REFERENCES
1. Merchant, A.; Batzner, S.; Schoenholz, S. S.; Aykol, M.; Cheon, G.; Cubuk, E. D. Scaling deep learning for materials discovery. Nature 2023, 624, 80-5.
2. Zeni, C.; Pinsler, R.; Zügner, D.; et al. A generative model for inorganic materials design. Nature 2025, 639, 624-32.
3. Xu, P.; Ma, Y.; Lu, W.; Li, M.; Zhao, W.; Dai, Z. Multi-objective optimization in machine learning assisted materials design and discovery. J. Mater. Inf. 2025, 5, 26.
4. Westermayr, J.; Gilkes, J.; Barrett, R.; Maurer, R. J. High-throughput property-driven generative design of functional organic molecules. Nat. Comput. Sci. 2023, 3, 139-48.
5. Biyela, S.; Dihal, K.; Gero, K. I.; et al. Generative AI and science communication in the physical sciences. Nat. Rev. Phys. 2024, 6, 162-5.
6. Njirjak, M.; Žužić, L.; Babić, M.; et al. Reshaping the discovery of self-assembling peptides with generative AI guided by hybrid deep learning. Nat. Mach. Intell. 2024, 6, 1487-500.
7. Li, Z.; Yang, M.; Park, J.; Wei, S.; Berry, J. J.; Zhu, K. Stabilizing perovskite structures by tuning tolerance factor: formation of formamidinium and cesium lead iodide solid-state alloys. Chem. Mater. 2016, 28, 284-92.
8. Liu, X.; Luo, D.; Lu, Z. H.; et al. Stabilization of photoactive phases for perovskite photovoltaics. Nat. Rev. Chem. 2023, 7, 462-79.
9. Song, Z.; Liu, Q. Tolerance factor and phase stability of the normal spinel structure. Cryst. Growth. Des. 2020, 20, 2014-8.
10. Song, Z.; Zhou, D.; Liu, Q. Tolerance factor and phase stability of the garnet structure. Acta. Crystallogr. C. Struct. Chem. 2019, 75, 1353-8.
11. Wang, Z.; Lin, X.; Han, Y.; et al. Harnessing artificial intelligence to holistic design and identification for solid electrolytes. Nano. Energy. 2021, 89, 106337.
12. Zhu, T.; Huhn, W. P.; Wessler, G. C.; et al. I2–II–IV–VI4 (I = Cu, Ag; II = Sr, Ba; IV = Ge, Sn; VI = S, Se): chalcogenides for thin-film photovoltaics. Chem. Mater. 2017, 29, 7868-79.
13. Wang, Z.; Cai, J.; Wang, Q.; Wu, S.; Li, J. Unsupervised discovery of thin-film photovoltaic materials from unlabeled data. npj. Comput. Mater. 2021, 7, 596.
14. Curtarolo, S.; Hart, G. L.; Nardelli, M. B.; Mingo, N.; Sanvito, S.; Levy, O. The high-throughput highway to computational materials design. Nat. Mater. 2013, 12, 191-201.
15. Griesemer, S. D.; Xia, Y.; Wolverton, C. Accelerating the prediction of stable materials with machine learning. Nat. Comput. Sci. 2023, 3, 934-45.
16. Wu, Z.; Zhang, O.; Wang, X.; et al. Leveraging language model for advanced multiproperty molecular optimization via prompt engineering. Nat. Mach. Intell. 2024, 6, 1359-69.
17. Jiang, X.; Wang, W.; Tian, S.; Wang, H.; Lookman, T.; Su, Y. Applications of natural language processing and large language models in materials discovery. npj. Comput. Mater. 2025, 11, 1554.
18. Bartel, C. J.; Sutton, C.; Goldsmith, B. R.; et al. New tolerance factor to predict the stability of perovskite oxides and halides. Sci. Adv. 2019, 5, eaav0693.
19. Bassen, G.; Wilfong, B.; Bunstine, W.; Edmiston, N.; Siegler, M. A.; McQueen, T. M. Tolerance factor approach for the design of quaternary materials as applied to the A2Ln4Cu2nQ7+n homologous series. J. Am. Chem. Soc. 2024, 146, 25190-9.
