DFT Study of Hydrogen Evolution Reactions of Water Molecule with In7 and In6Al Clusters

DFT Study of Hydrogen Evolution Reactions of Water Molecule with In7 and In6Al Clusters | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article DFT Study of Hydrogen Evolution Reactions of Water Molecule with In7 and In6Al Clusters Bing Xin Liu, Dan Lei, Shun Ping Shi, You Wen Xue, Zhan Jiang Duan, and 3 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-2844902/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 11 Feb, 2024 Read the published version in Journal of Cluster Science → Version 1 posted 7 You are reading this latest preprint version Abstract The specific process of hydrogen generation by the reaction of In 7 and In 6 Al clusters with H 2 O molecules is explored through density functional theory in this study. Based on the prediction of the lowest energy structure of In 7 and In 6 Al clusters, the geometric and electronic structures of In 7 @H 2 O and In 6 Al@H 2 O are obtained by using the dispersion-corrected density functional theory B3LYP-D3. The corresponding reaction paths are constructed according to the transition states in the searched reactions. Then we discuss the reaction path, energy barrier and reaction energy release. The results show that both In 7 and In 6 Al clusters can react with H 2 O molecules and release hydrogen. Both reactions are exothermic reactions, and the structure of the reaction product are very similar. The comparison of adsorption energy, energy barrier and reaction release energy show that the Al-doped In 7 cluster can significantly improve its ability to react with H 2 O and reduce the energy barrier that has to be overcome for the reaction process. The generated H 2 exists on the cluster surface in the form of physical adsorption, which is judged by the adsorption energy, the distance between the H 2 molecule and the cluster surface, and the interaction region indicator. Hydrogen evolution reaction Indium clusters NBO analysis Reaction mechanism Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Introduction Hydrogen energy is a green, efficient and clean energy, and a large amount of hydrogen on the earth exists in the form of water. Decomposing water to produce hydrogen will become an important way to solve energy and environmental problems. Hydrogen can be produced by electrocatalytic water splitting [ 1 , 2 ], but these methods are expensive and inefficient [ 3 ], and much attention has been paid to the efficient and cost-effective separation of hydrogen from water molecules. Several clusters are anticipated to have strong photocatalytic characteristics in the hydrogen evolution reaction of water molecules by a significant number of prior studies on the hydrogen evolution reaction (HER), and the effect of the reaction of Al clusters with H2O to produce hydrogen is particularly significant [ 4 – 11 ]. For example, the study of Alvarez-Barcia et al. [ 4 ] showed that the reaction of Al atoms with water would produce intermediates for the production of hydrogen, and their production was a key step in the production of hydrogen. Liu et al. [ 5 , 6 ] also systematically studied the adsorption of water molecules by Aln (n = 2–25) clusters. In addition to the study of pure Al clusters, the performance of the hydrogen evolution reaction of Al clusters doped with different elements has also become the focus of research [ 7 – 11 ]. The research on clusters such as GaAl12 had proved that doping was beneficial to lower the reaction energy barrier [ 7 ], thereby reducing the energy consumption required for the reaction and making the reaction easier. The ability of Al12X (X = Al, Mg, Zn, Ga, Ni, Fe, B, C, Si, P) clusters to dissociate water can be tuned by controllable X doping [ 8 ]. Al16Bi clusters can enhance H2 generation rate and yield [ 9 ]. At present, the research on the generation of H2 by dissociating water with Al clusters has been relatively comprehensive. From the research results of Xie et al., it can be found that Pt, Ge, and Ga clusters also have good performance in hydrogen evolution reaction [ 12 – 15 ]. Many theoretical research on indium in recent years have demonstrated that indium clusters have many great qualities in the areas of methane dehydrogenation, enhancing the stability of clusters like InnN 2 , and enhancing the photoactivity of TiO 2 [ 16 – 18 ]. Indium element also has a good performance in photocatalytic reaction, studies have shown that ZnInxSy, ZnO, and other clusters doping with appropriate amount of In can improve the photocatalytic hydrogen evolution activity [ 19 – 21 ]. To expand the research on hydrogen production from cluster dissociation of water, in view of the excellent properties of In clusters in many aspects, this research will start with In clusters to study the hydrogen evolution principle of the reaction between In clusters and H2O, and explore its performance in dissociating water to produce hydrogen. In previous theoretical studies on indium clusters, Zhang et al. have calculated the binding energy, second-order energy difference, etc. of Inn (n = 2–16) clusters through density functional theory, indicating that in small clusters In7, In8 and In13 are relatively more stable [ 22 – 24 ]. Considering the superior performance of Al clusters to dissociate water to produce H2, we first investigate the hydrogen evolution reaction of In7 and In6Al with a single H2O. This study systematically expounds the reaction mechanism of In7 and In6Al clusters in the hydrogen evolution reaction, including the adsorption of H2O, the extraction process of H2, and the structural analysis of the product. Computational Methods All calculations use density functional theory (DFT) to study the cluster structure and reaction process. The B3LYP [ 25 , 26 ] method is adopted as a whole, the SDD [ 27 ] basis set for In atoms and Al atom, the 6-311G [ 28 ] basis set for H atoms and O atom. Before studying the reaction process, the structure optimization and frequency analysis of various isomers of the In 7 and In 6 Al clusters are carried out to obtain the lowest energy structures of the two clusters, and then study the reactions of the In7 and In6Al clusters with a single H2O. At the same theoretical level, the dispersion-corrected density functional theory B3LYP-D3 [ 29 – 32 ] is used in the study of In 7 and In 6 Al clusters reacting with a single H 2 O to improve the calculation accuracy and solve the problem of poor functional ability to describe the dispersion effect. Considering the effect of different adsorption sites on the stability of the clusters, every possible configuration should be investigated, and then the most stable In7@H2O and In6Al@H2O complexes are obtained by optimization and frequency analysis. Natural bond orbital (NBO) [ 33 ] analysis at the same theoretical level is performed to clearly describe the intensity of electron transfer and interaction between H 2 O and In 7 or In 6 Al. The specific process of the reaction between clusters and water molecules to generate hydrogen is further investigated according to frequency analysis, structure optimization, and other methods, including looking for the transition states in the reaction, based on the lowest energy structures of In 7 @H 2 O and In 6 Al@H 2 O as the reactants for the hydrogen evolution reaction. Based on the Newton-Raphson algorithm, the reaction transition state is searched, and the reactant and product of the transition state connection are determined by the intrinsic reaction coordinate (IRC) [ 34 , 35 ]. The properties of the dissociate water of In 7 @H 2 O and In 6 Al@H 2 O are studied in terms of adsorption energies, energy barriers and reaction energies release. All the calculations are performed on the Gaussian 09 [ 36 ] program. Results and Discussion Different isomers of In 7 and In 6 Al clusters are constructed according to previous studies, and the optimization and frequency analysis are carried out for each structure respectively, and then the lowest energy structures of the In 7 and In 6 Al clusters are obtained by comparing the energies. In 7 has Cs symmetry and In 6 Al has C 1 symmetry, the spin multiplicity is doublet for both In 7 and In 6 Al, as shown in Fig. 1 . The results show that the structure of the In 6 Al cluster after replacing one In atom on one side of the In 7 cluster with an Al atom is relatively similar to the most stable structure of the In 7 cluster, and the most stable structure of the In 7 cluster is consistent with