Application of machine learning in high-throughput screening of binary alloys for the hydrogenation of benzene

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In this study, the adsorption energies of benzene and hydrogen over random 150 alloys are determined using density functional theory (DFT) calculation, and varied physical properties of alloys are used as descriptors. Four machine learning (ML) models, light gradient boosting machine (LGBM), extreme gradient boosting (XGBT), multilayer perceptron (MLP) and support vector machine (SVM) are employed to predict the adsorption energies. After feature selection and parameter optimization, LGBM model shows the highest prediction accuracy, with correlation coefficient (R 2 ) and root mean square error (RMSE) of 0.813 and 0.415 eV for benzene, as well as 0.874 and 0.176 eV for hydrogen. Therefore, LGBM model is selected to predict the adsorption energies of benzene and hydrogen (ΔE B and ΔE H ), and Cu 2 Ni 2 has excellent ΔE B and ΔE H of -4.97 and − 1.81 eV. benzene hydrogenation adsorption energy machine learning LGBM Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 1. Introduction The hydrogenation of benzene is of crucial significance in industrial synthesis [ 1 , 2 ]. For instance, millions of tons of benzene are hydrogenated to cyclohexane, which is known as a vital intermediate in the preparation of Nylon-6 and Nylon-66 [ 3 , 4 ]. However, owning to the resonance stabilization resulting from the strong π-conjugation of aromatic ring [ 5 ], this reaction typically uses Group VIII and IB elements including Fe, Co, Ni, Cu, Ru, Rh, Pd, Ag, Ir, Pt and Au as catalysts with temperature and hydrogen pressure over 100 ℃ and 3 MPa in Scheme S1 [ 6 – 8 ]. Among which, Fe, Co, Cu and Ag show low activities, requiring harsh reaction temperatures and pressures [ 9 , 10 ]. Ni exhibits good activity but tends to coke deposition and metal agglomeration during the reaction [ 11 , 12 ]. Ru, Rh, Pd, Ir, Pt and Au possess excellent activities, but they are too high-cost to widely applied in industry [ 13 , 14 ]. Therefore, it is reasonable to utilize binary alloys composed of two metals instead of single metal for the hydrogenation of benzene. Surprisingly, in binary alloys, the interaction between different elements (synergistic effect) and the distinctions in adsorption configurations between two metals (affinity) can increase catalytic activity [ 15 , 16 ]. But, due to numerous combinations of two metals, many potentially excellent alloys have not been developed yet. Thus, supervised learning methods in machine learning (ML) is employed to explore relationships between input and output data through data selection, feature engineering and algorithm optimization [ 17 , 18 ], including decision trees, support vector machines, Gaussian process regression and neural networks [ 19 , 20 ]. On the other hand, numerical descriptors directly related to catalytic performance are required [ 21 , 22 ]. In terms of the hydrogenation of benzene, the adsorption energies of benzene and hydrogen on the surface has been proven to effectively describe catalytic activity [ 23 , 24 ]. Nonetheless, traditional experiments are inefficient, which cannot promptly screen and evaluate potential catalysts. Hence, density functional theory (DFT) calculation can avoid issues arising from diverse experimental conditions and unclear structure-activity relationships, as it can handle surface reactions and predict the adsorption energies [ 25 , 26 ]. In previous studies, Toyao et al. demonstrated the workflow for DFT/ML screening of alloys, accurately predicting the adsorption energy of CH 3 * on single atom and obtaining the optimal catalyst [ 27 ]. Moreover, Lu et al. introduced specific geometric descriptors combined with basic property descriptors, to accurately predict the adsorption energy of OH* on high-entropy alloys using neural network algorithms [ 28 ]. Besides, Ma et al. studied the adsorption energy of CO* on binary alloy surfaces and introduced d -band distribution-related descriptors into ML model [ 29 ]. It was found that DFT/ML not only allowed large-scale screening of binary alloys within a short period, but also identified factors affecting catalytic activity. In this submission, 1155 types of binary alloys are constructed, including 11 active metals (A) and 35 dopant metals (B) with three ratios (1:3, 2:2, 3:1). The adsorption structures of benzene and hydrogen on alloys (111) surface are determined, and data sets and descriptors are formed through DFT calculations and metallic physical properties, respectively. Feature importance analysis is used to simplify the descriptors, and four different ML models (LGBM, XGBT, MLP, SVM) are compared for their prediction accuracy (correlation coefficient (R 2 ) and root mean square error (RMSE)) in predicting adsorption energies of benzene and hydrogen (ΔE B and ΔE H ) over random 150 binary alloys (training set). After parameter adjustment, LGBM model with the highest prediction is used to predict adsorption energies of benzene and hydrogen for the rest of 1005 binary alloys. Finally, Cu 2 Ni 2 constituted of earth-abundant metals has prominent ΔE B and ΔE H , which makes it a candidate for the hydrogenation of benzene (Scheme 1 ). 2. Experiments 2.1. Binary alloy model construction A x B 4− x -type binary alloys are constructed. Metal A are active sites (including Group VIII and IB elements), specifically Fe, Co, Ni, Cu, Ru, Rh, Pd, Ag, Ir, Pt and Au (11 types) as shown in the green section of Fig. 1 [ 30 , 31 ]. Metal B are dopants, which include all A metals and an aggregate of 35 types, as shown in both green and red sections of Fig. 1 . The value of x can be 1, 2 or 3, forming binary alloys with different ratios. Combining them produces a data space with 1155 binary alloys. Among them, 150 alloys are randomly selected for the training set, and the remaining 1005 alloys are used as the test set. To simplify the metallic crystal structure, both Metal A and B are assumed to adopt face-centered cubic (FCC) packing, and structural optimization is performed using the Vienna Ab-initio Simulation Package (VASP) software. Next, the binary alloy (111) plane is cleaved by the “Cleave Surface” function in Material Studio (MS), and the (111) surface is modeled via 6×6 five-layer periodic model with a vacuum layer of at least 20 Å, as shown in Fig. S1 . 2.2. Density functional theory calculation Density functional theory (DFT) calculation is conducted using the Vienna Ab initio Software Package (VASP). The Projector Augmented Wave (PAW) method is carried out to describe the interaction between the electrons and ionic cores. The electron exchange correlation is evaluated via the functional of Perdew-Burke- Ernzerhof (PBE) of generalized gradient approximation. The construction of the binary alloy (111) plane utilizes a 6×6 four-layer periodic model with a vacuum layer of at least 20 Å, and the energy cutoff is set to 400 eV with a k-point mesh of 6×6×6. The atomic force and electronic step convergence criterions are 3×10 − 2 eV·Å −1 and 1×10 − 5 eV·Å −1 . The adsorption energy (E adsorption ) is calculated as follows, where E total , E adsorbate and E slab represents the total energies of the slab model with adsorbate, adsorbate and slab model. E adsorption = E total - E adsorbate - E slab (1) 2.3. Dataset construction Machine learning modeling aims to establish a function y = f model ( x ) between input and output and make f model ( x ) as close to the real function