End-to-end machine-learned interatomic potentials for modeling functionalized mesoporous aluminosilicates

TL;DR

The study tackles structure–property relationships in functionalized metallosilicates by introducing an end-to-end workflow that couples de novo synthesis, surface functionalization, and property evaluation with two domain-specific MTPs (syn-MTP for synthesis and eq-MTP for equilibrium properties). Leveraging active learning and multiple DFT functionals, the approach achieves near-DFT accuracy while enabling large-scale MD of complex porous materials, validated against experimental densities, PDFs, IR spectra, and dehydrogenation energies. The framework also demonstrates predictive infrared spectra for functionalized mesopores, offering a robust path to operando-relevant modeling in metallosilicates. Overall, the work provides a computationally efficient, experimentally anchored route to explore composition, porosity, and surface chemistry in realistic aluminosilicate systems. This end-to-end strategy broadens the design space for catalytic and adsorption applications where precise control of pore surfaces and hydroxyl groups is crucial.

Abstract

The structural hierarchy and chemical flexibility of metallosilicates enable broad technological applications, yet they also make it challenging to uncover structure--property relations. Previous large-scale atomistic simulations have provided mechanistic insight, but their accuracy and achievable model complexity remain constrained by the available interatomic potentials. Here, we present an end-to-end workflow for developing accurate and efficient machine-learning potentials, specifically moment tensor potentials (MTPs), tailored for structurally and chemically complex systems such as metallosilicates. The workflow integrates de novo structure generation, surface functionalization, and property evaluation. A domain-specific training strategy is employed: Configurations associated with melt--quench generation and subsequent functionalization train the syn-MTP, whereas configurations near equilibrium train the eq-MTP. We apply the workflow to prototypical metallosilicates, i.e., aluminosilicates, which we also experimentally synthesize and characterize for benchmarking the simulations. The syn-MTP reliably generates amorphous aluminosilicates that match experimental density and pair distribution functions measured with synchrotron X-ray diffraction. The eq-MTP reproduces experimental infrared spectra and surface hydroxyl densities, along with density-functional-theory-derived dehydrogenation energies, demonstrating meta-GGA-level accuracy and validating the end-to-end workflow. Finally, we showcase the applicability of the developed potentials by predicting infrared spectra of functionalized porous aluminosilicates. This study establishes a robust path toward accurate modeling of realistic metallosilicates under operando-relevant conditions.

Figures (6)