the research results of Shi et al [ 24 ]. The stability of In 7 and In 6 Al clusters is evaluated by calculating the energy of the following reactions: In 7 + Al→In 6 Al + In E= [E(In 7 ) + E(Al)]-[E(In 6 Al) + E(In)] Where E(In) is the energy of In atom, E(Al) is the energy of Al atom, E(In7) is the energy of In7 cluster and E(In 6 Al) is the energy of In6Al cluster. The whole reaction is an exothermic reaction with a reaction energy of -0.26eV. This calculation result shows that the stability of the cluster is slightly improved after Al-doping. Based on the lowest energy structure of In 7 and In 6 Al, a water molecule is adsorbed at different sites of In 7 and In 6 Al to obtain the lowest energy structure of the In 7 @H 2 O and In 6 Al@H 2 O complexes. The following formula is used to calculate the adsorption energy in the process of adsorbing water molecules by the clusters: Ea = E(InxAly@H2O)-E(InxAly)-E(H2O) The lowest energy structures of In 7 @H 2 O and In 6 Al@H 2 O obtained through frequency analysis and structure optimization, as shown in Fig. 1 . The spin multiplicity of In 7 @H 2 O and In 6 Al@H 2 O is doublet, and the subsequent research is carried out in this spin. The most stable structure is when the H2O molecule is adsorbed on top of the In7 cluster, where the In-O bond length is 2.38Å. For In6Al clusters, the structure is most stable when H2O molecule is attached to Al atom, and the Al-O bond length is 2.05Å. The adsorption energies of In 7 @H 2 O and In 6 Al@H 2 O are − 0.89eV and − 0.93eV, respectively. During the whole process, both of the adsorption of H 2 O molecule by In 7 cluster and In 6 Al cluster are exothermic, and the latter reaction releases more energy, which indicates that H 2 O molecule is more likely to be adsorbed on Al-doped In 7 cluster to form a stable complex. To gain a more advanced understanding of the underlying mechanics governing the transfer of electrons between clusters and water molecules, we have employed the analytical technique of NBO analysis. This sophisticated tool provides a comprehensive characterization of the degree of orbital overlap present between donor and acceptor orbitals in the system and affords a detailed quantitative evaluation of the second-order stabilization energy resulting from electron delocalization. By using Multiwfn [ 37 ] to generate lattice data of NBO and related orbital wave functions, and then using VMD [ 38 ] to draw the donor-acceptor orbital overlap of In 7 @H 2 O and In 6 Al@H 2 O as shown in Fig. 2 , it can be seen that the orbital overlap degree of In 6 Al@H 2 O is higher. In In7@H2O, the strongest interaction of H2O with In7 is due to the electron transfer of LPO8→LP*In6 (value of E(2) is 10.71kcal/mol), the contribution of BDH10-O8→LP*In6 and BDH9-O8 → LP*In6 to the stabilization energy is small, which are 3.06kcal/mol and 1.77kcal/mol. For In6Al@H2O, the strongest interaction of H2O with In6Al is due to the electron transfer of LPO8→LP*Al7 (28.85kcal/mol), where the contributions of BDH10-O8→LP*Al7 and BDH9-O8→LP*Al7 to the stabilization energy are 7.16kcal/mol and 7.63kacl/mol. The adsorption energies of In 7 @H 2 O and In 6 Al@H 2 O complexes are − 0.89eV and − 0.93eV, respectively. The calculated results show that the second-order stabilization energy is positively correlated with the adsorption energy [ 39 ]. It can be seen that the interaction between Al-doped In 7 and H 2 O is stronger, and the comparison shows that Al-doped is beneficial to improve the adsorption capacity of the cluster for water and the stability of the molecules. The Mayer bond order of the O-H bond in the complexes and water molecule is shown in Table 1 . An intriguing observation from the NBO analysis is that while the electron transfer from the BDH10-O8 and BDH9-O8 orbitals to the vacant antibonding orbitals of the cluster's lone pair electrons is substantially lower than that from the LPO8 orbital, it still results in a notable reduction of O-H bond order, which in turn affects the strength of the O-H bond. Table 1 The Mayer bond order of the O-H bond in the complexes and water molecule is completed at the B3LYP-D3/mixed basis sets (the SDD basis set for In atoms and Al atom, the 6-311G basis set for H atoms and O atom). Mayer bond order Cluster In 7 @H 2 O In6Al@H2O H 2 O BD O8−H9 0.741 0.804 0.814 BD O8−H10 0.769 0.803 0.814 Based on the study of the lowest energy structure of In 7 and In 6 AL clusters and the lowest energy structure of complexes In 7 @H 2 O and In 6 Al@H 2 O, the hydrogen evolution reactions of complexes In 7 @H 2 O and In 6 Al@H 2 O as reactants and their bond order changes are predicted. The reaction pathways of In 7 and In 6 Al reacting with a single water molecule to generate hydrogen are discovered by looking for transition states in the reaction and then connecting the desired reactants and product structures via the Intrinsic Reaction Coordinate (IRC), and the reaction energy barriers, reaction energies, number of reaction steps, and final products are obtained. The reaction energy barriers and reaction energies in the reactions are shown in Table 2 . Table 2 The energy barriers and the reaction energy of In7@H2O and In6Al@H2O. Ebn(n = 1, 2, 3, 4) is energy barriers. Energy(eV) Reaction E b1 E b2 E b3 E b4 Reaction energy In 7 + H 2 O 1.597 0.866 \ \ -1.025 In 6 Al + H 2 O 0.775 0.144 0.077 0.625 -1.381 The reaction path of In7 with H2O The reaction path of In 7 and H 2 O is divided into two steps, and the highest reaction energy barrier to be overcome is 1.597eV. The reaction shows that In 7 can completely dissociate the H 2 O molecule and finally generate In 7 O and H 2 , and the whole reaction is an exothermic reaction with a reaction energy of -1.913eV. The reaction process is shown in Fig. 3 . The first step of the reaction, breaking an H-O bond, the separated H atom forms a bond with an In atom at the top of the cluster, and the remaining O and H atoms move towards the interior of the cluster. The second step of the reaction, the In-H bond and the second H-O bond are broken, the two H atoms are close to each other and form a bond, the formed H 2 breaks out of the cluster, and the remaining O atom is embedded in the cluster and interact with the surrounding In atoms form bonds. During the whole process, the structure of In 7 clusters do not undergo obvious deformation. The reaction path of In6Al with H2O The reaction path of In 6 Al and H 2 O is divided into four steps, and the highest reaction energy barrier to be overcome is 0.775eV. The reaction shows that In 6 Al can completely dissociate the H 2 O molecule and finally generate In 6 AlO and H 2 , and the whole reaction is also an exothermic reaction. The reaction energy is -2.310eV. The reaction process is shown in Fig. 4 . The reaction process is similar to the reaction of In 7 with H 2 O. First step, one H-O bond is broken, and the separated H atom forms a bond with an In atom at the top of the cluster. The second step, take the Al atom connected to the O atom as the center, rotate the whole H-O around the Al atom to the direction of the first H atom by about 49°, so that the two H atoms are close to each other. The third step, continue to rotate the H-O whole to the inside of the cluster by about 46°, so that the two H atoms get closer. The fourth step, the In-H bond and the second H-O bond are broken, the two H atoms form H 2 and break away from the cluster, while the remaining O atom bond with the surrounding atoms. During the whole process, the structure of In 6 Al clusters do not undergo obvious deformation. The second and third steps of the whole reaction are to rotate the hydrogen atoms, the purpose is to shorten the distance between the two hydrogen atoms, so that the two hydrogen atoms can bond and form H 2 in the later stage and then leave the cluster. The reaction mechanism of In 7 + H 2 O reveals that the rate-determining step is the A 1 →B 1 elementary reaction, with an electronic energy barrier of 1.597 eV. The hydrogen evolution reaction of Ge 7 cluster involves a slowest step with an electronic energy barrier of 3.174 eV [ 14 ], while in the case of Pt 4 gas-phase clusters, the corresponding free-energy barrier is around 2.7 eV [ 40 ]. This observation indicates that the surface active sites of In 7 clusters are more potent than those of Ge 7 and Pt 4 clusters. As for the reaction mechanism of In 6 Al + H 2 O, the A 2 →B 2 elementary reaction is rate-limiting, with an electronic energy barrier of 0.775 eV. This finding suggests that