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Page 4 of 14 Pei et al. J Mater Inf 2023;3:26 https://dx.doi.org/10.20517/jmi.2023.35

[57]
the k-point using a 2 × 2 × 1 grid . Ab initio molecular dynamics (AIMD) simulations were performed at a
temperature of 300 K in an NVT ensemble for a duration of 10 ps in order to estimate the thermodynamic
stability of the TM @C N systems.
3
3
3
The binding energies (E ) were calculated to judge the thermodynamic stabilities of the designed TM @C N 3
3
b
3
systems, as follows:
E = E TM 3 @C 3 N 3 - E C 3 N 3 - E TM 3 (1)
b

denote the total energy of C N substrate anchored with transition-metal
where E TM 3 @C 3 N 3, E C 3 N 3, and E TM 3 3 3
trimeric clusters, the optimized pristine C N , and the isolated transition-metal trimeric clusters,
3
3
respectively. The electronic adsorption energy (E ) of reaction intermediates on TM @C N substrates can
3
3
3
ads
be computed by the following formula:
E = E - E - E adsorbate (2)
ads
tot
cat
where E is the total energy of TM @C N substrates adsorbed by the intermediate, and E and E adsorbate are
cat
tot
3
3
3
the energy of TM @C N and the adsorbed intermediate, respectively. According to the proposal by
3
3
3
Nørskov et al. [58-60] , the calculated hydrogen electrode (CHE) model can be employed to determine the Gibbs
free energy change (∆G) for each individual step in the electrochemical hydrogenation process, and the ∆G
value is calculated by employing the formula as follows:
∆G = ∆E + ∆E - T∆S + ∆G + ∆G pH (3)
ZPE
U
where ∆E is the total reaction energy gained from the DFT calculations. ∆E and ∆S are the changes in
ZPE
zero-point energy and entropy, respectively. The zero-point energy and entropy were determined by
calculating the vibrational frequencies. The temperature (T) was set to 298.15 K in this research. ∆G U
denotes the impact of the applied potential (U) and is equal to -neU, where n corresponds to the number of
electrons transferred. The correction of pH, ∆G , represents the free energy and can be calculated
pH
according to the formula: ∆G = -K T × pH × ln10. The pH value is assumed to be 0, and K refers to the
pH
B
B
Boltzmann constant. The quantities of transferred electrons and the potential of the applied electrode are
represented by e and U, respectively. The potential determination step (PDS), which has the maximum ∆G
value, can be used to determine the limiting potential (U limiting ) of the entire reduction process in an acid
solution using the following formula:
U limiting = -∆G /e (4)
max
RESULTS AND DISCUSSION
Geometry and stability of TM @C N
3 3 3
Since the NRR is a complex process including various reactive species, the use of effective screening
descriptors is crucial. As illustrated in Figure 1, we propose a standard strategy for screening candidate
catalysts for N reduction reaction. (1) Thermodynamic stability: TACs should have thermodynamics (∆E <
b
2
0 eV, where ∆E is the binding energy of TM atoms on C N ). Additionally, their dynamic stability should
3
3
3
b
be confirmed through AIMD simulations at 300 K, ensuring that the structure remains stable without
< 0.50 eV, indicating
2
deformation; (2) Surficial activity: N should undergo complete activation (∆G *N 2
chemical adsorption of N , where the asterisk * denotes the adsorption site) ; (3) Energy cost: the potential
[61]
2
range of NRR reaction on Ru-based catalysts with high catalytic performance under mild conditions is