• Figure 1: Development of accurate and efficient MLIPs via end-to-end machine-learning and domain-specific training for modeling functionalized mesoporous aluminosilicates with confined water.a, Generation of the syn-MTP training set. The dataset includes both bulk aluminosilicate and pore configurations. Amorphous aluminosilicates are generated in silico by molecular dynamics (MD) simulations of precursor reactions and melt--quench procedures of silica--alumina mixtures. Active learning is performed in MD with syn-MTP to explore the complex configurational space. Additional structures are obtained from ab initio MD. To describe aluminosilicate interacting with water, liquid water and H$_2$O--aluminosilicate interface structures are included. MD simulations with active learning are conducted up to 1000K to further enrich the dataset. b, Resolving the realistic porous aluminosilicate structures obtained from experiments using syn-MTP. An artificial repulsive potential is applied to define a one-dimensional pore, followed by precursor filling and melt--quench amorphization. After the removal of repulsive potential, the pore surface is functionalized with hydroxyl (--OH) groups using syn-MTP. c, Generation of the eq-MTP training set via equilibrium-state sampling. MD-driven active learning up to 400K is used to sample water-infiltrated porous aluminosilicates, as well as slab and dehydrogenated structures. d, Large-scale MD simulations of realistic mesoporous aluminosilicates interacting with water. The trained lightweight yet accurate eq-MTP enables efficient prediction of target material properties. Some water molecules at the interface are not visualized to highlight the surface --OH groups. e, Experimental characterization of the synthesized mesoporous aluminosilicates, providing quantitative validation of the trained MTPs. Upon validation, the eq-MTP can be applied to predict a wide range of properties of mesoporous aluminosilicates. A representative transmission electron microscopy image of the synthesized mesoporous silica is shown.
• Figure 2: Training datasets and training of syn-MTP and eq-MTP based on the r$^2$SCAN-D4 functional. a, Radial distribution functions (RDFs) of Si--O pairs in 100 randomly selected configurations in the corresponding training datasets. The syn-MTP configurations exhibit greater variation in the RDFs, reflecting the broader structural diversity required to describe the synthesis processes. b, Distribution of energies and force norms from DFT calculations for all configurations in the training datasets. Energies are referenced to the 0 K relaxed energies of $\alpha$-quartz (SiO2), $\alpha$-alumina (Al2O3), a H2O molecule, and an O2 molecule in vacuum. The syn-MTP training set spans a broader range of relative energies and atomic forces. c, Distributions of training errors in energy and force vector, given as deviations of MTP predictions from DFT values. For both energy and force, more configurations in the training set of syn-MTP show a larger training error. d, Predicted densities of bulk amorphous aluminosilicate at 300K with an Al/Si molar ratio of 0.17, obtained from ensemble syn-MTP candidates trained on the same dataset. The error bars represent the 95% confidence intervals from multiple melt--quench runs. The syn-MTP with density closest to the experiment value from Hanada hanada1989 and a relatively low root-mean-square error (RMSE) was selected for production runs. e, RMSE in dehydrogenation energy at 0K for ensemble eq-MTP candidates fitted to the same training set. The eq-MTP exhibiting low RMSE in both training and dehydrogenation energies was chosen for predictive simulations. The final eq-MTP achieves an average relative deviation of $\sim$10% in the dehydrogenation energy, less than the RMSE for the dehydrogenation energies between r2SCAN-D4 and an available ReaxFF potential Zhang_Liu_van_Duin_Lu_Meijer_2024, 1.98eV.
• Figure 3: Validation of syn-MTP on bulk amorphous aluminosilicates. a, Comparison of aluminosilicate densities at 300K as a function of Al$_2$O$_3$ concentration between simulation and experiment. Experimental data are taken from Ando ando2018, Morikawa morikawa1982, Khemis khemis2024, Hanada hanada1989, and Ohira ohira2016. The syn-MTPs trained to both exchange--correlation functionals (vdW-DF-cx and r$^2$SCAN-D4) agree well with the experimental values. GRACE models PhysRevX.14.021036 trained to the PBE functional underestimate the density by about 10%. For comparison, a syn-MTP trained to PBE shows results consistent with the GRACE model. Error bars indicate the 95% confidence intervals from multiple melt--quench simulations. The label "fast" denotes a tenfold increase in the cooling rate during the melt--quench process, which results in a higher uncertainty and a minor change in the average density. b, Comparison of pair distribution functions (PDFs) for aluminosilicate with a molar Al/Si molar ratio of 0.2 at 300K. Atomic model synthesized in silico with syn-MTP reproduces experimental total PDFs accurately. Partial PDFs derived from simulations are also shown, offering atomic insights in aluminosilicates.
• Figure 4: Validation of the end-to-end modeling workflow and eq-MTP. a, Comparison of the infrared spectrum of bulk amorphous aluminosilicate with the Al/Si molar ratio of 0.05 predicted by eq-MTP and measured experimentally. Syn-MTP and eq-MTP trained on r$^2$SCAN data were employed in the end-to-end modeling workflow. The close match of the characteristic Si--O--Si peak confirms the accuracy of both the r$^2$SCAN-D4 functional and eq-MTP. b, Comparison of dehydrogenation energies at 0K predicted by eq-MTP and DFT. Dehydrogenation was modeled at the surfaces of pores with a diameter of 1.5nm in in silico--synthesized aluminosilicate with an Al/Si molar ratio of 0.2. Error bars represent the standard deviation arising from multiple hydrogen sites on the pore surface. The agreement demonstrates that eq-MTP retains near-ab initio accuracy. Dehydrogenation energies are similar for the single and geminal hydroxyl groups and generally lower for the bridging hydroxyl groups. Illustrative structural formulas and atomic sites for different types of dehydrogenation are shown.
• Figure 5: Predictions with the trained MTPs and the end-to-end modeling workflow. Infrared spectra of aluminosilicates with 1.5nm diameter pores and an Al/Si molar ratio of 0.2 are shown. Spectra from ten MD snapshots were averaged to mimic experimental conditions. One chosen snapshot is shown in the inset with an enlarged intensity scale. Six vibrational modes associated with the --OH functional groups are highlighted, with their displacement patterns visualized by black arrows in the atomic model.