the incorporation of Al results in a further reduction of the electronic energy barrier, corroborating the outcomes obtained from the previous NBO analysis. Notably, for the doped clusters Ge 6 Al and Al 6 Cu [ 14 , 11 ], the electronic energy barriers of their respective hydrogen evolution reactions' rate-determining steps are measured to be 2.766 eV and 3.254 eV, respectively. Through the study of the two reactions, we can see that during the step-by-step dissociation of H2O to generate H2, the structure of the In7 and In6Al clusters does not change significantly, but the O atoms are continuously embedded in the clusters, Finally, stable In7O, In6AlO and H2 are generated, and the structures of In7O and In6AlO products are also very similar, as shown in Fig. 5 . The results show that both In7 and In6Al clusters can stably react with H2O molecules and completely decompose H2O molecules into hydrogen. By exploring the reaction process, the reaction energy barrier and reaction energy of each step were determined. Both reactions are exothermic reactions, which are beneficial for us to use this cluster to dissociate water to generate hydrogen. By comparison, it is found that the reaction of In7 with H2O molecules needs to overcome a higher energy barrier (1.597eV), which means that more energy is required to make the reaction proceed. However, the energy barrier to be overcome for the reaction of In6Al and H2O molecule is lower, and the energy barrier values are all lower than 1eV, and the heat released by the reaction is increased compared with that of In7, indicating that In6Al cluster is superior to In7 cluster in dissociating water for hydrogen production. That is, the In7 cluster doping with Al atom is beneficial to the progress of the reaction. The product analysis The structural analysis of the reaction products is critical for understanding whether hydrogen molecules have formed and how they exist on the cluster surface. In this study, the geometric structure of the products and the interaction types on the surface were comprehensively analyzed using complementary methods, including bond lengths, adsorption energies, and IRI analyses [ 41 ]. Both the 2D and 3D IRI plots in Fig. 6 exhibit clear indications that H-H bonds have formed, suggesting that hydrogen molecules have indeed been generated on the cluster surface. The bond length between the two H atoms in the product is measured to be 0.6 Å, further confirming this conclusion. Additionally, the weak interaction between the hydrogen molecules and the cluster surface sites, as revealed by the prominent van der Waals interaction region in the plots, also sheds light on the physical adsorption form of H 2 molecules on the cluster surface. The study shows that the distances of H 2 molecules to the surface of In 7 O and In 6 AlO clusters (2.46A and 2.527 A, respectively) do not reach bonding distances [ 42 ]. The calculated adsorption energies (-0.089 eV and − 0.075 eV, respectively) support this observation, which is crucial for understanding the subsequent hydrogen desorption process. Conclusion Based on density functional theory, the geometric configuration, stability and hydrogen evolution reaction process of In7 and In6Al clusters with a single H2O are studied in detail. The adsorption energies of In 7 @H 2 O and In 6 Al@H 2 O are -0.89eV and -0.93eV during the complex formation process of water molecules adsorbed by clusters. The relationship between the donor and acceptor orbitals of In 7 @H 2 O and In 6 Al@H 2 O after water molecules adsorption is obtained by NBO analysis. The results show that Al-doped is beneficial to improve the adsorption capacity of the cluster to water and the stability of the molecules. And then the reaction pathways are constructed by finding transition states and generating the IRC. Our results show that both In7 and In6Al clusters can stably react with water molecules to generate H2, and both reactions are exothermic (-1.913eV and -2.310eV, respectively). In terms of binding energy, energy barrier and reaction energy, the stability of Al-doped In7 clusters is improved, the energy barrier to be overcome for the reaction is lower, and the energy released for the reaction is more. It shows that In7 doped with Al shows excellent performance in the production of hydrogen from dissociated water. From the perspective of the reaction process, the H atoms on In7@H2O or In6Al@H2O keep approaching to form H2, and the O atom move to the inside of the cluster to finally form oxide, which is conducive to the spontaneous progress of the reaction. And the generated H2 exists on the surface of the clusters in the form of physical adsorption, which is very beneficial for the later extraction of H2. Declarations Declarations of ethical approval all analyses were based on previous published studied, thus no ethical approval and patient consent are required. Declarations of competing interests The authors declare that they have no known competing financial interests or relationships that could have appeared to influence the work reported in the paper. Declarations of authorship contribution Bingxin Liu : Calculation, Writing – original draft. Shunping Shi and Dan Lei : Investigation, Supervision. Youwen Xue and Jing Jiang: Investigation. Jing Jiang and Chunyu Yao: Writing – draft improving. Yuanyuan Li: Provide calculations. Declarations of funding This project is supported by the Open Research Fund of Computational Physics Key Laboratory of Sichuan Province, Yibin University (Grant No. YB XYJSWL-ZD-2020-005). This work is also supported by the Student’s Platform for Innovation and Entrepreneurship Training Program (No. S202110616084). Declarations of availability of data and materials Encourages Data Sharing. References J. Chi and H. M. Yu (2018). Chin. J. Catal. 39, 390. Y. Xu and B. Zhang (2019). ChemElectroChem 6, 3214. C. Wang, H. Y. Shang, L. J. Jin, H. Xu and Y. K. Du (2021). Nanoscale 13, 7897. S. Alvarez-Barcia and J. R. Flores (2009). J. Chem. Phy.131, 174307. Y. L. Liu, Y. W. Hua, M. Jiang, G. Jiang and J. Chen (2012). J. Chem. Phy.136, 084703. J. Y. Zhao, F. Q. Zhao, H. X. Gao and X. H. Ju (2013). J. Mol. Model. 19, 1789. J. Chen and Z. Luo (2019). ChemPhysChem 20, 499. J. Y. Zhao, F. Q. Zhao, S. Y. Xu and X. H. Ju (2013). J. Phys. Chem. 117, 2213. F. Li, L. 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Cite Share Download PDF Status: Published Journal Publication published 11 Feb, 2024 Read the published version in Journal of Cluster Science → Version 1 posted Editorial decision: Major revision 24 Jun, 2023 Reviews received at journal 21 Jun, 2023 Reviewers agreed at journal 13 Jun, 2023 Reviewers invited by journal 06 Jun, 2023 Editor assigned by journal 05 May, 2023 Submission checks completed at journal 05 May, 2023 First submitted to journal 21 Apr, 2023 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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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-2844902","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":197719780,"identity":"a62d7ab7-0c39-44e2-b8d4-faaa39476f2d","order_by":0,"name":"Bing Xin Liu","email":"","orcid":"","institution":"Chengdu University of Technology","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Bing","middleName":"Xin","lastName":"Liu","suffix":""},{"id":197719781,"identity":"5c397d61-8249-41ff-b7fe-1d6e290bd157","order_by":1,"name":"Dan Lei","email":"","orcid":"","institution":"Chengdu University of Technology","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Dan","middleName":"","lastName":"Lei","suffix":""},{"id":197719782,"identity":"1f584546-c1ed-495a-a9af-16f5f7776a3a","order_by":2,"name":"Shun Ping Shi","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABDElEQVRIiWNgGAWjYDACCcYGZhDNBsQHP1QwMDaAeDxEamE8LHEGqIWNoBYGBmYok/kAbxsRWuRnNzd/Lmy7k8cn3X7hgOQ8O9kN9xsYH7xtY5A3x6HF4M7BNumZbc+K2WTOFBwo3JZsvOEYA7Ph3DYGw50NOLRIJLYx87YdTmyTyEk4ILntQCJQC5s00IUJBgdwOGxGYvNnuBbeOWAt7L/xaWG4kdggDdGSfuAAbwPEFmZ8WgxuJLZJ85w7XMwmkcNwWOJYsvHMY4nNknPOSRhuwOmw9MefecoO54EYHz/U2Mn2HT588MObMht5nA6DggRgXBhA2eAEIIFfPUQL+wOCqkbBKBgFo2BkAgBq3GMKkIkSNQAAAABJRU5ErkJggg==","orcid":"","institution":"Chengdu University of Technology","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Shun","middleName":"Ping","lastName":"Shi","suffix":""},{"id":197719783,"identity":"195d1723-5863-4974-a7b2-17c951522548","order_by":3,"name":"You Wen Xue","email":"","orcid":"","institution":"Chengdu University of