relationship f real ( x ) as possible by optimizing model parameters. The input variable x represents the physical properties as the descriptors of binary alloys. The first category includes the atomic radius ratio of metals B and A (R A /R B ), atomic radius of metal A (R A ), atomic numbers of metals A and B (N A , N B ) and relative atomic mass (M A , M B ), which represent the atomic structure of binary alloys. The second category contains the number of outer electrons (S A , S B ), number of valence electrons (V A , V B ), electronegativity (X A , X B ), first ionization energy (I A , I B ) and first electron affinity (E A , E B ) of metals A and B, which embody the electronic structure of binary alloys. In addition, the percentage of A metal atoms (A%) is introduced to differentiate between binary alloys with different metal ratios. The data are shown in Table S1 . Besides, the output variable y represents the adsorption energies of benzene and hydrogen (ΔE B and ΔE H ) for random 150 binary alloys according to DFT calculation. Based on the reaction pathway in Scheme S2 [ 32 , 33 ], the rate-determining steps are the transformation from stable benzene (B) and hydrogen (H₂) to activated benzene (B*) and hydrogen (H*). Considering the configurations of A x B 4− x alloys, the adsorption structures of benzene on (111) surface of binary alloys are illustrated in Fig. 2 . As for A 1 B 3 alloys, a conjugated π bond of benzene adsorbs at the bridge site formed by adjacent A and B metals on (111) surface and the top site of the B metal. In terms of A 2 B 2 alloys, a conjugated π bond adsorbs at the bridge site formed by adjacent A and B metals on (111) surface and the top site of the A metal. With regard to A 3 B 1 alloys, a conjugated π bond adsorbs at the bridge site formed by two adjacent A metals on (111) surface and the top site of the A metal. On the other hand, the adsorption structures of hydrogen on the (111) surface of binary alloys are demonstrated in Fig. 3 . With regard to A 1 B 3 alloys, hydrogen adsorbs at the FCC site formed by one A metal and two B metals. As for A 2 B 2 alloys, hydrogen adsorbs at the FCC site formed by two A metals and one B metal. As for A 3 B 1 alloys, hydrogen adsorbs at the FCC site formed by three A metals. 2.4. Model selection and training The machine learning algorithms are implemented in Python 3.10 using the machine learning framework Scikit-learn [ 34 ]. Four different supervised learning methods including light gradient boosting Machine (LGBM) [ 35 ], extreme gradient boosting (XGBT) [ 36 ], multilayer perceptron (MLP) [ 37 ], and support vector machine (SVM) [ 38 ] are used for training. Following this, model performance is determined by correlation coefficient (R 2 ) and root mean square error (RMSE), described as follows. After parameter adjustment, the model with best prediction is selected to predict the rest of 1005 binary alloys. 3. Results and discussion 3.1. Selection and optimization of descriptors To optimize the feature set and streamline the machine learning descriptors, the importance analysis function of LGBM model is used to rank the importance of each feature variable, selecting only key descriptors [ 28 , 39 ]. The feature and target set of data points including random 150 binary alloys are input into LGBM algorithm, and four models (LGBM, XGBT, MLP and SVM) are constructed and evaluated using R 2 and RMSE to assess the accuracy of predicting target variables ΔE B and ΔE H . It can be found that the descriptors M B , M A , E A , S A and R A have relatively low importances for model training in the adsorption energy of benzene in Fig. S2a. After sequentially removing these descriptors, R 2 values of four models gradually increase in Fig. S2b. As these five non-significant descriptors are eliminated one by one, the prediction accuracy of LGBM model expands when the number of descriptors reduces to 14, and becomes stable while decreases to 13 and 12, reaching R 2 of 0.802 in Fig. 4 a. As for XGBT model, its prediction accuracy rises when the number of descriptors falls to 13, and reaches its maximum of 0.653 as reduces to 12 descriptors. With regard to MLP model, its prediction accuracy gradually grows as the number of descriptors drops, and gets steady when slips to 12 descriptors with R 2 of 0.621. In terms of SVM model, the enhancement of prediction accuracy with a decline in the number of descriptors is slight, with R 2 of 0.547 when the number of descriptors goes down to 12. Furthermore, R A /R B , I B , V B , X B and V A are five most pivotal descriptors because of their high importances. It is observed that the descriptors M B , M A , X A , S A , V A , S B , X B , I A and E A possess relatively low importances for model training in the adsorption energy of hydrogen in Fig. S3a. Following gradually deleting these descriptors, R 2 values of four models subsequently rise in Fig. S3b. As these nine descriptors are withdrew one by one, R 2 of LGBM model improves when the number of descriptors decreases to 13, and continues to enhance until it reaches maximum of 0.773 when the number of descriptors reduces to 8 in Fig. 4 b. As for XGBT, MLP and SVM models, R 2 values also gradually grow as the number of descriptors drops, reaching their respective maximums when the number of descriptors falls to 8. The maximum R 2 values for XGBT, SVM and MLP models are 0.383, 0.516 and 0.631, respectively. Moreover, R A /R B , I B , R A , N B and V B are five most vital descriptors owing to their high importances. 3.3. Parameters optimization and training prediction To obtain more accurate machine learning models, parameters tuning is performed on each model, and the key hyperparameters for the adsorption energies of benzene and hydrogen are shown in Tables S2 to S5. On the one hand, the prediction of four models for the adsorption energy of benzene (ΔE B ) is shown in Fig. 5 . It is found that LGBM model exhibits the highest R 2 and lowest RMSE of 0.813 and 0.415 eV, thereby demonstrating the best prediction. In comparison, the prediction accuracy of XGBT and MLP models are lower, with XGBT model achieving R 2 and RMSE of 0.711 and 0.565 eV as well as MLP model having R 2 and RMSE of 0.628 and 0.664 eV. Besides, SVM model shows the lowest prediction accuracy with R 2 and RMSE of 0.603 and 0.693 eV. And these data are listed in Table 1 . Table 1 Prediction accuracy via four models for the adsorption energy of benzene. Model Source R 2 RMSE (eV) LGBM Training 0.843 0.353 Test 0.813 0.415 XGBT Training 0.802 0.422 Test 0.711 0.565 MLP Training 0.792 0.429 Test 0.628 0.664 SVM Training 0.769 0.446 Test 0.603 0.693 On the other hand, the prediction of four models for the adsorption energy of hydrogen (ΔE H ) is exhibited in Fig. 6 . It can be observed that LGBM model has the highest R 2 and lowest RMSE of 0.874 and 0.176 eV, showing the best prediction. By contrast, the prediction accuracy of MLP and SVM models are lower than that of LGBM model, with MLP model achieving R 2 and RMSE of 0.762 and 0.252 eV, whereas SVM model owns R 2 and RMSE of 0.708 and 0.297 eV. Additionally, XGBT model shows the worst prediction accuracy, with R 2 and RMSE of 0.521 and 0.438 eV. And these data are listed in Table 2 . Table 2 Prediction accuracy via four models for the adsorption energy of hydrogen. Model Source R 2 RMSE (eV) LGBM Training 0.953 0.082 Test 0.874 0.176 MLP Training 0.836 0.192 Test 0.762 0.252 SVM Training 0.781 0.229 Test 0.708 0.297 XGBT Training 0.609 0.344 Test 0.521 0.438 Among four models, LGBM demonstrates the best prediction for the adsorption energies of both benzene and hydrogen (ΔE B and ΔE H ). Therefore, it is selected to predict the adsorption energies of the remaining 1005 binary alloys for ΔE B and ΔE H , as shown in Figs. 7 and 8 . Figure 7 shows the predicted ΔE B for 1155 A x B 4− x alloys. It is found that Pt 1 Ti 3 (Fig. 7 a (30, 9)), Cu 2 Ni 2 (Fig. 7 b (19, 4)) and Pt 3 In 1 (Fig. 7 c (13, 9)) display excellent ΔE B of -4.97 eV. Among these alloys, Cu 2 Ni 2 does not contain noble metals, so it is chosen for the hydrogenation of benzene. Figure 8 depicts the predicted ΔE H for 1155 A x B 4− x alloys. It is observed that Rh 1 Tc 3 (Fig. 8 a (29, 10)), Pd 2 Pb 2 (Fig. 8 b (20, 8)) and Au 3 Mg 1 (Fig. 8 c (15, 2)) illustrates prominent ΔE H of -1.84 eV. Besides, Cu 2 Ni 2 (Fig. 8 b (19, 4)) also has − 1.81 eV for ΔE H . Therefore, Cu 2 Ni 2 made of earth-abundant metals could be applied in the hydrogenation of benzene. 