Interpretable, Physics-Informed Learning Reveals Sulfur Adsorption and Poisoning Mechanisms in 13-Atom Icosahedra Nanoclusters

TL;DR

This work addresses sulfur poisoning of subnanometer transition-metal nanoclusters by combining dispersion-corrected DFT with interpretable physics-informed ML to map sulfur adsorption across 13-atom icosahedral clusters (TM13) of 3$d$–5$d$ elements. The approach uses a rich descriptor set spanning energetics, structure, vibrational dynamics, and electronic structure, enabling unsupervised clustering and model-agnostic feature importance analyses that reveal transferable trends and identify Ti13, Zr13, and Hf13 as balanced, chemically resilient platforms. Explicit SO2 adsorption calculations validate the ML-guided selection, showing predominantly dissociative binding with strong interfacial interactions yet preservation of the ICO framework, consistent with Sabatier principles. Overall, the study provides data-driven design rules linking electronic states and lattice response to sulfur tolerance, offering practical guidance for subnanometer catalyst development.

Abstract

Transition-metal nanoclusters exhibit structural and electronic properties that depend on their size, often making them superior to bulk materials for heterogeneous catalysis. However, their performance can be limited by sulfur poisoning. Here, we use dispersion-corrected density functional theory (DFT) and physics-informed machine learning to map how atomic sulfur adsorbs and causes poisoning on 13-atom icosahedral clusters from 30 different transition metals (3$d$ to 5$d$). We measure which sites sulfur prefers to adsorb to, the thermodynamics and energy breakdown, changes in structure, such as bond lengths and coordination, and electronic properties, such as $\varepsilon_d$, the HOMO-LUMO gap, and charge transfer. Vibrational analysis reveals true energy minima and provides ZPE-based descriptors that reflect the lattice stiffening upon sulfur adsorption. For most metals, the metal-sulfur interaction mainly determines adsorption energy. At the same time, distortion penalties are usually moderate but can be significant for a few metals, suggesting these are more likely to restructure when sulfur is adsorbed. Using unsupervised \textit{k}-means clustering, we identify periodic trends and group metals based on their adsorption responses. Supervised regression models with leave-one-feature-out analysis identify the descriptors that best predict adsorption for new samples. Our results highlight the isoelectronic triad \ce{Ti}, \ce{Zr}, and \ce{Hf} as a balanced group that combines strong sulfur binding with minimal structural change. Additional DFT calculations for \ce{SO2} adsorption reveal strong binding and a clear tendency toward dissociation on these clusters, linking electronic states, lattice response, and poisoning strength. These findings offer data-driven guidelines for designing sulfur-tolerant nanocatalysts at the subnanometer scale.

Figures (7)

• Figure 1: Schematic workflow illustrating the combined first-principles and machine-learning strategy adopted in this work. Starting from DFT calculations, 13.0-atom ICO TM-NCs in pristine form (TM13) and after atomic S adsorption (S/TM$_{13}$), considering top, bridge, and hollow binding sites. Structural, energetic, electronic, and vibrational descriptors extracted from DFT calculations were subsequently standardized and used as input for unsupervised clustering analyses using k-means and principal component analysis (PCA), enabling the identification of chemically similar groups across the TM series. Based on the clustering outcomes, selected nanoclusters (Ti13, Zr13, and Hf13) were further employed in explicit SO2 adsorption calculations. Finally, the descriptor set was used to train the ElasticNet regression models, allowing the prediction and rationalization of S adsorption energetics to provide a selection of chemically resilient NCs.
• Figure 2: Vibrational and energetic trends of TM13 and S/TM$_{13}$ across the 3.0$d$--5.0$d$ series. (a) Vibrational frequencies for pristine TM13 (blue) and S/TM$_{13}$ (black) systems. (b) Per-atom $E_{\text{b}}^{\ce{TM13}}$ (blue) and $E_{\text{b}}^{\ce{S{\text{/}}TM13}}$ (black), compared with bulk cohesive energies ($E_{\text{coh}}^{\ce{TM}}$, green).
• Figure 3: Energetic, structural, and electronic descriptors for S adsorption on TM13 NCs across the 3.0$d$, 4.0$d$, and 5.0$d$ series. (a) Adsorption energy decomposition into interaction ($\Delta E_\text{int}$) and distortion ($\Delta E_\text{dis}^{\ce{TM13}}$) contributions, together with total adsorption energies ($E_\text{ads}$). (b) Effective coordination number (ECN) and average TM-TM bond length ($d_\text{av}$) before and after S adsorption. (c) TM-S bond distance ($d_{\ce{TM}-\ce{S}}$) for each TM. (d) Center of gravity of the occupied $d$-states ($\varepsilon_{\text{d}}$) for pristine and S-adsorbed NCs.
• Figure 4: (a) Two-dimensional PCA projections of standardized DFT-derived descriptors for pristine TM13 (left) and S/TM$_{13}$ (right) NCs. Colors denote k-means cluster assignments, while ellipses indicate the dispersion of each cluster in descriptor space. (b) Cluster membership of TM-NCs obtained from k-means classification for TM13 (left) and S/TM$_{13}$ (right) systems. Each point represents a TM element, identified by its atomic number, and elements that remain grouped in both classifications exhibit similar responses to S adsorption.
• Figure 5: Leave-one-feature-out (LOFO) analysis measures how removing each pristine nanocluster descriptor affects model generalization when predicting atomic sulfur adsorption energies on TM13 icosahedra. The panels show performance drops as (a) $\Delta R^{2}$, (b) $\Delta$MAE, and (c) $\Delta$RMSE, all evaluated with group cross-validation using three regression models: ElasticNetCV, RidgeCV, and Explainable Boosting Machine (EBM). The heatmaps on the left display effects for each model, while the bar plots on the right show the average impact across models, ranking feature importance (y-axis is the same as in the left panels).