Technology","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"You","middleName":"Wen","lastName":"Xue","suffix":""},{"id":197719784,"identity":"1ede37d6-9b9f-4ff5-a63f-432e96f75537","order_by":4,"name":"Zhan Jiang Duan","email":"","orcid":"","institution":"Chengdu University of Technology","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Zhan","middleName":"Jiang","lastName":"Duan","suffix":""},{"id":197719785,"identity":"45a22bd6-96b2-4031-a845-14c16513781a","order_by":5,"name":"Jing Jiang","email":"","orcid":"","institution":"Chengdu University of Technology","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Jing","middleName":"","lastName":"Jiang","suffix":""},{"id":197719786,"identity":"17699250-2b3d-4d66-86ed-9c7951148366","order_by":6,"name":"Chun Yu Yao","email":"","orcid":"","institution":"Chengdu University of Technology","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Chun","middleName":"Yu","lastName":"Yao","suffix":""},{"id":197719787,"identity":"3e84bf62-6159-4455-9674-1251b316624c","order_by":7,"name":"Yuan Yuan Li","email":"","orcid":"","institution":"Sichuan University of Science and Engineering","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Yuan","middleName":"Yuan","lastName":"Li","suffix":""}],"badges":[],"createdAt":"2023-04-21 10:14:22","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-2844902/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-2844902/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s10876-024-02580-6","type":"published","date":"2024-02-11T11:28:31+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":36742894,"identity":"f7a4f095-c217-4c46-9028-456266eff1ba","added_by":"auto","created_at":"2023-05-09 13:41:04","extension":"jpeg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":320515,"visible":true,"origin":"","legend":"\u003cp\u003eThe lowest energy structure of In\u003csub\u003e7\u003c/sub\u003e(a), In\u003csub\u003e6\u003c/sub\u003eAl(b), In\u003csub\u003e7\u003c/sub\u003e@H\u003csub\u003e2\u003c/sub\u003eO(c) and In\u003csub\u003e6\u003c/sub\u003eAl@H\u003csub\u003e2\u003c/sub\u003eO(d).\u003c/p\u003e","description":"","filename":"floatimage1.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-2844902/v1/6d366f1f13e309ac8e9d967f.jpeg"},{"id":36741887,"identity":"577ceea1-14b8-4a48-98e4-7d2573945580","added_by":"auto","created_at":"2023-05-09 13:33:04","extension":"jpeg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":993961,"visible":true,"origin":"","legend":"\u003cp\u003eThe donor-acceptor orbital overlaps of In7@H2O(a) and In6Al@H2O(b)\u003c/p\u003e","description":"","filename":"floatimage2.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-2844902/v1/4e04de4c8a95978372a502bb.jpeg"},{"id":36741885,"identity":"6b444aea-995e-4c64-921a-f90140a51f15","added_by":"auto","created_at":"2023-05-09 13:33:04","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":384429,"visible":true,"origin":"","legend":"\u003cp\u003eThe reaction paths between In\u003csub\u003e7\u003c/sub\u003e and H\u003csub\u003e2\u003c/sub\u003eO. The structure and energy changes of the reactant A\u003csub\u003e1\u003c/sub\u003e, intermediate states B\u003csub\u003e1\u003c/sub\u003e, transition states TS\u003csub\u003e1\u003c/sub\u003e1 and TS\u003csub\u003e1\u003c/sub\u003e2, product C\u003csub\u003e1\u003c/sub\u003e are included, and equilibrium constant(EC).\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-2844902/v1/38de0ed7fa49c9af45ab1403.png"},{"id":36741886,"identity":"0a461d98-ca1d-4568-9923-6f4093ac7e6e","added_by":"auto","created_at":"2023-05-09 13:33:04","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":523451,"visible":true,"origin":"","legend":"\u003cp\u003eThe reaction paths between In\u003csub\u003e6\u003c/sub\u003eAl and H\u003csub\u003e2\u003c/sub\u003eO. The structure and energy changes of the reactant A\u003csub\u003e2\u003c/sub\u003e, intermediate states B\u003csub\u003e2\u003c/sub\u003e, C\u003csub\u003e2\u003c/sub\u003e, and D\u003csub\u003e2\u003c/sub\u003e, transition states TS\u003csub\u003e2\u003c/sub\u003e1, TS\u003csub\u003e2\u003c/sub\u003e2, TS\u003csub\u003e2\u003c/sub\u003e3, and TS\u003csub\u003e2\u003c/sub\u003e4, and product E\u003csub\u003e2\u003c/sub\u003e are included, and equilibrium constant(EC).\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-2844902/v1/31c6614e9e9b276510a75ec3.png"},{"id":36741889,"identity":"25247322-67f4-447a-aa87-bac180d257bb","added_by":"auto","created_at":"2023-05-09 13:33:04","extension":"jpeg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":143651,"visible":true,"origin":"","legend":"\u003cp\u003eProducts of two reactions (In\u003csub\u003e7\u003c/sub\u003eO, In\u003csub\u003e6\u003c/sub\u003eAlO and H\u003csub\u003e2\u003c/sub\u003e)\u003c/p\u003e","description":"","filename":"floatimage5.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-2844902/v1/e85e4979c298b430d9897b01.jpeg"},{"id":36742895,"identity":"ccc1b958-3ce2-431b-b2ee-5d9bd7aa5d45","added_by":"auto","created_at":"2023-05-09 13:41:04","extension":"jpeg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":656654,"visible":true,"origin":"","legend":"\u003cp\u003eBonding Characteristics of the In\u003csub\u003e7\u003c/sub\u003eO@H\u003csub\u003e2\u003c/sub\u003e and In\u003csub\u003e6\u003c/sub\u003eAlO@H\u003csub\u003e2\u003c/sub\u003e complexes. The top row is IRI 2D plot, and the bottom row is IRI 3D plot. IRI = 1.0 a.u. The blue color of the isosurface represents the chemical bond action, the green is the van der Waals here, and the bright red color represents the strong steric hindrance here.\u003c/p\u003e","description":"","filename":"floatimage6.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-2844902/v1/ba6995761cddbed902d80e15.jpeg"},{"id":56598854,"identity":"b4dfe589-dbc7-42b2-9b6a-fa069c8c40c7","added_by":"auto","created_at":"2024-05-16 11:28:37","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3250105,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-2844902/v1/4f327770-44a8-416e-a9a2-28b82244d3c4.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"DFT Study of Hydrogen Evolution Reactions of Water Molecule with In7 and In6Al Clusters","fulltext":[{"header":"Introduction","content":"\u003cp\u003eHydrogen energy is a green, efficient and clean energy, and a large amount of hydrogen on the earth exists in the form of water. Decomposing water to produce hydrogen will become an important way to solve energy and environmental problems. Hydrogen can be produced by electrocatalytic water splitting [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e], but these methods are expensive and inefficient [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e], and much attention has been paid to the efficient and cost-effective separation of hydrogen from water molecules.\u003c/p\u003e \u003cp\u003eSeveral clusters are anticipated to have strong photocatalytic characteristics in the hydrogen evolution reaction of water molecules by a significant number of prior studies on the hydrogen evolution reaction (HER), and the effect of the reaction of Al clusters with H2O to produce hydrogen is particularly significant [\u003cspan additionalcitationids=\"CR5 CR6 CR7 CR8 CR9 CR10\" citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. For example, the study of Alvarez-Barcia et al. [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e] showed that the reaction of Al atoms with water would produce intermediates for the production of hydrogen, and their production was a key step in the production of hydrogen. Liu et al. [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e] also systematically studied the adsorption of water molecules by Aln (n\u0026thinsp;=\u0026thinsp;2\u0026ndash;25) clusters. In addition to the study of pure Al clusters, the performance of the hydrogen evolution reaction of Al clusters doped with different elements has also become the focus of research [\u003cspan additionalcitationids=\"CR8 CR9 CR10\" citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. The research on clusters such as GaAl12 had proved that doping was beneficial to lower the reaction energy barrier [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e], thereby reducing the energy consumption required for the reaction and making the reaction easier. The ability of Al12X (X\u0026thinsp;=\u0026thinsp;Al, Mg, Zn, Ga, Ni, Fe, B, C, Si, P) clusters to dissociate water can be tuned by controllable X doping [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. Al16Bi clusters can enhance H2 generation rate and yield [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. At present, the research on the generation of H2 by dissociating water with Al clusters has been relatively comprehensive. From the research results of Xie et al., it can be found that Pt, Ge, and Ga clusters also have good performance in hydrogen evolution reaction [\u003cspan additionalcitationids=\"CR13 CR14\" citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eMany theoretical research on indium in recent years have demonstrated that indium clusters have many great qualities in the areas of methane dehydrogenation, enhancing the stability of clusters like InnN\u003csub\u003e2\u003c/sub\u003e, and enhancing the photoactivity of TiO\u003csub\u003e2\u003c/sub\u003e [\u003cspan additionalcitationids=\"CR17\" citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. Indium element also has a good performance in photocatalytic reaction, studies have shown that ZnInxSy, ZnO, and other clusters doping with appropriate amount of In can improve the photocatalytic hydrogen evolution activity [\u003cspan additionalcitationids=\"CR20\" citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]. To expand the research on hydrogen production from cluster dissociation of water, in view of the excellent properties of In clusters in many aspects, this research will start with In clusters to study the hydrogen evolution principle of the reaction between In clusters and H2O, and explore its performance in dissociating water to produce hydrogen. In previous theoretical studies on indium clusters, Zhang et al. have calculated the binding energy, second-order energy difference, etc. of Inn (n\u0026thinsp;=\u0026thinsp;2\u0026ndash;16) clusters through density functional theory, indicating that in small clusters In7, In8 and In13 are relatively more stable [\u003cspan additionalcitationids=\"CR23\" citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]. Considering the superior performance of Al clusters to dissociate water to produce H2, we first investigate the hydrogen evolution reaction of In7 and In6Al with a single H2O. This study systematically expounds the reaction mechanism of In7 and In6Al clusters in the hydrogen evolution reaction, including the adsorption of H2O, the extraction process of H2, and the structural analysis of the product.\u003c/p\u003e"},{"header":"Computational Methods","content":"\u003cp\u003eAll calculations use density functional theory (DFT) to study the cluster structure and reaction process. The B3LYP [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e] method is adopted as a whole, the SDD [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e] basis set for In atoms and Al atom, the 6-311G [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e] basis set for H atoms and O atom. Before studying the reaction process, the structure optimization and frequency analysis of various isomers of the In\u003csub\u003e7\u003c/sub\u003e and In\u003csub\u003e6\u003c/sub\u003eAl clusters are carried out to obtain the lowest energy structures of the two clusters, and then study the reactions of the In7 and In6Al clusters with a single H2O. At the same theoretical level, the dispersion-corrected density functional theory B3LYP-D3 [\u003cspan additionalcitationids=\"CR30 CR31\" citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e] is used in the study of In\u003csub\u003e7\u003c/sub\u003e and In\u003csub\u003e6\u003c/sub\u003eAl clusters reacting with a single H\u003csub\u003e2\u003c/sub\u003eO to improve the calculation accuracy and solve the problem of poor functional ability to describe the dispersion effect. Considering the effect of different adsorption sites on the stability of the clusters, every possible configuration should be investigated, and then the most stable In7@H2O and In6Al@H2O complexes are obtained by optimization and frequency analysis. Natural bond orbital (NBO) [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e] analysis at the same theoretical level is performed to clearly describe the intensity of electron transfer and interaction between H\u003csub\u003e2\u003c/sub\u003eO and In\u003csub\u003e7\u003c/sub\u003e or In\u003csub\u003e6\u003c/sub\u003eAl. The specific process of the reaction between clusters and water molecules to generate hydrogen is further investigated according to frequency analysis, structure optimization, and other methods, including looking for the transition states in the reaction, based on the lowest energy structures of In\u003csub\u003e7\u003c/sub\u003e@H\u003csub\u003e2\u003c/sub\u003eO and In\u003csub\u003e6\u003c/sub\u003eAl@H\u003csub\u003e2\u003c/sub\u003eO as the reactants for the hydrogen evolution reaction. Based on the Newton-Raphson algorithm, the reaction transition state is searched, and the reactant and product of the transition state connection are determined by the intrinsic reaction coordinate (IRC) [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e, \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e]. The properties of the dissociate water of In\u003csub\u003e7\u003c/sub\u003e@H\u003csub\u003e2\u003c/sub\u003eO and In\u003csub\u003e6\u003c/sub\u003eAl@H\u003csub\u003e2\u003c/sub\u003eO are studied in terms of adsorption energies, energy barriers and reaction energies release. All the calculations are performed on the Gaussian 09 [\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e] program.\u003c/p\u003e"},{"header":"Results and Discussion","content":"\u003cp\u003eDifferent isomers of In\u003csub\u003e7\u003c/sub\u003e and In\u003csub\u003e6\u003c/sub\u003eAl clusters are constructed according to previous studies, and the optimization and frequency analysis are carried out for each structure respectively, and then the lowest energy structures of the In\u003csub\u003e7\u003c/sub\u003e and In\u003csub\u003e6\u003c/sub\u003eAl clusters are obtained by comparing the energies. In\u003csub\u003e7\u003c/sub\u003e has Cs symmetry and In\u003csub\u003e6\u003c/sub\u003eAl has C\u003csub\u003e1\u003c/sub\u003e symmetry, the spin multiplicity is doublet for both In\u003csub\u003e7\u003c/sub\u003e and In\u003csub\u003e6\u003c/sub\u003eAl, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. The results show that the structure of the In\u003csub\u003e6\u003c/sub\u003eAl cluster after replacing one In atom on one side of the In\u003csub\u003e7\u003c/sub\u003e cluster with an Al atom is relatively similar to the most stable structure of the In\u003csub\u003e7\u003c/sub\u003e cluster, and the most stable structure of the In\u003csub\u003e7\u003c/sub\u003e cluster is consistent with the research results of Shi et al [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]. The stability of In\u003csub\u003e7\u003c/sub\u003e and In\u003csub\u003e6\u003c/sub\u003eAl clusters is evaluated by calculating the energy of the following reactions:\u003c/p\u003e \u003cp\u003eIn\u003csub\u003e7\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;Al\u0026rarr;In\u003csub\u003e6\u003c/sub\u003eAl\u0026thinsp;+\u0026thinsp;In\u003c/p\u003e \u003cp\u003eE= [E(In\u003csub\u003e7\u003c/sub\u003e)\u0026thinsp;+\u0026thinsp;E(Al)]-[E(In\u003csub\u003e6\u003c/sub\u003eAl)\u0026thinsp;+\u0026thinsp;E(In)]\u003c/p\u003e \u003cp\u003eWhere E(In) is the energy of In atom, E(Al) is the energy of Al atom, E(In7) is the energy of In7 cluster and E(In\u003csub\u003e6\u003c/sub\u003eAl) is the energy of In6Al cluster. The whole reaction is an exothermic reaction with a reaction energy of -0.26eV. This calculation result shows that the stability of the cluster is slightly improved after Al-doping.