4. Conclusions In summary, a high-throughput screening process of binary alloys for the hydrogenation of benzene is conducted using a combination of DFT calculation and ML models. A total of 1155 binary alloys composed of 11 active metals and 35 dopant metals with three ratios are constructed. Four machine learning models, LGBM, XGBT, MLP and SVM are employed to predict the adsorption energies, with the accuracy evaluated by R² and RMSE. After parameter tuning and descriptor optimization, LGBM model demonstrates the greatest prediction accuracy for ΔE B and ΔE H , with R 2 reaching 0.813 and 0.874, and RMSE being only 0.415 and 0.176 eV, respectively. Finally, LGBM model is chosen to predict ΔE B and ΔE H over the remaining 1005 binary alloys, and earth-abundant metals constituted Cu 2 Ni 2 possesses remarkable ΔE B and ΔE H of -4.97 and − 1.81 eV, which makes it a candidate for the hydrogenation of benzene. Declarations Declaration of Competing Interest The author declare that no known competing financial interests or personal relationships may have appeared to influence the work reported in this paper. Funding We thank the Joint Fund of Henan Province Science and Technology (235200810100), and the Start-up Project Funding of Henan Academy of Sciences (No. 231817062). 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7387859","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":504428847,"identity":"0b63da90-9789-40cd-8239-b2b535faaddd","order_by":0,"name":"Zhili Chang","email":"","orcid":"","institution":"Petrochemical Research Institute","correspondingAuthor":false,"prefix":"","firstName":"Zhili","middleName":"","lastName":"Chang","suffix":""},{"id":504428848,"identity":"01e103e5-10cd-44c7-8fa7-0112d9b4d37f","order_by":1,"name":"Guangquan Li","email":"","orcid":"","institution":"Petrochemical Research 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13:53:13","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7387859/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7387859/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":90204861,"identity":"567d4dbf-a5a3-4501-b74b-4808ed024b33","added_by":"auto","created_at":"2025-08-29 20:45:32","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":111872,"visible":true,"origin":"","legend":"\u003cp\u003eSchematic diagram of Metal A (11 types) and Metal B (35 types).\u003c/p\u003e","description":"","filename":"Picture1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7387859/v1/ac3b4bae2bf852c54eabcd65.jpg"},{"id":90204862,"identity":"9cd3859e-aad3-4473-85ba-a69e79e4a9e9","added_by":"auto","created_at":"2025-08-29 20:45:32","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":114821,"visible":true,"origin":"","legend":"\u003cp\u003eAdsorption structures of benzene over (a) A\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sub\u003e, (b) A\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e and (c) A\u003csub\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e alloys.\u003c/p\u003e","description":"","filename":"Picture2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7387859/v1/f0ef0ad06d35c4f0cafdd466.jpg"},{"id":90204871,"identity":"d884a5f3-be34-461e-af97-a6a9d33075f1","added_by":"auto","created_at":"2025-08-29 20:45:32","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":111201,"visible":true,"origin":"","legend":"\u003cp\u003eAdsorption structures of hydrogen over (a) A\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sub\u003e, (b) A\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e and (c) A\u003csub\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e alloys.\u003c/p\u003e","description":"","filename":"Picture3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7387859/v1/fff271f94599567a25e78fc1.jpg"},{"id":90204868,"identity":"61bc1a06-0a75-4e0b-b6ef-60aa0dc951fc","added_by":"auto","created_at":"2025-08-29 20:45:32","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":100054,"visible":true,"origin":"","legend":"\u003cp\u003eRelationship between the number of descriptors and model accuracy for the adsorption energies of (a) benzene and (b) hydrogen\u003c/p\u003e","description":"","filename":"Picture4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7387859/v1/c3f99b3e8a709c4087b67053.jpg"},{"id":90205155,"identity":"b0b36805-2d75-4375-9ee2-970eaad85bdd","added_by":"auto","created_at":"2025-08-29 20:53:32","extension":"jpg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":347840,"visible":true,"origin":"","legend":"\u003cp\u003ePrediction results for the adsorption energy of benzene \u003cem\u003evia\u003c/em\u003e four models of (a) LGBM, (b) XGBT, (c) MLP and (d) SVM\u003c/p\u003e","description":"","filename":"Picture5.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7387859/v1/0cb1c1b52a230d0774ca688b.jpg"},{"id":90205159,"identity":"e846214c-d77b-4020-b1f7-d87257727426","added_by":"auto","created_at":"2025-08-29 20:53:32","extension":"jpg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":358945,"visible":true,"origin":"","legend":"\u003cp\u003ePrediction results for the adsorption energy of hydrogen \u003cem\u003eby\u003c/em\u003e four models of (a) LGBM, (b) MLP, (c) SVM and (d) XGBT.\u003c/p\u003e","description":"","filename":"Picture6.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7387859/v1/18d8dc86b21d1109c3dea76e.jpg"},{"id":90204892,"identity":"85d56493-68c4-4a94-94cb-ff2663cc1b8d","added_by":"auto","created_at":"2025-08-29 20:45:33","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":191536,"visible":true,"origin":"","legend":"\u003cp\u003eThe prediction of ΔE\u003csub\u003e\u003cem\u003eB\u003c/em\u003e\u003c/sub\u003e over (a) A\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sub\u003e, (b) A\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e and (c) A\u003csub\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e.\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-7387859/v1/90f267390e408d9167016d81.png"},{"id":90204873,"identity":"d6765c96-7cf7-487c-84aa-fde021f3e644","added_by":"auto","created_at":"2025-08-29 20:45:32","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":196215,"visible":true,"origin":"","legend":"\u003cp\u003eThe prediction of ΔE\u003csub\u003e\u003cem\u003eH\u003c/em\u003e\u003c/sub\u003e over (a) A\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sub\u003e, (b) A\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e and (c) A\u003csub\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e.