REFERENCES
1. Gao, D.; Xu, Y.; Liu, Z.; et al. Understanding of strain effect on Mo-based MXenes for electrocatalytic CO2 reduction. Appl. Surf. Sci. 2024, 654, 159501.
2. Löffler, T.; Savan, A.; Garzón-manjón, A.; et al. Toward a paradigm shift in electrocatalysis using complex solid solution nanoparticles. ACS. Energy. Lett. 2019, 4, 1206-14.
3. Lu, Z.; Chen, Z. W.; Singh, C. V. Neural network-assisted development of high-entropy alloy catalysts: decoupling ligand and coordination effects. Matter 2020, 3, 1318-33.
4. Li, G.; Yang, Q.; Rao, J.; et al. In situ induction of strain in iron phosphide (FeP2) catalyst for enhanced hydroxide adsorption and water oxidation. Adv. Funct. Mater. 2020, 30, 1907791.
5. Price, C. C.; Singh, A.; Frey, N. C.; Shenoy, V. B. Efficient catalyst screening using graph neural networks to predict strain effects on adsorption energy. Sci. Adv. 2022, 8, eabq5944.
6. Gariepy, Z.; Chen, Z.; Tamblyn, I.; Singh, C. V.; Tetsassi Feugmo, C. G. Automatic graph representation algorithm for heterogeneous catalysis. APL. Mach. Learn. 2023, 1, 036103.
7. Clausen, C. M.; Rossmeisl, J.; Ulissi, Z. W. Adapting OC20-trained equiformerV2 models for high-entropy materials. J. Phys. Chem. C. 2024, 128, 11190-5.
8. Dewyer, A. L.; Argüelles, A. J.; Zimmerman, P. M. Methods for exploring reaction space in molecular systems. WIREs. Comput. Mol. Sci. 2017, 8, e1354.
9. Choi, S. Prediction of transition state structures of gas-phase chemical reactions via machine learning. Nat. Commun. 2023, 14, 1168.
10. Kim, J.; Kang, M.; Yoon, J. H.; Kim, S. K. Tracking the structural change of the predissociating molecule near the transition state. Nat. Commun. 2025, 16, 210.
11. Wander, B.; Shuaibi, M.; Kitchin, J. R.; Ulissi, Z. W.; Zitnick, C. L. CatTSunami: accelerating transition state energy calculations with pretrained graph neural networks. ACS. Catal. 2025, 15, 5283-94.
12. Sun, Y.; Dai, S. High-entropy materials for catalysis: a new frontier. Sci. Adv. 2021, 7, eabg1600.
13. Butler, K. T.; Davies, D. W.; Cartwright, H.; Isayev, O.; Walsh, A. Machine learning for molecular and materials science. Nature 2018, 559, 547-55.
14. Jinnouchi, R.; Karsai, F.; Kresse, G. On-the-fly machine learning force field generation: application to melting points. Phys. Rev. B. 2019, 100, 014105.
15. Jingchen, L.; Xiao, F.; Xuhe, G.; Ruijuan, X.; Hong, L. High-throughput NEB for Li-ion conductor discovery via fine-tuned CHGNet potential. arXiv 2025, arXiv:2507.02334. Available online: https://doi.org/10.48550/arXiv.2507.02334. (accessed 10 July 2025).
16. Wander, B.; Broderick, K.; Ulissi, Z. W. Catlas: an automated framework for catalyst discovery demonstrated for direct syngas conversion. Catal. Sci. Technol. 2022, 12, 6256-67.
17. Lan, J.; Palizhati, A.; Shuaibi, M.; et al. AdsorbML: a leap in efficiency for adsorption energy calculations using generalizable machine learning potentials. NPJ. Comput. Mater. 2023, 9, 172.
18. Hu, Y.; Chen, J.; Wei, Z.; He, Q.; Zhao, Y. Recent advances and applications of machine learning in electrocatalysis. J. Mater. Inf. 2023, 3, 18.
19. Jain, A.; Ong, S. P.; Hautier, G.; et al. Commentary: the materials project: a materials genome approach to accelerating materials innovation. APL. Mater. 2013, 1, 011002.
20. Chanussot, L.; Das, A.; Goyal, S.; et al. Open Catalyst 2020 (OC20) Dataset and community challenges. ACS. Catal. 2021, 11, 6059-72.
21. Tran, R.; Lan, J.; Shuaibi, M.; et al. The Open Catalyst 2022 (OC22) Dataset and challenges for oxide electrocatalysts. ACS. Catal. 2023, 13, 3066-84.
