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Han et al. J Mater Inf 2023;3:24 https://dx.doi.org/10.20517/jmi.2023.32 Page 3 of 11

a single atom (M ) and a bimetallic atom (M ) site. In this work, we replaced the precious metal Ag atoms in
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Ag @C with Mo/Fe atoms and obtained the Mo /Fe @C monolayer. Through theoretical studies of the
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eNRR process, we found that Mo @C is not suitable for eNRR due to its strong N adsorption; in contrast,
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Fe @C is a good eNRR catalyst (the limiting potential U = -0.59 V). With the demonstration that Fe @C
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L
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can be used as an electrocatalyst for eNRR, we substituted the C bonded with Fe by N to tune the
coordination environment of the metal sites in order to further improve the catalytic efficiency. The limiting
potential was further changed to -0.45 V when the N doping of the Fe site was the maximum; i.e., all the
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four C bonded with Fe sites were replaced by N with the stoichiometry of Fe @N C .
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MATERIALS AND METHODS
All density functional theory (DFT) calculations were carried out using the Vienna ab initio Simulation
Package (VASP) . The Perdew, Burke, and Ernzerhof (PBE) parameterization of the generalized
[48]
[47]
gradient approximation (GGA) was used to describe the exchange-correlation function. The DFT-D2
dispersion correction scheme was applied for van der Waals (vdW) interactions . A cut-off energy of
[49]
600 eV was used (convergence tests are shown in Supplementary Figure 1). The convergence parameters for
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force and energy were 0.02 eV/Å and 10 eV, respectively, and the convergence parameters were set the
same as those in previous NRR calculations . The Brillouin zone was sampled using a Monkhorst-Pack k-
[50]
point grid of 3 × 5 × 1. The Bader charge analysis was employed to evaluate the charge transfer.
[51]
[52]
The adsorption energy of N was calculated by E = E - E - E , where E , E , and E are the total energy
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N2
tot
*
N2
tot
ads
*
of N adsorbed on the catalyst, the clean catalyst, and free N , respectively. The free energy G was obtained
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2
based on the computational hydrogen electrode (CHE) model proposed by Nørskov et al. , with the
[53]
formula:
ΔG = ΔE + ΔE - TΔS + ΔG + ΔG pH
U
ZPE
[54]
In the above equation, E is the DFT energy, E and S are the zero-point energy and entropy , respectively,
ZPE
E and TS can be obtained by VASPKIT post-processing program , ΔG = -eU, ΔG = -k Tln10 × pH, k
[55]
B
U
B
ZPE
pH
is the Boltzmann constant, T is 298.15 K , and the pH is zero in this study. The corrected values of the gas
[56]
molecules and intermediates were given in Supplementary Tables 1 and 2, respectively. The limiting
potential (U ) of the entire reduction process was determined by the potential limiting step and was
L
computed by U = -ΔG /e .
[57]
max
L
We used the following equation for the formation energy of N doping:
E = E Fe3@NxC20-x - E Fe3@C20 - xE + xE C
N
f
where E Fe3@NxC20-x and E Fe3@C20 are the energies of N-doped and pure Fe @C , respectively, x is the number
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of N atoms, and E and E represent the energies of a free N/C atom. All the details of the calculations and
C
N
the results of the energy difference calculations are presented in Supplementary Table 3.
RESULTS AND DISCUSSION
The structure and the eNRR performance of the M @C (M = Mo and Fe) monolayers
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After structural optimization, the structures are represented by the Fe @C shown in Figure 1A with
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rectangular lattice constants of a = 11.14 Å and b = 7.95 Å, and a = 11.59 Å and b = 8.45 Å for Mo @C ,
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