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eBased on the lowest energy structure of In\u003csub\u003e7\u003c/sub\u003e and In\u003csub\u003e6\u003c/sub\u003eAl, a water molecule is adsorbed at different sites of In\u003csub\u003e7\u003c/sub\u003e and In\u003csub\u003e6\u003c/sub\u003eAl to obtain the lowest energy structure of the In\u003csub\u003e7\u003c/sub\u003e@H\u003csub\u003e2\u003c/sub\u003eO and In\u003csub\u003e6\u003c/sub\u003eAl@H\u003csub\u003e2\u003c/sub\u003eO complexes. The following formula is used to calculate the adsorption energy in the process of adsorbing water molecules by the clusters:\u003c/p\u003e \u003cp\u003eEa\u0026thinsp;=\u0026thinsp;E(InxAly@H2O)-E(InxAly)-E(H2O)\u003c/p\u003e \u003cp\u003eThe lowest energy structures of In\u003csub\u003e7\u003c/sub\u003e@H\u003csub\u003e2\u003c/sub\u003eO and In\u003csub\u003e6\u003c/sub\u003eAl@H\u003csub\u003e2\u003c/sub\u003eO obtained through frequency analysis and structure optimization, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. The spin multiplicity of In\u003csub\u003e7\u003c/sub\u003e@H\u003csub\u003e2\u003c/sub\u003eO and In\u003csub\u003e6\u003c/sub\u003eAl@H\u003csub\u003e2\u003c/sub\u003eO is doublet, and the subsequent research is carried out in this spin. The most stable structure is when the H2O molecule is adsorbed on top of the In7 cluster, where the In-O bond length is 2.38\u0026Aring;. For In6Al clusters, the structure is most stable when H2O molecule is attached to Al atom, and the Al-O bond length is 2.05\u0026Aring;. The adsorption energies of In\u003csub\u003e7\u003c/sub\u003e@H\u003csub\u003e2\u003c/sub\u003eO and In\u003csub\u003e6\u003c/sub\u003eAl@H\u003csub\u003e2\u003c/sub\u003eO are \u0026minus;\u0026thinsp;0.89eV and \u0026minus;\u0026thinsp;0.93eV, respectively. During the whole process, both of the adsorption of H\u003csub\u003e2\u003c/sub\u003eO molecule by In\u003csub\u003e7\u003c/sub\u003e cluster and In\u003csub\u003e6\u003c/sub\u003eAl cluster are exothermic, and the latter reaction releases more energy, which indicates that H\u003csub\u003e2\u003c/sub\u003eO molecule is more likely to be adsorbed on Al-doped In\u003csub\u003e7\u003c/sub\u003e cluster to form a stable complex.\u003c/p\u003e \u003cp\u003eTo gain a more advanced understanding of the underlying mechanics governing the transfer of electrons between clusters and water molecules, we have employed the analytical technique of NBO analysis. This sophisticated tool provides a comprehensive characterization of the degree of orbital overlap present between donor and acceptor orbitals in the system and affords a detailed quantitative evaluation of the second-order stabilization energy resulting from electron delocalization. By using Multiwfn [\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e] to generate lattice data of NBO and related orbital wave functions, and then using VMD [\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e] to draw the donor-acceptor orbital overlap of In\u003csub\u003e7\u003c/sub\u003e@H\u003csub\u003e2\u003c/sub\u003eO and In\u003csub\u003e6\u003c/sub\u003eAl@H\u003csub\u003e2\u003c/sub\u003eO as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, it can be seen that the orbital overlap degree of In\u003csub\u003e6\u003c/sub\u003eAl@H\u003csub\u003e2\u003c/sub\u003eO is higher. In In7@H2O, the strongest interaction of H2O with In7 is due to the electron transfer of LPO8\u0026rarr;LP*In6 (value of E(2) is 10.71kcal/mol), the contribution of BDH10-O8\u0026rarr;LP*In6 and BDH9-O8 \u0026rarr; LP*In6 to the stabilization energy is small, which are 3.06kcal/mol and 1.77kcal/mol. For In6Al@H2O, the strongest interaction of H2O with In6Al is due to the electron transfer of LPO8\u0026rarr;LP*Al7 (28.85kcal/mol), where the contributions of BDH10-O8\u0026rarr;LP*Al7 and BDH9-O8\u0026rarr;LP*Al7 to the stabilization energy are 7.16kcal/mol and 7.63kacl/mol. The adsorption energies of In\u003csub\u003e7\u003c/sub\u003e@H\u003csub\u003e2\u003c/sub\u003eO and In\u003csub\u003e6\u003c/sub\u003eAl@H\u003csub\u003e2\u003c/sub\u003eO complexes are \u0026minus;\u0026thinsp;0.89eV and \u0026minus;\u0026thinsp;0.93eV, respectively. The calculated results show that the second-order stabilization energy is positively correlated with the adsorption energy [\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e]. It can be seen that the interaction between Al-doped In\u003csub\u003e7\u003c/sub\u003e and H\u003csub\u003e2\u003c/sub\u003eO is stronger, and the comparison shows that Al-doped is beneficial to improve the adsorption capacity of the cluster for water and the stability of the molecules. The Mayer bond order of the O-H bond in the complexes and water molecule is shown in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. An intriguing observation from the NBO analysis is that while the electron transfer from the BDH10-O8 and BDH9-O8 orbitals to the vacant antibonding orbitals of the cluster's lone pair electrons is substantially lower than that from the LPO8 orbital, it still results in a notable reduction of O-H bond order, which in turn affects the strength of the O-H bond.\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\u003eThe Mayer bond order of the O-H bond in the complexes and water molecule is completed at the B3LYP-D3/mixed basis sets (the SDD basis set for In atoms and Al atom, the 6-311G basis set for H atoms and O atom).\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=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colspan=\"4\" nameend=\"c4\" namest=\"c1\"\u003e \u003cp\u003eMayer bond order\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCluster\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eIn\u003csub\u003e7\u003c/sub\u003e@H\u003csub\u003e2\u003c/sub\u003eO\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eIn6Al@H2O\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eH\u003csub\u003e2\u003c/sub\u003eO\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBD\u003csub\u003eO8\u0026minus;H9\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.741\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.804\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.814\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBD\u003csub\u003eO8\u0026minus;H10\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.769\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.803\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.814\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\u003eBased on the study of the lowest energy structure of In\u003csub\u003e7\u003c/sub\u003e and In\u003csub\u003e6\u003c/sub\u003eAL clusters and the lowest energy structure of complexes In\u003csub\u003e7\u003c/sub\u003e@H\u003csub\u003e2\u003c/sub\u003eO and In\u003csub\u003e6\u003c/sub\u003eAl@H\u003csub\u003e2\u003c/sub\u003eO, the hydrogen evolution reactions of complexes In\u003csub\u003e7\u003c/sub\u003e@H\u003csub\u003e2\u003c/sub\u003eO and In\u003csub\u003e6\u003c/sub\u003eAl@H\u003csub\u003e2\u003c/sub\u003eO as reactants and their bond order changes are predicted. The reaction pathways of In\u003csub\u003e7\u003c/sub\u003e and In\u003csub\u003e6\u003c/sub\u003eAl reacting with a single water molecule to generate hydrogen are discovered by looking for transition states in the reaction and then connecting the desired reactants and product structures via the Intrinsic Reaction Coordinate (IRC), and the reaction energy barriers, reaction energies, number of reaction steps, and final products are obtained. The reaction energy barriers and reaction energies in the reactions are shown in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\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\u003eThe energy barriers and the reaction energy of In7@H2O and In6Al@H2O. Ebn(n\u0026thinsp;=\u0026thinsp;1, 2, 3, 4) is energy barriers.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\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=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colspan=\"6\" nameend=\"c6\" namest=\"c1\"\u003e \u003cp\u003eEnergy(eV)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eReaction\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eE\u003csub\u003eb1\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eE\u003csub\u003eb2\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eE\u003csub\u003eb3\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eE\u003csub\u003eb4\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eReaction energy\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eIn\u003csub\u003e7\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;H\u003csub\u003e2\u003c/sub\u003eO\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.597\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.866\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\\\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\\\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-1.025\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eIn\u003csub\u003e6\u003c/sub\u003eAl\u0026thinsp;+\u0026thinsp;H\u003csub\u003e2\u003c/sub\u003eO\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.775\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.144\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.077\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.625\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-1.381\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003eThe