on the testing set: (a) Result of r, (b) result of R², (c) result of RMSE.

  下载: 全尺寸图片 幻灯片
  

  Figure 4  The E_f, ΔG(NO₃) and ΔG of 15 configurations. Red data represents predicted values, green data represents true values.

  下载: 全尺寸图片 幻灯片
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