\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-7387859/v1/b87e9498e47973a750b79bf4.png"},{"id":90205626,"identity":"05675ea1-0310-42d3-b3d5-b545820fbca0","added_by":"auto","created_at":"2025-08-29 21:09:33","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2169018,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7387859/v1/e8fabd77-25a9-4e79-8a64-c51e10ce26a6.pdf"},{"id":90204865,"identity":"1c9b5382-af01-4fed-865c-4f95ff7f6ef1","added_by":"auto","created_at":"2025-08-29 20:45:32","extension":"docx","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":517064,"visible":true,"origin":"","legend":"","description":"","filename":"SupportingInformation.docx","url":"https://assets-eu.researchsquare.com/files/rs-7387859/v1/227d993cf36886cb769ebc70.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Application of machine learning in high-throughput screening of binary alloys for the hydrogenation of benzene","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eThe hydrogenation of benzene is of crucial significance in industrial synthesis [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. For instance, millions of tons of benzene are hydrogenated to cyclohexane, which is known as a vital intermediate in the preparation of Nylon-6 and Nylon-66 [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e, \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. However, owning to the resonance stabilization resulting from the strong π-conjugation of aromatic ring [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e], this reaction typically uses Group VIII and IB elements including Fe, Co, Ni, Cu, Ru, Rh, Pd, Ag, Ir, Pt and Au as catalysts with temperature and hydrogen pressure over 100 ℃ and 3 MPa in Scheme S1 [\u003cspan additionalcitationids=\"CR7\" citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. Among which, Fe, Co, Cu and Ag show low activities, requiring harsh reaction temperatures and pressures [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. Ni exhibits good activity but tends to coke deposition and metal agglomeration during the reaction [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. Ru, Rh, Pd, Ir, Pt and Au possess excellent activities, but they are too high-cost to widely applied in industry [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. Therefore, it is reasonable to utilize binary alloys composed of two metals instead of single metal for the hydrogenation of benzene.\u003c/p\u003e\u003cp\u003eSurprisingly, in binary alloys, the interaction between different elements (synergistic effect) and the distinctions in adsorption configurations between two metals (affinity) can increase catalytic activity [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. But, due to numerous combinations of two metals, many potentially excellent alloys have not been developed yet. Thus, supervised learning methods in machine learning (ML) is employed to explore relationships between input and output data through data selection, feature engineering and algorithm optimization [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e], including decision trees, support vector machines, Gaussian process regression and neural networks [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eOn the other hand, numerical descriptors directly related to catalytic performance are required [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e, \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]. In terms of the hydrogenation of benzene, the adsorption energies of benzene and hydrogen on the surface has been proven to effectively describe catalytic activity [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]. Nonetheless, traditional experiments are inefficient, which cannot promptly screen and evaluate potential catalysts. Hence, density functional theory (DFT) calculation can avoid issues arising from diverse experimental conditions and unclear structure-activity relationships, as it can handle surface reactions and predict the adsorption energies [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eIn previous studies, Toyao et al. demonstrated the workflow for DFT/ML screening of alloys, accurately predicting the adsorption energy of CH\u003csub\u003e3\u003c/sub\u003e\u003csup\u003e*\u003c/sup\u003e on single atom and obtaining the optimal catalyst [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e]. Moreover, Lu et al. introduced specific geometric descriptors combined with basic property descriptors, to accurately predict the adsorption energy of OH* on high-entropy alloys using neural network algorithms [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e]. Besides, Ma et al. studied the adsorption energy of CO* on binary alloy surfaces and introduced \u003cem\u003ed\u003c/em\u003e-band distribution-related descriptors into ML model [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]. It was found that DFT/ML not only allowed large-scale screening of binary alloys within a short period, but also identified factors affecting catalytic activity.\u003c/p\u003e\u003cp\u003eIn this submission, 1155 types of binary alloys are constructed, including 11 active metals (A) and 35 dopant metals (B) with three ratios (1:3, 2:2, 3:1). The adsorption structures of benzene and hydrogen on alloys (111) surface are determined, and data sets and descriptors are formed through DFT calculations and metallic physical properties, respectively. Feature importance analysis is used to simplify the descriptors, and four different ML models (LGBM, XGBT, MLP, SVM) are compared for their prediction accuracy (correlation coefficient (R\u003csup\u003e2\u003c/sup\u003e) and root mean square error (RMSE)) in predicting adsorption energies of benzene and hydrogen (ΔE\u003csub\u003e\u003cem\u003eB\u003c/em\u003e\u003c/sub\u003e and ΔE\u003csub\u003e\u003cem\u003eH\u003c/em\u003e\u003c/sub\u003e) over random 150 binary alloys (training set). After parameter adjustment, LGBM model with the highest prediction is used to predict adsorption energies of benzene and hydrogen for the rest of 1005 binary alloys. Finally, Cu\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003eNi\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e constituted of earth-abundant metals has prominent ΔE\u003csub\u003e\u003cem\u003eB\u003c/em\u003e\u003c/sub\u003e and ΔE\u003csub\u003e\u003cem\u003eH\u003c/em\u003e\u003c/sub\u003e, which makes it a candidate for the hydrogenation of benzene (Scheme \u003cspan refid=\"Sch1\" class=\"InternalRef\"\u003e1\u003c/span\u003e).\u003c/p\u003e\u003cp\u003e\u003c/p\u003e"},{"header":"2. Experiments","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\u003ch2\u003e2.1. Binary alloy model construction\u003c/h2\u003e\u003cp\u003eA\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e4\u0026minus;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003e-type binary alloys are constructed. Metal A are active sites (including Group VIII and IB elements), specifically Fe, Co, Ni, Cu, Ru, Rh, Pd, Ag, Ir, Pt and Au (11 types) as shown in the green section of Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e, \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e]. Metal B are dopants, which include all A metals and an aggregate of 35 types, as shown in both green and red sections of Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. The value of \u003cem\u003ex\u003c/em\u003e can be 1, 2 or 3, forming binary alloys with different ratios. Combining them produces a data space with 1155 binary alloys. Among them, 150 alloys are randomly selected for the training set, and the remaining 1005 alloys are used as the test set.