reaction path of In7 with H2O\u003c/h2\u003e \u003cp\u003eThe reaction path of In\u003csub\u003e7\u003c/sub\u003e and H\u003csub\u003e2\u003c/sub\u003eO is divided into two steps, and the highest reaction energy barrier to be overcome is 1.597eV. The reaction shows that In\u003csub\u003e7\u003c/sub\u003e can completely dissociate the H\u003csub\u003e2\u003c/sub\u003eO molecule and finally generate In\u003csub\u003e7\u003c/sub\u003eO and H\u003csub\u003e2\u003c/sub\u003e, and the whole reaction is an exothermic reaction with a reaction energy of -1.913eV. The reaction process is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eThe first step of the reaction, breaking an H-O bond, the separated H atom forms a bond with an In atom at the top of the cluster, and the remaining O and H atoms move towards the interior of the cluster. The second step of the reaction, the In-H bond and the second H-O bond are broken, the two H atoms are close to each other and form a bond, the formed H\u003csub\u003e2\u003c/sub\u003e breaks out of the cluster, and the remaining O atom is embedded in the cluster and interact with the surrounding In atoms form bonds. During the whole process, the structure of In\u003csub\u003e7\u003c/sub\u003e clusters do not undergo obvious deformation.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003eThe reaction path of In6Al with H2O\u003c/h2\u003e \u003cp\u003eThe reaction path of In\u003csub\u003e6\u003c/sub\u003eAl and H\u003csub\u003e2\u003c/sub\u003eO is divided into four steps, and the highest reaction energy barrier to be overcome is 0.775eV. The reaction shows that In\u003csub\u003e6\u003c/sub\u003eAl can completely dissociate the H\u003csub\u003e2\u003c/sub\u003eO molecule and finally generate In\u003csub\u003e6\u003c/sub\u003eAlO and H\u003csub\u003e2\u003c/sub\u003e, and the whole reaction is also an exothermic reaction. The reaction energy is -2.310eV. The reaction process is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eThe reaction process is similar to the reaction of In\u003csub\u003e7\u003c/sub\u003e with H\u003csub\u003e2\u003c/sub\u003eO. First step, one H-O bond is broken, and the separated H atom forms a bond with an In atom at the top of the cluster. The second step, take the Al atom connected to the O atom as the center, rotate the whole H-O around the Al atom to the direction of the first H atom by about 49\u0026deg;, so that the two H atoms are close to each other. The third step, continue to rotate the H-O whole to the inside of the cluster by about 46\u0026deg;, so that the two H atoms get closer. The fourth step, the In-H bond and the second H-O bond are broken, the two H atoms form H\u003csub\u003e2\u003c/sub\u003e and break away from the cluster, while the remaining O atom bond with the surrounding atoms. During the whole process, the structure of In\u003csub\u003e6\u003c/sub\u003eAl clusters do not undergo obvious deformation. The second and third steps of the whole reaction are to rotate the hydrogen atoms, the purpose is to shorten the distance between the two hydrogen atoms, so that the two hydrogen atoms can bond and form H\u003csub\u003e2\u003c/sub\u003e in the later stage and then leave the cluster.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe reaction mechanism of In\u003csub\u003e7\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;H\u003csub\u003e2\u003c/sub\u003eO reveals that the rate-determining step is the A\u003csub\u003e1\u003c/sub\u003e\u0026rarr;B\u003csub\u003e1\u003c/sub\u003e elementary reaction, with an electronic energy barrier of 1.597 eV. The hydrogen evolution reaction of Ge\u003csub\u003e7\u003c/sub\u003e cluster involves a slowest step with an electronic energy barrier of 3.174 eV [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e], while in the case of Pt\u003csub\u003e4\u003c/sub\u003e gas-phase clusters, the corresponding free-energy barrier is around 2.7 eV [\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e]. This observation indicates that the surface active sites of In\u003csub\u003e7\u003c/sub\u003e clusters are more potent than those of Ge\u003csub\u003e7\u003c/sub\u003e and Pt\u003csub\u003e4\u003c/sub\u003e clusters. As for the reaction mechanism of In\u003csub\u003e6\u003c/sub\u003eAl\u0026thinsp;+\u0026thinsp;H\u003csub\u003e2\u003c/sub\u003eO, the A\u003csub\u003e2\u003c/sub\u003e\u0026rarr;B\u003csub\u003e2\u003c/sub\u003e elementary reaction is rate-limiting, with an electronic energy barrier of 0.775 eV. This finding suggests that the incorporation of Al results in a further reduction of the electronic energy barrier, corroborating the outcomes obtained from the previous NBO analysis. Notably, for the doped clusters Ge\u003csub\u003e6\u003c/sub\u003eAl and Al\u003csub\u003e6\u003c/sub\u003eCu [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e], the electronic energy barriers of their respective hydrogen evolution reactions' rate-determining steps are measured to be 2.766 eV and 3.254 eV, respectively.\u003c/p\u003e \u003cp\u003eThrough the study of the two reactions, we can see that during the step-by-step dissociation of H2O to generate H2, the structure of the In7 and In6Al clusters does not change significantly, but the O atoms are continuously embedded in the clusters, Finally, stable In7O, In6AlO and H2 are generated, and the structures of In7O and In6AlO products are also very similar, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e. The results show that both In7 and In6Al clusters can stably react with H2O molecules and completely decompose H2O molecules into hydrogen.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eBy exploring the reaction process, the reaction energy barrier and reaction energy of each step were determined. Both reactions are exothermic reactions, which are beneficial for us to use this cluster to dissociate water to generate hydrogen. By comparison, it is found that the reaction of In7 with H2O molecules needs to overcome a higher energy barrier (1.597eV), which means that more energy is required to make the reaction proceed. However, the energy barrier to be overcome for the reaction of In6Al and H2O molecule is lower, and the energy barrier values are all lower than 1eV, and the heat released by the reaction is increased compared with that of In7, indicating that In6Al cluster is superior to In7 cluster in dissociating water for hydrogen production. That is, the In7 cluster doping with Al atom is beneficial to the progress of the reaction.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003eThe product analysis\u003c/h2\u003e \u003cp\u003eThe structural analysis of the reaction products is critical for understanding whether hydrogen molecules have formed and how they exist on the cluster surface. In this study, the geometric structure of the products and the interaction types on the surface were comprehensively analyzed using complementary methods, including bond lengths, adsorption energies, and IRI analyses [\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e]. Both the 2D and 3D IRI plots in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e exhibit clear indications that H-H bonds have formed, suggesting that hydrogen molecules have indeed been generated on the cluster surface. The bond length between the two H atoms in the product is measured to be 0.6 \u0026Aring;, further confirming this conclusion. Additionally, the weak interaction between the hydrogen molecules and the cluster surface sites, as revealed by the prominent van der Waals interaction region in the plots, also sheds light on the physical adsorption form of H\u003csub\u003e2\u003c/sub\u003e molecules on the cluster surface. The study shows that the distances of H\u003csub\u003e2\u003c/sub\u003e molecules to the surface of In\u003csub\u003e7\u003c/sub\u003eO and In\u003csub\u003e6\u003c/sub\u003eAlO clusters (2.46A and 2.527 A, respectively) do not reach bonding distances [\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e]. The calculated adsorption energies (-0.089 eV and \u0026minus;\u0026thinsp;0.075 eV, respectively) support this observation, which is crucial for understanding the subsequent hydrogen desorption process.