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Pei et al. J Mater Inf 2023;3:26 https://dx.doi.org/10.20517/jmi.2023.35 Page 3 of 14

Atomic clusters [36-38] , on the other hand, possess unique geometric and electronic properties owing to their
strong quantum size effects, rendering them highly promising for catalytic applications. The catalytic
activities and product selectivity of supported metal nanoclusters (NCs) were governed with atomic
precision by tuning the size and composition of metal NCs. Experimentally, the use of well-dispersed Pt
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dimers on graphene resulted in a unique catalytic system that significantly increased the aqueous
hydrogenation rate of ammonia-borane in comparison to isolated individual Pt-ions. Specifically, the
specific rate of the reaction was found to be approximately 17 times higher when using the Pt dimers .
[39]
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Furthermore, a Mo trimer on graphdiyne nanosheets was observed to exhibit the highest activity,
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selectivity, and stability towards NRR based on the designed screening criteria, involving a calculated initial
[40]
voltage of -0.32 V . More importantly, the presence of several active sites in a catalyst is essential to
broaden the range of adsorbate binding capabilities and to facilitate the catalysis of a broader spectrum of
complex reactions to yield diverse products. Tian et al. fabricated diatomic Fe NCs anchored on
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mesoporous carbon nitride, which demonstrated remarkable catalytic activity in the conversion of
substilbene to oxide, achieving a high selection of 93% while maintaining a transformation rate of 91% .
[41]
Ru stabilized on nitrogen-doped carbon nanosheets was reported to efficiently catalyze the selective
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oxidation of alcohols . Moreover, theoretical studies have suggested that supported metal NCs exhibit
[42]
remarkable abilities in catalyzing reactions involving the activation of inert reactant molecules or requiring
multiple reaction centers [43-47] . For example, a tetramer immobilized in nitrogen-doped graphene
monolayers shows optimal surface activities for N activation and subsequent reaction to yielding NH
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products, involving the calculational on-set potential of -0.45 V, significantly lower than that of supported
single atoms and dimers . Li et al. discovered that Rh -C N exhibited superior catalytic performance in the
[47]
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[48]
enzymatic pathway with a limiting voltage of only -0.45 V compared to Rh -C N and Rh -C N .
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Furthermore, Zheng et al. have designed a set of electrocatalysts known as triple-atom catalysts (TACs). The
theoretical insights suggest that the Co -N system has a superior catalytic activity, attaining a boundary
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potential of -0.41 V via the enzymatic mechanism for NRR .
[46]
Motivated by the substantial progress in both experimental and theoretical studies, we have systematically
investigated the stability of 3d-5d TM trimers embedded on C N nanosheets (marked as TM @C N ) using
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DFT calculations and evaluated their electrocatalytic performances for NRR. The theoretical results indicate
that TM @C N (TM = Re, Ru, Pt) holds significant promise electrocatalysts for the NRR, demonstrating
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excellent performance and feasibility. Significantly, the Re @C N system demonstrates exceptional catalytic
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activity, surpassing other catalysts, with a limiting potential of -0.11 V using the consecutive mechanism.
Furthermore, we established a correlation between the inherent electronic characteristics of TM @C N and
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its catalytic performance, identifying significant physical parameters. Additionally, we advocate the concept
of designing TACs as a strategic approach to drive the development of advanced electrocatalysts within the
framework of green hydrogen economics.
MATERIALS AND METHODS
The Vienna ab initio simulation package (VASP) was utilized to conduct spin-polarized DFT computations,
employing the plane wave basis set [49,50] . We employed projector augmented wave (PAW) potentials along
with an energy cutoff of 500 eV [51,52] . The Perdew-Burke-Ernzerhof (PBE) functional of generalized gradient
approximation (GGA) was employed as the exchange-correlation functional . It has been extensively
[53]
tested and successfully applied to an array of solid-state and molecular systems [22-26,54] . The van der Waals
(vdW) interaction was investigated using Grimme’s semiempirical DFT-D3 scheme with dispersion
correction [55,56] . The energy and force convergence thresholds were established at 10 eV and 0.02 eV·Å ,
-1
-4
correspondingly. To avoid any interaction between two periodic units, a (2 × 2) supercell of C N monolayer
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with a 16 Å vacuum space along the z-direction was employed. Moreover, the Brillouin zone was sampled at