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eTo simplify the metallic crystal structure, both Metal A and B are assumed to adopt face-centered cubic (FCC) packing, and structural optimization is performed using the Vienna Ab-initio Simulation Package (VASP) software. Next, the binary alloy (111) plane is cleaved \u003cem\u003eby\u003c/em\u003e the \u0026ldquo;Cleave Surface\u0026rdquo; function in Material Studio (MS), and the (111) surface is modeled \u003cem\u003evia\u003c/em\u003e 6\u0026times;6 five-layer periodic model with a vacuum layer of at least 20 \u0026Aring;, as shown in Fig. \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003e.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\u003ch2\u003e2.2. Density functional theory calculation\u003c/h2\u003e\u003cp\u003eDensity functional theory (DFT) calculation is conducted using the Vienna Ab initio Software Package (VASP). The Projector Augmented Wave (PAW) method is carried out to describe the interaction between the electrons and ionic cores. The electron exchange correlation is evaluated \u003cem\u003evia\u003c/em\u003e the functional of Perdew-Burke- Ernzerhof (PBE) of generalized gradient approximation.\u003c/p\u003e\u003cp\u003eThe construction of the binary alloy (111) plane utilizes a 6\u0026times;6 four-layer periodic model with a vacuum layer of at least 20 \u0026Aring;, and the energy cutoff is set to 400 eV with a k-point mesh of 6\u0026times;6\u0026times;6. The atomic force and electronic step convergence criterions are 3\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e eV\u0026middot;\u0026Aring;\u003csup\u003e\u0026minus;1\u003c/sup\u003e and 1\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;5\u003c/sup\u003e eV\u0026middot;\u0026Aring;\u003csup\u003e\u0026minus;1\u003c/sup\u003e. The adsorption energy (E\u003csub\u003e\u003cem\u003eadsorption\u003c/em\u003e\u003c/sub\u003e) is calculated as follows, where E\u003csub\u003e\u003cem\u003etotal\u003c/em\u003e\u003c/sub\u003e, E\u003csub\u003e\u003cem\u003eadsorbate\u003c/em\u003e\u003c/sub\u003e and E\u003csub\u003e\u003cem\u003eslab\u003c/em\u003e\u003c/sub\u003e represents the total energies of the slab model with adsorbate, adsorbate and slab model.\u003c/p\u003e\u003cp\u003eE\u003csub\u003e\u003cem\u003eadsorption\u003c/em\u003e\u003c/sub\u003e = E\u003csub\u003e\u003cem\u003etotal\u003c/em\u003e\u003c/sub\u003e - E\u003csub\u003e\u003cem\u003eadsorbate\u003c/em\u003e\u003c/sub\u003e - E\u003csub\u003e\u003cem\u003eslab\u003c/em\u003e\u003c/sub\u003e (1)\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e\u003ch2\u003e2.3. Dataset construction\u003c/h2\u003e\u003cp\u003eMachine learning modeling aims to establish a function \u003cem\u003ey\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003ef\u003c/em\u003e\u003csub\u003emodel\u003c/sub\u003e(\u003cem\u003ex\u003c/em\u003e) between input and output and make \u003cem\u003ef\u003c/em\u003e\u003csub\u003emodel\u003c/sub\u003e(\u003cem\u003ex\u003c/em\u003e) as close to the real function relationship \u003cem\u003ef\u003c/em\u003e\u003csub\u003ereal\u003c/sub\u003e(\u003cem\u003ex\u003c/em\u003e) as possible by optimizing model parameters. The input variable \u003cem\u003ex\u003c/em\u003e represents the physical properties as the descriptors of binary alloys. The first category includes the atomic radius ratio of metals B and A (R\u003csub\u003e\u003cem\u003eA\u003c/em\u003e\u003c/sub\u003e/R\u003csub\u003e\u003cem\u003eB\u003c/em\u003e\u003c/sub\u003e), atomic radius of metal A (R\u003csub\u003e\u003cem\u003eA\u003c/em\u003e\u003c/sub\u003e), atomic numbers of metals A and B (N\u003csub\u003e\u003cem\u003eA\u003c/em\u003e\u003c/sub\u003e, N\u003csub\u003e\u003cem\u003eB\u003c/em\u003e\u003c/sub\u003e) and relative atomic mass (M\u003csub\u003e\u003cem\u003eA\u003c/em\u003e\u003c/sub\u003e, M\u003csub\u003e\u003cem\u003eB\u003c/em\u003e\u003c/sub\u003e), which represent the atomic structure of binary alloys. The second category contains the number of outer electrons (S\u003csub\u003e\u003cem\u003eA\u003c/em\u003e\u003c/sub\u003e, S\u003csub\u003e\u003cem\u003eB\u003c/em\u003e\u003c/sub\u003e), number of valence electrons (V\u003csub\u003e\u003cem\u003eA\u003c/em\u003e\u003c/sub\u003e, V\u003csub\u003e\u003cem\u003eB\u003c/em\u003e\u003c/sub\u003e), electronegativity (X\u003csub\u003e\u003cem\u003eA\u003c/em\u003e\u003c/sub\u003e, X\u003csub\u003e\u003cem\u003eB\u003c/em\u003e\u003c/sub\u003e), first ionization energy (I\u003csub\u003e\u003cem\u003eA\u003c/em\u003e\u003c/sub\u003e, I\u003csub\u003e\u003cem\u003eB\u003c/em\u003e\u003c/sub\u003e) and first electron affinity (E\u003csub\u003e\u003cem\u003eA\u003c/em\u003e\u003c/sub\u003e, E\u003csub\u003e\u003cem\u003eB\u003c/em\u003e\u003c/sub\u003e) of metals A and B, which embody the electronic structure of binary alloys. In addition, the percentage of A metal atoms (A%) is introduced to differentiate between binary alloys with different metal ratios. The data are shown in Table \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003e.\u003c/p\u003e\u003cp\u003eBesides, the output variable \u003cem\u003ey\u003c/em\u003e represents the adsorption energies of benzene and hydrogen (ΔE\u003csub\u003e\u003cem\u003eB\u003c/em\u003e\u003c/sub\u003e and ΔE\u003csub\u003e\u003cem\u003eH\u003c/em\u003e\u003c/sub\u003e) for random 150 binary alloys according to DFT calculation. Based on the reaction pathway in Scheme S2 [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e, \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e], the rate-determining steps are the transformation from stable benzene (B) and hydrogen (H₂) to activated benzene (B*) and hydrogen (H*). Considering the configurations of A\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e4\u0026minus;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003e alloys, the adsorption structures of benzene on (111) surface of binary alloys are illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. As for A\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sub\u003e alloys, a conjugated π bond of benzene adsorbs at the bridge site formed \u003cem\u003eby\u003c/em\u003e adjacent A and B metals on (111) surface and the top site of the B metal. In terms of A\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e alloys, a conjugated π bond adsorbs at the bridge site formed \u003cem\u003eby\u003c/em\u003e adjacent A and B metals on (111) surface and the top site of the A metal. With regard to A\u003csub\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e alloys, a conjugated π bond adsorbs at the bridge site formed \u003cem\u003eby\u003c/em\u003e two adjacent A metals on (111) surface and the top site of the A metal.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eOn the other hand, the adsorption structures of hydrogen on the (111) surface of binary alloys are demonstrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. With regard to A\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sub\u003e alloys, hydrogen adsorbs at the FCC site formed \u003cem\u003eby\u003c/em\u003e one A metal and two B metals. As for A\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e alloys, hydrogen adsorbs at the FCC site formed \u003cem\u003eby\u003c/em\u003e two A metals and one B metal. As for A\u003csub\u003e3\u003c/sub\u003eB\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e alloys, hydrogen adsorbs at the FCC site formed \u003cem\u003eby\u003c/em\u003e three A metals.