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Pei et al. J Mater Inf 2023;3:26 https://dx.doi.org/10.20517/jmi.2023.35 Page 5 of 14

Figure 1. The schematic diagram for screening candidate TACs for NRR. HER: Hydrogen evolution reactions; NRR: nitrogen reduction
reactions; TACs: triple-atom catalysts.

-0.50~-0.56 V. Therefore, in this paper, catalytic properties of NRR: the limit potential, U limiting , is used to
evaluate NRR activity. To ensure low energy costs, we use a standard of 0.55 eV. For the first and last
hydrogenation steps, which are typically the most likely limiting steps in a reaction, it is desirable to have
∆G values that are as low as possible (∆G N 2 →NNH ≤ 0.55 eV and ∆G NH 2 →NH 3 ≤ 0.55 eV) [61,62] . The calculation of
[61]
∆G is performed using Equation (3) ; (4) NRR vs. HER selectivity: to ensure high NRR selectivity, the
Gibbs free energy value of hydrogen adsorption should exceed that of nitrogen. These criteria collectively
form a robust filtration strategy for identifying potential NRR catalysts.

Next, we first consider the stability of the metal trimer on C N before delving into the electroreduction
3
3
process. Through extensive geometric optimization and configuration search, we obtained the structures of
TM @C N . As summarized in Figure 2A, these metal trimer clusters show the strong binding strength on
3
3
3
the C N monolayer, involving E of -9.57~-4.22 eV, which indicates decent thermodynamic stabilities. The
b
3
3
E is calculated by Equation (1) with the detailed data shown in Table 1. Furthermore, according to the
b
above calculation, it is worth noting that Pd @C N possesses the weakest binding strength among the 21
3
3
3
selected systems. In light of this, we conducted AIMD at 300 K for 10 ps to evaluate the stability of
TM @C N , with Pd @C N considered as a representative. Figure 2B and C illustrates the oscillations of the
3
3
3
3
3
3
DFT total energies (E) relative to the initial conditions and temperature (T), along with the d Pd-N and d Pd-Pd ,
indicating dynamic fluctuations near the initial condition. According to the captured structures of
Pd @C N under different times [Figure 2D], it is preserved well and maintains structural stability, in which
3
3
3
the vertical buckling exhibits minimal fluctuation, measuring less than 0.10 Å. Therefore, combined with the
above calculations, we can confidently assert that these TM @C N systems have robust structural stabilities.
3
3
3
Activation of N on TM @C N
2 3 3 3
In the overall electrochemical NRR process, the primary and critical step involves the adsorption and
activation of N molecules, a process of utmost importance as it is responsible for activating the N≡N triple
2
bond, laying the foundation for the smooth protonation to follow. Figure 3A shows that the activation of N 2
is facilitated via an electron transfer mechanism, where the partially filled d orbitals of TM atoms accept
electrons from N molecules while simultaneously donating d electrons to the anti-bonding orbitals (π*) of
2
*N in the reverse direction. Therefore, this interaction strengthens the TM–N bond while attenuating N≡N.
2
Notably, the metal double or triple-atom centers are critical to maximizing the activation effect by donating
a greater number of electrons to N in comparison to monatomic active sites [63-66] . Using dual-metal or
2
triple-atom centers proves to be a more effective approach in promoting N activation. Employing this
2
approach provides an advantage in surmounting the barrier encountered during the initial step in the