Stability and Dynamics of Zeolite-Confined Gold Nanoclusters

Abstract

Nanoengineered metal@zeolite materials have recently emerged as a promising class of catalysts for several industrially relevant reactions. These materials, which consist of small transition metal nanoclusters confined within three-dimensional zeolite pores, are interesting because they show higher stability and better sintering resistance under reaction conditions. While several such hybrid catalysts have been reported experimentally, key questions such as the impact of the zeolite frameworks on the properties of the metal clusters are not well understood. To address such knowledge gaps, in this study, we report a robust and transferable machine learning-based potential (MLP) that is capable of describing the structure, stability, and dynamics of zeolite-confined gold nanoclusters. Specifically, we show that the resulting MLP maintains ab initio accuracy across a range of temperatures (300-1000 K) and can be used to investigate time scales (>10 ns), length scales (ca. 10,000 atoms), and phenomena (e.g., ensemble-averaged stability and diffusivity) that are typically inaccessible using density functional theory (DFT). Taken together, this study represents an important step in enabling the rational theory-guided design of metal@zeolite catalysts.

Figure 1

(a) Overview of the active learning curriculum used to develop NEP-based MLPs for Au@zeolites. The associated (b) force parity plots and (c) energy error histograms for the final NEP5 model. The blue boxes in (a) refer to DFT calculations, orange to MLP-based simulations, and UQ to uncertainty quantification using the σ_f metric. (d) The progression of the data set used for different iterations of the NEP model.

Figure 2

(a) σ_f uncertainty estimation for the 2nd to 4th iterations of the NEP model. (Inset: a zoomed-in comparison of NEP3 and NEP4.) (b) The σ_f uncertainty estimation for four different zeolites using the NEP4 model. (Inset is the structure that has the highest uncertainty, Au₆@MFI.) Dashed line in the graph is the maximum preferred σ_f = 0.3 eV/Å.

Figure 3

(a) Comparing the temporal evolution of NEP5- and DFT-calculated (black) relative energies for a 10 ns WTmetaD simulation of Au₃@LTA (orange) and Au₆@LTA (red). (b) Relative energy error histogram and (c) force parity plots for the Au₆@LTA system. Representative configurations from the transition state region for the diffusion of (d) Au₃ and (e) Au₆ nanoclusters across the LTA eight-membered ring (8MR) window.

Figure 4

(a) Trend of ΔÊ_disp for Au₁–Au₁₀ in a vacuum and five zeolite topologies. (b) The trend of ΔE_confinement for five different zeolite topologies.

Figure 5

Trends in the (a) Au–O and (b) Au–Au radial distribution functions (RDFs) obtained from the dynamics of Au₆ nanoclusters confined within RHO, LTA, and MFI zeolites. Similar analysis of the (c) Au–O and (d) Au–Au RDFs for Au_6–10@MFI.

Figure 6

(a) Positions of Au₃@LTA zeolite in the CV space (the CV is defined in eq 1). The blue region shows the region where free energy surface was estimated. (b) The free energy surfaces (FES) of Au₃@LTA at 300, 400, 450, and 500 K, respectively. (c) The pores occupied by an Au₃ nanocluster in a CHA zeolite from a 10 ns MD simulation conducted at 500 K.

Figure 7

(a) Pores occupied by each Au₃ nanocluster in an LTA zeolite from a 4 ns MD simulation conducted at 700 K. The system comprises 9228 atoms (128 zeolite pores) of which 12 are Au atoms, which corresponds to a near experimental catalyst weight of 1.26 wt %. (b) A plot showing the wall time required on a single NVIDIA RTX A4000 GPU to run a 10 ns MD simulation of different system sizes in terms of the number of atoms.