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Lu et al. J Mater Inf 2024;4:31 https://dx.doi.org/10.20517/jmi.2024.65 Page 3 of 16

[47]
limiting potential (U ) as low as -0.51 V .
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C N-h2D (C N), a two-dimensional porous carbon nitride material first synthesized in 2015, has garnered
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attention as an excellent substrate for anchoring metal atoms due to its wide band gap, high electron
mobility, and excellent thermal stability [50,51] . Its unique structure, characterized by electron-rich nitrogen
atoms exposed within a two-dimensional framework, offers an ideal platform for NHC functionalization,
facilitating the design of novel NCM. Unlike graphene, C N possesses distinct structural and electronic
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properties, providing a different local coordination environment that modulates the electronic properties of
the anchored metal atoms, potentially enhancing their catalytic performance [24,52,53] . Inspired by these
advantages, we systematically investigated C N-based NCMs as platforms for SACs and explored their
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potential in NRR catalysis.

In this study, we designed 28 SACs by embedding 3d, 4d, and 5d TMs into a C N-based NCM system,
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denoted as TM@C N-NCM. Using a combination of first-principles calculations and machine learning
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(ML), we systematically evaluated the NRR catalytic performance of these SACs. Through a multiple-step
screening process, eight candidates with high catalytic activity and selectivity for NRR were identified, all
exhibiting lower U than their TM@Graphene-NCM counterparts, demonstrating enhanced catalytic
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performance. Notably, Nb@C N-NCM showed the best performance, with a U of -0.29 V. ML models
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further revealed the intrinsic factors governing the varied NRR performance across different SACs.
Compared to graphene-based NCMs, the introduction of C N not only improved catalytic activity but also
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expanded the range of TMs that could be utilized as promising SACs for NRR. This study provides valuable
insights into the design of highly efficient NRR electrocatalysts and offers strategies for developing more
effective SACs in future research.

MATERIALS AND METHODS
All density functional theory (DFT) calculations were carried out using the Vienna Ab Initio Simulation
[54]
Package (VASP) , with the electronic interactions between ions and electrons described through the
projector augmented wave (PAW) method . The exchange-correlation effects were treated using the
[55]
generalized gradient approximation (GGA) combined with the Perdew-Burke-Ernzerhof (PBE)
functionals . For the plane-wave basis set, a kinetic energy cutoff of 500 eV was chosen to ensure
[56]
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computational accuracy. The energy convergence criterion was set at 10 eV, while the force convergence
threshold was fixed at 0.01 eV/Å. The Brillouin zone was sampled using 2 × 2 × 1 and 8 × 8 × 1 Gamma-
[57]
centered k-points for geometry optimizations and electronic property calculations . Spin polarization was
included in all calculations to account for potential magnetic effects. A vacuum layer of 18 Å along the
Z-direction was applied to eliminate spurious interactions between periodic images. The thermal stability of
the catalysts was evaluated using ab initio molecular dynamics (AIMD) simulations within the canonical
(NVT) ensemble. A Nosé thermostat was applied to maintain the temperature at 500 K, with a time step of
1 fs over a simulation period of 10 ps . To incorporate van der Waals forces between NRR intermediates
[58]
and the catalyst, we employed the DFT-D3 method for calculating free energy and electronic structure .
[59]
Charge transfer was analyzed through Bader charge calculations . Detailed methods for evaluating
[60]
adsorption energies (E ), Gibbs free energy changes (ΔG), and differential charge density are provided in
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the Supplementary Materials.
For the ML analysis, we utilized three non-linear regression algorithms: Random Forest Regression (RFR),
Gradient Boosting Regression (GBR), and Extreme GBR (XGBR) [61-65] . A grid search technique was applied
to optimize the hyperparameters for each model [66,67] . These algorithms were selected for their robustness
against overfitting, their ability to process high-dimensional datasets, and their superior predictive accuracy