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e\u003ch2\u003e2.4. Model selection and training\u003c/h2\u003e\u003cp\u003eThe machine learning algorithms are implemented in Python 3.10 using the machine learning framework Scikit-learn [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e]. Four different supervised learning methods including light gradient boosting Machine (LGBM) [\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e], extreme gradient boosting (XGBT) [\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e], multilayer perceptron (MLP) [\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e], and support vector machine (SVM) [\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e] are used for training. Following this, model performance is determined by correlation coefficient (R\u003csup\u003e2\u003c/sup\u003e) and root mean square error (RMSE), described as follows. After parameter adjustment, the model with best prediction is selected to predict the rest of 1005 binary alloys.\u003c/p\u003e\u003cp\u003e\u003cimg 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\"\u003e\u003c/p\u003e\u003c/div\u003e"},{"header":"3. Results and discussion","content":"\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\u003ch2\u003e3.1. Selection and optimization of descriptors\u003c/h2\u003e\u003cp\u003eTo optimize the feature set and streamline the machine learning descriptors, the importance analysis function of LGBM model is used to rank the importance of each feature variable, selecting only key descriptors [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e, \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e]. The feature and target set of data points including random 150 binary alloys are input into LGBM algorithm, and four models (LGBM, XGBT, MLP and SVM) are constructed and evaluated using R\u003csup\u003e2\u003c/sup\u003e and RMSE to assess the accuracy of predicting target variables ΔE\u003csub\u003e\u003cem\u003eB\u003c/em\u003e\u003c/sub\u003e and ΔE\u003csub\u003e\u003cem\u003eH\u003c/em\u003e\u003c/sub\u003e.\u003c/p\u003e\u003cp\u003eIt can be found that the descriptors M\u003csub\u003e\u003cem\u003eB\u003c/em\u003e\u003c/sub\u003e, M\u003csub\u003e\u003cem\u003eA\u003c/em\u003e\u003c/sub\u003e, E\u003csub\u003e\u003cem\u003eA\u003c/em\u003e\u003c/sub\u003e, S\u003csub\u003e\u003cem\u003eA\u003c/em\u003e\u003c/sub\u003e and R\u003csub\u003e\u003cem\u003eA\u003c/em\u003e\u003c/sub\u003e have relatively low importances for model training in the adsorption energy of benzene in Fig. S2a. After sequentially removing these descriptors, R\u003csup\u003e2\u003c/sup\u003e values of four models gradually increase in Fig. S2b. As these five non-significant descriptors are eliminated one \u003cem\u003eby\u003c/em\u003e one, the prediction accuracy of LGBM model expands when the number of descriptors reduces to 14, and becomes stable while decreases to 13 and 12, reaching R\u003csup\u003e2\u003c/sup\u003e of 0.802 in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ea. As for XGBT model, its prediction accuracy rises when the number of descriptors falls to 13, and reaches its maximum of 0.653 as reduces to 12 descriptors. With regard to MLP model, its prediction accuracy gradually grows as the number of descriptors drops, and gets steady when slips to 12 descriptors with R\u003csup\u003e2\u003c/sup\u003e of 0.621. In terms of SVM model, the enhancement of prediction accuracy with a decline in the number of descriptors is slight, with R\u003csup\u003e2\u003c/sup\u003e of 0.547 when the number of descriptors goes down to 12. Furthermore, R\u003csub\u003e\u003cem\u003eA\u003c/em\u003e\u003c/sub\u003e/R\u003csub\u003e\u003cem\u003eB\u003c/em\u003e\u003c/sub\u003e, I\u003csub\u003e\u003cem\u003eB\u003c/em\u003e\u003c/sub\u003e, V\u003csub\u003e\u003cem\u003eB\u003c/em\u003e\u003c/sub\u003e, X\u003csub\u003e\u003cem\u003eB\u003c/em\u003e\u003c/sub\u003e and V\u003csub\u003e\u003cem\u003eA\u003c/em\u003e\u003c/sub\u003e are five most pivotal descriptors because of their high importances.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eIt is observed that the descriptors M\u003csub\u003e\u003cem\u003eB\u003c/em\u003e\u003c/sub\u003e, M\u003csub\u003e\u003cem\u003eA\u003c/em\u003e\u003c/sub\u003e, X\u003csub\u003e\u003cem\u003eA\u003c/em\u003e\u003c/sub\u003e, S\u003csub\u003e\u003cem\u003eA\u003c/em\u003e\u003c/sub\u003e, V\u003csub\u003e\u003cem\u003eA\u003c/em\u003e\u003c/sub\u003e, S\u003csub\u003e\u003cem\u003eB\u003c/em\u003e\u003c/sub\u003e, X\u003csub\u003e\u003cem\u003eB\u003c/em\u003e\u003c/sub\u003e, I\u003csub\u003e\u003cem\u003eA\u003c/em\u003e\u003c/sub\u003e and E\u003csub\u003e\u003cem\u003eA\u003c/em\u003e\u003c/sub\u003e possess relatively low importances for model training in the adsorption energy of hydrogen in Fig. S3a. Following gradually deleting these descriptors, R\u003csup\u003e2\u003c/sup\u003e values of four models subsequently rise in Fig. S3b. As these nine descriptors are withdrew one \u003cem\u003eby\u003c/em\u003e one, R\u003csup\u003e2\u003c/sup\u003e of LGBM model improves when the number of descriptors decreases to 13, and continues to enhance until it reaches maximum of 0.773 when the number of descriptors reduces to 8 in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eb. As for XGBT, MLP and SVM models, R\u003csup\u003e2\u003c/sup\u003e values also gradually grow as the number of descriptors drops, reaching their respective maximums when the number of descriptors falls to 8. The maximum R\u003csup\u003e2\u003c/sup\u003e values for XGBT, SVM and MLP models are 0.383, 0.516 and 0.631, respectively. Moreover, R\u003csub\u003e\u003cem\u003eA\u003c/em\u003e\u003c/sub\u003e/R\u003csub\u003e\u003cem\u003eB\u003c/em\u003e\u003c/sub\u003e, I\u003csub\u003e\u003cem\u003eB\u003c/em\u003e\u003c/sub\u003e, R\u003csub\u003e\u003cem\u003eA\u003c/em\u003e\u003c/sub\u003e, N\u003csub\u003e\u003cem\u003eB\u003c/em\u003e\u003c/sub\u003e and V\u003csub\u003e\u003cem\u003eB\u003c/em\u003e\u003c/sub\u003e are five most vital descriptors owing to their high importances.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e\u003ch2\u003e3.3. Parameters optimization and training prediction\u003c/h2\u003e\u003cp\u003eTo obtain more accurate machine learning models, parameters tuning is performed on each model, and the key hyperparameters for the adsorption energies of benzene and hydrogen are shown in Tables S2 to S5.\u003c/p\u003e\u003cp\u003eOn the one hand, the prediction of four models for the adsorption energy of benzene (ΔE\u003csub\u003e\u003cem\u003eB\u003c/em\u003e\u003c/sub\u003e) is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e. It is found that LGBM model exhibits the highest R\u003csup\u003e2\u003c/sup\u003e and lowest RMSE of 0.813 and 0.415 eV, thereby demonstrating the best prediction. In comparison, the prediction accuracy of XGBT and MLP models are lower, with XGBT model achieving R\u003csup\u003e2\u003c/sup\u003e and RMSE of 0.711 and 0.565 eV as well as MLP model having R\u003csup\u003e2\u003c/sup\u003e and RMSE of 0.628 and 0.664 eV. Besides, SVM model shows the lowest prediction accuracy with R\u003csup\u003e2\u003c/sup\u003e and RMSE of 0.603 and 0.693 eV. And these data are listed in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003ePrediction accuracy \u003cem\u003evia\u003c/em\u003e four models for the adsorption energy of benzene.