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Page 4 of 16 Lu et al. J Mater Inf 2024;4:31 https://dx.doi.org/10.20517/jmi.2024.65

[68]
in material property modeling. All ML models were implemented using the Scikit-learn library . To
prevent overfitting, data normalization was performed prior to training, and a 5-fold cross-validation was
used to validate model performance. Model accuracy was evaluated using the coefficient of determination
2
2
(R ) and mean absolute error (MAE), with ideal models approaching an R value of 1 and an MAE close to
0. For feature selection, we applied both Pearson correlation coefficient heatmap analysis and Recursive
[69]
Feature Elimination (RFE) . The heatmap identifies highly correlated features, enabling us to eliminate
redundancy, while RFE iteratively removes the least important features, further refining the feature set. By
combining these two methods, we derived the optimal feature subset for input into the ML models. To
interpret the ML results and understand the influence of key descriptors on catalytic activity, the Shapley
Additive Explanations (SHAP) method was employed. SHAP provides the magnitude and direction of the
[70]
contribution of each feature to the model predictions . In the SHAP summary plot, each point
corresponds to a sample, with the horizontal axis showing the SHAP value, indicating the impact of the
feature on the prediction. Positive SHAP values contribute to an increase in the predicted value, while
negative values result in a decrease. The color of each point reflects the feature value, with red indicating
higher values and blue representing lower values.

RESULTS AND DISCUSSION
Structure of TM@C N-NCM
2
To construct the target catalysts, a C N-based NCM was designed by introducing three classic five-
2
membered NHC units into a 2 × 2 C N supercell. TM atoms from the 3d, 4d, and 5d series were
2
subsequently anchored into the pores of the C N-based NCM framework, resulting in the TM@C N-NCM
2
2
structure (see Figure 1A). The lattice constant is a = b = 16.63 Å. The TMs studied include 3d (Sc, Ti, V, Cr,
Mn, Fe, Co, Ni, Cu, Zn), 4d (Y, Zr, Nb, Mo, Ru, Rh, Pd, Ag, Cd), and 5d (Hf, Ta, W, Re, Os, Ir, Pt, Au, Hg)
elements [Figure 1B]. To gain a more comprehensive understanding of the role of the substrate and various
metals and identify broader trends, toxic Cd and Hg were also included in the study. Each TM atom is
stably coordinated by three NHC units, forming robust TM-C bonds. Due to the presence of three five-
membered rings, the non-planar TM@C N-NCM structures result in the exposure of these metal centers on
2
the surface, which is beneficial for N adsorption and catalytic activity.
2
To evaluate the stability of the metal atoms on the substrate, the binding energies (E ) of the TMs with the
b
C N-NCM were calculated. As shown in Figure 1C, all TMs exhibited negative E , except for Au, which had
2
b
a slightly positive value of 0.02 eV, indicating weak interaction between Au and the substrate. For the
remaining 27 TMs, the E values range from -10.03 eV (Os) to -0.75 eV (Hg). These negative values confirm
b
their stable adsorption on the C N-NCM substrate, with more negative values indicating stronger metal-
2
substrate interactions. Additionally, we found that the trend in E is strongly influenced by the d-electron
b
configuration of the TMs, which is consistent with observations from TM@graphene-NCM. Metals located
in the middle of each period (e.g., Fe, Ru, Os) exhibited more negative E values, which can be attributed to
b
a balanced electron donation from the metal to the NHC ligands and back-donation from the NHCs to the
d-orbitals of metal atoms. Early TMs (e.g., Ti, Zr, Ta) lack sufficient d-electrons for effective back-donation,
while late TMs (e.g., Zn, Cd, Hg) have fewer vacant d-orbitals to accept electron donation from the NHCs.
To further verify the thermodynamic stability of the catalysts, AIMD simulations were performed. Nb@C 2
N-NCM, which later demonstrated the best catalytic performance, was selected as a representative example
to further verify its stability. The results showed that the energy fluctuations remained near equilibrium
throughout the simulation, with the Nb atom firmly anchored in the NHC coordination environment,
confirming the favorable thermodynamic stability of the structure (see Supplementary Figure 1). Based on
these results, 27 SACs (excluding Au) were identified as stable candidates for further catalytic investigation.