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Page 4 of 12 Chi et al. J. Mater. Inf. 2025, 5, 11 https://dx.doi.org/10.20517/jmi.2024.49

[20]
correction was employed . The core treatment utilized a DFT semi-core pseudopotential with a basis set of
[21]
double numerical plus polarization (DNP) . Convergence was accelerated by adopting smearing with a
value of 0.005 Ha, while electron convergence accuracy was ensured with a real-space global orbital cutoff
radius of 4.9 Å. The convergence criteria for electronic relaxation, force, and displacement were set to
10 eV, 0.002 eV/Å, and 0.005 Å, respectively. To analyze the bonding nature of the N≡N, the crystal orbital
-5
Hamilton population (COHP) analysis was performed using the Lobster software [22,23] .

The substrate was modeled by a 2 × 2 monolayer of γ-GDY (18.92 × 18.92 Å ). A vacuum of 20 Å was
2
introduced along the z to avoid interactions from the periodic images in the direction normal to the
substrate. Sampling of the Brillouin zone was performed using a 2 × 2 × 1 Monkhorst-Pack k-points mesh.
*
The transition state (TS) analysis of the key intermediate ( NCON) formed by C-N coupling was
[24]
implemented using the linear synchronous transit (LST)/quadratic synchronous transit (QST) method .
The basic parameter settings are the same as those used in other calculations, with the root mean square
(RMS) convergence being set to 0.01 Ha/Å. The spin population and charge transfer were calculated using
the Hirshfeld population analysis . The Gibbs free energy changes for each reaction step in the
[25]
electrocatalytic synthesis of urea were evaluated based on the computational hydrogen electrode (CHE)
model proposed by Nørskov et al. . Under standard reaction conditions (pH = 0, 298.15 K, and 1 atm) and
[26]
at a potential of 0 V vs. reversible hydrogen electrode (RHE), the free energy associated with the transfer of a
[27]
proton and electron pair is defined as half the value of gaseous hydrogen ,
G(H + e ) = 1/2G(H ) (1)
-
+
2
The Gibbs free energy during the electrocatalytic synthesis process was calculated by

ΔG = ΔE + ΔZPE - TΔS (2)

where ΔE represents the change of free energy obtained directly from DFT calculations, ΔZPE denotes the
variation in zero-point energy, T is the Kelvin temperature (298.15 K), and ΔS indicates the change of
[28]
entropy. For N , CO, and H , the ZPE and S values are obtained from the experiments . The limiting
2
2
potential is computed as
U = -ΔG /e (3)
L
max
where the variable e represents the number of electrons transferred during potential limiting step (PLS) and
ΔG determines the PLS. The adsorption energy (E ) is calculated by
ad
max
E = E - E - E (4)
*
total
ads
ad
where E represents the total energy of the adsorption system, E is the energy of the adsorbed species,
total
ads
and E denotes the total energy of the pristine catalyst. The mass loading of TMs atoms on the substrate of
*
Fe Mo@γ-GDY is determined by
2
η = m /m catalyst × 100% (5)
TMs
where m and m catalyst denote the mass of Fe/Mo atoms loaded on the catalyst and the mass of the whole
TMs
catalyst system, respectively. In our catalyst system, there are 72 C atoms and three TMs; therefore, m =
TMs