LOCAL: A Locality-based Active Learning Framework for Predicting the Stability of Dual-Atom Catalysts

TL;DR

This work tackles the combinatorial problem of predicting the stability of dual-atom catalysts on N-doped graphene by introducing LOCAL, a locality-based active-learning framework. LOCAL combines two graph neural networks—POS2COHP for estimating local bond strengths via ICOHP and Graph2E for predicting the stability energy from both structural and local bonding information—within a chemistry-informed neural network architecture, enabling predictions directly from unrelaxed structures. The method achieves a test MAE of $0.15\ \mathrm{eV}$ while labeling only $16{,}704$ structures ($2.7\%$ of the dataset) with DFT, enabling large-scale phase diagrams to be constructed across $741$ bimetallic combinations and validated against experimental configurations. The framework is presented as general and transferable to other catalytically relevant materials, offering a scalable route to accelerate discovery and optimization of complex, locally variable catalysts beyond DAC/NG.

Abstract

Dual-atom catalysts supported on nitrogen-doped graphene (DAC/NG) are emerging as a family of promising catalysts that can overcome intrinsic limitations of single-atom catalysts. However, comprehensive assessment of their structural stability is prohibitively demanding due to a vast local configurational space. Here we introduce LOCAL, a locality-based framework that combines graph convolutional networks with active learning to efficiently predict DAC/NG stability by leveraging chemically intuitive locality quantified by crystal orbital Hamilton population analysis. We demonstrate the effectiveness of LOCAL over a comprehensive dataset of 611,648 DAC/NG structures, achieving a test mean absolute error of 0.15~eV while invoking density functional theory calculations for only 16,704 structures (2.7% of the dataset). Thus, LOCAL enables efficient and accurate construction of phase diagrams for DAC/NG across diverse compositions reciprocally validated with experimentally synthesized configurations for representative systems. Our framework composes an essential methodology for accelerating the discovery and optimization of high-performance complex catalysts.

Figures (5)

• Figure 1: The CINN architecture of LOCAL.
• Figure 2: The overall workflow of LOCAL.
• Figure 3: Construction of the DAC/NG dataset.
• Figure 4: (a) Distribution of predicted stability energies for the DAC/NG dataset. (b) Zoomed-in view of the 1–4 eV window in (a), highlighting finer details in the low-energy region with dashed lines marking the experimentally synthesized and effective DAC/NG structures. (c) Heatmap of averaged stability energies across all metal pair combinations to identify the element-dependent trends.
• Figure 5: Integrated thermodynamic–structural analysis of the Ru–Rh DAC/NG system. (a) Ru–Rh thermodynamic phase diagram with carbon chemical potential $\eta_{\mathrm{C}}$ as the $x$-axis and nitrogen chemical potential $\eta_{\mathrm{N}}$ as the $y$-axis. Two dashed guide lines, parallel to the axes, indicate the reference $\mu_{\mathrm{C}}$ and $\mu_{\mathrm{N}}$ (graphene for C; g-$\mathrm{C_3N_4}$ in equilibrium for N; both are at 0 K with no vibrational/$pV$ corrections; more details are provided in the Methods section); their intersection marks the chosen reference condition at which the dominant phase is identified as QV2_null_Ru_Rh. The five candidate phases are displayed as structural insets at the bottom, arranged from top-left to bottom-right, each outlined in the color corresponding to its representation in the phase diagram. R-space EXAFS fitting of (b) Ru and (c) Rh. In both cases, the coordination number of the first shell is four and that of the Rh–Ru path is one.