Unveiling the Structure–Surface Energy Relationship of Zeolites through Machine Learning

Understanding the intricate relationship between structure and surface energy is essential for a thorough comprehension of the external surface structure and crystal morphology of zeolites. In this study, we evaluated the surface energies of various zeolite surfaces across multiple representative frameworks with DFT calculations. Our analysis reveals a linear relationship between the calculated surface energy and the surface hydroxyl density, which is slightly disrupted due to the formation of hydrogen bonds. Using a symbolic regression approach, we establish a mathematical formula that correlates the surface energy with the density of surface hydroxyl groups and hydrogen bonds. We show that using the surface hydroxyl density alone can rapidly predict zeolite crystal morphologies with a high degree of accuracy, demonstrated by a promising Wulff similarity of 98%. The applicability and potential of our findings are demonstrated in estimating the Wulff shapes of 237 zeolite framework types in the database and predicting the crystal morphology evolution of a representative zeolite with pH, confirming the general validity of our approach based on straightforward structural analysis and thermodynamic principles. This work establishes a solid foundation for advancing the structural design of silica-based materials, particularly in applications requiring precise control of the surface structure and crystal habit.