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"Conclusion","content":"\u003cp\u003eBased on density functional theory, the geometric configuration, stability and hydrogen evolution reaction process of In7\u0026nbsp;and In6Al clusters with a single H2O are studied in detail. The adsorption energies of In\u003csub\u003e7\u003c/sub\u003e@H\u003csub\u003e2\u003c/sub\u003eO and In\u003csub\u003e6\u003c/sub\u003eAl@H\u003csub\u003e2\u003c/sub\u003eO are -0.89eV and -0.93eV during the complex formation process of water molecules adsorbed by clusters. The relationship between the donor and acceptor orbitals of In\u003csub\u003e7\u003c/sub\u003e@H\u003csub\u003e2\u003c/sub\u003eO and In\u003csub\u003e6\u003c/sub\u003eAl@H\u003csub\u003e2\u003c/sub\u003eO after water molecules adsorption is obtained by NBO analysis. The results show that Al-doped is beneficial to improve the adsorption capacity of the cluster to water and the stability of the molecules. And then the reaction pathways are constructed by finding transition states and generating the IRC. Our results show that both In7 and In6Al clusters can stably react with water molecules to generate H2, and both reactions are exothermic (-1.913eV and -2.310eV, respectively). In terms of binding energy, energy barrier and reaction energy, the stability of Al-doped In7 clusters is improved, the energy barrier to be overcome for the reaction is lower, and the energy released for the reaction is more. It shows that In7 doped with Al shows excellent performance in the production of hydrogen from dissociated water. From the perspective of the reaction process, the H atoms on In7@H2O or In6Al@H2O keep approaching to form H2, and the O atom move to the inside of the cluster to finally form oxide, which is conducive to the spontaneous progress of the reaction. And the generated H2 exists on the surface of the clusters in the form of physical adsorption, which is very beneficial for the later extraction of H2.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eDeclarations of ethical approval\u0026nbsp;\u003c/strong\u003eall analyses were based on previous published studied, thus no ethical approval and patient consent are required.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eDeclarations of competing interests\u0026nbsp;\u003c/strong\u003eThe authors declare that they have no known competing financial interests or relationships that could have appeared to influence the work reported in the paper.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eDeclarations\u003c/strong\u003e\u003cstrong\u003e\u0026nbsp;of authorship contribution\u0026nbsp;\u003c/strong\u003eBingxin Liu\u003cstrong\u003e:\u003c/strong\u003e Calculation, Writing \u0026ndash; original draft.\u0026nbsp;Shunping Shi and Dan Lei\u003cstrong\u003e:\u003c/strong\u003e Investigation, Supervision.\u0026nbsp;Youwen Xue and Jing Jiang: Investigation.\u0026nbsp;Jing Jiang and Chunyu Yao: Writing \u0026ndash; draft improving.\u0026nbsp;Yuanyuan Li: Provide calculations.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eDeclarations of funding\u003c/strong\u003e This project is supported by the Open Research Fund of Computational Physics Key Laboratory of Sichuan Province, Yibin University (Grant No. YB XYJSWL-ZD-2020-005). This work is also supported by the Student\u0026rsquo;s Platform for Innovation and Entrepreneurship Training Program (No. S202110616084).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eDeclarations of availability of data and materials\u0026nbsp;\u003c/strong\u003eEncourages Data Sharing.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n \u003cli\u003e\u003cspan\u003eJ. Chi and H. M. Yu (2018). Chin. J. Catal. 39, 390.\u003c/span\u003e\u003c/li\u003e\n \u003cli\u003e\u003cspan\u003eY. Xu and B. Zhang (2019). ChemElectroChem 6, 3214.\u003c/span\u003e\u003c/li\u003e\n \u003cli\u003e\u003cspan\u003eC. Wang, H. Y. Shang, L. J. Jin, H. Xu and Y. K. Du (2021). Nanoscale 13, 7897.\u003c/span\u003e\u003c/li\u003e\n \u003cli\u003e\u003cspan\u003eS. Alvarez-Barcia and J. R. Flores (2009). J. Chem. Phy.131, 174307.\u003c/span\u003e\u003c/li\u003e\n \u003cli\u003e\u003cspan\u003eY. L. Liu, Y. W. Hua, M. Jiang, G. Jiang and J. Chen (2012). J. Chem. 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Dalton Trans. 21, 2832.\u003c/span\u003e\u003c/li\u003e\n\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":"journal-of-cluster-science","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":" Learn more about [Journal of Cluster Science](https://www.springer.com/journal/10876) ","snPcode":"10876","submissionUrl":"https://mc.manuscriptcentral.com/jocl","title":"Journal of Cluster Science","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Hydrogen evolution reaction, Indium clusters, NBO analysis, Reaction mechanism ","lastPublishedDoi":"10.21203/rs.3.rs-2844902/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-2844902/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe specific process of hydrogen generation by the reaction of In\u003csub\u003e7\u003c/sub\u003e and In\u003csub\u003e6\u003c/sub\u003eAl clusters with H\u003csub\u003e2\u003c/sub\u003eO molecules is explored through density functional theory in this study. Based on the prediction of the lowest energy structure of In\u003csub\u003e7\u003c/sub\u003e and In\u003csub\u003e6\u003c/sub\u003eAl clusters, the geometric and electronic structures of In\u003csub\u003e7\u003c/sub\u003e@H\u003csub\u003e2\u003c/sub\u003eO and In\u003csub\u003e6\u003c/sub\u003eAl@H\u003csub\u003e2\u003c/sub\u003eO are obtained by using the dispersion-corrected density functional theory B3LYP-D3. The corresponding reaction paths are constructed according to the transition states in the searched reactions. Then we discuss the reaction path, energy barrier and reaction energy release. The results show that both In\u003csub\u003e7\u003c/sub\u003e and In\u003csub\u003e6\u003c/sub\u003eAl clusters can react with H\u003csub\u003e2\u003c/sub\u003eO molecules and release hydrogen. Both reactions are exothermic reactions, and the structure of the reaction product are very similar. The comparison of adsorption energy, energy barrier and reaction release energy show that the Al-doped In\u003csub\u003e7\u003c/sub\u003e cluster can significantly improve its ability to react with H\u003csub\u003e2\u003c/sub\u003eO and reduce the energy barrier that has to be overcome for the reaction process. The generated H\u003csub\u003e2\u003c/sub\u003e exists on the cluster surface in the form of physical adsorption, which is judged by the adsorption energy, the distance between the H\u003csub\u003e2\u003c/sub\u003e molecule and the cluster surface, and the interaction region indicator.\u003c/p\u003e","manuscriptTitle":"DFT Study of Hydrogen Evolution Reactions of Water Molecule with In7 and In6Al Clusters","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2023-05-09 13:32:59","doi":"10.21203/rs.3.rs-2844902/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Major revision","date":"2023-06-24T07:17:50+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2023-06-22T00:31:41+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"fb62424f-a7e5-4cab-a7eb-c538aef65692","date":"2023-06-13T12:13:02+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2023-06-06T06:45:12+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2023-05-05T13:17:48+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2023-05-05T11:35:40+00:00","index":"","fulltext":""},{"type":"submitted","content":"Journal of Cluster Science","date":"2023-04-21T10:08:16+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"journal-of-cluster-science","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":" Learn more about [Journal of Cluster Science](https://www.springer.com/journal/10876) ","snPcode":"10876","submissionUrl":"https://mc.manuscriptcentral.com/jocl","title":"Journal of Cluster Science","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"d4e11089-175a-40a8-abbc-6277091d3061","owner":[],"postedDate":"May 9th, 2023","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2024-05-16T11:28:31+00:00","versionOfRecord":{"articleIdentity":"rs-2844902","link":"https://doi.org/10.1007/s10876-024-02580-6","journal":{"identity":"journal-of-cluster-science","isVorOnly":false,"title":"Journal of Cluster Science"},"publishedOn":"2024-02-11 11:28:31","publishedOnDateReadable":"February 11th, 2024"},"versionCreatedAt":"2023-05-09 13:32:59","video":"","vorDoi":"10.1007/s10876-024-02580-6","vorDoiUrl":"https://doi.org/10.1007/s10876-024-02580-6","workflowStages":[]},"version":"v1","identity":"rs-2844902","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-2844902","identity":"rs-2844902","version":["v1"]},"buildId":"WrCJVZZCHTDjtuVLN7oU0","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}