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"4\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eModel\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eSource\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eR\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eRMSE (eV)\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e\u003cp\u003eLGBM\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eTraining\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.843\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.353\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eTest\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.813\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.415\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e\u003cp\u003eXGBT\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eTraining\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.802\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.422\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eTest\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.711\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.565\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e\u003cp\u003eMLP\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eTraining\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.792\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.429\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eTest\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.628\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.664\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e\u003cp\u003eSVM\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eTraining\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.769\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.446\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eTest\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.603\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.693\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eOn the other hand, the prediction of four models for the adsorption energy of hydrogen (ΔE\u003csub\u003e\u003cem\u003eH\u003c/em\u003e\u003c/sub\u003e) is exhibited in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e. It can be observed that LGBM model has the highest R\u003csup\u003e2\u003c/sup\u003e and lowest RMSE of 0.874 and 0.176 eV, showing the best prediction. By contrast, the prediction accuracy of MLP and SVM models are lower than that of LGBM model, with MLP model achieving R\u003csup\u003e2\u003c/sup\u003e and RMSE of 0.762 and 0.252 eV, whereas SVM model owns R\u003csup\u003e2\u003c/sup\u003e and RMSE of 0.708 and 0.297 eV. Additionally, XGBT model shows the worst prediction accuracy, with R\u003csup\u003e2\u003c/sup\u003e and RMSE of 0.521 and 0.438 eV. And these data are listed in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003ePrediction accuracy \u003cem\u003evia\u003c/em\u003e four models for the adsorption energy of hydrogen.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"4\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eModel\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eSource\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eR\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eRMSE (eV)\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e\u003cp\u003eLGBM\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eTraining\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.953\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.082\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eTest\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.874\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.176\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e\u003cp\u003eMLP\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eTraining\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.836\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.192\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eTest\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.762\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.252\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e\u003cp\u003eSVM\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eTraining\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.781\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.229\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eTest\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.708\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.297\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e\u003cp\u003eXGBT\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eTraining\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.609\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.344\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eTest\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.521\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.438\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eAmong four models, LGBM demonstrates the best prediction for the adsorption energies of both benzene and hydrogen (ΔE\u003csub\u003e\u003cem\u003eB\u003c/em\u003e\u003c/sub\u003e and ΔE\u003csub\u003e\u003cem\u003eH\u003c/em\u003e\u003c/sub\u003e). Therefore, it is selected to predict the adsorption energies of the remaining 1005 binary alloys for ΔE\u003csub\u003e\u003cem\u003eB\u003c/em\u003e\u003c/sub\u003e and ΔE\u003csub\u003e\u003cem\u003eH\u003c/em\u003e\u003c/sub\u003e, as shown in Figs.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e and \u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e.\u003c/p\u003e\u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e shows the predicted ΔE\u003csub\u003e\u003cem\u003eB\u003c/em\u003e\u003c/sub\u003e for 1155 A\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e4\u0026minus;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003e alloys. It is found that Pt\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003eTi\u003csub\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sub\u003e (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003ea (30, 9)), Cu\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003eNi\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003eb (19, 4)) and Pt\u003csub\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sub\u003eIn\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e (Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003ec (13, 9)) display excellent ΔE\u003csub\u003e\u003cem\u003eB\u003c/em\u003e\u003c/sub\u003e of -4.97 eV. Among these alloys, Cu\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003eNi\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e does not contain noble metals, so it is chosen for the hydrogenation of benzene.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e depicts the predicted ΔE\u003csub\u003e\u003cem\u003eH\u003c/em\u003e\u003c/sub\u003e for 1155 A\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003eB\u003csub\u003e4\u0026minus;\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003e alloys. It is observed that Rh\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003eTc\u003csub\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sub\u003e (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003ea (29, 10)), Pd\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003ePb\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003eb (20, 8)) and Au\u003csub\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sub\u003eMg\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003ec (15, 2)) illustrates prominent ΔE\u003csub\u003e\u003cem\u003eH\u003c/em\u003e\u003c/sub\u003e of -1.84 eV. Besides, Cu\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003eNi\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003eb (19, 4)) also has \u0026minus;\u0026thinsp;1.81 eV for ΔE\u003csub\u003e\u003cem\u003eH\u003c/em\u003e\u003c/sub\u003e. Therefore, Cu\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003eNi\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e made of earth-abundant metals could be applied in the hydrogenation of benzene.