22. Liao, Y. -L.; Wood, B.; Das, A.; Smidt, T. EquiformerV2: improved equivariant transformer for scaling to higher-degree representations. arXiv 2024, arXiv:2306.12059. Available online: https://doi.org/10.48550/arXiv.2306.12059 (accessed 10 July 2025).
23. Batchelor, T. A.; Pedersen, J. K.; Winther, S. H.; Castelli, I. E.; Jacobsen, K. W.; Rossmeisl, J. High-entropy alloys as a discovery platform for electrocatalysis. Joule 2019, 3, 834-45.
24. Yang, X.; Wang, Y.; Tong, X.; Yang, N. Strain engineering in electrocatalysts: fundamentals, progress, and perspectives. Adv. Energy. Mater. 2021, 12, 2102261.
25. Kresse, G.; Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B. Condens. Matter. 1996, 54, 11169-86.
26. Kresse, G.; Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B. 1999, 59, 1758-75.
27. Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 1996, 77, 3865-8.
29. Henkelman, G.; Uberuaga, B. P.; Jónsson, H. A climbing image nudged elastic band method for finding saddle points and minimum energy paths. J. Chem. Phys. 2000, 113, 9901-4.
30. Smidstrup, S.; Pedersen, A.; Stokbro, K.; Jónsson, H. Improved initial guess for minimum energy path calculations. J. Chem. Phys. 2014, 140, 214106.
31. Boda, A.; Chandorkar, N.; Ali, S. M. Density functional theoretical assessment of titanium metal for adsorption of hydrogen, deuterium and tritium isotopes. Theor. Chem. Acc. 2023, 142, 46.
32. Montoya, A.; Schlunke, A.; Haynes, B. S. Reaction of hydrogen with Ag(111): binding states, minimum energy paths, and kinetics. J. Phys. Chem. B. 2006, 110, 17145-54.
33. Ignatov, S. K.; Okhapkin, A. I.; Gadzhiev, O. B.; Razuvaev, A. G.; Kunz, S.; Bäumer, M. Adsorption and diffusion of hydrogen on the surface of the Pt24 subnanoparticle. A DFT Study. J. Phys. Chem. C. 2016, 120, 18570-87.
34. Loshchilov, I.; Hutter, F. Decoupled weight decay regularization. arXiv 2019, arXiv:1711.05101. Available online: https://doi.org/10.48550/arXiv.1711.05101 (accessed 10 July 2025).
35. Loshchilov, I.; Hutter, F. SGDR: stochastic gradient descent with warm restarts. arXiv 2017, arXiv:1608.03983. Available online: https://doi.org/10.48550/arXiv.1608.03983. (accessed 10 July 2025).
36. Wang, Z.; Hu, S.; Wang, D.; et al. A HER-inhibiting layer based on M‐H bond regulation for achieving stable zinc anodes in aqueous zinc-ion batteries. Adv. Funct. Mater. 2025, 35, 2502186.
37. Wei, J.; Zhou, M.; Long, A.; et al. Heterostructured electrocatalysts for hydrogen evolution reaction under alkaline conditions. Nanomicro. Lett. 2018, 10, 75.
38. Li, Q.; Zou, X.; Ai, X.; Chen, H.; Sun, L.; Zou, X. Revealing activity trends of metal diborides toward pH-universal hydrogen evolution electrocatalysts with Pt-like activity. Adv. Energy. Mater. 2018, 9, 1803369.
39. Tang, S.; Xu, L.; Dong, K.; et al. Curvature effect on graphene-based Co/Ni single-atom catalysts. Appl. Surf. Sci. 2023, 615, 156357.
40. Liu, G.; Shih, A. J.; Deng, H.; et al. Site-specific reactivity of stepped Pt surfaces driven by stress release. Nature 2024, 626, 1005-10.
41. Khorshidi, A.; Violet, J.; Hashemi, J.; Peterson, A. A. How strain can break the scaling relations of catalysis. Nat. Catal. 2018, 1, 263-8.
42. Wang, L.; Zhou, X.; Luo, Z.; et al. Review of external field effects on electrocatalysis: machine learning guided design. Adv. Funct. Mater. 2024, 34, 2408870.
43. Plenge, M. K.; Pedersen, J. K.; Bagger, A.; Rossmeisl, J. Catalysis of C-N coupling on high-entropy alloys. J. Catal. 2024, 430, 115322.
44. Cao, G.; Yang, S.; Ren, J. C.; Liu, W. Electronic descriptors for designing high-entropy alloy electrocatalysts by leveraging local chemical environments. Nat. Commun. 2025, 16, 1251.
45. Yan, L.; Yamamoto, Y.; Shiga, M.; Sugino, O. Nuclear quantum effect for hydrogen adsorption on Pt(111). Phys. Rev. B. 2020, 101, 165414.
