Spin density symmetry breaking-mediated hydrogen evolution in single-atom catalysts

doi:10.1016/S1872-2067(25)64837-6

Abstract

Abstract:

Symmetry-broken single-atom catalysts (SACs) are pivotal due to their asymmetric electronic environments, which enhance the activity of the hydrogen evolution reaction (HER). This study investigated how symmetry breaking in SACs affects HER performance using density functional theory (DFT) and variable selection machine learning (ML). The study revealed a nearly volcano-shaped correlation between the degree of spin density symmetry breaking (D_asym) and HER activity, with catalysts at the base of the volcano showing enhanced HER activity. Spin density symmetry breaking facilitates the enrichment of unpaired electrons on the active sites and reduces HER energy barriers, resulting in up to a 40-fold enhancement in HER performance of symmetry-broken SACs compared to symmetric SACs. The ML model accurately identified key descriptors, such as symmetry breaking and electronic transfer effects, allowing spin density symmetry breaking on M-N3C-SWCNTs to be further condensed into an effect term with a structure-property relationship. A weaker symmetry breaking effect and a stronger electron transfer enhance HER performance. ML-guided analysis highlighted a spin selection-related Volmer-Heyrovsky pathway with a dual activation mechanism involving surface atom displacement and para-activation. These findings offer critical insights into the design of advanced HER catalysts by elucidating the interplay between symmetry-breaking properties and catalytic behavior.

Key words: Symmetry breaking, Spin density, Hydrogen evolution reaction, Interpretable machine learning, Single-atom catalyst

Xin Song, Zhonghua Li, Li Sheng, Yang Liu. Spin density symmetry breaking-mediated hydrogen evolution in single-atom catalysts[J]. Chinese Journal of Catalysis, 2026, 80: 213-226.

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URL: https://www.cjcatal.com/EN/10.1016/S1872-2067(25)64837-6

https://www.cjcatal.com/EN/Y2026/V80/I1/213

Figures/Tables 7

Scheme 1. Overview of research process.

Fig. 1. HER performance and stability analysis of M-N3C-SWCNTs. (a) Calculated ΔGH* values, with the dashed line representing the |ΔGH*| of the Pt catalyst. (b) Comparison of ΔGH* between pristine SWCNT and M-N3C-SWCNT (M = Sc, Mn, Pd, and Pt). (c) Calculated volcano curve. (d) Calculated Eb and Ef. (e) Analysis of single-atom stability (ΔEb). (f) Calculated dissolution potential (Udiss) values. (g)-(i) AIMD simulations conducted at 300 K.

Fig. 2. The relationship between spin density symmetry breaking and HER activity on M-N3C-SWCNTs. (a)-(f) Schematic diagrams of spin density symmetry breaking. Yellow represents spin up, while cyan represents spin down. The isosurface value is 0.01 e/Bohr3 for Mn SACs, whereas for Pd and Pt SACs, it is 0.0001 e/Bohr3. (g) Simplified illustration of Dasym calculation using OpenCV. (h) The relationship between |ΔGH*| and Dasym. (i) The relationship between TOF and Dasym.

Fig. 3. 2D spin density distribution and reaction pathways. (a) 2D spin density distribution for M-N3C-SWCNT and M-N4-SWCNT (M = Mn, Pd and Pt). Positive and negative values represent spin up and spin down, respectively. The V-T and V-H pathways on Mn-N3C-SWCNT (b), Pd-N3C-SWCNT (c), and Pt-N3C-SWCNT (d).

Fig. 4. Feature selection and hyperparameter optimization of the VS-SISSO model applied to M-N3C-SWCNTs. (a) Feature selection diagram. (b) Optimal feature set selection using the elastic net method. (c) RMSE as a function of model complexity across various dimensions. (d) Distribution of absolute prediction errors for various hyperparameter combinations. (e)-(j) Performance comparison of the VS-SISSO model across different combinations of D and F.

Fig. 5. Correlation of model compositions with HER activity in M-N3C-SWCNTs. (a) Correlation of |c1·β1| with |ΔGH*|. (b) Correlation of |c2·β2| with |ΔGH*|. (c,d) HER performance comparison based on from |c1·β1| and |c2·β2| for M-N3C-SWCNT (M = Mn, Pd, and Pt). (e) Comparison of contributions from |c1·β1| and |c2·β2| for M-N3C-SWCNTs. (f) Importance analysis of features in the prediction model. (g) Evolutionary route of symmetry breaking.

Fig. 6. Relationship between composite descriptors and DFT calculation results. (a) Correlation of HER activity with ICOHPM-N2. (b) Correlation of HER activity with TDOS at Fermi level. (c) Diagram of dual activation mechanism. (d)-(i) Planar-average charge density difference of M-N3C-SWCNTs and M-N4-SWCNTs along the tube axis direction. Green represents regions of electron depletion, whereas pink denotes regions of electron accumulation. The isosurface value of all structures is 0.003 e/Bohr3. ΔΔρ = Δρadsorption site - Δρmetal atom.

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