High-throughput design of bimetallic materials via the multimodal machine learning and accessibility index

There is a great challenge for efficient exploration of bimetallic systems containing miscible or even immiscible elements (e.g., Au/Ni, Au/Rh) due to the difficulty in screening candidates with favorable formation energy (E_form) from the vast combination space of different metal pairs and ligands or coordination environments. The importance of the coordination environment is highlighted through the multilevel attention mechanism within the graph convolutional neural network (GCNN) and the Shapley additive explanation (SHAP) analysis for 8-feature scheme in E_form prediction. To further reduce the prediction error of formation energy in test set, the multimodal machine learning (MML) is applied to 11,186 bimetallic nanocluster data by integrating the molecule graph of the metal core and the physical property features such as mixing enthalpy (H_mix) of the bimetallic pair and SMLES strings and solubility (logP) of ligand. The present MML model could predict nanoclusters with up to more than one thousand atoms rapidly. To evaluate the experimental accessibility of bimetallic porous materials, alloys, and 2D materials in a general way, an accessibility index, φ, is defined as the combination of the electronegativity (χ_env) and the reduced atomic distance index (D) without the need of density functional theory (DFT) calculations. Larger values of φ indicate that the bimetallic materials are more accessible, owing to the energetically favorable interatomic charge tranfer and optimal reduced distance around 0.3 (~3.5 Å metal-metal distance) for nanoclusters and 0.1 (~2.5 Å) for zeolites, respectively. Among the 100 external test samples, three nanoclusters (Au₃₆Ag₃₈((CF₃)₂PhC≡C)₃₀Cl₁₀, Au₃₈Ag₃₃((CF₃)₂PhC≡C)₃₀Cl₈, and Au₉AgRh(PPh₃)₈Cl) and three 2D materials (Au/Ni@NC, Ni/Pt@NC, and Cu/Gd@NC) were synthesized in this work, in good agreement with that their accessibility indices (φ) are in the favorable range (φ > -0.30) and low formation energies below -1 eV/atom. The proposed MML scheme and accessibility index hold promise in facilitating the high-throughput discovery and bimetallic material design.