46. Henkelman, G.; Jónsson, H. Improved tangent estimate in the nudged elastic band method for finding minimum energy paths and saddle points. J. Chem. Phys. 2000, 113, 9978-85.
47. Bhatia, B.; Sholl, D. S. Chemisorption and diffusion of hydrogen on surface and subsurface sites of flat and stepped nickel surfaces. J. Chem. Phys. 2005, 122, 204707.
48. Wang, L.; Zeng, Z.; Gao, W.; et al. Tunable intrinsic strain in two-dimensional transition metal electrocatalysts. Science 2019, 363, 870-4.
49. Hsiao, Y. C.; Wu, C. Y.; Lee, C. H.; et al. A library of seed@high-entropy-alloy core-shell nanocrystals with controlled facets for catalysis. Adv. Mater. 2025, 37, e2411464.
50. Wang, C.; Huang, Z.; Ding, Y.; Xie, M.; Chi, M.; Xia, Y. Facet-controlled synthesis of platinum-group-metal quaternary alloys: the case of nanocubes and {100} facets. J. Am. Chem. Soc. 2023, 145, 2553-60.
51. Altantzis, T.; Lobato, I.; De Backer, A.; et al. Three-dimensional quantification of the facet evolution of Pt nanoparticles in a variable gaseous environment. Nano. Lett. 2019, 19, 477-81.
52. Boukouvala, C.; Daniel, J.; Ringe, E. Approaches to modelling the shape of nanocrystals. Nano. Converg. 2021, 8, 26.
53. Karlberg, G. S.; Jaramillo, T. F.; Skúlason, E.; Rossmeisl, J.; Bligaard, T.; Nørskov, J. K. Cyclic voltammograms for H on Pt(111) and Pt(100) from first principles. Phys. Rev. Lett. 2007, 99, 126101.
54. Miller, D. J.; Öberg, H.; Kaya, S.; et al. Oxidation of Pt(111) under near-ambient conditions. Phys. Rev. Lett. 2011, 107, 195502.
55. Kormányos, A.; Dong, Q.; Xiao, B.; et al. Stability of high-entropy alloys under electrocatalytic conditions. iScience 2023, 26, 107775.
56. Lu, S.; Cao, J.; Zhang, Y.; Lou, F.; Yu, Z. Transition metal single-atom supported on PC3 monolayer for highly efficient hydrogen evolution reaction by combined density functional theory and machine learning study. Appl. Surf. Sci. 2022, 606, 154945.
57. Yang, Y.; Qian, Y.; Li, H.; et al. O-coordinated W-Mo dual-atom catalyst for pH-universal electrocatalytic hydrogen evolution. Sci. Adv. 2020, 6, eaba6586.
58. Fung, V.; Hu, G.; Wu, Z.; Jiang, D. Descriptors for hydrogen evolution on single atom catalysts in nitrogen-doped graphene. J. Phys. Chem. C. 2020, 124, 19571-8.
59. Wang, Y.; Qiu, W.; Song, E.; et al. Adsorption-energy-based activity descriptors for electrocatalysts in energy storage applications. Natl. Sci. Rev. 2018, 5, 327-41.
60. Oh, N. K.; Seo, J.; Lee, S.; et al. Highly efficient and robust noble-metal free bifunctional water electrolysis catalyst achieved via complementary charge transfer. Nat. Commun. 2021, 12, 4606.
61. Di Liberto, G.; Cipriano, L. A.; Pacchioni, G. Universal principles for the rational design of single atom electrocatalysts? Handle with care. ACS. Catal. 2022, 12, 5846-56.
62. Wu, T.; Stone, M. L.; Shearer, M. J.; et al. Crystallographic facet dependence of the hydrogen evolution reaction on CoPS: theory and experiments. ACS. Catal. 2018, 8, 1143-52.
63. Zhang, Y.; Lee, S.; Jeong, S.; et al. Phase-bridged hierarchical catalysts for efficient and stable water electrolysis. Adv. Funct. Mater. 2023, 34, 2309250.
64. Nazari, S.; Najmi, A.; Kumar, P.; et al. Configuring a liquid state high-entropy metal alloy electrocatalyst. Small 2025, 21, e2504087.
65. Chang, C.; Ting, Y.; Yen, F.; Li, G.; Lin, K.; Lu, S. High performance anion exchange membrane water electrolysis driven by atomic scale synergy of non-precious high entropy catalysts. Energy. Mater. 2025, 5, 500117.
66. Moon, J.; Beker, W.; Siek, M.; et al. Active learning guides discovery of a champion four-metal perovskite oxide for oxygen evolution electrocatalysis. Nat. Mater. 2024, 23, 108-15.