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e"},{"header":"4. Conclusions","content":"\u003cp\u003eIn summary, a high-throughput screening process of binary alloys for the hydrogenation of benzene is conducted using a combination of DFT calculation and ML models. A total of 1155 binary alloys composed of 11 active metals and 35 dopant metals with three ratios are constructed. Four machine learning models, LGBM, XGBT, MLP and SVM are employed to predict the adsorption energies, with the accuracy evaluated \u003cem\u003eby\u003c/em\u003e R\u0026sup2; and RMSE. After parameter tuning and descriptor optimization, LGBM model demonstrates the greatest prediction accuracy for ΔE\u003csub\u003e\u003cem\u003eB\u003c/em\u003e\u003c/sub\u003e and ΔE\u003csub\u003e\u003cem\u003eH\u003c/em\u003e\u003c/sub\u003e, with R\u003csup\u003e2\u003c/sup\u003e reaching 0.813 and 0.874, and RMSE being only 0.415 and 0.176 eV, respectively. Finally, LGBM model is chosen to predict ΔE\u003csub\u003e\u003cem\u003eB\u003c/em\u003e\u003c/sub\u003e and ΔE\u003csub\u003e\u003cem\u003eH\u003c/em\u003e\u003c/sub\u003e over the remaining 1005 binary alloys, and earth-abundant metals constituted Cu\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003eNi\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e possesses remarkable ΔE\u003csub\u003e\u003cem\u003eB\u003c/em\u003e\u003c/sub\u003e and ΔE\u003csub\u003e\u003cem\u003eH\u003c/em\u003e\u003c/sub\u003e of -4.97 and \u0026minus;\u0026thinsp;1.81 eV, which makes it a candidate for the hydrogenation of benzene.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003ch2\u003eDeclaration of Competing Interest\u003c/h2\u003e\u003cp\u003eThe author declare that no known competing financial interests or personal relationships may have appeared to influence the work reported in this paper.\u003c/p\u003e\u003c/p\u003e\u003ch2\u003eFunding\u003c/h2\u003e\u003cp\u003eWe thank the Joint Fund of Henan Province Science and Technology (235200810100), and the Start-up Project Funding of Henan Academy of Sciences (No. 231817062).\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eZhili Chang: Investigation, Methodology, Data curation, Formal analysis, Writing \u0026ndash; Original Draft.Guangquan Li: Validation, Formal analysis, Supervision.Wenjun Cai: Validation, Software, Formal analysis.Haolan Liu: Formal analysis, Supervision, Funding acquisition.Guangcheng Zhang: Software, Supervision, Funding acquisition.Weitao Ou: Conceptualization, Methodology, Resources, Writing \u0026ndash; review \u0026amp; editing.\u003c/p\u003e\u003ch2\u003eAcknowledgement\u003c/h2\u003e\u003cp\u003eThis work was also financially supported by Zhejiang Hengyi Petrochemical Research Institute Co., Ltd.\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eThe data will be made available on request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eLiu H, Fang R, Li Z, Li Y (2015) Solventless hydrogenation of benzene to cyclohexane over a heterogeneous Ru\u0026ndash;Pt bimetallic catalyst. 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ACS Appl Mater Inter 13:50878\u0026ndash;50891\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"catalysis-letters","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [Catalysis Letters](https://link.springer.com/journal/10562)","snPcode":"10562","submissionUrl":"https://submission.springernature.com/new-submission/10562/3","title":"Catalysis Letters","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"benzene hydrogenation, adsorption energy, machine learning, LGBM","lastPublishedDoi":"10.21203/rs.3.rs-7387859/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7387859/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe hydrogenation of benzene is a key reaction in industry, and binary alloys are promising candidates for improving the catalytic efficiency of this process. In this study, the adsorption energies of benzene and hydrogen over random 150 alloys are determined using density functional theory (DFT) calculation, and varied physical properties of alloys are used as descriptors. Four machine learning (ML) models, light gradient boosting machine (LGBM), extreme gradient boosting (XGBT), multilayer perceptron (MLP) and support vector machine (SVM) are employed to predict the adsorption energies. After feature selection and parameter optimization, LGBM model shows the highest prediction accuracy, with correlation coefficient (R\u003csup\u003e2\u003c/sup\u003e) and root mean square error (RMSE) of 0.813 and 0.415 eV for benzene, as well as 0.874 and 0.176 eV for hydrogen. Therefore, LGBM model is selected to predict the adsorption energies of benzene and hydrogen (ΔE\u003csub\u003e\u003cem\u003eB\u003c/em\u003e\u003c/sub\u003e and ΔE\u003csub\u003e\u003cem\u003eH\u003c/em\u003e\u003c/sub\u003e), and Cu\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003eNi\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e has excellent ΔE\u003csub\u003e\u003cem\u003eB\u003c/em\u003e\u003c/sub\u003e and ΔE\u003csub\u003e\u003cem\u003eH\u003c/em\u003e\u003c/sub\u003e of -4.97 and \u0026minus;\u0026thinsp;1.81 eV.\u003c/p\u003e","manuscriptTitle":"Application of machine learning in high-throughput screening of binary alloys for the hydrogenation of benzene","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-08-29 20:45:27","doi":"10.21203/rs.3.rs-7387859/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-09-09T19:55:37+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-09-09T12:00:10+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-09-01T04:33:11+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"200363542953689293482848444800976616439","date":"2025-08-23T02:05:59+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"286279446685533465499594050727455204317","date":"2025-08-21T01:05:36+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"318296564337707491082048375676716971338","date":"2025-08-20T21:01:17+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-08-20T15:35:05+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-08-20T12:57:35+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-08-20T12:56:50+00:00","index":"","fulltext":""},{"type":"submitted","content":"Catalysis Letters","date":"2025-08-16T13:38:38+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"catalysis-letters","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [Catalysis Letters](https://link.springer.com/journal/10562)","snPcode":"10562","submissionUrl":"https://submission.springernature.com/new-submission/10562/3","title":"Catalysis Letters","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"03fcb393-514c-40d1-816c-d51e18d8bbee","owner":[],"postedDate":"August 29th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2025-10-17T19:23:20+00:00","versionOfRecord":[],"versionCreatedAt":"2025-08-29 20:45:27","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7387859","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7387859","identity":"rs-7387859","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}