20. Molokeev, M. S.; Kuznetsov, S. O. Tolerance factor for huntite-family compounds. Phys. Solid. State. 2020, 62, 2058-62.
21. Mouta, R.; Silva, R. X.; Paschoal, C. W. Tolerance factor for pyrochlores and related structures. Acta. Crystallogr. B. Struct. Sci. Cryst. Eng. Mater. 2013, 69, 439-45.
22. Smith, M.; Li, Z.; Landry, L.; Merz, K. M. Jr.; Li, P. Consequences of overfitting the van der Waals radii of ions. J. Chem. Theory. Comput. 2023, 19, 2064-74.
23. Marchenko, E. I.; Fateev, S. A.; Eremin, N. N.; Chen, Q.; Goodilin, E. A.; Tarasov, A. B. Crystal chemical insights on lead iodide perovskites doping from revised effective radii of metal ions. ACS. Materials. Lett. 2021, 3, 1377-84.
24. Turnley, J. W.; Agarwal, S.; Agrawal, R. Rethinking tolerance factor analysis for chalcogenide perovskites. Mater. Horiz. 2024, 11, 4802-8.
25. Mondal, D.; Mahadevan, P. Structural distortions in hybrid perovskites revisited. Chem. Mater. 2024, 36, 4254-61.
26. Antoniuk, E. R.; Cheon, G.; Wang, G.; Bernstein, D.; Cai, W.; Reed, E. J. Predicting the synthesizability of crystalline inorganic materials from the data of known material compositions. npj. Comput. Mater. 2023, 9, 1114.
27. Vasylenko, A.; Antypov, D.; Gusev, V. V.; Gaultois, M. W.; Dyer, M. S.; Rosseinsky, M. J. Element selection for functional materials discovery by integrated machine learning of elemental contributions to properties. npj. Comput. Mater. 2023, 9, 1072.
28. Jha, D.; Ward, L.; Paul, A.; et al. ElemNet: deep learning the chemistry of materials from only elemental composition. Sci. Rep. 2018, 8, 17593.
29. Hargreaves, C. J.; Gaultois, M. W.; Daniels, L. M.; et al. A database of experimentally measured lithium solid electrolyte conductivities evaluated with machine learning. npj. Comput. Mater. 2023, 9, 951.
30. Kang, Y.; Kim, J. ChatMOF: an artificial intelligence system for predicting and generating metal-organic frameworks using large language models. Nat. Commun. 2024, 15, 4705.
31. Zheng, Y.; Koh, H. Y.; Ju, J.; et al. Large language models for scientific discovery in molecular property prediction. Nat. Mach. Intell. 2025, 7, 437-47.
32. Butler, K. T.; Davies, D. W.; Cartwright, H.; Isayev, O.; Walsh, A. Machine learning for molecular and materials science. Nature 2018, 559, 547-55.
33. Dass KT, Hossain MK, Marasamy L. Highly efficient emerging Ag2BaTiSe4 solar cells using a new class of alkaline earth metal-based chalcogenide buffers alternative to CdS. Sci. Rep. 2024, 14, 1473.
34. Talirz, L.; Kumbhar, S.; Passaro, E.; et al. Materials Cloud, a platform for open computational science. Sci. Data. 2020, 7, 299.
35. Curtarolo, S.; Setyawan, W.; Hart, G. L.; et al. AFLOW: an automatic framework for high-throughput materials discovery. Comput. Mater. Sci. 2012, 58, 218-26.
36. Sbailò, L.; Fekete, Á.; Ghiringhelli, L. M.; Scheffler, M. The NOMAD Artificial-Intelligence Toolkit: turning materials-science data into knowledge and understanding. npj. Comput. Mater. 2022, 8, 935.
37. Szymanski, N. J.; Smith, A.; Daoutidis, P.; Bartel, C. J. Topological descriptors for the electron density of inorganic solids. ACS. Materials. Lett. 2025, 7, 2158-64.
38. Hylton-Farrington, C. M.; Remsing, R. C. Dynamic local symmetry fluctuations of electron density in halide perovskites. Chem. Mater. 2024, 36, 9442-59.
39. Feng, C.; Zhang, Y.; Jiang, B. Efficient sampling for machine learning electron density and its response in real space. J. Chem. Theory. Comput. 2025, 21, 691-702.





